An analysis of numerical convergence in discrete velocity gas dynamics for internal flows

NASA Astrophysics Data System (ADS)

Sekaran, Aarthi; Varghese, Philip; Goldstein, David

2018-07-01

The Discrete Velocity Method (DVM) for solving the Boltzmann equation has significant advantages in the modeling of non-equilibrium and near equilibrium flows as compared to other methods in terms of reduced statistical noise, faster solutions and the ability to handle transient flows. Yet the DVM performance for rarefied flow in complex, small-scale geometries, in microelectromechanical (MEMS) devices for instance, is yet to be studied in detail. The present study focuses on the performance of the DVM for locally large Knudsen number flows of argon around sharp corners and other sources for discontinuities in the distribution function. Our analysis details the nature of the solution for some benchmark cases and introduces the concept of solution convergence for the transport terms in the discrete velocity Boltzmann equation. The limiting effects of the velocity space discretization are also investigated and the constraints on obtaining a robust, consistent solution are derived. We propose techniques to maintain solution convergence and demonstrate the implementation of a specific strategy and its effect on the fidelity of the solution for some benchmark cases.

Convergence characteristics of nonlinear vortex-lattice methods for configuration aerodynamics

NASA Technical Reports Server (NTRS)

Seginer, A.; Rusak, Z.; Wasserstrom, E.

1983-01-01

Nonlinear panel methods have no proof for the existence and uniqueness of their solutions. The convergence characteristics of an iterative, nonlinear vortex-lattice method are, therefore, carefully investigated. The effects of several parameters, including (1) the surface-paneling method, (2) an integration method of the trajectories of the wake vortices, (3) vortex-grid refinement, and (4) the initial conditions for the first iteration on the computed aerodynamic coefficients and on the flow-field details are presented. The convergence of the iterative-solution procedure is usually rapid. The solution converges with grid refinement to a constant value, but the final value is not unique and varies with the wing surface-paneling and wake-discretization methods within some range in the vicinity of the experimental result.

Multiple-grid convergence acceleration of viscous and inviscid flow computations

NASA Technical Reports Server (NTRS)

Johnson, G. M.

1983-01-01

A multiple-grid algorithm for use in efficiently obtaining steady solution to the Euler and Navier-Stokes equations is presented. The convergence of a simple, explicit fine-grid solution procedure is accelerated on a sequence of successively coarser grids by a coarse-grid information propagation method which rapidly eliminates transients from the computational domain. This use of multiple-gridding to increase the convergence rate results in substantially reduced work requirements for the numerical solution of a wide range of flow problems. Computational results are presented for subsonic and transonic inviscid flows and for laminar and turbulent, attached and separated, subsonic viscous flows. Work reduction factors as large as eight, in comparison to the basic fine-grid algorithm, were obtained. Possibilities for further performance improvement are discussed.

Reliability enhancement of Navier-Stokes codes through convergence acceleration

NASA Technical Reports Server (NTRS)

Merkle, Charles L.; Dulikravich, George S.

1995-01-01

Methods for enhancing the reliability of Navier-Stokes computer codes through improving convergence characteristics are presented. The improving of these characteristics decreases the likelihood of code unreliability and user interventions in a design environment. The problem referred to as a 'stiffness' in the governing equations for propulsion-related flowfields is investigated, particularly in regard to common sources of equation stiffness that lead to convergence degradation of CFD algorithms. Von Neumann stability theory is employed as a tool to study the convergence difficulties involved. Based on the stability results, improved algorithms are devised to ensure efficient convergence in different situations. A number of test cases are considered to confirm a correlation between stability theory and numerical convergence. The examples of turbulent and reacting flow are presented, and a generalized form of the preconditioning matrix is derived to handle these problems, i.e., the problems involving additional differential equations for describing the transport of turbulent kinetic energy, dissipation rate and chemical species. Algorithms for unsteady computations are considered. The extension of the preconditioning techniques and algorithms derived for Navier-Stokes computations to three-dimensional flow problems is discussed. New methods to accelerate the convergence of iterative schemes for the numerical integration of systems of partial differential equtions are developed, with a special emphasis on the acceleration of convergence on highly clustered grids.

Development of a pressure based multigrid solution method for complex fluid flows

NASA Technical Reports Server (NTRS)

Shyy, Wei

1991-01-01

In order to reduce the computational difficulty associated with a single grid (SG) solution procedure, the multigrid (MG) technique was identified as a useful means for improving the convergence rate of iterative methods. A full MG full approximation storage (FMG/FAS) algorithm is used to solve the incompressible recirculating flow problems in complex geometries. The algorithm is implemented in conjunction with a pressure correction staggered grid type of technique using the curvilinear coordinates. In order to show the performance of the method, two flow configurations, one a square cavity and the other a channel, are used as test problems. Comparisons are made between the iterations, equivalent work units, and CPU time. Besides showing that the MG method can yield substantial speed-up with wide variations in Reynolds number, grid distributions, and geometry, issues such as the convergence characteristics of different grid levels, the choice of convection schemes, and the effectiveness of the basic iteration smoothers are studied. An adaptive grid scheme is also combined with the MG procedure to explore the effects of grid resolution on the MG convergence rate as well as the numerical accuracy.

Numerical Computation of Subsonic Conical Diffuser Flows with Nonuniform Turbulent Inlet Conditions

DTIC Science & Technology

1977-09-01

Gauss - Seidel Point Iteration Method . . . . . . . . . . . . . . . 7.0 FACTORS AFFECTING THE RATE OF CONVERGENCE OF THE POINT...can be solved in several ways. For simplicity, a standard Gauss - Seidel iteration method is used to obtain the solution . The method updates the...FACTORS AFFECTING THE RATE OF CONVERGENCE OF THE POINT ITERATION ,ŘETHOD The advantage of using the Gauss - Seidel point iteration method to

An efficient iteration strategy for the solution of the Euler equations

NASA Technical Reports Server (NTRS)

Walters, R. W.; Dwoyer, D. L.

1985-01-01

A line Gauss-Seidel (LGS) relaxation algorithm in conjunction with a one-parameter family of upwind discretizations of the Euler equations in two-dimensions is described. The basic algorithm has the property that convergence to the steady-state is quadratic for fully supersonic flows and linear otherwise. This is in contrast to the block ADI methods (either central or upwind differenced) and the upwind biased relaxation schemes, all of which converge linearly, independent of the flow regime. Moreover, the algorithm presented here is easily enhanced to detect regions of subsonic flow embedded in supersonic flow. This allows marching by lines in the supersonic regions, converging each line quadratically, and iterating in the subsonic regions, thus yielding a very efficient iteration strategy. Numerical results are presented for two-dimensional supersonic and transonic flows containing both oblique and normal shock waves which confirm the efficiency of the iteration strategy.

Application of 1 D Finite Element Method in Combination with Laminar Solution Method for Pipe Network Analysis

NASA Astrophysics Data System (ADS)

Dudar, O. I.; Dudar, E. S.

2017-11-01

The features of application of the 1D dimensional finite element method (FEM) in combination with the laminar solutions method (LSM) for the calculation of underground ventilating networks are considered. In this case the processes of heat and mass transfer change the properties of a fluid (binary vapour-air mix). Under the action of gravitational forces it leads to such phenomena as natural draft, local circulation, etc. The FEM relations considering the action of gravity, the mass conservation law, the dependence of vapour-air mix properties on the thermodynamic parameters are derived so that it allows one to model the mentioned phenomena. The analogy of the elastic and plastic rod deformation processes to the processes of laminar and turbulent flow in a pipe is described. Owing to this analogy, the guaranteed convergence of the elastic solutions method for the materials of plastic type means the guaranteed convergence of the LSM for any regime of a turbulent flow in a rough pipe. By means of numerical experiments the convergence rate of the FEM - LSM is investigated. This convergence rate appeared much higher than the convergence rate of the Cross - Andriyashev method. Data of other authors on the convergence rate comparison for the finite element method, the Newton method and the method of gradient are provided. These data allow one to conclude that the FEM in combination with the LSM is one of the most effective methods of calculation of hydraulic and ventilating networks. The FEM - LSM has been used for creation of the research application programme package “MineClimate” allowing to calculate the microclimate parameters in the underground ventilating networks.

Converging flow joint insert system at an intersection between adjacent transitions extending between a combustor and a turbine assembly in a gas turbine engine

DOE Office of Scientific and Technical Information (OSTI.GOV)

Wiebe, David J.; Carlson, Andrew; Stoker, Kyle C.

A transition duct system for routing a gas flow in a combustion turbine engine is provided. The transition duct system includes one or more converging flow joint inserts forming a trailing edge at an intersection between adjacent transition ducts. The converging flow joint insert may be contained within a converging flow joint insert receiver and may be disconnected from the transition duct bodies by which the converging flow joint insert is positioned. Being disconnected eliminates stress formation within the converging flow joint insert, thereby enhancing the life of the insert. The converging flow joint insert may be removable such thatmore » the insert can be replaced once worn beyond design limits.« less

Appliance of Inertial Gas-Dynamic Separation of Gas-Dispersion Flows in the Curvilinear Convergent-Divergent Channels for Compressor Equipment Reliability Improvement

NASA Astrophysics Data System (ADS)

Liaposhchenko, O. O.; Sklabinskyi, V. I.; Zavialov, V. L.; Pavlenko, I. V.; Nastenko, O. V.; Demianenko, M. M.

2017-08-01

The new methods of vibration and inertial gas-dynamic separation of gas-condensate and dusty flows and the corresponding separation devices are proposed in order to avoid emergencies and premature wear of parts and components of the compressor equipment. The formation of the gas flow and disperse particles in the curvilinear convergent-divergent channels are investigated. The optimizing hydrodynamic profiling of a geometrical configuration of curvilinear separation channels with rigid and flexible walls of baffles is carried out.

Characteristics of Perforated Diffusers at Free-stream Mach Number 1.90

NASA Technical Reports Server (NTRS)

Hunczak, Henry R; Kremzier, Emil J

1950-01-01

An investigation was conducted at Mach number 1.90 to determine pressure recovery and mass-flow characteristics of series of perforated convergent-divergent supersonic diffusers. Pressure recoveries as high as 96 percent were obtained, but at reduced mass flows through the diffuser. Theoretical considerations of effect of perforation distribution on shock stability in converging section of diffuser are presented and correlated with experimental data. A method of estimating relative importance of pressure recovery and mass flow on internal thrust coefficient basis is given and a comparison of various diffusers investigated is made.

DOE Office of Scientific and Technical Information (OSTI.GOV)

Sen, Oishik, E-mail: oishik-sen@uiowa.edu; Gaul, Nicholas J., E-mail: nicholas-gaul@ramdosolutions.com; Choi, K.K., E-mail: kyung-choi@uiowa.edu

Macro-scale computations of shocked particulate flows require closure laws that model the exchange of momentum/energy between the fluid and particle phases. Closure laws are constructed in this work in the form of surrogate models derived from highly resolved mesoscale computations of shock-particle interactions. The mesoscale computations are performed to calculate the drag force on a cluster of particles for different values of Mach Number and particle volume fraction. Two Kriging-based methods, viz. the Dynamic Kriging Method (DKG) and the Modified Bayesian Kriging Method (MBKG) are evaluated for their ability to construct surrogate models with sparse data; i.e. using the leastmore » number of mesoscale simulations. It is shown that if the input data is noise-free, the DKG method converges monotonically; convergence is less robust in the presence of noise. The MBKG method converges monotonically even with noisy input data and is therefore more suitable for surrogate model construction from numerical experiments. This work is the first step towards a full multiscale modeling of interaction of shocked particle laden flows.« less

Simulation of the Flow Through Porous Layers Composed of Converging-Diverging Capillary Fissures or Tubes

NASA Astrophysics Data System (ADS)

Walicka, A.

2018-02-01

In this paper, a porous medium is modelled by a network of converging-diverging capillaries which may be considered as fissures or tubes. This model makes it necessary to consider flows through capillary fissures or tubes. Therefore an analytical method for deriving the relationships between pressure drops, volumetric flow rates and velocities for the following fluids: Newtonian, polar, power-law, pseudoplastic (DeHaven and Sisko types) and Shulmanian, was developed. Next, considerations on the models of pore network for Newtonian and non-Newtonian fluids were presented. The models, similar to the schemes of central finite differences may provide a good basis for transforming the governing equations of a flow through the porous medium into a set of linear or quasi-linear algebraic equations. It was shown that the some coefficients in these algebraic equations depend on the kind of the capillary convergence.

Convergence acceleration of the Proteus computer code with multigrid methods

NASA Technical Reports Server (NTRS)

Demuren, A. O.; Ibraheem, S. O.

1992-01-01

Presented here is the first part of a study to implement convergence acceleration techniques based on the multigrid concept in the Proteus computer code. A review is given of previous studies on the implementation of multigrid methods in computer codes for compressible flow analysis. Also presented is a detailed stability analysis of upwind and central-difference based numerical schemes for solving the Euler and Navier-Stokes equations. Results are given of a convergence study of the Proteus code on computational grids of different sizes. The results presented here form the foundation for the implementation of multigrid methods in the Proteus code.

Efficient self-consistent viscous-inviscid solutions for unsteady transonic flow

NASA Technical Reports Server (NTRS)

Howlett, J. T.

1985-01-01

An improved method is presented for coupling a boundary layer code with an unsteady inviscid transonic computer code in a quasi-steady fashion. At each fixed time step, the boundary layer and inviscid equations are successively solved until the process converges. An explicit coupling of the equations is described which greatly accelerates the convergence process. Computer times for converged viscous-inviscid solutions are about 1.8 times the comparable inviscid values. Comparison of the results obtained with experimental data on three airfoils are presented. These comparisons demonstrate that the explicitly coupled viscous-inviscid solutions can provide efficient predictions of pressure distributions and lift for unsteady two-dimensional transonic flows.

Efficient self-consistent viscous-inviscid solutions for unsteady transonic flow

NASA Technical Reports Server (NTRS)

Howlett, J. T.

1985-01-01

An improved method is presented for coupling a boundary layer code with an unsteady inviscid transonic computer code in a quasi-steady fashion. At each fixed time step, the boundary layer and inviscid equations are successively solved until the process converges. An explicit coupling of the equations is described which greatly accelerates the convergence process. Computer times for converged viscous-inviscid solutions are about 1.8 times the comparable inviscid values. Comparison of the results obtained with experimental data on three airfoils are presented. These comparisons demonstrate that the explicitly coupled viscous-inviscid solutions can provide efficient predictions of pressure distributions and lift for unsteady two-dimensional transonic flow.

Flows of Newtonian and Power-Law Fluids in Symmetrically Corrugated Cappilary Fissures and Tubes

NASA Astrophysics Data System (ADS)

Walicka, A.

2018-02-01

In this paper, an analytical method for deriving the relationships between the pressure drop and the volumetric flow rate in laminar flow regimes of Newtonian and power-law fluids through symmetrically corrugated capillary fissures and tubes is presented. This method, which is general with regard to fluid and capillary shape, can also be used as a foundation for different fluids, fissures and tubes. It can also be a good base for numerical integration when analytical expressions are hard to obtain due to mathematical complexities. Five converging-diverging or diverging-converging geometrics, viz. wedge and cone, parabolic, hyperbolic, hyperbolic cosine and cosine curve, are used as examples to illustrate the application of this method. For the wedge and cone geometry the present results for the power-law fluid were compared with the results obtained by another method; this comparison indicates a good compatibility between both the results.

Grid-converged solution and analysis of the unsteady viscous flow in a two-dimensional shock tube

NASA Astrophysics Data System (ADS)

Zhou, Guangzhao; Xu, Kun; Liu, Feng

2018-01-01

The flow in a shock tube is extremely complex with dynamic multi-scale structures of sharp fronts, flow separation, and vortices due to the interaction of the shock wave, the contact surface, and the boundary layer over the side wall of the tube. Prediction and understanding of the complex fluid dynamics are of theoretical and practical importance. It is also an extremely challenging problem for numerical simulation, especially at relatively high Reynolds numbers. Daru and Tenaud ["Evaluation of TVD high resolution schemes for unsteady viscous shocked flows," Comput. Fluids 30, 89-113 (2001)] proposed a two-dimensional model problem as a numerical test case for high-resolution schemes to simulate the flow field in a square closed shock tube. Though many researchers attempted this problem using a variety of computational methods, there is not yet an agreed-upon grid-converged solution of the problem at the Reynolds number of 1000. This paper presents a rigorous grid-convergence study and the resulting grid-converged solutions for this problem by using a newly developed, efficient, and high-order gas-kinetic scheme. Critical data extracted from the converged solutions are documented as benchmark data. The complex fluid dynamics of the flow at Re = 1000 are discussed and analyzed in detail. Major phenomena revealed by the numerical computations include the downward concentration of the fluid through the curved shock, the formation of the vortices, the mechanism of the shock wave bifurcation, the structure of the jet along the bottom wall, and the Kelvin-Helmholtz instability near the contact surface. Presentation and analysis of those flow processes provide important physical insight into the complex flow physics occurring in a shock tube.

Unified gas-kinetic scheme with multigrid convergence for rarefied flow study

NASA Astrophysics Data System (ADS)

Zhu, Yajun; Zhong, Chengwen; Xu, Kun

2017-09-01

The unified gas kinetic scheme (UGKS) is based on direct modeling of gas dynamics on the mesh size and time step scales. With the modeling of particle transport and collision in a time-dependent flux function in a finite volume framework, the UGKS can connect the flow physics smoothly from the kinetic particle transport to the hydrodynamic wave propagation. In comparison with the direct simulation Monte Carlo (DSMC) method, the current equation-based UGKS can implement implicit techniques in the updates of macroscopic conservative variables and microscopic distribution functions. The implicit UGKS significantly increases the convergence speed for steady flow computations, especially in the highly rarefied and near continuum regimes. In order to further improve the computational efficiency, for the first time, a geometric multigrid technique is introduced into the implicit UGKS, where the prediction step for the equilibrium state and the evolution step for the distribution function are both treated with multigrid acceleration. More specifically, a full approximate nonlinear system is employed in the prediction step for fast evaluation of the equilibrium state, and a correction linear equation is solved in the evolution step for the update of the gas distribution function. As a result, convergent speed has been greatly improved in all flow regimes from rarefied to the continuum ones. The multigrid implicit UGKS (MIUGKS) is used in the non-equilibrium flow study, which includes microflow, such as lid-driven cavity flow and the flow passing through a finite-length flat plate, and high speed one, such as supersonic flow over a square cylinder. The MIUGKS shows 5-9 times efficiency increase over the previous implicit scheme. For the low speed microflow, the efficiency of MIUGKS is several orders of magnitude higher than the DSMC. Even for the hypersonic flow at Mach number 5 and Knudsen number 0.1, the MIUGKS is still more than 100 times faster than the DSMC method for obtaining a convergent steady state solution.

Convergence of Defect-Correction and Multigrid Iterations for Inviscid Flows

NASA Technical Reports Server (NTRS)

Diskin, Boris; Thomas, James L.

2011-01-01

Convergence of multigrid and defect-correction iterations is comprehensively studied within different incompressible and compressible inviscid regimes on high-density grids. Good smoothing properties of the defect-correction relaxation have been shown using both a modified Fourier analysis and a more general idealized-coarse-grid analysis. Single-grid defect correction alone has some slowly converging iterations on grids of medium density. The convergence is especially slow for near-sonic flows and for very low compressible Mach numbers. Additionally, the fast asymptotic convergence seen on medium density grids deteriorates on high-density grids. Certain downstream-boundary modes are very slowly damped on high-density grids. Multigrid scheme accelerates convergence of the slow defect-correction iterations to the extent determined by the coarse-grid correction. The two-level asymptotic convergence rates are stable and significantly below one in most of the regions but slow convergence is noted for near-sonic and very low-Mach compressible flows. Multigrid solver has been applied to the NACA 0012 airfoil and to different flow regimes, such as near-tangency and stagnation. Certain convergence difficulties have been encountered within stagnation regions. Nonetheless, for the airfoil flow, with a sharp trailing-edge, residuals were fast converging for a subcritical flow on a sequence of grids. For supercritical flow, residuals converged slower on some intermediate grids than on the finest grid or the two coarsest grids.

A theoretical method for the analysis and design of axisymmetric bodies. [flow distribution and incompressible fluids

NASA Technical Reports Server (NTRS)

Beatty, T. D.

1975-01-01

A theoretical method is presented for the computation of the flow field about an axisymmetric body operating in a viscous, incompressible fluid. A potential flow method was used to determine the inviscid flow field and to yield the boundary conditions for the boundary layer solutions. Boundary layer effects in the forces of displacement thickness and empirically modeled separation streamlines are accounted for in subsequent potential flow solutions. This procedure is repeated until the solutions converge. An empirical method was used to determine base drag allowing configuration drag to be computed.

Method of making a rocket nozzle

NASA Technical Reports Server (NTRS)

Campbell, D. H. (Inventor)

1969-01-01

A method is described for forming the interior of a nozzle having uneven walls so that a throat of smooth converging and diverging sides is provided for passing flow. A metallic insert material is placed within the flow passageway adjacent to the area where the sharper throat constriction is to be formed, so that the material will flow through the inlet into the throat space when liquefied.

Accuracy and Numerical Stabilty Analysis of Lattice Boltzmann Method with Multiple Relaxation Time for Incompressible Flows

NASA Astrophysics Data System (ADS)

Pradipto; Purqon, Acep

2017-07-01

Lattice Boltzmann Method (LBM) is the novel method for simulating fluid dynamics. Nowadays, the application of LBM ranges from the incompressible flow, flow in the porous medium, until microflows. The common collision model of LBM is the BGK with a constant single relaxation time τ. However, BGK suffers from numerical instabilities. These instabilities could be eliminated by implementing LBM with multiple relaxation time. Both of those scheme have implemented for incompressible 2 dimensions lid-driven cavity. The stability analysis has done by finding the maximum Reynolds number and velocity for converged simulations. The accuracy analysis is done by comparing the velocity profile with the benchmark results from Ghia, et al and calculating the net velocity flux. The tests concluded that LBM with MRT are more stable than BGK, and have a similar accuracy. The maximum Reynolds number that converges for BGK is 3200 and 7500 for MRT respectively.

Two-phase flow pressure drop and heat transfer during condensation in microchannels with uniform and converging cross-sections

NASA Astrophysics Data System (ADS)

Kuo, Ching Yi; Pan, Chin

2010-09-01

This study experimentally investigates steam condensation in rectangular microchannels with uniform and converging cross-sections and a mean hydraulic diameter of 135 µm. The steam flow in the microchannels was cooled by water cross-flowing along its bottom surface, which is different from other methods reported in the literature. The flow patterns, two-phase flow pressure drop and condensation heat transfer coefficient are determined. The microchannels with the uniform cross-section design have a higher heat transfer coefficient than those with the converging cross-section under condensation in the mist/annular flow regimes, although the latter work best for draining two-phase fluids composed of uncondensed steam and liquid water, which is consistent with the result of our previous study. From the experimental results, dimensionless correlations of condensation heat transfer for the mist and annular flow regions and a two-phase frictional multiplier are developed for the microchannels with both types of cross-section designs. The experimental data agree well with the obtained correlations, with the maximum mean absolute errors of 6.4% for the two-phase frictional multiplier and 6.0% for the condensation heat transfer.

On the POD based reduced order modeling of high Reynolds flows

NASA Astrophysics Data System (ADS)

Behzad, Fariduddin; Helenbrook, Brian; Ahmadi, Goodarz

2012-11-01

Reduced-order modeling (ROM) of a high Reynolds fluid flow using the proper orthogonal decomposition (POD) was studied. Particular attention was given to incompressible, unsteady flow over a two-dimensional NACA0015 airfoil. The Reynolds number is 105 and the angle of attacked of the airfoil is 12°. For DNS solution, hp-finite element method is employed to drive flow samples from which the POD modes are extracted. Particular attention is paid on two issues. First, the stability of POD-ROM resimulation of the turbulent flow is studied. High Reynolds flow contains a lot of fluctuating modes. So, to reach a certain amount of error, more POD modes are needed and the effect of truncation of POD modes is more important. Second, the role of convergence rate on the results of POD. Due to complexity of the flow, convergence of the governing equations is more difficult and the influences of weak convergence appear in the results of POD-ROM. For each issue, the capability of the POD-ROM is assessed in terms of predictions quality of times upon which the POD model was derived. The results are compared with DNS solution and the accuracy and efficiency of different cases are evaluated.

Approximation methods for stochastic petri nets

NASA Technical Reports Server (NTRS)

Jungnitz, Hauke Joerg

1992-01-01

Stochastic Marked Graphs are a concurrent decision free formalism provided with a powerful synchronization mechanism generalizing conventional Fork Join Queueing Networks. In some particular cases the analysis of the throughput can be done analytically. Otherwise the analysis suffers from the classical state explosion problem. Embedded in the divide and conquer paradigm, approximation techniques are introduced for the analysis of stochastic marked graphs and Macroplace/Macrotransition-nets (MPMT-nets), a new subclass introduced herein. MPMT-nets are a subclass of Petri nets that allow limited choice, concurrency and sharing of resources. The modeling power of MPMT is much larger than that of marked graphs, e.g., MPMT-nets can model manufacturing flow lines with unreliable machines and dataflow graphs where choice and synchronization occur. The basic idea leads to the notion of a cut to split the original net system into two subnets. The cuts lead to two aggregated net systems where one of the subnets is reduced to a single transition. A further reduction leads to a basic skeleton. The generalization of the idea leads to multiple cuts, where single cuts can be applied recursively leading to a hierarchical decomposition. Based on the decomposition, a response time approximation technique for the performance analysis is introduced. Also, delay equivalence, which has previously been introduced in the context of marked graphs by Woodside et al., Marie's method and flow equivalent aggregation are applied to the aggregated net systems. The experimental results show that response time approximation converges quickly and shows reasonable accuracy in most cases. The convergence of Marie's method and flow equivalent aggregation are applied to the aggregated net systems. The experimental results show that response time approximation converges quickly and shows reasonable accuracy in most cases. The convergence of Marie's is slower, but the accuracy is generally better. Delay equivalence often fails to converge, while flow equivalent aggregation can lead to potentially bad results if a strong dependence of the mean completion time on the interarrival process exists.

Apparatus and method for spraying liquid materials

DOEpatents

Alvarez, J.L.; Watson, L.D.

1988-01-21

A method for spraying liquids involving a flow of gas which shears the liquid. A flow of gas is introduced in a converging-diverging nozzle where it meets and shears the liquid into small particles which are of a size and uniformity which can be controlled through adjustment of pressures and gas velocity. 5 figs.

Apparatus and method for spraying liquid materials

DOEpatents

Alvarez, Joseph L.; Watson, Lloyd D.

1990-01-01

A method for spraying liquids involving a flow of gas which shears the liquid. A flow of gas is introduced in a converging-diverging nozzle where it meets and shears the liquid into small particles which are of a size and uniformity which can be controlled through adjustment of pressures and gas velocity.

Method and apparatus for automatically generating airfoil performance tables

NASA Technical Reports Server (NTRS)

van Dam, Cornelis P. (Inventor); Mayda, Edward A. (Inventor); Strawn, Roger Clayton (Inventor)

2006-01-01

One embodiment of the present invention provides a system that facilitates automatically generating a performance table for an object, wherein the object is subject to fluid flow. The system operates by first receiving a description of the object and testing parameters for the object. The system executes a flow solver using the testing parameters and the description of the object to produce an output. Next, the system determines if the output of the flow solver indicates negative density or pressure. If not, the system analyzes the output to determine if the output is converging. If converging, the system writes the output to the performance table for the object.

Converging flow joint insert system at an intersection between adjacent transitions extending between a combustor and a turbine assembly in a gas turbine engine

DOE Office of Scientific and Technical Information (OSTI.GOV)

Brooks, Robert T.

A transition duct system (100) for routing a gas flow from a combustor (102) to the first stage (104) of a turbine section (106) in a combustion turbine engine (108), wherein the transition duct system (100) includes one or more converging flow joint inserts (120) forming a trailing edge (122) at an intersection (124) between adjacent transition ducts (126, 128) is disclosed. The transition duct system (100) may include a transition duct (126, 128) having an internal passage (130) extending between an inlet (132, 184) to an outlet (134, 186) and may expel gases into the first stage turbine (104)more » with a tangential component. The converging flow joint insert (120) may be contained within a converging flow joint insert receiver (136) and disconnected from the transition duct bodies (126, 128) by which the converging flow joint insert (120) is positioned. Being disconnected eliminates stress formation within the converging flow joint insert (120), thereby enhancing the life of the insert. The converging flow joint insert (120) may be removable such that the insert (120) can be replaced once worn beyond design limits.« less

Gas ultrasonic flow rate measurement through genetic-ant colony optimization based on the ultrasonic pulse received signal model

NASA Astrophysics Data System (ADS)

Hou, Huirang; Zheng, Dandan; Nie, Laixiao

2015-04-01

For gas ultrasonic flowmeters, the signals received by ultrasonic sensors are susceptible to noise interference. If signals are mingled with noise, a large error in flow measurement can be caused by triggering mistakenly using the traditional double-threshold method. To solve this problem, genetic-ant colony optimization (GACO) based on the ultrasonic pulse received signal model is proposed. Furthermore, in consideration of the real-time performance of the flow measurement system, the improvement of processing only the first three cycles of the received signals rather than the whole signal is proposed. Simulation results show that the GACO algorithm has the best estimation accuracy and ant-noise ability compared with the genetic algorithm, ant colony optimization, double-threshold and enveloped zero-crossing. Local convergence doesn’t appear with the GACO algorithm until -10 dB. For the GACO algorithm, the converging accuracy and converging speed and the amount of computation are further improved when using the first three cycles (called GACO-3cycles). Experimental results involving actual received signals show that the accuracy of single-gas ultrasonic flow rate measurement can reach 0.5% with GACO-3 cycles, which is better than with the double-threshold method.

Discontinuous Galerkin method for multicomponent chemically reacting flows and combustion

NASA Astrophysics Data System (ADS)

Lv, Yu; Ihme, Matthias

2014-08-01

This paper presents the development of a discontinuous Galerkin (DG) method for application to chemically reacting flows in subsonic and supersonic regimes under the consideration of variable thermo-viscous-diffusive transport properties, detailed and stiff reaction chemistry, and shock capturing. A hybrid-flux formulation is developed for treatment of the convective fluxes, combining a conservative Riemann-solver and an extended double-flux scheme. A computationally efficient splitting scheme is proposed, in which advection and diffusion operators are solved in the weak form, and the chemically stiff substep is advanced in the strong form using a time-implicit scheme. The discretization of the viscous-diffusive transport terms follows the second form of Bassi and Rebay, and the WENO-based limiter due to Zhong and Shu is extended to multicomponent systems. Boundary conditions are developed for subsonic and supersonic flow conditions, and the algorithm is coupled to thermochemical libraries to account for detailed reaction chemistry and complex transport. The resulting DG method is applied to a series of test cases of increasing physico-chemical complexity. Beginning with one- and two-dimensional multispecies advection and shock-fluid interaction problems, computational efficiency, convergence, and conservation properties are demonstrated. This study is followed by considering a series of detonation and supersonic combustion problems to investigate the convergence-rate and the shock-capturing capability in the presence of one- and multistep reaction chemistry. The DG algorithm is then applied to diffusion-controlled deflagration problems. By examining convergence properties for polynomial order and spatial resolution, and comparing these with second-order finite-volume solutions, it is shown that optimal convergence is achieved and that polynomial refinement provides advantages in better resolving the localized flame structure and complex flow-field features associated with multidimensional and hydrodynamic/thermo-diffusive instabilities in deflagration and detonation systems. Comparisons with standard third- and fifth-order WENO schemes are presented to illustrate the benefit of the DG scheme for application to detonation and multispecies flow/shock-interaction problems.

Second order upwind Lagrangian particle method for Euler equations

DOE PAGES

Samulyak, Roman; Chen, Hsin -Chiang; Yu, Kwangmin

2016-06-01

A new second order upwind Lagrangian particle method for solving Euler equations for compressible inviscid fluid or gas flows is proposed. Similar to smoothed particle hydrodynamics (SPH), the method represents fluid cells with Lagrangian particles and is suitable for the simulation of complex free surface / multiphase flows. The main contributions of our method, which is different from SPH in all other aspects, are (a) significant improvement of approximation of differential operators based on a polynomial fit via weighted least squares approximation and the convergence of prescribed order, (b) an upwind second-order particle-based algorithm with limiter, providing accuracy and longmore » term stability, and (c) accurate resolution of states at free interfaces. In conclusion, numerical verification tests demonstrating the convergence order for fixed domain and free surface problems are presented.« less

Second order upwind Lagrangian particle method for Euler equations

DOE Office of Scientific and Technical Information (OSTI.GOV)

Samulyak, Roman; Chen, Hsin -Chiang; Yu, Kwangmin

A new second order upwind Lagrangian particle method for solving Euler equations for compressible inviscid fluid or gas flows is proposed. Similar to smoothed particle hydrodynamics (SPH), the method represents fluid cells with Lagrangian particles and is suitable for the simulation of complex free surface / multiphase flows. The main contributions of our method, which is different from SPH in all other aspects, are (a) significant improvement of approximation of differential operators based on a polynomial fit via weighted least squares approximation and the convergence of prescribed order, (b) an upwind second-order particle-based algorithm with limiter, providing accuracy and longmore » term stability, and (c) accurate resolution of states at free interfaces. In conclusion, numerical verification tests demonstrating the convergence order for fixed domain and free surface problems are presented.« less

An efficient method for solving the steady Euler equations

NASA Technical Reports Server (NTRS)

Liou, M. S.

1986-01-01

An efficient numerical procedure for solving a set of nonlinear partial differential equations is given, specifically for the steady Euler equations. Solutions of the equations were obtained by Newton's linearization procedure, commonly used to solve the roots of nonlinear algebraic equations. In application of the same procedure for solving a set of differential equations we give a theorem showing that a quadratic convergence rate can be achieved. While the domain of quadratic convergence depends on the problems studied and is unknown a priori, we show that firstand second-order derivatives of flux vectors determine whether the condition for quadratic convergence is satisfied. The first derivatives enter as an implicit operator for yielding new iterates and the second derivatives indicates smoothness of the flows considered. Consequently flows involving shocks are expected to require larger number of iterations. First-order upwind discretization in conjunction with the Steger-Warming flux-vector splitting is employed on the implicit operator and a diagonal dominant matrix results. However the explicit operator is represented by first- and seond-order upwind differencings, using both Steger-Warming's and van Leer's splittings. We discuss treatment of boundary conditions and solution procedures for solving the resulting block matrix system. With a set of test problems for one- and two-dimensional flows, we show detailed study as to the efficiency, accuracy, and convergence of the present method.

Development and evaluation of a local grid refinement method for block-centered finite-difference groundwater models using shared nodes

USGS Publications Warehouse

Mehl, S.; Hill, M.C.

2002-01-01

A new method of local grid refinement for two-dimensional block-centered finite-difference meshes is presented in the context of steady-state groundwater-flow modeling. The method uses an iteration-based feedback with shared nodes to couple two separate grids. The new method is evaluated by comparison with results using a uniform fine mesh, a variably spaced mesh, and a traditional method of local grid refinement without a feedback. Results indicate: (1) The new method exhibits quadratic convergence for homogeneous systems and convergence equivalent to uniform-grid refinement for heterogeneous systems. (2) Coupling the coarse grid with the refined grid in a numerically rigorous way allowed for improvement in the coarse-grid results. (3) For heterogeneous systems, commonly used linear interpolation of heads from the large model onto the boundary of the refined model produced heads that are inconsistent with the physics of the flow field. (4) The traditional method works well in situations where the better resolution of the locally refined grid has little influence on the overall flow-system dynamics, but if this is not true, lack of a feedback mechanism produced errors in head up to 3.6% and errors in cell-to-cell flows up to 25%. ?? 2002 Elsevier Science Ltd. All rights reserved.

On conforming mixed finite element methods for incompressible viscous flow problems

NASA Technical Reports Server (NTRS)

Gunzburger, M. D; Nicolaides, R. A.; Peterson, J. S.

1982-01-01

The application of conforming mixed finite element methods to obtain approximate solutions of linearized Navier-Stokes equations is examined. Attention is given to the convergence rates of various finite element approximations of the pressure and the velocity field. The optimality of the convergence rates are addressed in terms of comparisons of the approximation convergence to a smooth solution in relation to the best approximation available for the finite element space used. Consideration is also devoted to techniques for efficient use of a Gaussian elimination algorithm to obtain a solution to a system of linear algebraic equations derived by finite element discretizations of linear partial differential equations.

Application of a multi-level grid method to transonic flow calculations

NASA Technical Reports Server (NTRS)

South, J. C., Jr.; Brandt, A.

1976-01-01

A multi-level grid method was studied as a possible means of accelerating convergence in relaxation calculations for transonic flows. The method employs a hierarchy of grids, ranging from very coarse to fine. The coarser grids are used to diminish the magnitude of the smooth part of the residuals. The method was applied to the solution of the transonic small disturbance equation for the velocity potential in conservation form. Nonlifting transonic flow past a parabolic arc airfoil is studied with meshes of both constant and variable step size.

The Application of Simulation Method in Isothermal Elastic Natural Gas Pipeline

NASA Astrophysics Data System (ADS)

Xing, Chunlei; Guan, Shiming; Zhao, Yue; Cao, Jinggang; Chu, Yanji

2018-02-01

This Elastic pipeline mathematic model is of crucial importance in natural gas pipeline simulation because of its compliance with the practical industrial cases. The numerical model of elastic pipeline will bring non-linear complexity to the discretized equations. Hence the Newton-Raphson method cannot achieve fast convergence in this kind of problems. Therefore A new Newton Based method with Powell-Wolfe Condition to simulate the Isothermal elastic pipeline flow is presented. The results obtained by the new method aregiven based on the defined boundary conditions. It is shown that the method converges in all cases and reduces significant computational cost.

Grid Convergence of High Order Methods for Multiscale Complex Unsteady Viscous Compressible Flows

NASA Technical Reports Server (NTRS)

Sjoegreen, B.; Yee, H. C.

2001-01-01

Grid convergence of several high order methods for the computation of rapidly developing complex unsteady viscous compressible flows with a wide range of physical scales is studied. The recently developed adaptive numerical dissipation control high order methods referred to as the ACM and wavelet filter schemes are compared with a fifth-order weighted ENO (WENO) scheme. The two 2-D compressible full Navier-Stokes models considered do not possess known analytical and experimental data. Fine grid solutions from a standard second-order TVD scheme and a MUSCL scheme with limiters are used as reference solutions. The first model is a 2-D viscous analogue of a shock tube problem which involves complex shock/shear/boundary-layer interactions. The second model is a supersonic reactive flow concerning fuel breakup. The fuel mixing involves circular hydrogen bubbles in air interacting with a planar moving shock wave. Both models contain fine scale structures and are stiff in the sense that even though the unsteadiness of the flows are rapidly developing, extreme grid refinement and time step restrictions are needed to resolve all the flow scales as well as the chemical reaction scales.

Nozzle Flow with Vibrational Nonequilibrium. Ph.D. Thesis

NASA Technical Reports Server (NTRS)

Landry, John Gary

1995-01-01

Flow of nitrogen gas through a converging-diverging nozzle is simulated. The flow is modeled using the Navier-Stokes equations that have been modified for vibrational nonequilibrium. The energy equation is replaced by two equations. One equation accounts for energy effects due to the translational and rotational degrees of freedom, and the other accounts for the affects due to the vibrational degree of freedom. The energy equations are coupled by a relaxation time which measures the time required for the vibrational energy component to equilibrate with the translational and rotational energy components. An improved relaxation time is used in this thesis. The equations are solved numerically using the Steger-Warming flux vector splitting method and the Implicit MacCormack method. The results show that uniform flow is produced outside of the boundary layer. Nonequilibrium exists in both the converging and diverging nozzle sections. The boundary layer region is characterized by a marked increase in translational-rotational temperature. The vibrational temperature remains frozen downstream of the nozzle, except in the boundary layer.

A coupled implicit method for chemical non-equilibrium flows at all speeds

NASA Technical Reports Server (NTRS)

Shuen, Jian-Shun; Chen, Kuo-Huey; Choi, Yunho

1993-01-01

The present time-accurate coupled-solution procedure addresses the chemical nonequilibrium Navier-Stokes equations over a wide Mach-number range uses, in conjunction with the strong conservation form of the governing equations, five unknown primitive variables. The numerical tests undertaken address steady convergent-divergent nozzle flows with air dissociation/recombination, dump combustor flows with n-pentane/air chemistry, and unsteady nonreacting cavity flows.

Slip flow through a converging microchannel: experiments and 3D simulations

NASA Astrophysics Data System (ADS)

Varade, Vijay; Agrawal, Amit; Pradeep, A. M.

2015-02-01

An experimental and 3D numerical study of gaseous slip flow through a converging microchannel is presented in this paper. The measurements reported are with nitrogen gas flowing through the microchannel with convergence angles (4°, 8° and 12°), hydraulic diameters (118, 147 and 177 µm) and lengths (10, 20 and 30 mm). The measurements cover the entire slip flow regime and a part of the continuum and transition regimes (the Knudsen number is between 0.0004 and 0.14); the flow is laminar (the Reynolds number is between 0.5 and 1015). The static pressure drop is measured for various mass flow rates. The overall pressure drop increases with a decrease in the convergence angle and has a relatively large contribution of the viscous component. The numerical solutions of the Navier-Stokes equations with Maxwell’s slip boundary condition explore two different flow behaviors: uniform centerline velocity with linear pressure variation in the initial and the middle part of the microchannel and flow acceleration with nonlinear pressure variation in the last part of the microchannel. The centerline velocity and the wall shear stress increase with a decrease in the convergence angle. The concept of a characteristic length scale for a converging microchannel is also explored. The location of the characteristic length is a function of the Knudsen number and approaches the microchannel outlet with rarefaction. These results on gaseous slip flow through converging microchannels are observed to be considerably different than continuum flow.

Three-dimensional unstructured grid Euler computations using a fully-implicit, upwind method

NASA Technical Reports Server (NTRS)

Whitaker, David L.

1993-01-01

A method has been developed to solve the Euler equations on a three-dimensional unstructured grid composed of tetrahedra. The method uses an upwind flow solver with a linearized, backward-Euler time integration scheme. Each time step results in a sparse linear system of equations which is solved by an iterative, sparse matrix solver. Local-time stepping, switched evolution relaxation (SER), preconditioning and reuse of the Jacobian are employed to accelerate the convergence rate. Implicit boundary conditions were found to be extremely important for fast convergence. Numerical experiments have shown that convergence rates comparable to that of a multigrid, central-difference scheme are achievable on the same mesh. Results are presented for several grids about an ONERA M6 wing.

Hybrid Method for Power Control Simulation of a Single Fluid Plasma Thruster

NASA Astrophysics Data System (ADS)

Jaisankar, S.; Sheshadri, T. S.

2018-05-01

Propulsive plasma flow through a cylindrical-conical diverging thruster is simulated by a power controlled hybrid method to obtain the basic flow, thermodynamic and electromagnetic variables. Simulation is based on a single fluid model with electromagnetics being described by the equations of potential Poisson, Maxwell and the Ohm's law while the compressible fluid dynamics by the Navier Stokes in cylindrical form. The proposed method solved the electromagnetics and fluid dynamics separately, both to segregate the two prominent scales for an efficient computation and for the delivery of voltage controlled rated power. The magnetic transport is solved for steady state while fluid dynamics is allowed to evolve in time along with an electromagnetic source using schemes based on generalized finite difference discretization. The multistep methodology with power control is employed for simulating fully ionized propulsive flow of argon plasma through the thruster. Numerical solution shows convergence of every part of the solver including grid stability causing the multistep hybrid method to converge for a rated power delivery. Simulation results are reasonably in agreement with the reported physics of plasma flow in the thruster thus indicating the potential utility of this hybrid computational framework, especially when single fluid approximation of plasma is relevant.

Convergence speeding up in the calculation of the viscous flow about an airfoil

NASA Technical Reports Server (NTRS)

Radespiel, R.; Rossow, C.

1988-01-01

A finite volume method to solve the three dimensional Navier-Stokes equations was developed. It is based on a cell-vertex scheme with central differences and explicit Runge-Kutta time steps. A good convergence for a stationary solution was obtained by the use of local time steps, implicit smoothing of the residues, a multigrid algorithm, and a carefully controlled artificial dissipative term. The method is illustrated by results for transonic profiles and airfoils. The method allows a routine solution of the Navier-Stokes equations.

Modeling sediment trapping in a vegetative filter accounting for converging overland flow

Treesearch

M. J. Helmers; D. E. Eisenhauer; T. G. Franti; M. G. Dosskey

2005-01-01

Vegetative filters (VF) are used to remove sediment and other pollutants from overland flow. When modeling the hydrology of VF, it is often assumed that overland flow is planar, but our research indicated that it can be two-dimensional with converging and diverging pathways. Our hypothesis is that flow convergence will negatively influence the sediment trapping...

Vortex methods for separated flows

NASA Technical Reports Server (NTRS)

Spalart, Philippe R.

1988-01-01

The numerical solution of the Euler or Navier-Stokes equations by Lagrangian vortex methods is discussed. The mathematical background is presented and includes the relationship with traditional point-vortex studies, convergence to smooth solutions of the Euler equations, and the essential differences between two and three-dimensional cases. The difficulties in extending the method to viscous or compressible flows are explained. Two-dimensional flows around bluff bodies are emphasized. Robustness of the method and the assessment of accuracy, vortex-core profiles, time-marching schemes, numerical dissipation, and efficient programming are treated. Operation counts for unbounded and periodic flows are given, and two algorithms designed to speed up the calculations are described.

Application of high-order numerical schemes and Newton-Krylov method to two-phase drift-flux model

DOE Office of Scientific and Technical Information (OSTI.GOV)

Zou, Ling; Zhao, Haihua; Zhang, Hongbin

This study concerns the application and solver robustness of the Newton-Krylov method in solving two-phase flow drift-flux model problems using high-order numerical schemes. In our previous studies, the Newton-Krylov method has been proven as a promising solver for two-phase flow drift-flux model problems. However, these studies were limited to use first-order numerical schemes only. Moreover, the previous approach to treating the drift-flux closure correlations was later revealed to cause deteriorated solver convergence performance, when the mesh was highly refined, and also when higher-order numerical schemes were employed. In this study, a second-order spatial discretization scheme that has been tested withmore » two-fluid two-phase flow model was extended to solve drift-flux model problems. In order to improve solver robustness, and therefore efficiency, a new approach was proposed to treating the mean drift velocity of the gas phase as a primary nonlinear variable to the equation system. With this new approach, significant improvement in solver robustness was achieved. With highly refined mesh, the proposed treatment along with the Newton-Krylov solver were extensively tested with two-phase flow problems that cover a wide range of thermal-hydraulics conditions. Satisfactory convergence performances were observed for all test cases. Numerical verification was then performed in the form of mesh convergence studies, from which expected orders of accuracy were obtained for both the first-order and the second-order spatial discretization schemes. Finally, the drift-flux model, along with numerical methods presented, were validated with three sets of flow boiling experiments that cover different flow channel geometries (round tube, rectangular tube, and rod bundle), and a wide range of test conditions (pressure, mass flux, wall heat flux, inlet subcooling and outlet void fraction).« less

Application of high-order numerical schemes and Newton-Krylov method to two-phase drift-flux model

DOE PAGES

Zou, Ling; Zhao, Haihua; Zhang, Hongbin

2017-08-07

This study concerns the application and solver robustness of the Newton-Krylov method in solving two-phase flow drift-flux model problems using high-order numerical schemes. In our previous studies, the Newton-Krylov method has been proven as a promising solver for two-phase flow drift-flux model problems. However, these studies were limited to use first-order numerical schemes only. Moreover, the previous approach to treating the drift-flux closure correlations was later revealed to cause deteriorated solver convergence performance, when the mesh was highly refined, and also when higher-order numerical schemes were employed. In this study, a second-order spatial discretization scheme that has been tested withmore » two-fluid two-phase flow model was extended to solve drift-flux model problems. In order to improve solver robustness, and therefore efficiency, a new approach was proposed to treating the mean drift velocity of the gas phase as a primary nonlinear variable to the equation system. With this new approach, significant improvement in solver robustness was achieved. With highly refined mesh, the proposed treatment along with the Newton-Krylov solver were extensively tested with two-phase flow problems that cover a wide range of thermal-hydraulics conditions. Satisfactory convergence performances were observed for all test cases. Numerical verification was then performed in the form of mesh convergence studies, from which expected orders of accuracy were obtained for both the first-order and the second-order spatial discretization schemes. Finally, the drift-flux model, along with numerical methods presented, were validated with three sets of flow boiling experiments that cover different flow channel geometries (round tube, rectangular tube, and rod bundle), and a wide range of test conditions (pressure, mass flux, wall heat flux, inlet subcooling and outlet void fraction).« less

An efficient and general numerical method to compute steady uniform vortices

NASA Astrophysics Data System (ADS)

Luzzatto-Fegiz, Paolo; Williamson, Charles H. K.

2011-07-01

Steady uniform vortices are widely used to represent high Reynolds number flows, yet their efficient computation still presents some challenges. Existing Newton iteration methods become inefficient as the vortices develop fine-scale features; in addition, these methods cannot, in general, find solutions with specified Casimir invariants. On the other hand, available relaxation approaches are computationally inexpensive, but can fail to converge to a solution. In this paper, we overcome these limitations by introducing a new discretization, based on an inverse-velocity map, which radically increases the efficiency of Newton iteration methods. In addition, we introduce a procedure to prescribe Casimirs and remove the degeneracies in the steady vorticity equation, thus ensuring convergence for general vortex configurations. We illustrate our methodology by considering several unbounded flows involving one or two vortices. Our method enables the computation, for the first time, of steady vortices that do not exhibit any geometric symmetry. In addition, we discover that, as the limiting vortex state for each flow is approached, each family of solutions traces a clockwise spiral in a bifurcation plot consisting of a velocity-impulse diagram. By the recently introduced "IVI diagram" stability approach [Phys. Rev. Lett. 104 (2010) 044504], each turn of this spiral is associated with a loss of stability for the steady flows. Such spiral structure is suggested to be a universal feature of steady, uniform-vorticity flows.

Study of effects of injector geometry on fuel-air mixing and combustion

NASA Technical Reports Server (NTRS)

Bangert, L. H.; Roach, R. L.

1977-01-01

An implicit finite-difference method has been developed for computing the flow in the near field of a fuel injector as part of a broader study of the effects of fuel injector geometry on fuel-air mixing and combustion. Detailed numerical results have been obtained for cases of laminar and turbulent flow without base injection, corresponding to the supersonic base flow problem. These numerical results indicated that the method is stable and convergent, and that significant savings in computer time can be achieved, compared with explicit methods.

Improved numerical methods for turbulent viscous recirculating flows

NASA Technical Reports Server (NTRS)

Turan, A.; Vandoormaal, J. P.

1988-01-01

The performance of discrete methods for the prediction of fluid flows can be enhanced by improving the convergence rate of solvers and by increasing the accuracy of the discrete representation of the equations of motion. This report evaluates the gains in solver performance that are available when various acceleration methods are applied. Various discretizations are also examined and two are recommended because of their accuracy and robustness. Insertion of the improved discretization and solver accelerator into a TEACH mode, that has been widely applied to combustor flows, illustrates the substantial gains to be achieved.

Quantification of mitral and tricuspid regurgitation by the proximal flow convergence method using two-dimensional colour Doppler and colour Doppler M-mode: influence of the mechanism of regurgitation.

PubMed

Grossmann, G; Giesler, M; Stein, M; Kochs, M; Höher, M; Hombach, V

1998-10-30

In patients with mitral (n=77: organic=49, functional=28) and tricuspid regurgitation (n=55: functional=54) quantified by angiography, the temporal variation of the proximal flow convergence region throughout systole was assessed by colour Doppler M-Mode, and peak and mean radius of the proximal isovelocity surface area for 28 cm/s blood flow velocity were measured. Additionally, the peak radius derived from two-dimensional colour Doppler was obtained. About 50% of the patients with mitral and tricuspid regurgitation showed a typical temporal variation of the flow convergence region related to the mechanism of regurgitation. The different proximal isovelocity surface area radii were similarly correlated to the angiographic grade in mitral and tricuspid regurgitation (rank correlation coefficients 0.55-0.89) and they differentiated mild to moderate (grade < or =II) from severe (grade > or =III) mitral and tricuspid regurgitation with comparable accuracy (82-96%). However, moderate mitral regurgitation due to leaflet prolapse in two patients was correctly classified by the mean M-mode radius and overestimated by both peak radii. Only half of the patients showed a typical variation of the flow convergence region related to the mechanism of regurgitation. The different proximal isovelocity surface area radii were suitable to quantify mitral and tricuspid regurgitation in most patients. However, in mitral regurgitation due to leaflet prolapse the use of the mean M-mode radius may avoid overestimation.

Distinct wind convergence patterns in the Mexico City basin due to the interaction of the gap winds with the synoptic flow

NASA Astrophysics Data System (ADS)

de Foy, B.; Clappier, A.; Molina, L. T.; Molina, M. J.

2006-04-01

Mexico City lies in a high altitude basin where air quality and pollutant fate is strongly influenced by local winds. The combination of high terrain with weak synoptic forcing leads to weak and variable winds with complex circulation patterns. A gap wind entering the basin in the afternoon leads to very different wind convergence lines over the city depending on the meteorological conditions. Surface and upper-air meteorological observations are analysed during the MCMA-2003 field campaign to establish the meteorological conditions and obtain an index of the strength and timing of the gap wind. A mesoscale meteorological model (MM5) is used in combination with high-resolution satellite data for the land surface parameters and soil moisture maps derived from diurnal ground temperature range. A simple method to map the lines of wind convergence both in the basin and on the regional scale is used to show the different convergence patterns according to episode types. The gap wind is found to occur on most days of the campaign and is the result of a temperature gradient across the southern basin rim which is very similar from day to day. Momentum mixing from winds aloft into the surface layer is much more variable and can determine both the strength of the flow and the pattern of the convergence zones. Northerly flows aloft lead to a weak jet with an east-west convergence line that progresses northwards in the late afternoon and early evening. Westerlies aloft lead to both stronger gap flows due to channelling and winds over the southern and western basin rim. This results in a north-south convergence line through the middle of the basin starting in the early afternoon. Improved understanding of basin meteorology will lead to better air quality forecasts for the city and better understanding of the chemical regimes in the urban atmosphere.

Artificial dissipation and central difference schemes for the Euler and Navier-Stokes equations

NASA Technical Reports Server (NTRS)

Swanson, R. C.; Turkel, Eli

1987-01-01

An artificial dissipation model, including boundary treatment, that is employed in many central difference schemes for solving the Euler and Navier-Stokes equations is discussed. Modifications of this model such as the eigenvalue scaling suggested by upwind differencing are examined. Multistage time stepping schemes with and without a multigrid method are used to investigate the effects of changes in the dissipation model on accuracy and convergence. Improved accuracy for inviscid and viscous airfoil flow is obtained with the modified eigenvalue scaling. Slower convergence rates are experienced with the multigrid method using such scaling. The rate of convergence is improved by applying a dissipation scaling function that depends on mesh cell aspect ratio.

Numerical solution of Euler's equation by perturbed functionals

NASA Technical Reports Server (NTRS)

Dey, S. K.

1985-01-01

A perturbed functional iteration has been developed to solve nonlinear systems. It adds at each iteration level, unique perturbation parameters to nonlinear Gauss-Seidel iterates which enhances its convergence properties. As convergence is approached these parameters are damped out. Local linearization along the diagonal has been used to compute these parameters. The method requires no computation of Jacobian or factorization of matrices. Analysis of convergence depends on properties of certain contraction-type mappings, known as D-mappings. In this article, application of this method to solve an implicit finite difference approximation of Euler's equation is studied. Some representative results for the well known shock tube problem and compressible flows in a nozzle are given.

The role of boundary layer momentum advection in the mean location of the ITCZ

NASA Astrophysics Data System (ADS)

Dixit, Vishal; Srinivasan, J.

2017-08-01

The inter-tropical convergence zones (ITCZ) form closer to the equator during equinoxes while they form well away from the equator during the boreal summer. A simple three-way balance between the pressure gradients, Coriolis force and effective Rayleigh friction has been classically used to diagnose the location of maximum boundary layer convergence in the near equatorial ITCZ. If such a balance can capture the dynamics of off-equatorial convergence was not known. We used idealized aqua planet simulations with fixed, zonally symmetric sea surface temperature boundary conditions to simulate the near equatorial and off-equatorial ITCZ. As opposed to the convergence of inter-hemispheric flows in the near equatorial convergence, the off-equatorial convergence forms due to the deceleration of cross-equatorial meridional flow. The detailed momentum budget of the off-equatorial convergence zone reveals that the simple balance is not sufficient to capture the relevant dynamics. The deceleration of the meridional flow is strongly modulated by the inertial effects due to the meridional advection of zonal momentum in addition to the terms in the simple balance. The simple balance predicts a spurious near equatorial convergence and a consistent off-equatorial convergence of the meridional flow. The spurious convergence disappears when inertial effects are included in the balance. As cross equatorial meridional flow decelerates to form convergence, the inertial effects cancel the pressure gradient effects near the equator while they add away from the equator. The contribution to the off-equatorial convergence induced by the pressure gradients is significantly larger than the contribution due to the inertial effects and hence pressure gradients appear to be the primary factor in anchoring the strength and location of the off-equatorial convergence.

The Finite-Surface Method for incompressible flow: a step beyond staggered grid

NASA Astrophysics Data System (ADS)

Hokpunna, Arpiruk; Misaka, Takashi; Obayashi, Shigeru

2017-11-01

We present a newly developed higher-order finite surface method for the incompressible Navier-Stokes equations (NSE). This method defines the velocities as a surface-averaged value on the surfaces of the pressure cells. Consequently, the mass conservation on the pressure cells becomes an exact equation. The only things left to approximate is the momentum equation and the pressure at the new time step. At certain conditions, the exact mass conservation enables the explicit n-th order accurate NSE solver to be used with the pressure treatment that is two or four order less accurate without loosing the apparent convergence rate. This feature was not possible with finite volume of finite difference methods. We use Fourier analysis with a model spectrum to determine the condition and found that the range covers standard boundary layer flows. The formal convergence and the performance of the proposed scheme is compared with a sixth-order finite volume method. Finally, the accuracy and performance of the method is evaluated in turbulent channel flows. This work is partially funded by a research colloaboration from IFS, Tohoku university and ASEAN+3 funding scheme from CMUIC, Chiang Mai University.

A two-dimensional, TVD numerical scheme for inviscid, high Mach number flows in chemical equilibrium

NASA Technical Reports Server (NTRS)

Eberhardt, S.; Palmer, G.

1986-01-01

A new algorithm has been developed for hypervelocity flows in chemical equilibrium. Solutions have been achieved for Mach numbers up to 15 with no adverse effect on convergence. Two methods of coupling an equilibrium chemistry package have been tested, with the simpler method proving to be more robust. Improvements in boundary conditions are still required for a production-quality code.

High Fidelity Modeling of Field-Reversed Configuration (FRC) Thrusters (Briefing Charts)

DTIC Science & Technology

2017-05-24

Converged Math → Irrelevant Solutions? Validation: Fluids Example Stoke’s Flow MARTIN, SOUSA, TRAN (AFRL/RQRS) DISTRIBUTION A - APPROVED FOR PUBLIC RELEASE...Convergence Tests Converged Math → Irrelevant Solutions? Must be Aware of Valid Assumption Regions Validation: Fluids Example Stoke’s Flow Potential...AND VALIDATION Verification: Asymptotic Models → Analytical Solutions Yields Exact Convergence Tests Converged Math → Irrelevant Solutions? Must be

Convergence Acceleration of a Navier-Stokes Solver for Efficient Static Aeroelastic Computations

NASA Technical Reports Server (NTRS)

Obayashi, Shigeru; Guruswamy, Guru P.

1995-01-01

New capabilities have been developed for a Navier-Stokes solver to perform steady-state simulations more efficiently. The flow solver for solving the Navier-Stokes equations is based on a combination of the lower-upper factored symmetric Gauss-Seidel implicit method and the modified Harten-Lax-van Leer-Einfeldt upwind scheme. A numerically stable and efficient pseudo-time-marching method is also developed for computing steady flows over flexible wings. Results are demonstrated for transonic flows over rigid and flexible wings.

Hybrid Upwinding for Two-Phase Flow in Heterogeneous Porous Media with Buoyancy and Capillarity

NASA Astrophysics Data System (ADS)

Hamon, F. P.; Mallison, B.; Tchelepi, H.

2016-12-01

In subsurface flow simulation, efficient discretization schemes for the partial differential equations governing multiphase flow and transport are critical. For highly heterogeneous porous media, the temporal discretization of choice is often the unconditionally stable fully implicit (backward-Euler) method. In this scheme, the simultaneous update of all the degrees of freedom requires solving large algebraic nonlinear systems at each time step using Newton's method. This is computationally expensive, especially in the presence of strong capillary effects driven by abrupt changes in porosity and permeability between different rock types. Therefore, discretization schemes that reduce the simulation cost by improving the nonlinear convergence rate are highly desirable. To speed up nonlinear convergence, we present an efficient fully implicit finite-volume scheme for immiscible two-phase flow in the presence of strong capillary forces. In this scheme, the discrete viscous, buoyancy, and capillary spatial terms are evaluated separately based on physical considerations. We build on previous work on Implicit Hybrid Upwinding (IHU) by using the upstream saturations with respect to the total velocity to compute the relative permeabilities in the viscous term, and by determining the directionality of the buoyancy term based on the phase density differences. The capillary numerical flux is decomposed into a rock- and geometry-dependent transmissibility factor, a nonlinear capillary diffusion coefficient, and an approximation of the saturation gradient. Combining the viscous, buoyancy, and capillary terms, we obtain a numerical flux that is consistent, bounded, differentiable, and monotone for homogeneous one-dimensional flow. The proposed scheme also accounts for spatially discontinuous capillary pressure functions. Specifically, at the interface between two rock types, the numerical scheme accurately honors the entry pressure condition by solving a local nonlinear problem to compute the numerical flux. Heterogeneous numerical tests demonstrate that this extended IHU scheme is non-oscillatory and convergent upon refinement. They also illustrate the superior accuracy and nonlinear convergence rate of the IHU scheme compared with the standard phase-based upstream weighting approach.

Solving coupled groundwater flow systems using a Jacobian Free Newton Krylov method

NASA Astrophysics Data System (ADS)

Mehl, S.

2012-12-01

Jacobian Free Newton Kyrlov (JFNK) methods can have several advantages for simulating coupled groundwater flow processes versus conventional methods. Conventional methods are defined here as those based on an iterative coupling (rather than a direct coupling) and/or that use Picard iteration rather than Newton iteration. In an iterative coupling, the systems are solved separately, coupling information is updated and exchanged between the systems, and the systems are re-solved, etc., until convergence is achieved. Trusted simulators, such as Modflow, are based on these conventional methods of coupling and work well in many cases. An advantage of the JFNK method is that it only requires calculation of the residual vector of the system of equations and thus can make use of existing simulators regardless of how the equations are formulated. This opens the possibility of coupling different process models via augmentation of a residual vector by each separate process, which often requires substantially fewer changes to the existing source code than if the processes were directly coupled. However, appropriate perturbation sizes need to be determined for accurate approximations of the Frechet derivative, which is not always straightforward. Furthermore, preconditioning is necessary for reasonable convergence of the linear solution required at each Kyrlov iteration. Existing preconditioners can be used and applied separately to each process which maximizes use of existing code and robust preconditioners. In this work, iteratively coupled parent-child local grid refinement models of groundwater flow and groundwater flow models with nonlinear exchanges to streams are used to demonstrate the utility of the JFNK approach for Modflow models. Use of incomplete Cholesky preconditioners with various levels of fill are examined on a suite of nonlinear and linear models to analyze the effect of the preconditioner. Comparisons of convergence and computer simulation time are made using conventional iteratively coupled methods and those based on Picard iteration to those formulated with JFNK to gain insights on the types of nonlinearities and system features that make one approach advantageous. Results indicate that nonlinearities associated with stream/aquifer exchanges are more problematic than those resulting from unconfined flow.

A method for modifying two-dimensional adaptive wind-tunnel walls including analytical and experimental verification

NASA Technical Reports Server (NTRS)

Everhart, J. L.

1983-01-01

The theoretical development of a simple and consistent method for removing the interference in adaptive-wall wind tunnels is reported. A Cauchy integral formulation of the velocities in an imaginary infinite extension of the real wind-tunnel flow is obtained and evaluated on a closed contour dividing the real and imaginary flow. The contour consists of the upper and lower effective wind-tunnel walls (wall plus boundary-layer displacement thickness) and upstream and downstream boundaries perpendicular to the axial tunnel flow. The resulting integral expressions for the streamwise and normal perturbation velocities on the contour are integrated by assuming a linear variation of the velocities between data-measurement stations along the contour. In an iterative process, the velocity components calculated on the upper and lower boundaries are then used to correct the shape of the wall to remove the interference. Convergence of the technique is shown numerically for the cases of a circular cylinder and a lifting and nonlifting NACA 0012 airfoil in incompressible flow. Experimental convergence at a transonic Mach number is demonstrated by using an NACA 0012 airfoil at zero lift.

Rotor cascade shape optimization with unsteady passing wakes using implicit dual time stepping method

NASA Astrophysics Data System (ADS)

Lee, Eun Seok

2000-10-01

An improved aerodynamics performance of a turbine cascade shape can be achieved by an understanding of the flow-field associated with the stator-rotor interaction. In this research, an axial gas turbine airfoil cascade shape is optimized for improved aerodynamic performance by using an unsteady Navier-Stokes solver and a parallel genetic algorithm. The objective of the research is twofold: (1) to develop a computational fluid dynamics code having faster convergence rate and unsteady flow simulation capabilities, and (2) to optimize a turbine airfoil cascade shape with unsteady passing wakes for improved aerodynamic performance. The computer code solves the Reynolds averaged Navier-Stokes equations. It is based on the explicit, finite difference, Runge-Kutta time marching scheme and the Diagonalized Alternating Direction Implicit (DADI) scheme, with the Baldwin-Lomax algebraic and k-epsilon turbulence modeling. Improvements in the code focused on the cascade shape design capability, convergence acceleration and unsteady formulation. First, the inverse shape design method was implemented in the code to provide the design capability, where a surface transpiration concept was employed as an inverse technique to modify the geometry satisfying the user specified pressure distribution on the airfoil surface. Second, an approximation storage multigrid method was implemented as an acceleration technique. Third, the preconditioning method was adopted to speed up the convergence rate in solving the low Mach number flows. Finally, the implicit dual time stepping method was incorporated in order to simulate the unsteady flow-fields. For the unsteady code validation, the Stokes's 2nd problem and the Poiseuille flow were chosen and compared with the computed results and analytic solutions. To test the code's ability to capture the natural unsteady flow phenomena, vortex shedding past a cylinder and the shock oscillation over a bicircular airfoil were simulated and compared with experiments and other research results. The rotor cascade shape optimization with unsteady passing wakes was performed to obtain an improved aerodynamic performance using the unsteady Navier-Stokes solver. Two objective functions were defined as minimization of total pressure loss and maximization of lift, while the mass flow rate was fixed. A parallel genetic algorithm was used as an optimizer and the penalty method was introduced. Each individual's objective function was computed simultaneously by using a 32 processor distributed memory computer. One optimization took about four days.

Implicit unified gas-kinetic scheme for steady state solutions in all flow regimes

NASA Astrophysics Data System (ADS)

Zhu, Yajun; Zhong, Chengwen; Xu, Kun

2016-06-01

This paper presents an implicit unified gas-kinetic scheme (UGKS) for non-equilibrium steady state flow computation. The UGKS is a direct modeling method for flow simulation in all regimes with the updates of both macroscopic flow variables and microscopic gas distribution function. By solving the macroscopic equations implicitly, a predicted equilibrium state can be obtained first through iterations. With the newly predicted equilibrium state, the evolution equation of the gas distribution function and the corresponding collision term can be discretized in a fully implicit way for fast convergence through iterations as well. The lower-upper symmetric Gauss-Seidel (LU-SGS) factorization method is implemented to solve both macroscopic and microscopic equations, which improves the efficiency of the scheme. Since the UGKS is a direct modeling method and its physical solution depends on the mesh resolution and the local time step, a physical time step needs to be fixed before using an implicit iterative technique with a pseudo-time marching step. Therefore, the physical time step in the current implicit scheme is determined by the same way as that in the explicit UGKS for capturing the physical solution in all flow regimes, but the convergence to a steady state speeds up through the adoption of a numerical time step with large CFL number. Many numerical test cases in different flow regimes from low speed to hypersonic ones, such as the Couette flow, cavity flow, and the flow passing over a cylinder, are computed to validate the current implicit method. The overall efficiency of the implicit UGKS can be improved by one or two orders of magnitude in comparison with the explicit one.

Efficient C1-continuous phase-potential upwind (C1-PPU) schemes for coupled multiphase flow and transport with gravity

NASA Astrophysics Data System (ADS)

Jiang, Jiamin; Younis, Rami M.

2017-10-01

In the presence of counter-current flow, nonlinear convergence problems may arise in implicit time-stepping when the popular phase-potential upwinding (PPU) scheme is used. The PPU numerical flux is non-differentiable across the co-current/counter-current flow regimes. This may lead to cycles or divergence in the Newton iterations. Recently proposed methods address improved smoothness of the numerical flux. The objective of this work is to devise and analyze an alternative numerical flux scheme called C1-PPU that, in addition to improving smoothness with respect to saturations and phase potentials, also improves the level of scalar nonlinearity and accuracy. C1-PPU involves a novel use of the flux limiter concept from the context of high-resolution methods, and allows a smooth variation between the co-current/counter-current flow regimes. The scheme is general and applies to fully coupled flow and transport formulations with an arbitrary number of phases. We analyze the consistency property of the C1-PPU scheme, and derive saturation and pressure estimates, which are used to prove the solution existence. Several numerical examples for two- and three-phase flows in heterogeneous and multi-dimensional reservoirs are presented. The proposed scheme is compared to the conventional PPU and the recently proposed Hybrid Upwinding schemes. We investigate three properties of these numerical fluxes: smoothness, nonlinearity, and accuracy. The results indicate that in addition to smoothness, nonlinearity may also be critical for convergence behavior and thus needs to be considered in the design of an efficient numerical flux scheme. Moreover, the numerical examples show that the C1-PPU scheme exhibits superior convergence properties for large time steps compared to the other alternatives.

Comparison between iteration schemes for three-dimensional coordinate-transformed saturated-unsaturated flow model

NASA Astrophysics Data System (ADS)

An, Hyunuk; Ichikawa, Yutaka; Tachikawa, Yasuto; Shiiba, Michiharu

2012-11-01

SummaryThree different iteration methods for a three-dimensional coordinate-transformed saturated-unsaturated flow model are compared in this study. The Picard and Newton iteration methods are the common approaches for solving Richards' equation. The Picard method is simple to implement and cost-efficient (on an individual iteration basis). However it converges slower than the Newton method. On the other hand, although the Newton method converges faster, it is more complex to implement and consumes more CPU resources per iteration than the Picard method. The comparison of the two methods in finite-element model (FEM) for saturated-unsaturated flow has been well evaluated in previous studies. However, two iteration methods might exhibit different behavior in the coordinate-transformed finite-difference model (FDM). In addition, the Newton-Krylov method could be a suitable alternative for the coordinate-transformed FDM because it requires the evaluation of a 19-point stencil matrix. The formation of a 19-point stencil is quite a complex and laborious procedure. Instead, the Newton-Krylov method calculates the matrix-vector product, which can be easily approximated by calculating the differences of the original nonlinear function. In this respect, the Newton-Krylov method might be the most appropriate iteration method for coordinate-transformed FDM. However, this method involves the additional cost of taking an approximation at each Krylov iteration in the Newton-Krylov method. In this paper, we evaluated the efficiency and robustness of three iteration methods—the Picard, Newton, and Newton-Krylov methods—for simulating saturated-unsaturated flow through porous media using a three-dimensional coordinate-transformed FDM.

An investigation of several factors involved in a finite difference procedure for analyzing the transonic flow about harmonically oscillating airfoils and wings

NASA Technical Reports Server (NTRS)

Ehlers, F. E.; Sebastian, J. D.; Weatherill, W. H.

1979-01-01

Analytical and empirical studies of a finite difference method for the solution of the transonic flow about harmonically oscillating wings and airfoils are presented. The procedure is based on separating the velocity potential into steady and unsteady parts and linearizing the resulting unsteady equations for small disturbances. Since sinusoidal motion is assumed, the unsteady equation is independent of time. Three finite difference investigations are discussed including a new operator for mesh points with supersonic flow, the effects on relaxation solution convergence of adding a viscosity term to the original differential equation, and an alternate and relatively simple downstream boundary condition. A method is developed which uses a finite difference procedure over a limited inner region and an approximate analytical procedure for the remaining outer region. Two investigations concerned with three-dimensional flow are presented. The first is the development of an oblique coordinate system for swept and tapered wings. The second derives the additional terms required to make row relaxation solutions converge when mixed flow is present. A finite span flutter analysis procedure is described using the two-dimensional unsteady transonic program with a full three-dimensional steady velocity potential.

An efficient strongly coupled immersed boundary method for deforming bodies

NASA Astrophysics Data System (ADS)

Goza, Andres; Colonius, Tim

2016-11-01

Immersed boundary methods treat the fluid and immersed solid with separate domains. As a result, a nonlinear interface constraint must be satisfied when these methods are applied to flow-structure interaction problems. This typically results in a large nonlinear system of equations that is difficult to solve efficiently. Often, this system is solved with a block Gauss-Seidel procedure, which is easy to implement but can require many iterations to converge for small solid-to-fluid mass ratios. Alternatively, a Newton-Raphson procedure can be used to solve the nonlinear system. This typically leads to convergence in a small number of iterations for arbitrary mass ratios, but involves the use of large Jacobian matrices. We present an immersed boundary formulation that, like the Newton-Raphson approach, uses a linearization of the system to perform iterations. It therefore inherits the same favorable convergence behavior. However, we avoid large Jacobian matrices by using a block LU factorization of the linearized system. We derive our method for general deforming surfaces and perform verification on 2D test problems of flow past beams. These test problems involve large amplitude flapping and a wide range of mass ratios. This work was partially supported by the Jet Propulsion Laboratory and Air Force Office of Scientific Research.

Oscillatory supersonic kernel function method for interfering surfaces

NASA Technical Reports Server (NTRS)

Cunningham, A. M., Jr.

1974-01-01

In the method presented in this paper, a collocation technique is used with the nonplanar supersonic kernel function to solve multiple lifting surface problems with interference in steady or oscillatory flow. The pressure functions used are based on conical flow theory solutions and provide faster solution convergence than is possible with conventional functions. In the application of the nonplanar supersonic kernel function, an improper integral of a 3/2 power singularity along the Mach hyperbola is described and treated. The method is compared with other theories and experiment for two wing-tail configurations in steady and oscillatory flow.

A novel potential/viscous flow coupling technique for computing helicopter flow fields

NASA Technical Reports Server (NTRS)

Summa, J. Michael; Strash, Daniel J.; Yoo, Sungyul

1990-01-01

Because of the complexity of helicopter flow field, a zonal method of analysis of computational aerodynamics is required. Here, a new procedure for coupling potential and viscous flow is proposed. An overlapping, velocity coupling technique is to be developed with the unique feature that the potential flow surface singularity strengths are obtained directly from the Navier-Stokes at a smoother inner fluid boundary. The closed-loop iteration method proceeds until the velocity field is converged. This coupling should provide the means of more accurate viscous computations of the near-body and rotor flow fields with resultant improved analysis of such important performance parameters as helicopter fuselage drag and rotor airloads.

A fully-coupled discontinuous Galerkin spectral element method for two-phase flow in petroleum reservoirs

NASA Astrophysics Data System (ADS)

Taneja, Ankur; Higdon, Jonathan

2018-01-01

A high-order spectral element discontinuous Galerkin method is presented for simulating immiscible two-phase flow in petroleum reservoirs. The governing equations involve a coupled system of strongly nonlinear partial differential equations for the pressure and fluid saturation in the reservoir. A fully implicit method is used with a high-order accurate time integration using an implicit Rosenbrock method. Numerical tests give the first demonstration of high order hp spatial convergence results for multiphase flow in petroleum reservoirs with industry standard relative permeability models. High order convergence is shown formally for spectral elements with up to 8th order polynomials for both homogeneous and heterogeneous permeability fields. Numerical results are presented for multiphase fluid flow in heterogeneous reservoirs with complex geometric or geologic features using up to 11th order polynomials. Robust, stable simulations are presented for heterogeneous geologic features, including globally heterogeneous permeability fields, anisotropic permeability tensors, broad regions of low-permeability, high-permeability channels, thin shale barriers and thin high-permeability fractures. A major result of this paper is the demonstration that the resolution of the high order spectral element method may be exploited to achieve accurate results utilizing a simple cartesian mesh for non-conforming geological features. Eliminating the need to mesh to the boundaries of geological features greatly simplifies the workflow for petroleum engineers testing multiple scenarios in the face of uncertainty in the subsurface geology.

Conjugate gradient method for phase retrieval based on the Wirtinger derivative.

PubMed

Wei, Zhun; Chen, Wen; Qiu, Cheng-Wei; Chen, Xudong

2017-05-01

A conjugate gradient Wirtinger flow (CG-WF) algorithm for phase retrieval is proposed in this paper. It is shown that, compared with recently reported Wirtinger flow and its modified methods, the proposed CG-WF algorithm is able to dramatically accelerate the convergence rate while keeping the dominant computational cost of each iteration unchanged. We numerically illustrate the effectiveness of our method in recovering 1D Gaussian signals and 2D natural color images under both Gaussian and coded diffraction pattern models.

An all-at-once reduced Hessian SQP scheme for aerodynamic design optimization

NASA Technical Reports Server (NTRS)

Feng, Dan; Pulliam, Thomas H.

1995-01-01

This paper introduces a computational scheme for solving a class of aerodynamic design problems that can be posed as nonlinear equality constrained optimizations. The scheme treats the flow and design variables as independent variables, and solves the constrained optimization problem via reduced Hessian successive quadratic programming. It updates the design and flow variables simultaneously at each iteration and allows flow variables to be infeasible before convergence. The solution of an adjoint flow equation is never needed. In addition, a range space basis is chosen so that in a certain sense the 'cross term' ignored in reduced Hessian SQP methods is minimized. Numerical results for a nozzle design using the quasi-one-dimensional Euler equations show that this scheme is computationally efficient and robust. The computational cost of a typical nozzle design is only a fraction more than that of the corresponding analysis flow calculation. Superlinear convergence is also observed, which agrees with the theoretical properties of this scheme. All optimal solutions are obtained by starting far away from the final solution.

Evaluation of a Multigrid Scheme for the Incompressible Navier-Stokes Equations

NASA Technical Reports Server (NTRS)

Swanson, R. C.

2004-01-01

A fast multigrid solver for the steady, incompressible Navier-Stokes equations is presented. The multigrid solver is based upon a factorizable discrete scheme for the velocity-pressure form of the Navier-Stokes equations. This scheme correctly distinguishes between the advection-diffusion and elliptic parts of the operator, allowing efficient smoothers to be constructed. To evaluate the multigrid algorithm, solutions are computed for flow over a flat plate, parabola, and a Karman-Trefftz airfoil. Both nonlifting and lifting airfoil flows are considered, with a Reynolds number range of 200 to 800. Convergence and accuracy of the algorithm are discussed. Using Gauss-Seidel line relaxation in alternating directions, multigrid convergence behavior approaching that of O(N) methods is achieved. The computational efficiency of the numerical scheme is compared with that of Runge-Kutta and implicit upwind based multigrid methods.

A characteristic based volume penalization method for general evolution problems applied to compressible viscous flows

NASA Astrophysics Data System (ADS)

Brown-Dymkoski, Eric; Kasimov, Nurlybek; Vasilyev, Oleg V.

2014-04-01

In order to introduce solid obstacles into flows, several different methods are used, including volume penalization methods which prescribe appropriate boundary conditions by applying local forcing to the constitutive equations. One well known method is Brinkman penalization, which models solid obstacles as porous media. While it has been adapted for compressible, incompressible, viscous and inviscid flows, it is limited in the types of boundary conditions that it imposes, as are most volume penalization methods. Typically, approaches are limited to Dirichlet boundary conditions. In this paper, Brinkman penalization is extended for generalized Neumann and Robin boundary conditions by introducing hyperbolic penalization terms with characteristics pointing inward on solid obstacles. This Characteristic-Based Volume Penalization (CBVP) method is a comprehensive approach to conditions on immersed boundaries, providing for homogeneous and inhomogeneous Dirichlet, Neumann, and Robin boundary conditions on hyperbolic and parabolic equations. This CBVP method can be used to impose boundary conditions for both integrated and non-integrated variables in a systematic manner that parallels the prescription of exact boundary conditions. Furthermore, the method does not depend upon a physical model, as with porous media approach for Brinkman penalization, and is therefore flexible for various physical regimes and general evolutionary equations. Here, the method is applied to scalar diffusion and to direct numerical simulation of compressible, viscous flows. With the Navier-Stokes equations, both homogeneous and inhomogeneous Neumann boundary conditions are demonstrated through external flow around an adiabatic and heated cylinder. Theoretical and numerical examination shows that the error from penalized Neumann and Robin boundary conditions can be rigorously controlled through an a priori penalization parameter η. The error on a transient boundary is found to converge as O(η), which is more favorable than the error convergence of the already established Dirichlet boundary condition.

A fast and accurate method to predict 2D and 3D aerodynamic boundary layer flows

NASA Astrophysics Data System (ADS)

Bijleveld, H. A.; Veldman, A. E. P.

2014-12-01

A quasi-simultaneous interaction method is applied to predict 2D and 3D aerodynamic flows. This method is suitable for offshore wind turbine design software as it is a very accurate and computationally reasonably cheap method. This study shows the results for a NACA 0012 airfoil. The two applied solvers converge to the experimental values when the grid is refined. We also show that in separation the eigenvalues remain positive thus avoiding the Goldstein singularity at separation. In 3D we show a flow over a dent in which separation occurs. A rotating flat plat is used to show the applicability of the method for rotating flows. The shown capabilities of the method indicate that the quasi-simultaneous interaction method is suitable for design methods for offshore wind turbine blades.

Acoustic tests of a 15.2 centimeter-diameter potential flow convergent nozzle

NASA Technical Reports Server (NTRS)

Karchmer, A. M.; Dorsch, R. G.; Friedman, R.

1974-01-01

An experimental investigation of the jet noise radiated to the far field from a 15.2-cm-diam potential flow convergent nozzle has been conducted. Tests were made with unheated airflow over a range of subsonic nozzle exhaust velocities from 62 to 310m/sec. Mean and turbulent velocity measurements in the flow field of the nozzle exhaust indicated no apparent flow anomalies. Acoustic measurements yielded data uncontaminated by internal and/or background noise to velocities as low as 152m/sec. Finally, no significantly different acoustic characteristics between the potential flow nozzle and simple convergent nozzles were found.

Pseudo-compressibility methods for the incompressible flow equations

NASA Technical Reports Server (NTRS)

Turkel, Eli; Arnone, A.

1993-01-01

Preconditioning methods to accelerate convergence to a steady state for the incompressible fluid dynamics equations are considered. The analysis relies on the inviscid equations. The preconditioning consists of a matrix multiplying the time derivatives. Thus the steady state of the preconditioned system is the same as the steady state of the original system. The method is compared to other types of pseudo-compressibility. For finite difference methods preconditioning can change and improve the steady state solutions. An application to viscous flow around a cascade with a non-periodic mesh is presented.

Extension of a GIS procedure for calculating the RUSLE equation LS factor

NASA Astrophysics Data System (ADS)

Zhang, Hongming; Yang, Qinke; Li, Rui; Liu, Qingrui; Moore, Demie; He, Peng; Ritsema, Coen J.; Geissen, Violette

2013-03-01

The Universal Soil Loss Equation (USLE) and revised USLE (RUSLE) are often used to estimate soil erosion at regional landscape scales, however a major limitation is the difficulty in extracting the LS factor. The geographic information system-based (GIS-based) methods which have been developed for estimating the LS factor for USLE and RUSLE also have limitations. The unit contributing area-based estimation method (UCA) converts slope length to unit contributing area for considering two-dimensional topography, however is not able to predict the different zones of soil erosion and deposition. The flowpath and cumulative cell length-based method (FCL) overcomes this disadvantage but does not consider channel networks and flow convergence in two-dimensional topography. The purpose of this research was to overcome these limitations and extend the FCL method through inclusion of channel networks and convergence flow. We developed LS-TOOL in Microsoft's.NET environment using C♯ with a user-friendly interface. Comparing the LS factor calculated with the three methodologies (UCA, FCL and LS-TOOL), LS-TOOL delivers encouraging results. In particular, LS-TOOL uses breaks in slope identified from the DEM to locate soil erosion and deposition zones, channel networks and convergence flow areas. Comparing slope length and LS factor values generated using LS-TOOL with manual methods, LS-TOOL corresponds more closely with the reality of the Xiannangou catchment than results using UCA or FCL. The LS-TOOL algorithm can automatically calculate slope length, slope steepness, L factor, S factor, and LS factors, providing the results as ASCII files which can be easily used in some GIS software. This study is an important step forward in conducting more accurate large area erosion evaluation.

Variational Methods in Sensitivity Analysis and Optimization for Aerodynamic Applications

NASA Technical Reports Server (NTRS)

Ibrahim, A. H.; Hou, G. J.-W.; Tiwari, S. N. (Principal Investigator)

1996-01-01

Variational methods (VM) sensitivity analysis, which is the continuous alternative to the discrete sensitivity analysis, is employed to derive the costate (adjoint) equations, the transversality conditions, and the functional sensitivity derivatives. In the derivation of the sensitivity equations, the variational methods use the generalized calculus of variations, in which the variable boundary is considered as the design function. The converged solution of the state equations together with the converged solution of the costate equations are integrated along the domain boundary to uniquely determine the functional sensitivity derivatives with respect to the design function. The determination of the sensitivity derivatives of the performance index or functional entails the coupled solutions of the state and costate equations. As the stable and converged numerical solution of the costate equations with their boundary conditions are a priori unknown, numerical stability analysis is performed on both the state and costate equations. Thereafter, based on the amplification factors obtained by solving the generalized eigenvalue equations, the stability behavior of the costate equations is discussed and compared with the state (Euler) equations. The stability analysis of the costate equations suggests that the converged and stable solution of the costate equation is possible only if the computational domain of the costate equations is transformed to take into account the reverse flow nature of the costate equations. The application of the variational methods to aerodynamic shape optimization problems is demonstrated for internal flow problems at supersonic Mach number range. The study shows, that while maintaining the accuracy of the functional sensitivity derivatives within the reasonable range for engineering prediction purposes, the variational methods show a substantial gain in computational efficiency, i.e., computer time and memory, when compared with the finite difference sensitivity analysis.

Measurement of LNAPL flow using single-well tracer dilution techniques.

PubMed

Sale, Tom; Taylor, Geoffrey Ryan; Iltis, Gabriel; Lyverse, Mark

2007-01-01

This paper describes the use of single-well tracer dilution techniques to resolve the rate of light nonaqueous phase liquid (LNAPL) flow through wells and the adjacent geologic formation. Laboratory studies are presented in which a fluorescing tracer is added to LNAPL in wells. An in-well mixer keeps the tracer well mixed in the LNAPL. Tracer concentrations in LNAPL are measured through time using a fiber optic cable and a spectrometer. Results indicate that the rate of tracer depletion is proportional to the rate of LNAPL flow through the well and the adjacent formation. Tracer dilution methods are demonstrated for vertically averaged LNAPL Darcy velocities of 0.00048 to 0.11 m/d and LNAPL thicknesses of 9 to 24 cm. Over the range of conditions studied, results agree closely with steady-state LNAPL flow rates imposed by pumping. A key parameter for estimating LNAPL flow rates in the formation is the flow convergence factor alpha. Measured convergence factors for 0.030-inch wire wrap, 0.030-inch-slotted polyvinyl chloride (PVC), and 0.010-inch-slotted PVC are 1.7, 0.91, and 0.79, respectively. In addition, methods for using tracer dilution data to determine formation transmissivity to LNAPL are presented. Results suggest that single-well tracer dilution techniques are a viable approach for measuring in situ LNAPL flow and formation transmissivity to LNAPL.

Hypersonic blunt body computations including real gas effects

NASA Technical Reports Server (NTRS)

Montagne, J.-L.; Yee, H. C.; Klopfer, G. H.; Vinokur, M.

1989-01-01

Various second-order explicit and implicit TVD shock-capturing methods, a generalization of Roe's approximate Riemann solver, and a generalized flux-vector splitting scheme are used to study two-dimensional hypersonic real-gas flows. Special attention is given to the identification of some of the elements and parameters which can affect the convergence rate for high Mach numbers or real gases, but have negligible effect for low Mach numbers, for cases involving steady-state inviscid blunt flows. Blunt body calculations at Mach numbers of greater than 15 are performed to treat real-gas effects, and impinging shock results are obtained to test the treatment of slip surfaces and complex structures. Even with the addition of improvements, the convergence rate of algorithms in the hypersonic flow regime is found to be generally slower for a real gas than for a perfect gas.

An efficient method for solving the steady Euler equations

NASA Technical Reports Server (NTRS)

Liou, M.-S.

1986-01-01

An efficient numerical procedure for solving a set of nonlinear partial differential equations, the steady Euler equations, using Newton's linearization procedure is presented. A theorem indicating quadratic convergence for the case of differential equations is demonstrated. A condition for the domain of quadratic convergence Omega(2) is obtained which indicates that whether an approximation lies in Omega(2) depends on the rate of change and the smoothness of the flow vectors, and hence is problem-dependent. The choice of spatial differencing, of particular importance for the present method, is discussed. The treatment of boundary conditions is addressed, and the system of equations resulting from the foregoing analysis is summarized and solution strategies are discussed. The convergence of calculated solutions is demonstrated by comparing them with exact solutions to one and two-dimensional problems.

Multigrid for hypersonic viscous two- and three-dimensional flows

NASA Technical Reports Server (NTRS)

Turkel, E.; Swanson, R. C.; Vatsa, V. N.; White, J. A.

1991-01-01

The use of a multigrid method with central differencing to solve the Navier-Stokes equations for hypersonic flows is considered. The time dependent form of the equations is integrated with an explicit Runge-Kutta scheme accelerated by local time stepping and implicit residual smoothing. Variable coefficients are developed for the implicit process that removes the diffusion limit on the time step, producing significant improvement in convergence. A numerical dissipation formulation that provides good shock capturing capability for hypersonic flows is presented. This formulation is shown to be a crucial aspect of the multigrid method. Solutions are given for two-dimensional viscous flow over a NACA 0012 airfoil and three-dimensional flow over a blunt biconic.

The technique of numerical research of cooling medium flow in the water jacket of self-lubricated bearing

NASA Astrophysics Data System (ADS)

Raikovskiy, N. A.; Tretyakov, A. V.; Abramov, S. A.; Nazmeev, F. G.; Pavlichev, S. V.

2017-08-01

The paper presents a numerical study method of the cooling medium flowing in the water jacket of self-lubricating sliding bearing based on ANSYS CFX. The results of numerical calculations have satisfactory convergence with the empirical data obtained on the testbed. Verification data confirm the possibility of applying this numerical technique for the analysis of coolant flowings in the self-lubricating bearing containing the water jacket.

Nonlinear initial-boundary value solutions by the finite element method. [for Navier-Stokes equations of two dimensional flow

NASA Technical Reports Server (NTRS)

Baker, A. J.

1974-01-01

The finite-element method is used to establish a numerical solution algorithm for the Navier-Stokes equations for two-dimensional flows of a viscous compressible fluid. Numerical experiments confirm the advection property for the finite-element equivalent of the nonlinear convection term for both unidirectional and recirculating flowfields. For linear functionals, the algorithm demonstrates good accuracy using coarse discretizations and h squared convergence with discretization refinement.

A Study on Market-based Strategic Procurement Planning in Convergent Supply Networks

NASA Astrophysics Data System (ADS)

Opadiji, Jayeola Femi; Kaihara, Toshiya

We present a market-based decentralized approach which uses a market-oriented programming algorithm to obtain Pareto-optimal allocation of resources traded among agents which represent enterprise units in a supply network. The proposed method divides the network into a series of Walrsian markets in order to obtain procurement budgets for enterprises in the network. An interaction protocol based on market value propagation is constructed to coordinate the flow of resources across the network layers. The method mitigates the effect of product complementarity in convergent network by allowing for enterprises to hold private valuations of resources in the markets.

The development of three-dimensional adjoint method for flow control with blowing in convergent-divergent nozzle flows

NASA Astrophysics Data System (ADS)

Sikarwar, Nidhi

The noise produced by the low bypass ratio turbofan engines used to power fighter aircraft is a problem for communities near military bases and for personnel working in close proximity to the aircraft. For example, carrier deck personnel are subject to noise exposure that can result in Noise-Induced Hearing Loss which in-turn results in over a billion dollars of disability payments by the Veterans Administration. Several methods have been proposed to reduce the jet noise at the source. These methods include microjet injection of air or water downstream of the jet exit, chevrons, and corrugated nozzle inserts. The last method involves the insertion of corrugated seals into the diverging section of a military-style convergent-divergent jet nozzle (to replace the existing seals). This has been shown to reduce both the broadband shock-associated noise as well as the mixing noise in the peak noise radiation direction. However, the original inserts were designed to be effective for a take-off condition where the jet is over-expanded. The nozzle performance would be expected to degrade at other conditions, such as in cruise at altitude. A new method has been proposed to achieve the same effects as corrugated seals, but using fluidic inserts. This involves injection of air, at relatively low pressures and total mass flow rates, into the diverging section of the nozzle. These fluidic inserts" deflect the flow in the same way as the mechanical inserts. The fluidic inserts represent an active control method, since the injectors can be modified or turned off depending on the jet operating conditions. Noise reductions in the peak noise direction of 5 to 6 dB have been achieved and broadband shock-associated noise is effectively suppressed. There are multiple parameters to be considered in the design of the fluidic inserts. This includes the number and location of the injectors and the pressures and mass flow rates to be used. These could be optimized on an ad hoc basis with multiple experiments or numerical simulations. Alternatively an inverse design method can be used. An adjoint optimization method can be used to achieve the optimum blowing rate. It is shown that the method works for both geometry optimization and active control of the flow in order to deflect the flow in desirable ways. An adjoint optimization method is described. It is used to determine the blowing distribution in the diverging section of a convergent-divergent nozzle that gives a desired pressure distribution in the nozzle. Both the direct and adjoint problems and their associated boundary conditions are developed. The adjoint method is used to determine the blowing distribution required to minimize the shock strength in the nozzle to achieve a known target pressure and to achieve close to an ideally expanded flow pressure. A multi-block structured solver is developed to calculate the flow solution and associated adjoint variables. Two and three-dimensional calculations are performed for internal and external of the nozzle domains. A two step MacCormack scheme based on predictor- corrector technique is was used for some calculations. The four and five stage Runge-Kutta schemes are also used to artificially march in time. A modified Runge-Kutta scheme is used to accelerate the convergence to a steady state. Second order artificial dissipation has been added to stabilize the calculations. The steepest decent method has been used for the optimization of the blowing velocity after the gradients of the cost function with respect to the blowing velocity are calculated using adjoint method. Several examples are given of the optimization of blowing using the adjoint method.

A hybridized method for computing high-Reynolds-number hypersonic flow about blunt bodies

NASA Technical Reports Server (NTRS)

Weilmuenster, K. J.; Hamilton, H. H., II

1979-01-01

A hybridized method for computing the flow about blunt bodies is presented. In this method the flow field is split into its viscid and inviscid parts. The forebody flow field about a parabolic body is computed. For the viscous solution, the Navier-Stokes equations are solved on orthogonal parabolic coordinates using explicit finite differencing. The inviscid flow is determined by using a Moretti type scheme in which the Euler equations are solved, using explicit finite differences, on a nonorthogonal coordinate system which uses the bow shock as an outer boundary. The two solutions are coupled along a common data line and are marched together in time until a converged solution is obtained. Computed results, when compared with experimental and analytical results, indicate the method works well over a wide range of Reynolds numbers and Mach numbers.

C1-Continuous relative permeability and hybrid upwind discretization of three phase flow in porous media

NASA Astrophysics Data System (ADS)

Lee, S. H.; Efendiev, Y.

2016-10-01

Three-phase flow in a reservoir model has been a major challenge in simulation studies due to slowly convergent iterations in Newton solution of nonlinear transport equations. In this paper, we examine the numerical characteristics of three-phase flow and propose a consistent, "C1-continuous discretization" (to be clarified later) of transport equations that ensures a convergent solution in finite difference approximation. First, we examine three-phase relative permeabilities that are critical in solving nonlinear transport equations. Three-phase relative permeabilities are difficult to measure in the laboratory, and they are often correlated with two-phase relative permeabilities (e.g., oil-gas and water-oil systems). Numerical convergence of non-linear transport equations entails that three-phase relative permeability correlations are a monotonically increasing function of the phase saturation and the consistency conditions of phase transitions are satisfied. The Modified Stone's Method II and the Linear Interpolation Method for three-phase relative permeability are closely examined for their mathematical properties. We show that the Linear Interpolation Method yields C1-continuous three-phase relative permeabilities for smooth solutions if the two phase relative permeabilities are monotonic and continuously differentiable. In the second part of the paper, we extend a Hybrid-Upwinding (HU) method of two-phase flow (Lee, Efendiev and Tchelepi, ADWR 82 (2015) 27-38) to three phase flow. In the HU method, the phase flux is divided into two parts based on the driving forces (in general, it can be divided into several parts): viscous and buoyancy. The viscous-driven and buoyancy-driven fluxes are upwinded differently. Specifically, the viscous flux, which is always co-current, is upwinded based on the direction of the total velocity. The pure buoyancy-induced flux is shown to be only dependent on saturation distributions and counter-current. In three-phase flow, the buoyancy effect can be expressed as a sum of two buoyancy effects from two-phase flows, i.e., oil-water and oil-gas systems. We propose an upwind scheme for the buoyancy flux term from three-phase flow as a sum of two buoyancy terms from two-phase flows. The upwind direction of the buoyancy flux in two phase flow is always fixed such that the heavier fluid goes downward and the lighter fluid goes upward. It is shown that the Implicit Hybrid-Upwinding (IHU) scheme for three-phase flow is locally conservative and produces physically-consistent numerical solutions. As in two phase flow, the primary advantage of the IHU scheme is that the flux of a fluid phase remains continuous and differentiable as the flow regime changes between co-current and counter-current conditions as a function of time, or (Newton) iterations. This is in contrast to the standard phase-potential-based upwinding scheme, in which the overall fractional-flow (flux) function is non-differentiable across the transition between co-current and counter-current flows.

Effect of Finite Particle Size on Convergence of Point Particle Models in Euler-Lagrange Multiphase Dispersed Flow

NASA Astrophysics Data System (ADS)

Nili, Samaun; Park, Chanyoung; Haftka, Raphael T.; Kim, Nam H.; Balachandar, S.

2017-11-01

Point particle methods are extensively used in simulating Euler-Lagrange multiphase dispersed flow. When particles are much smaller than the Eulerian grid the point particle model is on firm theoretical ground. However, this standard approach of evaluating the gas-particle coupling at the particle center fails to converge as the Eulerian grid is reduced below particle size. We present an approach to model the interaction between particles and fluid for finite size particles that permits convergence. We use the generalized Faxen form to compute the force on a particle and compare the results against traditional point particle method. We apportion the different force components on the particle to fluid cells based on the fraction of particle volume or surface in the cell. The application is to a one-dimensional model of shock propagation through a particle-laden field at moderate volume fraction, where the convergence is achieved for a well-formulated force model and back coupling for finite size particles. Comparison with 3D direct fully resolved numerical simulations will be used to check if the approach also improves accuracy compared to the point particle model. Work supported by the U.S. Department of Energy, National Nuclear Security Administration, Advanced Simulation and Computing Program, as a Cooperative Agreement under the Predictive Science Academic Alliance Program, under Contract No. DE-NA0002378.

Robust phase retrieval of complex-valued object in phase modulation by hybrid Wirtinger flow method

NASA Astrophysics Data System (ADS)

Wei, Zhun; Chen, Wen; Yin, Tiantian; Chen, Xudong

2017-09-01

This paper presents a robust iterative algorithm, known as hybrid Wirtinger flow (HWF), for phase retrieval (PR) of complex objects from noisy diffraction intensities. Numerical simulations indicate that the HWF method consistently outperforms conventional PR methods in terms of both accuracy and convergence rate in multiple phase modulations. The proposed algorithm is also more robust to low oversampling ratios, loose constraints, and noisy environments. Furthermore, compared with traditional Wirtinger flow, sample complexity is largely reduced. It is expected that the proposed HWF method will find applications in the rapidly growing coherent diffractive imaging field for high-quality image reconstruction with multiple modulations, as well as other disciplines where PR is needed.

Depressurization and two-phase flow of water containing high levels of dissolved nitrogen gas

NASA Technical Reports Server (NTRS)

Simoneau, R. J.

1981-01-01

Depressurization of water containing various concentrations of dissolved nitrogen gas was studied. In a nonflow depressurization experiment, water with very high nitrogen content was depressurized at rates from 0.09 to 0.50 MPa per second and a metastable behavior which was a strong function of the depressurization rate was observed. Flow experiments were performed in an axisymmetric, converging diverging nozzle, a two dimensional, converging nozzle with glass sidewalls, and a sharp edge orifice. The converging diverging nozzle exhibited choked flow behavior even at nitrogen concentration levels as low as 4 percent of the saturation level. The flow rates were independent of concentration level. Flow in the two dimensional, converging, visual nozzle appeared to have a sufficient pressure drop at the throat to cause nitrogen to come out of solution, but choking occurred further downstream. The orifice flow motion pictures showed considerable oscillation downstream of the orifice and parallel to the flow. Nitrogen bubbles appeared in the flow at back pressures as high as 3.28 MPa, and the level at which bubbles were no longer visible was a function of nitrogen concentration.

Vortical structures and development of laminar flow over convergent-divergent riblets

NASA Astrophysics Data System (ADS)

Xu, Fang; Zhong, Shan; Zhang, Shanying

2018-05-01

In this work, the development of a laminar boundary layer over a rectangular convergent-divergent riblet section with a finite streamwise length is studied experimentally using dye visualization and particle image velocimetry in a water flume. The flow topology over this highly directional spanwise roughness is established from this study. It is shown that convergent-divergent riblets generate a spanwise flow above the riblets from the diverging line toward the adjacent converging line. This consequently leads to the formation of a weak recirculating secondary flow in cross-stream planes across the boundary layer that creates a downwash motion over the diverging line and an upwash motion over the converging line. It is found that the fluid inside the riblet valley follows a helicoidal path and it also interacts with the crossflow boundary layer hence playing a key role in determining the structure of the secondary flow across the boundary layer. The impact of riblet wavelength on vortical structures is also revealed for the first time. A larger riblet wavelength is seen to produce a stronger upwash/downwash and hence a more intense secondary flow as well as a stronger deceleration effect on the crossflow. Furthermore, the streamwise development of the flow over the riblet section can be divided into a developing stage followed by a developed stage. In the developing stage, the magnitude of induced streamwise velocity and vorticity over the converging line continues to increase, whereas in the developed stage the values of these parameters remain essentially unchanged.

A hybrid numerical technique for predicting the aerodynamic and acoustic fields of advanced turboprops

NASA Technical Reports Server (NTRS)

Homicz, G. F.; Moselle, J. R.

1985-01-01

A hybrid numerical procedure is presented for the prediction of the aerodynamic and acoustic performance of advanced turboprops. A hybrid scheme is proposed which in principle leads to a consistent simultaneous prediction of both fields. In the inner flow a finite difference method, the Approximate-Factorization Alternating-Direction-Implicit (ADI) scheme, is used to solve the nonlinear Euler equations. In the outer flow the linearized acoustic equations are solved via a Boundary-Integral Equation (BIE) method. The two solutions are iteratively matched across a fictitious interface in the flow so as to maintain continuity. At convergence the resulting aerodynamic load prediction will automatically satisfy the appropriate free-field boundary conditions at the edge of the finite difference grid, while the acoustic predictions will reflect the back-reaction of the radiated field on the magnitude of the loading source terms, as well as refractive effects in the inner flow. The equations and logic needed to match the two solutions are developed and the computer program implementing the procedure is described. Unfortunately, no converged solutions were obtained, due to unexpectedly large running times. The reasons for this are discussed and several means to alleviate the situation are suggested.

A nonlinear relaxation/quasi-Newton algorithm for the compressible Navier-Stokes equations

NASA Technical Reports Server (NTRS)

Edwards, Jack R.; Mcrae, D. S.

1992-01-01

A highly efficient implicit method for the computation of steady, two-dimensional compressible Navier-Stokes flowfields is presented. The discretization of the governing equations is hybrid in nature, with flux-vector splitting utilized in the streamwise direction and central differences with flux-limited artificial dissipation used for the transverse fluxes. Line Jacobi relaxation is used to provide a suitable initial guess for a new nonlinear iteration strategy based on line Gauss-Seidel sweeps. The applicability of quasi-Newton methods as convergence accelerators for this and other line relaxation algorithms is discussed, and efficient implementations of such techniques are presented. Convergence histories and comparisons with experimental data are presented for supersonic flow over a flat plate and for several high-speed compression corner interactions. Results indicate a marked improvement in computational efficiency over more conventional upwind relaxation strategies, particularly for flowfields containing large pockets of streamwise subsonic flow.

Efficient Multi-Stage Time Marching for Viscous Flows via Local Preconditioning

NASA Technical Reports Server (NTRS)

Kleb, William L.; Wood, William A.; vanLeer, Bram

1999-01-01

A new method has been developed to accelerate the convergence of explicit time-marching, laminar, Navier-Stokes codes through the combination of local preconditioning and multi-stage time marching optimization. Local preconditioning is a technique to modify the time-dependent equations so that all information moves or decays at nearly the same rate, thus relieving the stiffness for a system of equations. Multi-stage time marching can be optimized by modifying its coefficients to account for the presence of viscous terms, allowing larger time steps. We show it is possible to optimize the time marching scheme for a wide range of cell Reynolds numbers for the scalar advection-diffusion equation, and local preconditioning allows this optimization to be applied to the Navier-Stokes equations. Convergence acceleration of the new method is demonstrated through numerical experiments with circular advection and laminar boundary-layer flow over a flat plate.

The piecewise-linear predictor-corrector code - A Lagrangian-remap method for astrophysical flows

NASA Technical Reports Server (NTRS)

Lufkin, Eric A.; Hawley, John F.

1993-01-01

We describe a time-explicit finite-difference algorithm for solving the nonlinear fluid equations. The method is similar to existing Eulerian schemes in its use of operator-splitting and artificial viscosity, except that we solve the Lagrangian equations of motion with a predictor-corrector and then remap onto a fixed Eulerian grid. The remap is formulated to eliminate errors associated with coordinate singularities, with a general prescription for remaps of arbitrary order. We perform a comprehensive series of tests on standard problems. Self-convergence tests show that the code has a second-order rate of convergence in smooth, two-dimensional flow, with pressure forces, gravity, and curvilinear geometry included. While not as accurate on idealized problems as high-order Riemann-solving schemes, the predictor-corrector Lagrangian-remap code has great flexibility for application to a variety of astrophysical problems.

Persistent magnetic vortex flow at a supergranular vertex

NASA Astrophysics Data System (ADS)

Requerey, Iker S.; Cobo, Basilio Ruiz; Gošić, Milan; Bellot Rubio, Luis R.

2018-03-01

Context. Photospheric vortex flows are thought to play a key role in the evolution of magnetic fields. Recent studies show that these swirling motions are ubiquitous in the solar surface convection and occur in a wide range of temporal and spatial scales. Their interplay with magnetic fields is poorly characterized, however. Aims: We study the relation between a persistent photospheric vortex flow and the evolution of a network magnetic element at a supergranular vertex. Methods: We used long-duration sequences of continuum intensity images acquired with Hinode and the local correlation-tracking method to derive the horizontal photospheric flows. Supergranular cells are detected as large-scale divergence structures in the flow maps. At their vertices, and cospatial with network magnetic elements, the velocity flows converge on a central point. Results: One of these converging flows is observed as a vortex during the whole 24 h time series. It consists of three consecutive vortices that appear nearly at the same location. At their core, a network magnetic element is also detected. Its evolution is strongly correlated to that of the vortices. The magnetic feature is concentrated and evacuated when it is caught by the vortices and is weakened and fragmented after the whirls disappear. Conclusions: This evolutionary behavior supports the picture presented previously, where a small flux tube becomes stable when it is surrounded by a vortex flow. A movie attached to Fig. 2 is available at http://https://www.aanda.org

Computation of aerodynamic interference effects on oscillating airfoils with controls in ventilated subsonic wind tunnels

NASA Technical Reports Server (NTRS)

Fromme, J. A.; Golberg, M. A.

1979-01-01

Lift interference effects are discussed based on Bland's (1968) integral equation. A mathematical existence theory is utilized for which convergence of the numerical method has been proved for general (square-integrable) downwashes. Airloads are computed using orthogonal airfoil polynomial pairs in conjunction with a collocation method which is numerically equivalent to Galerkin's method and complex least squares. Convergence exhibits exponentially decreasing error with the number n of collocation points for smooth downwashes, whereas errors are proportional to 1/n for discontinuous downwashes. The latter can be reduced to 1/n to the m+1 power with mth-order Richardson extrapolation (by using m = 2, hundredfold error reductions were obtained with only a 13% increase of computer time). Numerical results are presented showing acoustic resonance, as well as the effect of Mach number, ventilation, height-to-chord ratio, and mode shape on wind-tunnel interference. Excellent agreement with experiment is obtained in steady flow, and good agreement is obtained for unsteady flow.

Time-asymptotic solutions of the Navier-Stokes equation for free shear flows using an alternating-direction implicit method

NASA Technical Reports Server (NTRS)

Rudy, D. H.; Morris, D. J.

1976-01-01

An uncoupled time asymptotic alternating direction implicit method for solving the Navier-Stokes equations was tested on two laminar parallel mixing flows. A constant total temperature was assumed in order to eliminate the need to solve the full energy equation; consequently, static temperature was evaluated by using algebraic relationship. For the mixing of two supersonic streams at a Reynolds number of 1,000, convergent solutions were obtained for a time step 5 times the maximum allowable size for an explicit method. The solution diverged for a time step 10 times the explicit limit. Improved convergence was obtained when upwind differencing was used for convective terms. Larger time steps were not possible with either upwind differencing or the diagonally dominant scheme. Artificial viscosity was added to the continuity equation in order to eliminate divergence for the mixing of a subsonic stream with a supersonic stream at a Reynolds number of 1,000.

Preconditioned upwind methods to solve 3-D incompressible Navier-Stokes equations for viscous flows

NASA Technical Reports Server (NTRS)

Hsu, C.-H.; Chen, Y.-M.; Liu, C. H.

1990-01-01

A computational method for calculating low-speed viscous flowfields is developed. The method uses the implicit upwind-relaxation finite-difference algorithm with a nonsingular eigensystem to solve the preconditioned, three-dimensional, incompressible Navier-Stokes equations in curvilinear coordinates. The technique of local time stepping is incorporated to accelerate the rate of convergence to a steady-state solution. An extensive study of optimizing the preconditioned system is carried out for two viscous flow problems. Computed results are compared with analytical solutions and experimental data.

Evaluation of new techniques for the calculation of internal recirculating flows

NASA Technical Reports Server (NTRS)

Van Doormaal, J. P.; Turan, A.; Raithby, G. D.

1987-01-01

The performance of discrete methods for the prediction of fluid flows can be enhanced by improving the convergence rate of solvers and by increasing the accuracy of the discrete representation of the equations of motion. This paper evaluates the gains in solver performance that are available when various acceleration methods are applied. Various discretizations are also examined and two are recommended because of their accuracy and robustness. Insertion of the improved discretization and solver accelerator into a TEACH code, that has been widely applied to combustor flows, illustrates the substantial gains that can be achieved.

Effective regurgitant orifice area by the color Doppler flow convergence method for evaluating the severity of chronic aortic regurgitation. An animal study.

PubMed

Shiota, T; Jones, M; Yamada, I; Heinrich, R S; Ishii, M; Sinclair, B; Holcomb, S; Yoganathan, A P; Sahn, D J

1996-02-01

The aim of the present study was to evaluate dynamic changes in aortic regurgitant (AR) orifice area with the use of calibrated electromagnetic (EM) flowmeters and to validate a color Doppler flow convergence (FC) method for evaluating effective AR orifice area and regurgitant volume. In 6 sheep, 8 to 20 weeks after surgically induced AR, 22 hemodynamically different states were studied. Instantaneous regurgitant flow rates were obtained by aortic and pulmonary EM flowmeters balanced against each other. Instantaneous AR orifice areas were determined by dividing these actual AR flow rates by the corresponding continuous wave velocities (over 25 to 40 points during each diastole) matched for each steady state. Echo studies were performed to obtain maximal aliasing distances of the FC in a low range (0.20 to 0.32 m/s) and a high range (0.70 to 0.89 m/s) of aliasing velocities; the corresponding maximal AR flow rates were calculated using the hemispheric flow convergence assumption for the FC isovelocity surface. AR orifice areas were derived by dividing the maximal flow rates by the maximal continuous wave Doppler velocities. AR orifice sizes obtained with the use of EM flowmeters showed little change during diastole. Maximal and time-averaged AR orifice areas during diastole obtained by EM flowmeters ranged from 0.06 to 0.44 cm2 (mean, 0.24 +/- 0.11 cm2) and from 0.05 to 0.43 cm2 (mean, 0.21 +/- 0.06 cm2), respectively. Maximal AR orifice areas by FC using low aliasing velocities overestimated reference EM orifice areas; however, at high AV, FC predicted the reference areas more reliably (0.25 +/- 0.16 cm2, r = .82, difference = 0.04 +/- 0.07 cm2). The product of the maximal orifice area obtained by the FC method using high AV and the velocity time integral of the regurgitant orifice velocity showed good agreement with regurgitant volumes per beat (r = .81, difference = 0.9 +/- 7.9 mL/beat). This study, using strictly quantified AR volume, demonstrated little change in AR orifice size during diastole. When high aliasing velocities are chosen, the FC method can be useful for determining effective AR orifice size and regurgitant volume.

Scalability and performance of data-parallel pressure-based multigrid methods for viscous flows

DOE Office of Scientific and Technical Information (OSTI.GOV)

Blosch, E.L.; Shyy, W.

1996-05-01

A full-approximation storage multigrid method for solving the steady-state 2-d incompressible Navier-Stokes equations on staggered grids has been implemented in Fortran on the CM-5, using the array aliasing feature in CM-Fortran to avoid declaring fine-grid-sized arrays on all levels while still allowing a variable number of grid levels. Thus, the storage cost scales with the number of unknowns, allowing us to consider significantly larger problems than would otherwise be possible. Timings over a range of problem sizes and numbers of processors, up to 4096 x 4096 on 512 nodes, show that the smoothing procedure, a pressure-correction technique, is scalable andmore » that the restriction and prolongation steps are nearly so. The performance obtained for the multigrid method is 333 Mflops out of the theoretical peak 4 Gflops on a 32-node CM-5. In comparison, a single-grid computation obtained 420 Mflops. The decrease is due to the inefficiency of the smoothing iterations on the coarse grid levels. W cycles cost much more and are much less efficient than V cycles, due to the increased contribution from the coarse grids. The convergence rate characteristics of the pressure-correction multigrid method are investigated in a Re = 5000 lid-driven cavity flow and a Re = 300 symmetric backward-facing step flow, using either a defect-correction scheme or a second-order upwind scheme. A heuristic technique relating the convergence tolerances for the course grids to the truncation error of the discretization has been found effective and robust. With second-order upwinding on all grid levels, a 5-level 320 x 80 step flow solution was obtained in 20 V cycles, which corresponds to a smoothing rate of 0.7, and required 25 s on a 32-node CM-5. Overall, the convergence rates obtained in the present work are comparable to the most competitive findings reported in the literature. 62 refs., 13 figs.« less

Scalability and Performance of Data-Parallel Pressure-Based Multigrid Methods for Viscous Flows

NASA Astrophysics Data System (ADS)

Blosch, Edwin L.; Shyy, Wei

1996-05-01

A full-approximation storage multigrid method for solving the steady-state 2-dincompressible Navier-Stokes equations on staggered grids has been implemented in Fortran on the CM-5,using the array aliasing feature in CM-Fortran to avoid declaring fine-grid-sized arrays on all levels while still allowing a variable number of grid levels. Thus, the storage cost scales with the number of unknowns,allowing us to consider significantly larger problems than would otherwise be possible. Timings over a range of problem sizes and numbers of processors, up to 4096 × 4096 on 512 nodes, show that the smoothing procedure, a pressure-correction technique, is scalable and that the restriction and prolongation steps are nearly so. The performance obtained for the multigrid method is 333 Mflops out of the theoretical peak 4 Gflops on a 32-node CM-5. In comparison, a single-grid computation obtained 420 Mflops. The decrease is due to the inefficiency of the smoothing iterations on the coarse grid levels. W cycles cost much more and are much less efficient than V cycles, due to the increased contribution from the coarse grids. The convergence rate characteristics of the pressure-correction multigrid method are investigated in a Re = 5000 lid-driven cavity flow and a Re = 300 symmetric backward-facing step flow, using either a defect-correction scheme or a second-order upwind scheme. A heuristic technique relating the convergence tolerances for the coarse grids to the truncation error of the discretization has been found effective and robust. With second-order upwinding on all grid levels, a 5-level 320× 80 step flow solution was obtained in 20 V cycles, which corresponds to a smoothing rate of 0.7, and required 25 s on a 32-node CM-5. Overall, the convergence rates obtained in the present work are comparable to the most competitive findings reported in the literature.

Anisotropic shear stress patterns predict the orientation of convergent tissue movements in the embryonic heart

PubMed Central

2017-01-01

Myocardial contractility and blood flow provide essential mechanical cues for the morphogenesis of the heart. In general, endothelial cells change their migratory behavior in response to shear stress patterns, according to flow directionality. Here, we assessed the impact of shear stress patterns and flow directionality on the behavior of endocardial cells, the specialized endothelial cells of the heart. At the early stages of zebrafish heart valve formation, we show that endocardial cells are converging to the valve-forming area and that this behavior depends upon mechanical forces. Quantitative live imaging and mathematical modeling allow us to correlate this tissue convergence with the underlying flow forces. We predict that tissue convergence is associated with the direction of the mean wall shear stress and of the gradient of harmonic phase-averaged shear stresses, which surprisingly do not match the overall direction of the flow. This contrasts with the usual role of flow directionality in vascular development and suggests that the full spatial and temporal complexity of the wall shear stress should be taken into account when studying endothelial cell responses to flow in vivo. PMID:29183943

Physics-Based Preconditioning of a Compressible Flow Solver for Large-Scale Simulations of Additive Manufacturing Processes

NASA Astrophysics Data System (ADS)

Weston, Brian; Nourgaliev, Robert; Delplanque, Jean-Pierre

2017-11-01

We present a new block-based Schur complement preconditioner for simulating all-speed compressible flow with phase change. The conservation equations are discretized with a reconstructed Discontinuous Galerkin method and integrated in time with fully implicit time discretization schemes. The resulting set of non-linear equations is converged using a robust Newton-Krylov framework. Due to the stiffness of the underlying physics associated with stiff acoustic waves and viscous material strength effects, we solve for the primitive-variables (pressure, velocity, and temperature). To enable convergence of the highly ill-conditioned linearized systems, we develop a physics-based preconditioner, utilizing approximate block factorization techniques to reduce the fully-coupled 3×3 system to a pair of reduced 2×2 systems. We demonstrate that our preconditioned Newton-Krylov framework converges on very stiff multi-physics problems, corresponding to large CFL and Fourier numbers, with excellent algorithmic and parallel scalability. Results are shown for the classic lid-driven cavity flow problem as well as for 3D laser-induced phase change. This work was performed under the auspices of the U.S. Department of Energy by Lawrence Livermore National Laboratory under Contract DE-AC52-07NA27344.

Local multiplicative Schwarz algorithms for convection-diffusion equations

NASA Technical Reports Server (NTRS)

Cai, Xiao-Chuan; Sarkis, Marcus

1995-01-01

We develop a new class of overlapping Schwarz type algorithms for solving scalar convection-diffusion equations discretized by finite element or finite difference methods. The preconditioners consist of two components, namely, the usual two-level additive Schwarz preconditioner and the sum of some quadratic terms constructed by using products of ordered neighboring subdomain preconditioners. The ordering of the subdomain preconditioners is determined by considering the direction of the flow. We prove that the algorithms are optimal in the sense that the convergence rates are independent of the mesh size, as well as the number of subdomains. We show by numerical examples that the new algorithms are less sensitive to the direction of the flow than either the classical multiplicative Schwarz algorithms, and converge faster than the additive Schwarz algorithms. Thus, the new algorithms are more suitable for fluid flow applications than the classical additive or multiplicative Schwarz algorithms.

Nozzle Free Jet Flows Within the Strong Curved Shock Regime

NASA Technical Reports Server (NTRS)

Shih, Tso-Shin

1975-01-01

A study based on inviscid analysis was conducted to examine the flow field produced from a convergent-divergent nozzle when a strong curved shock occurs. It was found that a certain constraint is imposed on the flow solution of the problem which is the unique feature of the flow within this flow regime, and provides the reason why the inverse method of calculation cannot be employed for these problems. An approximate method was developed to calculate the flow field, and results were obtained for two-dimensional flows. Analysis and calculations were performed for flows with axial symmetry. It is shown that under certain conditions, the vorticity generated at the jet boundary may become infinite and the viscous effect becomes important. Under other conditions, the asymptotic free jet height as well as the corresponding shock geometry were determined.

Method and apparatus for strip casting

DOEpatents

Follstaedt, Donald W.; Powell, John C.; Sussman, Richard C.; Williams, Robert S.

1991-01-01

Casting nozzles will provide improved flow conditions with the parameters controlled according to the present invention. The gap relationships between the nozzle slot and exit orifice must be controlled in combination with converging exit passageway to provide a smooth flow without shearing and turbulence in the stream. The nozzle lips are also rounded to improve flow and increase refractory life of the lips of the nozzle. The tundish walls are tapered to provide improve flow for supplying the melt to the nozzle. The nozzle is located about 45.degree. below top dead center for optimum conditions.

A finite difference method for the solution of the transonic flow around harmonically oscillating wings

NASA Technical Reports Server (NTRS)

Ehlers, E. F.

1974-01-01

A finite difference method for the solution of the transonic flow about a harmonically oscillating wing is presented. The partial differential equation for the unsteady transonic flow was linearized by dividing the flow into separate steady and unsteady perturbation velocity potentials and by assuming small amplitudes of harmonic oscillation. The resulting linear differential equation is of mixed type, being elliptic or hyperbolic whereever the steady flow equation is elliptic or hyperbolic. Central differences were used for all derivatives except at supersonic points where backward differencing was used for the streamwise direction. Detailed formulas and procedures are described in sufficient detail for programming on high speed computers. To test the method, the problem of the oscillating flap on a NACA 64A006 airfoil was programmed. The numerical procedure was found to be stable and convergent even in regions of local supersonic flow with shocks.

Thermodynamic evaluation of transonic compressor rotors using the finite volume approach

NASA Technical Reports Server (NTRS)

Nicholson, S.; Moore, J.

1986-01-01

A method was developed which calculates two-dimensional, transonic, viscous flow in ducts. The finite volume, time marching formulation is used to obtain steady flow solutions of the Reynolds-averaged form of the Navier Stokes equations. The entire calculation is performed in the physical domain. The method is currently limited to the calculation of attached flows. The features of the current method can be summarized as follows. Control volumes are chosen so that smoothing of flow properties, typically required for stability, is now needed. Different time steps are used in the different governing equations to improve the convergence speed of the viscous calculations. A new pressure interpolation scheme is introduced which improves the shock capturing ability of the method. A multi-volume method for pressure changes in the boundary layer allows calculations which use very long and thin control volumes. A special discretization technique is also used to stabilize these calculations. A special formulation of the energy equation is used to provide improved transient behavior of solutions which use the full energy equation. The method is then compared with a wide variety of test cases. The freestream Mach numbers range from 0.075 to 2.8 in the calculations. Transonic viscous flow in a converging diverging nozzle is calculated with the method; the Mach number upstream of the shock is approximately 1.25. The agreement between the calculated and measured shock strength and total pressure losses is good. Essentially incompressible turbulent boundary layer flow in a adverse pressure gradient is calculated and the computed distribution of mean velocity and shear stress are in good agreement with the measurements. At the other end of the Mach number range, a flat plate turbulent boundary layer with a freestream Mach number of 2.8 is calculated using the full energy equation; the computed total temperature distribution and recovery factor agree well with the measurements when a variable Prandtl number is used through the boundary layer.

Geometrically Flexible and Efficient Flow Analysis of High Speed Vehicles Via Domain Decomposition, Part 1: Unstructured-Grid Solver for High Speed Flows

NASA Technical Reports Server (NTRS)

White, Jeffery A.; Baurle, Robert A.; Passe, Bradley J.; Spiegel, Seth C.; Nishikawa, Hiroaki

2017-01-01

The ability to solve the equations governing the hypersonic turbulent flow of a real gas on unstructured grids using a spatially-elliptic, 2nd-order accurate, cell-centered, finite-volume method has been recently implemented in the VULCAN-CFD code. This paper describes the key numerical methods and techniques that were found to be required to robustly obtain accurate solutions to hypersonic flows on non-hex-dominant unstructured grids. The methods and techniques described include: an augmented stencil, weighted linear least squares, cell-average gradient method, a robust multidimensional cell-average gradient-limiter process that is consistent with the augmented stencil of the cell-average gradient method and a cell-face gradient method that contains a cell skewness sensitive damping term derived using hyperbolic diffusion based concepts. A data-parallel matrix-based symmetric Gauss-Seidel point-implicit scheme, used to solve the governing equations, is described and shown to be more robust and efficient than a matrix-free alternative. In addition, a y+ adaptive turbulent wall boundary condition methodology is presented. This boundary condition methodology is deigned to automatically switch between a solve-to-the-wall and a wall-matching-function boundary condition based on the local y+ of the 1st cell center off the wall. The aforementioned methods and techniques are then applied to a series of hypersonic and supersonic turbulent flat plate unit tests to examine the efficiency, robustness and convergence behavior of the implicit scheme and to determine the ability of the solve-to-the-wall and y+ adaptive turbulent wall boundary conditions to reproduce the turbulent law-of-the-wall. Finally, the thermally perfect, chemically frozen, Mach 7.8 turbulent flow of air through a scramjet flow-path is computed and compared with experimental data to demonstrate the robustness, accuracy and convergence behavior of the unstructured-grid solver for a realistic 3-D geometry on a non-hex-dominant grid.

Variable High Order Multiblock Overlapping Grid Methods for Mixed Steady and Unsteady Multiscale Viscous Flows

NASA Technical Reports Server (NTRS)

Sjogreen, Bjoern; Yee, H. C.

2007-01-01

Flows containing steady or nearly steady strong shocks in parts of the flow field, and unsteady turbulence with shocklets on other parts of the flow field are difficult to capture accurately and efficiently employing the same numerical scheme even under the multiblock grid or adaptive grid refinement framework. On one hand, sixth-order or higher shock-capturing methods are appropriate for unsteady turbulence with shocklets. On the other hand, lower order shock-capturing methods are more effective for strong steady shocks in terms of convergence. In order to minimize the shortcomings of low order and high order shock-capturing schemes for the subject flows,a multi- block overlapping grid with different orders of accuracy on different blocks is proposed. Test cases to illustrate the performance of the new solver are included.

Vadose zone flow convergence test suite

DOE Office of Scientific and Technical Information (OSTI.GOV)

Butcher, B. T.

Performance Assessment (PA) simulations for engineered disposal systems at the Savannah River Site involve highly contrasting materials and moisture conditions at and near saturation. These conditions cause severe convergence difficulties that typically result in unacceptable convergence or long simulation times or excessive analyst effort. Adequate convergence is usually achieved in a trial-anderror manner by applying under-relaxation to the Saturation or Pressure variable, in a series of everdecreasing RELAxation values. SRNL would like a more efficient scheme implemented inside PORFLOW to achieve flow convergence in a more reliable and efficient manner. To this end, a suite of test problems that illustratemore » these convergence problems is provided to facilitate diagnosis and development of an improved convergence strategy. The attached files are being transmitted to you describing the test problem and proposed resolution.« less

Regulation of Renewable Energy Sources to Optimal Power Flow Solutions Using ADMM

DOE Office of Scientific and Technical Information (OSTI.GOV)

Dall-Anese, Emiliano; Zhang, Yijian; Hong, Mingyi

This paper considers power distribution systems featuring renewable energy sources (RESs), and develops a distributed optimization method to steer the RES output powers to solutions of AC optimal power flow (OPF) problems. The design of the proposed method leverages suitable linear approximations of the AC-power flow equations, and is based on the Alternating Direction Method of Multipliers (ADMM). Convergence of the RES-inverter output powers to solutions of the OPF problem is established under suitable conditions on the stepsize as well as mismatches between the commanded setpoints and actual RES output powers. In a broad sense, the methods and results proposedmore » here are also applicable to other distributed optimization problem setups with ADMM and inexact dual updates.« less

Eddy Current Minimizing Flow Plug for Use in Flow Conditioning and Flow Metering

NASA Technical Reports Server (NTRS)

England, John Dwight (Inventor); Kelley, Anthony R. (Inventor)

2015-01-01

An eddy-current-minimizing flow plug has an outer radial wall with open flow channels formed between the plug's inlet and outlet. The plug has a central region coupled to the inner surface of the outer radial wall. Each open flow channel includes (i) a first portion originating at the inlet and converging to a location in the plug where convergence is contributed to by changes in thickness of the outer radial wall and divergence of the central region, and (ii) a second portion originating in the plug and diverging to the outlet where divergence is contributed to by changes in thickness of the outer radial wall and convergence of the central region. For at least a portion of the open flow channels, a central axis passing through the first and second portions is non-parallel with respect to the given direction of the flow.

Improved Boundary Conditions for Cell-centered Difference Schemes

NASA Technical Reports Server (NTRS)

VanderWijngaart, Rob F.; Klopfer, Goetz H.; Chancellor, Marisa K. (Technical Monitor)

1997-01-01

Cell-centered finite-volume (CCFV) schemes have certain attractive properties for the solution of the equations governing compressible fluid flow. Among others, they provide a natural vehicle for specifying flux conditions at the boundaries of the physical domain. Unfortunately, they lead to slow convergence for numerical programs utilizing them. In this report a method for investigating and improving the convergence of CCFV schemes is presented, which focuses on the effect of the numerical boundary conditions. The key to the method is the computation of the spectral radius of the iteration matrix of the entire demoralized system of equations, not just of the interior point scheme or the boundary conditions.

A Pseudo-Temporal Multi-Grid Relaxation Scheme for Solving the Parabolized Navier-Stokes Equations

NASA Technical Reports Server (NTRS)

White, J. A.; Morrison, J. H.

1999-01-01

A multi-grid, flux-difference-split, finite-volume code, VULCAN, is presented for solving the elliptic and parabolized form of the equations governing three-dimensional, turbulent, calorically perfect and non-equilibrium chemically reacting flows. The space marching algorithms developed to improve convergence rate and or reduce computational cost are emphasized. The algorithms presented are extensions to the class of implicit pseudo-time iterative, upwind space-marching schemes. A full approximate storage, full multi-grid scheme is also described which is used to accelerate the convergence of a Gauss-Seidel relaxation method. The multi-grid algorithm is shown to significantly improve convergence on high aspect ratio grids.

Numerical Speed of Sound and its Application to Schemes for all Speeds

NASA Technical Reports Server (NTRS)

Liou, Meng-Sing; Edwards, Jack R.

1999-01-01

The concept of "numerical speed of sound" is proposed in the construction of numerical flux. It is shown that this variable is responsible for the accurate resolution of' discontinuities, such as contacts and shocks. Moreover, this concept can he readily extended to deal with low speed and multiphase flows. As a results, the numerical dissipation for low speed flows is scaled with the local fluid speed, rather than the sound speed. Hence, the accuracy is enhanced the correct solution recovered, and the convergence rate improved. We also emphasize the role of mass flux and analyze the behavior of this flux. Study of mass flux is important because the numerical diffusivity introduced in it can be identified. In addition, it is the term common to all conservation equations. We show calculated results for a wide variety of flows to validate the effectiveness of using the numerical speed of sound concept in constructing the numerical flux. We especially aim at achieving these two goals: (1) improving accuracy and (2) gaining convergence rates for all speed ranges. We find that while the performance at high speed range is maintained, the flux now has the capability of performing well even with the low: speed flows. Thanks to the new numerical speed of sound, the convergence is even enhanced for the flows outside of the low speed range. To realize the usefulness of the proposed method in engineering problems, we have also performed calculations for complex 3D turbulent flows and the results are in excellent agreement with data.

Analysis of a Stabilized CNLF Method with Fast Slow Wave Splittings for Flow Problems

DOE PAGES

Jiang, Nan; Tran, Hoang A.

2015-04-01

In this work, we study Crank-Nicolson leap-frog (CNLF) methods with fast-slow wave splittings for Navier-Stokes equations (NSE) with a rotation/Coriolis force term, which is a simplification of geophysical flows. We propose a new stabilized CNLF method where the added stabilization completely removes the method's CFL time step condition. A comprehensive stability and error analysis is given. We also prove that for Oseen equations with the rotation term, the unstable mode (for which u(n+1) + u(n-1) equivalent to 0) of CNLF is asymptotically stable. Numerical results are provided to verify the stability and the convergence of the methods.

A space-time lower-upper symmetric Gauss-Seidel scheme for the time-spectral method

NASA Astrophysics Data System (ADS)

Zhan, Lei; Xiong, Juntao; Liu, Feng

2016-05-01

The time-spectral method (TSM) offers the advantage of increased order of accuracy compared to methods using finite-difference in time for periodic unsteady flow problems. Explicit Runge-Kutta pseudo-time marching and implicit schemes have been developed to solve iteratively the space-time coupled nonlinear equations resulting from TSM. Convergence of the explicit schemes is slow because of the stringent time-step limit. Many implicit methods have been developed for TSM. Their computational efficiency is, however, still limited in practice because of delayed implicit temporal coupling, multiple iterative loops, costly matrix operations, or lack of strong diagonal dominance of the implicit operator matrix. To overcome these shortcomings, an efficient space-time lower-upper symmetric Gauss-Seidel (ST-LU-SGS) implicit scheme with multigrid acceleration is presented. In this scheme, the implicit temporal coupling term is split as one additional dimension of space in the LU-SGS sweeps. To improve numerical stability for periodic flows with high frequency, a modification to the ST-LU-SGS scheme is proposed. Numerical results show that fast convergence is achieved using large or even infinite Courant-Friedrichs-Lewy (CFL) numbers for unsteady flow problems with moderately high frequency and with the use of moderately high numbers of time intervals. The ST-LU-SGS implicit scheme is also found to work well in calculating periodic flow problems where the frequency is not known a priori and needed to be determined by using a combined Fourier analysis and gradient-based search algorithm.

Convergent validity between willingness to pay elicitation methods: an application to Grand Canyon whitewater boaters

USGS Publications Warehouse

Neher, Christopher; Bair, Lucas S.; Duffield, John; Patterson, David A.; Neher, Katherine

2018-01-01

We directly compare trip willingness to pay (WTP) values between dichotomous choice contingent valuation (DCCV) and discrete choice experiment (DCE) stated preference surveys of private party Grand Canyon whitewater boaters. The consistency of DCCV and DCE estimates is debated in the literature, and this study contributes to the body of work comparing the methods. Comparisons were made of mean WTP estimates for four hypothetical Colorado River flow-level scenarios. Boaters were found to most highly value mid-range flows, with very low and very high flows eliciting lower WTP estimates across both DCE and DCCV surveys. Mean WTP precision was estimated through simulation. No statistically significant differences were detected between the two methods at three of the four hypothetical flow levels.

The Hubble flow of plateau inflation

DOE Office of Scientific and Technical Information (OSTI.GOV)

Coone, Dries; Roest, Diederik; Vennin, Vincent, E-mail: a.a.coone@rug.nl, E-mail: d.roest@rug.nl, E-mail: vincent.vennin@port.ac.uk

2015-11-01

In the absence of CMB precision measurements, a Taylor expansion has often been invoked to parametrize the Hubble flow function during inflation. The standard ''horizon flow'' procedure implicitly relies on this assumption. However, the recent Planck results indicate a strong preference for plateau inflation, which suggests the use of Padé approximants instead. We propose a novel method that provides analytic solutions of the flow equations for a given parametrization of the Hubble function. This method is illustrated in the Taylor and Padé cases, for low order expansions. We then present the results of a full numerical treatment scanning larger ordermore » expansions, and compare these parametrizations in terms of convergence, prior dependence, predictivity and compatibility with the data. Finally, we highlight the implications for potential reconstruction methods.« less

Flow in a planar convergent-divergent nozzle

NASA Astrophysics Data System (ADS)

Kotteda, V. M. K.; Mittal, S.

2017-05-01

Flow in a convergent-divergent nozzle is studied for pressure ratios (NPR) of 1-11 and exit-to-throat area ratios of 1.2 to 2.0. The unsteady compressible Navier-Stokes equations along with the Spalart-Allmaras turbulence model are solved using a stabilized finite element method in two dimensions. Asymmetric flow is observed at moderate NPR. The side loads due to the flow asymmetry increase with increases in NPR and area ratio. Various flow regimes that are possible in the entire parameter space are identified. The introduction of boundary layer bleed results in steady and symmetric flow conditions at all NPR. Consequently, the nozzle does not experience a lateral force for any NPR. Application of bleed leads to a significant downstream shift in the shock location at low to moderate NPR. Compared to no-bleed, the nozzle experiences a loss of thrust in this regime. The thrust performance for {NPR} > 6 is, however, unaffected by bleed. The effect of nozzle geometry on the flow at various NPR is studied. Four different geometries with the same area ratio and nozzle length are considered. These geometries differ from each other in terms of the nozzle surface profile, including the discontinuity in slope of the surface. Barring some minor differences at low to moderate NPR, the flow is similar for all the geometries considered.

Implicit solution of three-dimensional internal turbulent flows

NASA Technical Reports Server (NTRS)

Michelassi, V.; Liou, M.-S.; Povinelli, Louis A.; Martelli, F.

1991-01-01

The scalar form of the approximate factorization method was used to develop a new code for the solution of three dimensional internal laminar and turbulent compressible flows. The Navier-Stokes equations in their Reynolds-averaged form were iterated in time until a steady solution was reached. Evidence was given to the implicit and explicit artificial damping schemes that proved to be particularly efficient in speeding up convergence and enhancing the algorithm robustness. A conservative treatment of these terms at the domain boundaries was proposed in order to avoid undesired mass and/or momentum artificial fluxes. Turbulence effects were accounted for by the zero-equation Baldwin-Lomax turbulence model and the q-omega two-equation model. The flow in a developing S-duct was then solved in the laminar regime in a Reynolds number (Re) of 790 and in the turbulent regime at Re equals 40,000 by using the Baldwin-Lomax model. The Stanitz elbow was then solved by using an invicid version of the same code at M sub inlet equals 0.4. Grid dependence and convergence rate were investigated, showing that for this solver the implicit damping scheme may play a critical role for convergence characteristics. The same flow at Re equals 2.5 times 10(exp 6) was solved with the Baldwin-Lomax and the q-omega models. Both approaches show satisfactory agreement with experiments, although the q-omega model was slightly more accurate.

Development and application of a standardized flow measurement uncertainty analysis framework to various low-head short-converging intake types across the United States federal hydropower fleet

DOE Office of Scientific and Technical Information (OSTI.GOV)

Smith, Brennan T

2015-01-01

Turbine discharges at low-head short converging intakes are difficult to measure accurately. The proximity of the measurement section to the intake entrance admits large uncertainties related to asymmetry of the velocity profile, swirl, and turbulence. Existing turbine performance codes [10, 24] do not address this special case and published literature is largely silent on rigorous evaluation of uncertainties associated with this measurement context. The American Society of Mechanical Engineers (ASME) Committee investigated the use of Acoustic transit time (ATT), Acoustic scintillation (AS), and Current meter (CM) in a short converging intake at the Kootenay Canal Generating Station in 2009. Basedmore » on their findings, a standardized uncertainty analysis (UA) framework for velocity-area method (specifically for CM measurements) is presented in this paper given the fact that CM is still the most fundamental and common type of measurement system. Typical sources of systematic and random errors associated with CM measurements are investigated, and the major sources of uncertainties associated with turbulence and velocity fluctuations, numerical velocity integration technique (bi-cubic spline), and the number and placement of current meters are being considered for an evaluation. Since the velocity measurements in a short converging intake are associated with complex nonlinear and time varying uncertainties (e.g., Reynolds stress in fluid dynamics), simply applying the law of propagation of uncertainty is known to overestimate the measurement variance while the Monte Carlo method does not. Therefore, a pseudo-Monte Carlo simulation method (random flow generation technique [8]) which was initially developed for the purpose of establishing upstream or initial conditions in the Large-Eddy Simulation (LES) and the Direct Numerical Simulation (DNS) is used to statistically determine uncertainties associated with turbulence and velocity fluctuations. This technique is then combined with a bi-cubic spline interpolation method which converts point velocities into a continuous velocity distribution over the measurement domain. Subsequently the number and placement of current meters are simulated to investigate the accuracy of the estimated flow rates using the numerical velocity-area integration method outlined in ISO 3354 [12]. The authors herein consider that statistics on generated flow rates processed with bi-cubic interpolation and sensor simulations are the combined uncertainties which already accounted for the effects of all those three uncertainty sources. A preliminary analysis based on the current meter data obtained through an upgrade acceptance test of a single unit located in a mainstem plant has been presented.« less

DONBOL: A computer program for predicting axisymmetric nozzle afterbody pressure distributions and drag at subsonic speeds

NASA Technical Reports Server (NTRS)

Putnam, L. E.

1979-01-01

A Neumann solution for inviscid external flow was coupled to a modified Reshotko-Tucker integral boundary-layer technique, the control volume method of Presz for calculating flow in the separated region, and an inviscid one-dimensional solution for the jet exhaust flow in order to predict axisymmetric nozzle afterbody pressure distributions and drag. The viscous and inviscid flows are solved iteratively until convergence is obtained. A computer algorithm of this procedure was written and is called DONBOL. A description of the computer program and a guide to its use is given. Comparisons of the predictions of this method with experiments show that the method accurately predicts the pressure distributions of boattail afterbodies which have the jet exhaust flow simulated by solid bodies. For nozzle configurations which have the jet exhaust simulated by high-pressure air, the present method significantly underpredicts the magnitude of nozzle pressure drag. This deficiency results because the method neglects the effects of jet plume entrainment. This method is limited to subsonic free-stream Mach numbers below that for which the flow over the body of revolution becomes sonic.

A time-accurate finite volume method valid at all flow velocities

NASA Technical Reports Server (NTRS)

Kim, S.-W.

1993-01-01

A finite volume method to solve the Navier-Stokes equations at all flow velocities (e.g., incompressible, subsonic, transonic, supersonic and hypersonic flows) is presented. The numerical method is based on a finite volume method that incorporates a pressure-staggered mesh and an incremental pressure equation for the conservation of mass. Comparison of three generally accepted time-advancing schemes, i.e., Simplified Marker-and-Cell (SMAC), Pressure-Implicit-Splitting of Operators (PISO), and Iterative-Time-Advancing (ITA) scheme, are made by solving a lid-driven polar cavity flow and self-sustained oscillatory flows over circular and square cylinders. Calculated results show that the ITA is the most stable numerically and yields the most accurate results. The SMAC is the most efficient computationally and is as stable as the ITA. It is shown that the PISO is the most weakly convergent and it exhibits an undesirable strong dependence on the time-step size. The degenerated numerical results obtained using the PISO are attributed to its second corrector step that cause the numerical results to deviate further from a divergence free velocity field. The accurate numerical results obtained using the ITA is attributed to its capability to resolve the nonlinearity of the Navier-Stokes equations. The present numerical method that incorporates the ITA is used to solve an unsteady transitional flow over an oscillating airfoil and a chemically reacting flow of hydrogen in a vitiated supersonic airstream. The turbulence fields in these flow cases are described using multiple-time-scale turbulence equations. For the unsteady transitional over an oscillating airfoil, the fluid flow is described using ensemble-averaged Navier-Stokes equations defined on the Lagrangian-Eulerian coordinates. It is shown that the numerical method successfully predicts the large dynamic stall vortex (DSV) and the trailing edge vortex (TEV) that are periodically generated by the oscillating airfoil. The calculated streaklines are in very good comparison with the experimentally obtained smoke picture. The calculated turbulent viscosity contours show that the transition from laminar to turbulent state and the relaminarization occur widely in space as well as in time. The ensemble-averaged velocity profiles are also in good agreement with the measured data and the good comparison indicates that the numerical method as well as the multipletime-scale turbulence equations successfully predict the unsteady transitional turbulence field. The chemical reactions for the hydrogen in the vitiated supersonic airstream are described using 9 chemical species and 48 reaction-steps. Consider that a fast chemistry can not be used to describe the fine details (such as the instability) of chemically reacting flows while a reduced chemical kinetics can not be used confidently due to the uncertainty contained in the reaction mechanisms. However, the use of a detailed finite rate chemistry may make it difficult to obtain a fully converged solution due to the coupling between the large number of flow, turbulence, and chemical equations. The numerical results obtained in the present study are in good agreement with the measured data. The good comparison is attributed to the numerical method that can yield strongly converged results for the reacting flow and to the use of the multiple-time-scale turbulence equations that can accurately describe the mixing of the fuel and the oxidant.

The transmission of sound in nonuniform ducts. [carrying steady, compressible flow

NASA Technical Reports Server (NTRS)

Eversman, W.

1975-01-01

The method of weighted residuals in the form of a modified Galerkin method with boundary residuals was developed for the study of the transmission of sound in nonuniform ducts carrying a steady, compressible flow. In this development, the steady flow was modeled as essentially one dimensional but with a kinematic modification to force tangency of the flow at the duct walls. Three forms of the computational scheme were developed using for basis functions (1) the no-flow uniform duct modes, (2) positive running uniform duct modes, with flow, and (3) positive and negative running uniform duct modes, with flow. The formulation using the no-flow modes was the most highly developed, and has advantages primarily due to relative computational simplicity. Results using the three methods are shown to converge to known solutions for several special cases, and the most significant check case is against low frequency, one dimensional results over the complete subsonic Mach number range. Development of the method is continuing, with emphasis on assessing the relative accuracy and efficiency of the three implementations.

A comparison of discrete versus continuous adjoint states to invert groundwater flow in heterogeneous dual porosity systems

NASA Astrophysics Data System (ADS)

Delay, Frederick; Badri, Hamid; Fahs, Marwan; Ackerer, Philippe

2017-12-01

Dual porosity models become increasingly used for simulating groundwater flow at the large scale in fractured porous media. In this context, model inversions with the aim of retrieving the system heterogeneity are frequently faced with huge parameterizations for which descent methods of inversion with the assistance of adjoint state calculations are well suited. We compare the performance of discrete and continuous forms of adjoint states associated with the flow equations in a dual porosity system. The discrete form inherits from previous works by some of the authors, as the continuous form is completely new and here fully differentiated for handling all types of model parameters. Adjoint states assist descent methods by calculating the gradient components of the objective function, these being a key to good convergence of inverse solutions. Our comparison on the basis of synthetic exercises show that both discrete and continuous adjoint states can provide very similar solutions close to reference. For highly heterogeneous systems, the calculation grid of the continuous form cannot be too coarse, otherwise the method may show lack of convergence. This notwithstanding, the continuous adjoint state is the most versatile form as its non-intrusive character allows for plugging an inversion toolbox quasi-independent from the code employed for solving the forward problem.

Numerical study of combustion processes in afterburners

NASA Technical Reports Server (NTRS)

Zhou, Xiaoqing; Zhang, Xiaochun

1986-01-01

Mathematical models and numerical methods are presented for computer modeling of aeroengine afterburners. A computer code GEMCHIP is described briefly. The algorithms SIMPLER, for gas flow predictions, and DROPLET, for droplet flow calculations, are incorporated in this code. The block correction technique is adopted to facilitate convergence. The method of handling irregular shapes of combustors and flameholders is described. The predicted results for a low-bypass-ratio turbofan afterburner in the cases of gaseous combustion and multiphase spray combustion are provided and analyzed, and engineering guides for afterburner optimization are presented.

The calculation of steady non-linear transonic flow over finite wings with linear theory aerodynamics

NASA Technical Reports Server (NTRS)

Cunningham, A. M., Jr.

1976-01-01

The feasibility of calculating steady mean flow solutions for nonlinear transonic flow over finite wings with a linear theory aerodynamic computer program is studied. The methodology is based on independent solutions for upper and lower surface pressures that are coupled through the external flow fields. Two approaches for coupling the solutions are investigated which include the diaphragm and the edge singularity method. The final method is a combination of both where a line source along the wing leading edge is used to account for blunt nose airfoil effects; and the upper and lower surface flow fields are coupled through a diaphragm in the plane of the wing. An iterative solution is used to arrive at the nonuniform flow solution for both nonlifting and lifting cases. Final results for a swept tapered wing in subcritical flow show that the method converges in three iterations and gives excellent agreement with experiment at alpha = 0 deg and 2 deg. Recommendations are made for development of a procedure for routine application.

Mixed convection flow of viscoelastic fluid by a stretching cylinder with heat transfer.

PubMed

Hayat, Tasawar; Anwar, Muhammad Shoaib; Farooq, Muhammad; Alsaedi, Ahmad

2015-01-01

Flow of viscoelastic fluid due to an impermeable stretching cylinder is discussed. Effects of mixed convection and variable thermal conductivity are present. Thermal conductivity is taken temperature dependent. Nonlinear partial differential system is reduced into the nonlinear ordinary differential system. Resulting nonlinear system is computed for the convergent series solutions. Numerical values of skin friction coefficient and Nusselt number are computed and discussed. The results obtained with the current method are in agreement with previous studies using other methods as well as theoretical ideas. Physical interpretation reflecting the contribution of influential parameters in the present flow is presented. It is hoped that present study serves as a stimulus for modeling further stretching flows especially in polymeric and paper production processes.

Mixed Convection Flow of Viscoelastic Fluid by a Stretching Cylinder with Heat Transfer

PubMed Central

Hayat, Tasawar; Anwar, Muhammad Shoaib; Farooq, Muhammad; Alsaedi, Ahmad

2015-01-01

Flow of viscoelastic fluid due to an impermeable stretching cylinder is discussed. Effects of mixed convection and variable thermal conductivity are present. Thermal conductivity is taken temperature dependent. Nonlinear partial differential system is reduced into the nonlinear ordinary differential system. Resulting nonlinear system is computed for the convergent series solutions. Numerical values of skin friction coefficient and Nusselt number are computed and discussed. The results obtained with the current method are in agreement with previous studies using other methods as well as theoretical ideas. Physical interpretation reflecting the contribution of influential parameters in the present flow is presented. It is hoped that present study serves as a stimulus for modeling further stretching flows especially in polymeric and paper production processes. PMID:25775032

DAMAS Processing for a Phased Array Study in the NASA Langley Jet Noise Laboratory

NASA Technical Reports Server (NTRS)

Brooks, Thomas F.; Humphreys, William M.; Plassman, Gerald e.

2010-01-01

A jet noise measurement study was conducted using a phased microphone array system for a range of jet nozzle configurations and flow conditions. The test effort included convergent and convergent/divergent single flow nozzles, as well as conventional and chevron dual-flow core and fan configurations. Cold jets were tested with and without wind tunnel co-flow, whereas, hot jets were tested only with co-flow. The intent of the measurement effort was to allow evaluation of new phased array technologies for their ability to separate and quantify distributions of jet noise sources. In the present paper, the array post-processing method focused upon is DAMAS (Deconvolution Approach for the Mapping of Acoustic Sources) for the quantitative determination of spatial distributions of noise sources. Jet noise is highly complex with stationary and convecting noise sources, convecting flows that are the sources themselves, and shock-related and screech noise for supersonic flow. The analysis presented in this paper addresses some processing details with DAMAS, for the array positioned at 90 (normal) to the jet. The paper demonstrates the applicability of DAMAS and how it indicates when strong coherence is present. Also, a new approach to calibrating the array focus and position is introduced and demonstrated.

Preliminary study of the use of the STAR-100 computer for transonic flow calculations

NASA Technical Reports Server (NTRS)

Keller, J. D.; Jameson, A.

1977-01-01

An explicit method for solving the transonic small-disturbance potential equation is presented. This algorithm, which is suitable for the new vector-processor computers such as the CDC STAR-100, is compared to successive line over-relaxation (SLOR) on a simple test problem. The convergence rate of the explicit scheme is slower than that of SLOR, however, the efficiency of the explicit scheme on the STAR-100 computer is sufficient to overcome the slower convergence rate and allow an overall speedup compared to SLOR on the CYBER 175 computer.

An Investigation of Transonic Resonance in a Mach 2.2 Round Convergent-Divergent Nozzle

NASA Technical Reports Server (NTRS)

Dippold, Vance F., III; Zaman, Khairul B. M. Q.

2015-01-01

Hot-wire and acoustic measurements were taken for a round convergent nozzle and a round convergent-divergent (C-D) nozzle at a jet Mach number of 0.61. The C-D nozzle had a design Mach number of 2.2. Compared to the convergent nozzle jet flow, the Mach 2.2 nozzle jet flow produced excess broadband noise (EBBN). It also produced a transonic resonance tone at 1200 Herz. Computational simulations were performed for both nozzle flows. A steady Reynolds-Averaged Navier-Stokes simulation was performed for the convergent nozzle jet flow. For the Mach 2.2 nozzle flow, a steady RANS simulation, an unsteady RANS (URANS) simulation, and an unsteady Detached Eddy Simulation (DES) were performed. The RANS simulation of the convergent nozzle showed good agreement with the hot-wire velocity and turbulence measurements, though the decay of the potential core was over-predicted. The RANS simulation of the Mach 2.2 nozzle showed poor agreement with the experimental data, and more closely resembled an ideally-expanded jet. The URANS simulation also showed qualitative agreement with the hot-wire data, but predicted a transonic resonance at 1145 Herz. The DES showed good agreement with the hot-wire velocity and turbulence data. The DES also produced a transonic tone at 1135 Herz. The DES solution showed that the destabilization of the shock-induced separation region inside the nozzle produced increased levels of turbulence intensity. This is likely the source of the EBBN.

Method and apparatus for strip casting

DOEpatents

Follstaedt, D.W.; Powell, J.C.; Sussman, R.C.; Williams, R.S.

1991-11-12

Casting nozzles will provide improved flow conditions with the parameters controlled according to the present invention. The gap relationships between the nozzle slot and exit orifice must be controlled in combination with converging exit passageway to provide a smooth flow without shearing and turbulence in the stream. The nozzle lips are also rounded to improve flow and increase refractory life of the lips of the nozzle. The tundish walls are tapered to provide improve flow for supplying the melt to the nozzle. The nozzle is located about 45[degree] below top dead center for optimum conditions. 2 figures.

Grid Convergence for Turbulent Flows(Invited)

NASA Technical Reports Server (NTRS)

Diskin, Boris; Thomas, James L.; Rumsey, Christopher L.; Schwoppe, Axel

2015-01-01

A detailed grid convergence study has been conducted to establish accurate reference solutions corresponding to the one-equation linear eddy-viscosity Spalart-Allmaras turbulence model for two dimensional turbulent flows around the NACA 0012 airfoil and a flat plate. The study involved three widely used codes, CFL3D (NASA), FUN3D (NASA), and TAU (DLR), and families of uniformly refined structured grids that differ in the grid density patterns. Solutions computed by different codes on different grid families appear to converge to the same continuous limit, but exhibit different convergence characteristics. The grid resolution in the vicinity of geometric singularities, such as a sharp trailing edge, is found to be the major factor affecting accuracy and convergence of discrete solutions, more prominent than differences in discretization schemes and/or grid elements. The results reported for these relatively simple turbulent flows demonstrate that CFL3D, FUN3D, and TAU solutions are very accurate on the finest grids used in the study, but even those grids are not sufficient to conclusively establish an asymptotic convergence order.

Numerical Method for Darcy Flow Derived Using Discrete Exterior Calculus

NASA Astrophysics Data System (ADS)

Hirani, A. N.; Nakshatrala, K. B.; Chaudhry, J. H.

2015-05-01

We derive a numerical method for Darcy flow, and also for Poisson's equation in mixed (first order) form, based on discrete exterior calculus (DEC). Exterior calculus is a generalization of vector calculus to smooth manifolds and DEC is one of its discretizations on simplicial complexes such as triangle and tetrahedral meshes. DEC is a coordinate invariant discretization, in that it does not depend on the embedding of the simplices or the whole mesh. We start by rewriting the governing equations of Darcy flow using the language of exterior calculus. This yields a formulation in terms of flux differential form and pressure. The numerical method is then derived by using the framework provided by DEC for discretizing differential forms and operators that act on forms. We also develop a discretization for a spatially dependent Hodge star that varies with the permeability of the medium. This also allows us to address discontinuous permeability. The matrix representation for our discrete non-homogeneous Hodge star is diagonal, with positive diagonal entries. The resulting linear system of equations for flux and pressure are saddle type, with a diagonal matrix as the top left block. The performance of the proposed numerical method is illustrated on many standard test problems. These include patch tests in two and three dimensions, comparison with analytically known solutions in two dimensions, layered medium with alternating permeability values, and a test with a change in permeability along the flow direction. We also show numerical evidence of convergence of the flux and the pressure. A convergence experiment is included for Darcy flow on a surface. A short introduction to the relevant parts of smooth and discrete exterior calculus is included in this article. We also include a discussion of the boundary condition in terms of exterior calculus.

Entropic multirelaxation lattice Boltzmann models for turbulent flows

NASA Astrophysics Data System (ADS)

Bösch, Fabian; Chikatamarla, Shyam S.; Karlin, Ilya V.

2015-10-01

We present three-dimensional realizations of a class of lattice Boltzmann models introduced recently by the authors [I. V. Karlin, F. Bösch, and S. S. Chikatamarla, Phys. Rev. E 90, 031302(R) (2014), 10.1103/PhysRevE.90.031302] and review the role of the entropic stabilizer. Both coarse- and fine-grid simulations are addressed for the Kida vortex flow benchmark. We show that the outstanding numerical stability and performance is independent of a particular choice of the moment representation for high-Reynolds-number flows. We report accurate results for low-order moments for homogeneous isotropic decaying turbulence and second-order grid convergence for most assessed statistical quantities. It is demonstrated that all the three-dimensional lattice Boltzmann realizations considered herein converge to the familiar lattice Bhatnagar-Gross-Krook model when the resolution is increased. Moreover, thanks to the dynamic nature of the entropic stabilizer, the present model features less compressibility effects and maintains correct energy and enstrophy dissipation. The explicit and efficient nature of the present lattice Boltzmann method renders it a promising candidate for both engineering and scientific purposes for highly turbulent flows.

Approaches to the simulation of unconfined flow and perched groundwater flow in MODFLOW

USGS Publications Warehouse

Bedekar, Vivek; Niswonger, Richard G.; Kipp, Kenneth; Panday, Sorab; Tonkin, Matthew

2012-01-01

Various approaches have been proposed to manage the nonlinearities associated with the unconfined flow equation and to simulate perched groundwater conditions using the MODFLOW family of codes. The approaches comprise a variety of numerical techniques to prevent dry cells from becoming inactive and to achieve a stable solution focused on formulations of the unconfined, partially-saturated, groundwater flow equation. Keeping dry cells active avoids a discontinuous head solution which in turn improves the effectiveness of parameter estimation software that relies on continuous derivatives. Most approaches implement an upstream weighting of intercell conductance and Newton-Raphson linearization to obtain robust convergence. In this study, several published approaches were implemented in a stepwise manner into MODFLOW for comparative analysis. First, a comparative analysis of the methods is presented using synthetic examples that create convergence issues or difficulty in handling perched conditions with the more common dry-cell simulation capabilities of MODFLOW. Next, a field-scale three-dimensional simulation is presented to examine the stability and performance of the discussed approaches in larger, practical, simulation settings.

Numerical Modeling of a Vortex Stabilized Arcjet. Ph.D. Thesis, 1991 Final Report

NASA Technical Reports Server (NTRS)

Pawlas, Gary E.

1992-01-01

Arcjet thrusters are being actively considered for use in Earth orbit maneuvering applications. Experimental studies are currently the chief means of determining an optimal thruster configuration. Earlier numerical studies have failed to include all of the effects found in typical arcjets including complex geometries, viscosity, and swirling flow. Arcjet geometries are large area ratio converging nozzles with centerbodies in the subsonic portion of the nozzle. The nozzle walls serve as the anode while the centerbody functions as the cathode. Viscous effects are important because the Reynolds number, based on the throat radius, is typically less than 1,000. Experimental studies have shown that a swirl or circumferential velocity component stabilizes a constricted arc. This dissertation describes the equations governing flow through a constricted arcjet thruster. An assumption that the flowfield is in local thermodynamic equilibrium leads to a single fluid plasma temperature model. An order of magnitude analysis reveals the governing fluid mechanics equations are uncoupled from the electromagnetic field equations. A numerical method is developed to solve the governing fluid mechanics equations, the Thin Layer Navier-Stokes equations. A coordinate transformation is employed in deriving the governing equations to simplify the application of boundary conditions in complex geometries. An axisymmetric formulation is employed to include the swirl velocity component as well as the axial and radial velocity components. The numerical method is an implicit finite-volume technique and allows for large time steps to reach a converged steady-state solution. The inviscid fluxes are flux-split, and Gauss-Seidel line relaxation is used to accelerate convergence. Converging-diverging nozzles with exit-to-throat area ratios up to 100:1 and annular nozzles were examined. Quantities examined included Mach number and static wall pressure distributions, and oblique shock structures. As the level of swirl and viscosity in the flowfield increased the mass flow rate and thrust decreased. The technique was used to predict the flow through a typical arcjet thruster geometry. Results indicate swirl and viscosity play an important role in the complex geometry of an arcjet.

Numerical modeling of a vortex stabilized arcjet

NASA Astrophysics Data System (ADS)

Pawlas, Gary E.

1992-11-01

Arcjet thrusters are being actively considered for use in Earth orbit maneuvering applications. Experimental studies are currently the chief means of determining an optimal thruster configuration. Earlier numerical studies have failed to include all of the effects found in typical arcjets including complex geometries, viscosity, and swirling flow. Arcjet geometries are large area ratio converging nozzles with centerbodies in the subsonic portion of the nozzle. The nozzle walls serve as the anode while the centerbody functions as the cathode. Viscous effects are important because the Reynolds number, based on the throat radius, is typically less than 1,000. Experimental studies have shown that a swirl or circumferential velocity component stabilizes a constricted arc. This dissertation describes the equations governing flow through a constricted arcjet thruster. An assumption that the flowfield is in local thermodynamic equilibrium leads to a single fluid plasma temperature model. An order of magnitude analysis reveals the governing fluid mechanics equations are uncoupled from the electromagnetic field equations. A numerical method is developed to solve the governing fluid mechanics equations, the Thin Layer Navier-Stokes equations. A coordinate transformation is employed in deriving the governing equations to simplify the application of boundary conditions in complex geometries. An axisymmetric formulation is employed to include the swirl velocity component as well as the axial and radial velocity components. The numerical method is an implicit finite-volume technique and allows for large time steps to reach a converged steady-state solution. The inviscid fluxes are flux-split, and Gauss-Seidel line relaxation is used to accelerate convergence. Converging-diverging nozzles with exit-to-throat area ratios up to 100:1 and annular nozzles were examined. Quantities examined included Mach number and static wall pressure distributions, and oblique shock structures. As the level of swirl and viscosity in the flowfield increased the mass flow rate and thrust decreased.

Simple numerical method for predicting steady compressible flows

NASA Technical Reports Server (NTRS)

Vonlavante, Ernst; Nelson, N. Duane

1986-01-01

A numerical method for solving the isenthalpic form of the governing equations for compressible viscous and inviscid flows was developed. The method was based on the concept of flux vector splitting in its implicit form. The method was tested on several demanding inviscid and viscous configurations. Two different forms of the implicit operator were investigated. The time marching to steady state was accelerated by the implementation of the multigrid procedure. Its various forms very effectively increased the rate of convergence of the present scheme. High quality steady state results were obtained in most of the test cases; these required only short computational times due to the relative efficiency of the basic method.

Flow cytometry apparatus

DOEpatents

Pinkel, D.

1987-11-30

An obstruction across the flow chamber creates a one-dimensional convergence of a sheath fluid. A passageway in the obstruction directs flat cells near to the area of one-dimensional convergence in the sheath fluid to provide proper orientation of flat cells at fast rates. 6 figs.

Applying a general triclinic transpression model to highly partitioned brittle-ductile shear zones: A case study from the Torcal de Antequera massif, external Betics, southern Spain

NASA Astrophysics Data System (ADS)

Díaz-Azpiroz, M.; Barcos, L.; Balanyá, J. C.; Fernández, C.; Expósito, I.; Czeck, D. M.

2014-11-01

Oblique convergence and subsequent transpression kinematics can be considered as the general situation in most convergent and strike-slip tectonic boundaries. To better understand such settings, progressively more complex kinematic models have been proposed, which need to be tested against natural shear zones using standardized procedures that minimise subjectivism. In this work, a protocol to test a general triclinic transpression model is applied to the Torcal de Antequera massif (TAM), an essentially brittle shear zone. Our results, given as kinematic parameters of the transpressive flow (transpression obliquity, ϕ; extrusion obliquity, υ; and kinematic vorticity number, Wk), suggest that the bulk triclinic transpressive flow imposed on the TAM was partitioned into two different flow fields, following a general partitioning type. As such, one flow field produced narrow structural domains located at the limits of the TAM, where mainly dextral strike-slip simple-shear-dominated transpression took place (Outer domains, ODs). In contrast, the remaining part of the bulk flow produced pure-shear-dominated dextral triclinic transpression at the inner part of the TAM (Inner domain, ID). A graphical method relating internal (ϕ, Wk) to far-field (dip of the shear zone boundary, δ; angle of oblique convergence, α) transpression parameters is proposed to obtain the theoretical horizontal velocity vector (V→), which in the case of the TAM, ranges between 099 and 118. These results support the applicability of kinematic models of triclinic transpression to brittle-ductile shear zones and the potential utility of the proposed protocol.

A time-accurate algorithm for chemical non-equilibrium viscous flows at all speeds

NASA Technical Reports Server (NTRS)

Shuen, J.-S.; Chen, K.-H.; Choi, Y.

1992-01-01

A time-accurate, coupled solution procedure is described for the chemical nonequilibrium Navier-Stokes equations over a wide range of Mach numbers. This method employs the strong conservation form of the governing equations, but uses primitive variables as unknowns. Real gas properties and equilibrium chemistry are considered. Numerical tests include steady convergent-divergent nozzle flows with air dissociation/recombination chemistry, dump combustor flows with n-pentane-air chemistry, nonreacting flow in a model double annular combustor, and nonreacting unsteady driven cavity flows. Numerical results for both the steady and unsteady flows demonstrate the efficiency and robustness of the present algorithm for Mach numbers ranging from the incompressible limit to supersonic speeds.

Incompressible flow simulations on regularized moving meshfree grids

NASA Astrophysics Data System (ADS)

Vasyliv, Yaroslav; Alexeev, Alexander

2017-11-01

A moving grid meshfree solver for incompressible flows is presented. To solve for the flow field, a semi-implicit approximate projection method is directly discretized on meshfree grids using General Finite Differences (GFD) with sharp interface stencil modifications. To maintain a regular grid, an explicit shift is used to relax compressed pseudosprings connecting a star node to its cloud of neighbors. The following test cases are used for validation: the Taylor-Green vortex decay, the analytic and modified lid-driven cavities, and an oscillating cylinder enclosed in a container for a range of Reynolds number values. We demonstrate that 1) the grid regularization does not impede the second order spatial convergence rate, 2) the Courant condition can be used for time marching but the projection splitting error reduces the convergence rate to first order, and 3) moving boundaries and arbitrary grid distortions can readily be handled. Financial support provided by the National Science Foundation (NSF) Graduate Research Fellowship, Grant No. DGE-1148903.

Numerical Investigation of 'Transonic Resonance' with a Convergent-Divergent Nozzle

NASA Technical Reports Server (NTRS)

Loh, Ching Y.; Zaman, K. B. M. Q.

2002-01-01

At pressure ratios lower than the design value, convergent-divergent (C-D) nozzles often undergo a flow resonance accompanied by the emission of acoustic tones. The phenomenon, driven by the unsteady shock within the divergent section of the nozzle, has been studied experimentally by Zaman et al. In this paper, the space-time conservation element solution element (CE/SE) method is employed to numerically investigate the phenomenon. The computations are performed for a given nozzle geometry for several different pressure ratios. Sustained 'limit cycle' oscillations are encountered in all cases. The oscillation frequencies, their variation with pressure ratio including a 'stage jump', agree well with the experimental results. The unsteady flow data confirm that stage 1 of the resonance (fundamental) involves a one-quarter standing wave while stage 2 (third harmonic) involves a three-quarter standing wave within the divergent section of the nozzle. Details of the shock motion, and the flow and near acoustic field, are documented for one case each of stages 1 and 2.

Numerical modeling of a vortex stabilized arcjet

NASA Astrophysics Data System (ADS)

Pawlas, Gary Edward

Arcjet thrusters are being actively considered for use in Earth orbit maneuvering applications. Satellite station-keeping is an example of a maneuvering application requiring the low thrust, high specific impulse of an arcjet. Experimental studies are currently the chief means of determining an optimal thruster configuration. Earlier numerical studies have failed to include all of the effects found in typical arcjets including complex geometries, viscosity and swirling flow. Arcjet geometries are large area ratio converging-diverging nozzles with centerbodies in the subsonic portion of the nozzle. The nozzle walls serve as the anode while the centerbody functions as the cathode. Viscous effects are important because the Reynolds number, based on the throat radius, is typically less than 1,000. Experimental studies have shown a swirl or circumferential velocity component stabilizes a constricted arc. The equations are described which governs the flow through a constricted arcjet thruster. An assumption that the flowfield is in local thermodynamic equilibrium leads to a single fluid plasma temperature model. An order of magnitude analysis reveals the governing fluid mechanics equations are uncoupled from the electromagnetic field equations. A numerical method is developed to solve the governing fluid mechanics equations, the Thin Layer Navier-Stokes equations. A coordinate transformation is used in deriving the governing equations to simplify the application of boundary conditions in complex geometries. An axisymmetric formulation is employed to include the swirl velocity component as well as the axial and redial velocity components. The numerical method is an implicit finite-volume technique and allows for large time steps to reach a converged steady-state solution. The inviscid fluxes are flux-split and Gauss-Seidel line relaxation is used to accelerate convergence. 'Converging diverging' nozzles with exit-to-throat area ratios up to 100:1 and annual nozzles were examined. Comparisons with experimental data and previous numerical results were in excellent agreement. Quantities examined included Mach number and static wall pressure distributions, and oblique shock structures.

Focusing of active particles in a converging flow

DOE PAGES

Potomkin, Mykhailo; Kaiser, Andreas; Berlyand, Leonid; ...

2017-10-20

We consider active particles swimming in a convergent fluid flow in a trapezoid nozzle with no-slip walls. We use mathematical modeling to analyze trajectories of these particles inside the nozzle. By extensive Monte Carlo simulations, we show that trajectories are strongly affected by the background fluid flow and geometry of the nozzle leading to wall accumulation and upstream motion (rheotaxis). In particular, we describe the non-trivial focusing of active rods depending on physical and geometrical parameters. It is also established that the convergent component of the background flow leads to stability of both downstream and upstream swimming at the centerline.more » The stability of downstream swimming enhances focusing, and the stability of upstream swimming enables rheotaxis in the bulk.« less

A set of parallel, implicit methods for a reconstructed discontinuous Galerkin method for compressible flows on 3D hybrid grids

DOE PAGES

Xia, Yidong; Luo, Hong; Frisbey, Megan; ...

2014-07-01

A set of implicit methods are proposed for a third-order hierarchical WENO reconstructed discontinuous Galerkin method for compressible flows on 3D hybrid grids. An attractive feature in these methods are the application of the Jacobian matrix based on the P1 element approximation, resulting in a huge reduction of memory requirement compared with DG (P2). Also, three approaches -- analytical derivation, divided differencing, and automatic differentiation (AD) are presented to construct the Jacobian matrix respectively, where the AD approach shows the best robustness. A variety of compressible flow problems are computed to demonstrate the fast convergence property of the implemented flowmore » solver. Furthermore, an SPMD (single program, multiple data) programming paradigm based on MPI is proposed to achieve parallelism. The numerical results on complex geometries indicate that this low-storage implicit method can provide a viable and attractive DG solution for complicated flows of practical importance.« less

A hybrid incremental projection method for thermal-hydraulics applications

NASA Astrophysics Data System (ADS)

Christon, Mark A.; Bakosi, Jozsef; Nadiga, Balasubramanya T.; Berndt, Markus; Francois, Marianne M.; Stagg, Alan K.; Xia, Yidong; Luo, Hong

2016-07-01

A new second-order accurate, hybrid, incremental projection method for time-dependent incompressible viscous flow is introduced in this paper. The hybrid finite-element/finite-volume discretization circumvents the well-known Ladyzhenskaya-Babuška-Brezzi conditions for stability, and does not require special treatment to filter pressure modes by either Rhie-Chow interpolation or by using a Petrov-Galerkin finite element formulation. The use of a co-velocity with a high-resolution advection method and a linearly consistent edge-based treatment of viscous/diffusive terms yields a robust algorithm for a broad spectrum of incompressible flows. The high-resolution advection method is shown to deliver second-order spatial convergence on mixed element topology meshes, and the implicit advective treatment significantly increases the stable time-step size. The algorithm is robust and extensible, permitting the incorporation of features such as porous media flow, RANS and LES turbulence models, and semi-/fully-implicit time stepping. A series of verification and validation problems are used to illustrate the convergence properties of the algorithm. The temporal stability properties are demonstrated on a range of problems with 2 ≤ CFL ≤ 100. The new flow solver is built using the Hydra multiphysics toolkit. The Hydra toolkit is written in C++ and provides a rich suite of extensible and fully-parallel components that permit rapid application development, supports multiple discretization techniques, provides I/O interfaces, dynamic run-time load balancing and data migration, and interfaces to scalable popular linear solvers, e.g., in open-source packages such as HYPRE, PETSc, and Trilinos.

A hybrid incremental projection method for thermal-hydraulics applications

DOE Office of Scientific and Technical Information (OSTI.GOV)

Christon, Mark A.; Bakosi, Jozsef; Nadiga, Balasubramanya T.

In this paper, a new second-order accurate, hybrid, incremental projection method for time-dependent incompressible viscous flow is introduced in this paper. The hybrid finite-element/finite-volume discretization circumvents the well-known Ladyzhenskaya–Babuška–Brezzi conditions for stability, and does not require special treatment to filter pressure modes by either Rhie–Chow interpolation or by using a Petrov–Galerkin finite element formulation. The use of a co-velocity with a high-resolution advection method and a linearly consistent edge-based treatment of viscous/diffusive terms yields a robust algorithm for a broad spectrum of incompressible flows. The high-resolution advection method is shown to deliver second-order spatial convergence on mixed element topology meshes,more » and the implicit advective treatment significantly increases the stable time-step size. The algorithm is robust and extensible, permitting the incorporation of features such as porous media flow, RANS and LES turbulence models, and semi-/fully-implicit time stepping. A series of verification and validation problems are used to illustrate the convergence properties of the algorithm. The temporal stability properties are demonstrated on a range of problems with 2 ≤ CFL ≤ 100. The new flow solver is built using the Hydra multiphysics toolkit. The Hydra toolkit is written in C++ and provides a rich suite of extensible and fully-parallel components that permit rapid application development, supports multiple discretization techniques, provides I/O interfaces, dynamic run-time load balancing and data migration, and interfaces to scalable popular linear solvers, e.g., in open-source packages such as HYPRE, PETSc, and Trilinos.« less

A hybrid incremental projection method for thermal-hydraulics applications

DOE PAGES

Christon, Mark A.; Bakosi, Jozsef; Nadiga, Balasubramanya T.; ...

2016-07-01

In this paper, a new second-order accurate, hybrid, incremental projection method for time-dependent incompressible viscous flow is introduced in this paper. The hybrid finite-element/finite-volume discretization circumvents the well-known Ladyzhenskaya–Babuška–Brezzi conditions for stability, and does not require special treatment to filter pressure modes by either Rhie–Chow interpolation or by using a Petrov–Galerkin finite element formulation. The use of a co-velocity with a high-resolution advection method and a linearly consistent edge-based treatment of viscous/diffusive terms yields a robust algorithm for a broad spectrum of incompressible flows. The high-resolution advection method is shown to deliver second-order spatial convergence on mixed element topology meshes,more » and the implicit advective treatment significantly increases the stable time-step size. The algorithm is robust and extensible, permitting the incorporation of features such as porous media flow, RANS and LES turbulence models, and semi-/fully-implicit time stepping. A series of verification and validation problems are used to illustrate the convergence properties of the algorithm. The temporal stability properties are demonstrated on a range of problems with 2 ≤ CFL ≤ 100. The new flow solver is built using the Hydra multiphysics toolkit. The Hydra toolkit is written in C++ and provides a rich suite of extensible and fully-parallel components that permit rapid application development, supports multiple discretization techniques, provides I/O interfaces, dynamic run-time load balancing and data migration, and interfaces to scalable popular linear solvers, e.g., in open-source packages such as HYPRE, PETSc, and Trilinos.« less

Mantle downwelling and crustal convergence - A model for Ishtar Terra, Venus

NASA Technical Reports Server (NTRS)

Kiefer, Walter S.; Hager, Bradford H.

1991-01-01

Models of viscous crustal flow driven by gradients in topography are presented in order to explore quantitatively the implications of the hypothesis that Ishtar is a crustal convergence zone overlying a downwelling mantle. Assuming a free-slip surface boundary condition, it is found that, if the crustal convergence hypothesis is correct, then the crustal thickness in the plains surrounding Ishtar can be no more than about 25 km thick. If the geothermal gradient is larger or the rheology is weaker, the crust must be even thinner for net crustal convergence to be possible. This upper bound is in good agreement with the several independent estimates of crustal thickness of 15-30 km in the plains of Venus based on modeling of the spacing of tectonic features and of impact crater relaxation. Although Ishtar is treated as a crustal convergence zone, this crustal flow model shows that under some circumstances, near-surface material may actually flow away from Ishtar, providing a possible explanation for the grabenlike structures in Fortuna Tessera.

The Topographic Design of River Channels for Form-Process Linkages.

PubMed

Brown, Rocko A; Pasternack, Gregory B; Lin, Tin

2016-04-01

Scientists and engineers design river topography for a wide variety of uses, such as experimentation, site remediation, dam mitigation, flood management, and river restoration. A recent advancement has been the notion of topographical design to yield specific fluvial mechanisms in conjunction with natural or environmental flow releases. For example, the flow convergence routing mechanism, whereby shear stress and spatially convergent flow migrate or jump from the topographic high (riffle) to the low point (pool) from low to high discharge, is thought to be a key process able to maintain undular relief in gravel bedded rivers. This paper develops an approach to creating riffle-pool topography with a form-process linkage to the flow convergence routing mechanism using an adjustable, quasi equilibrium synthetic channel model. The link from form to process is made through conceptualizing form-process relationships for riffle-pool couplets into geomorphic covariance structures (GCSs) that are then quantitatively embedded in a synthetic channel model. Herein, GCSs were used to parameterize a geometric model to create five straight, synthetic river channels with varying combinations of bed and width undulations. Shear stress and flow direction predictions from 2D hydrodynamic modeling were used to determine if scenarios recreated aspects of the flow convergence routing mechanism. Results show that the creation of riffle-pool couplets that experience flow convergence in straight channels requires GCSs with covarying bed and width undulations in their topography as supported in the literature. This shows that GCSs are a useful way to translate conceptualizations of form-process linkages into quantitative models of channel form.

A parallel finite-difference method for computational aerodynamics

NASA Technical Reports Server (NTRS)

Swisshelm, Julie M.

1989-01-01

A finite-difference scheme for solving complex three-dimensional aerodynamic flow on parallel-processing supercomputers is presented. The method consists of a basic flow solver with multigrid convergence acceleration, embedded grid refinements, and a zonal equation scheme. Multitasking and vectorization have been incorporated into the algorithm. Results obtained include multiprocessed flow simulations from the Cray X-MP and Cray-2. Speedups as high as 3.3 for the two-dimensional case and 3.5 for segments of the three-dimensional case have been achieved on the Cray-2. The entire solver attained a factor of 2.7 improvement over its unitasked version on the Cray-2. The performance of the parallel algorithm on each machine is analyzed.

Breakdown of Burton Prim Slichter approach and lateral solute segregation in radially converging flows

NASA Astrophysics Data System (ADS)

Priede, J.; Gerbeth, G.

2005-11-01

A theoretical study is presented of the effect of a radially converging melt flow, which is directed away from the solidification front, on the radial solute segregation in simple solidification models. We show that the classical Burton-Prim-Slichter (BPS) solution describing the effect of a diverging flow on the solute incorporation into the solidifying material breaks down for the flows converging along the solidification front. The breakdown is caused by a divergence of the integral defining the effective boundary layer thickness which is the basic concept of the BPS theory. Although such a divergence can formally be avoided by restricting the axial extension of the melt to a layer of finite height, radially uniform solute distributions are possible only for weak melt flows with an axial velocity away from the solidification front comparable to the growth rate. There is a critical melt velocity for each growth rate at which the solution passes through a singularity and becomes physically inconsistent for stronger melt flows. To resolve these inconsistencies we consider a solidification front presented by a disk of finite radius R0 subject to a strong converging melt flow and obtain an analytic solution showing that the radial solute concentration depends on the radius r as ˜ln(R0/r) and ˜ln(R0/r) close to the rim and at large distances from it. The logarithmic increase of concentration is limited in the vicinity of the symmetry axis by the diffusion becoming effective at a distance comparable to the characteristic thickness of the solute boundary layer. The converging flow causes a solute pile-up forming a logarithmic concentration peak at the symmetry axis which might be an undesirable feature for crystal growth processes.

Time-derivative preconditioning for viscous flows

NASA Technical Reports Server (NTRS)

Choi, Yunho; Merkle, Charles L.

1991-01-01

A time-derivative preconditioning algorithm that is effective over a wide range of flow conditions from inviscid to very diffusive flows and from low speed to supersonic flows was developed. This algorithm uses a viscous set of primary dependent variables to introduce well-conditioned eigenvalues and to avoid having a nonphysical time reversal for viscous flow. The resulting algorithm also provides a mechanism for controlling the inviscid and viscous time step parameters to be of order one for very diffusive flows, thereby ensuring rapid convergence at very viscous flows as well as for inviscid flows. Convergence capabilities are demonstrated through computation of a wide variety of problems.

Accelerating global optimization of aerodynamic shapes using a new surrogate-assisted parallel genetic algorithm

NASA Astrophysics Data System (ADS)

Ebrahimi, Mehdi; Jahangirian, Alireza

2017-12-01

An efficient strategy is presented for global shape optimization of wing sections with a parallel genetic algorithm. Several computational techniques are applied to increase the convergence rate and the efficiency of the method. A variable fidelity computational evaluation method is applied in which the expensive Navier-Stokes flow solver is complemented by an inexpensive multi-layer perceptron neural network for the objective function evaluations. A population dispersion method that consists of two phases, of exploration and refinement, is developed to improve the convergence rate and the robustness of the genetic algorithm. Owing to the nature of the optimization problem, a parallel framework based on the master/slave approach is used. The outcomes indicate that the method is able to find the global optimum with significantly lower computational time in comparison to the conventional genetic algorithm.

Spectral element simulation of precession driven flows in the outer cores of spheroidal planets

NASA Astrophysics Data System (ADS)

Vormann, Jan; Hansen, Ulrich

2015-04-01

A common feature of the planets in the solar system is the precession of the rotation axes, driven by the gravitational influence of another body (e.g. the Earth's moon). In a precessing body, the rotation axis itself is rotating around another axis, describing a cone during one precession period. Similar to the coriolis and centrifugal force appearing from the transformation to a rotating system, the addition of precession adds another term to the Navier-Stokes equation, the so called Poincaré force. The main geophysical motivation in studying precession driven flows comes from their ability to act as magnetohydrodynamic dynamos in planets and moons. Precession may either act as the only driving force or operate together with other forces such as thermochemical convection. One of the challenges in direct numerical simulations of such flows lies in the spheroidal shape of the fluid volume, which should not be neglected since it contributes an additional forcing trough pressure torques. Codes developed for the simulation of flows in spheres mostly use efficient global spectral algorithms that converge fast, but lack geometric flexibility, while local methods are usable in more complex shapes, but often lack high accuracy. We therefore adapted the spectral element code Nek5000, developed at Argonne National Laboratory, to the problem. The spectral element method is capable of solving for the flow in arbitrary geometries while still offering spectral convergence. We present first results for the simulation of a purely hydrodynamic, precession-driven flow in a spheroid with no-slip boundaries and an inner core. The driving by the Poincaré force is in a range where theoretical work predicts multiple solutions for a laminar flow. Our simulations indicate a transition to turbulent flows for Ekman numbers of 10-6 and lower.

Comparison of an algebraic multigrid algorithm to two iterative solvers used for modeling ground water flow and transport

USGS Publications Warehouse

Detwiler, R.L.; Mehl, S.; Rajaram, H.; Cheung, W.W.

2002-01-01

Numerical solution of large-scale ground water flow and transport problems is often constrained by the convergence behavior of the iterative solvers used to solve the resulting systems of equations. We demonstrate the ability of an algebraic multigrid algorithm (AMG) to efficiently solve the large, sparse systems of equations that result from computational models of ground water flow and transport in large and complex domains. Unlike geometric multigrid methods, this algorithm is applicable to problems in complex flow geometries, such as those encountered in pore-scale modeling of two-phase flow and transport. We integrated AMG into MODFLOW 2000 to compare two- and three-dimensional flow simulations using AMG to simulations using PCG2, a preconditioned conjugate gradient solver that uses the modified incomplete Cholesky preconditioner and is included with MODFLOW 2000. CPU times required for convergence with AMG were up to 140 times faster than those for PCG2. The cost of this increased speed was up to a nine-fold increase in required random access memory (RAM) for the three-dimensional problems and up to a four-fold increase in required RAM for the two-dimensional problems. We also compared two-dimensional numerical simulations of steady-state transport using AMG and the generalized minimum residual method with an incomplete LU-decomposition preconditioner. For these transport simulations, AMG yielded increased speeds of up to 17 times with only a 20% increase in required RAM. The ability of AMG to solve flow and transport problems in large, complex flow systems and its ready availability make it an ideal solver for use in both field-scale and pore-scale modeling.

Comparison of three explicit multigrid methods for the Euler and Navier-Stokes equations

NASA Technical Reports Server (NTRS)

Chima, Rodrick V.; Turkel, Eli; Schaffer, Steve

1987-01-01

Three explicit multigrid methods, Ni's method, Jameson's finite-volume method, and a finite-difference method based on Brandt's work, are described and compared for two model problems. All three methods use an explicit multistage Runge-Kutta scheme on the fine grid, and this scheme is also described. Convergence histories for inviscid flow over a bump in a channel for the fine-grid scheme alone show that convergence rate is proportional to Courant number and that implicit residual smoothing can significantly accelerate the scheme. Ni's method was slightly slower than the implicitly-smoothed scheme alone. Brandt's and Jameson's methods are shown to be equivalent in form but differ in their node versus cell-centered implementations. They are about 8.5 times faster than Ni's method in terms of CPU time. Results for an oblique shock/boundary layer interaction problem verify the accuracy of the finite-difference code. All methods slowed considerably on the stretched viscous grid but Brandt's method was still 2.1 times faster than Ni's method.

Ordered roughness effects on NACA 0026 airfoil

NASA Astrophysics Data System (ADS)

Harun, Z.; Abbas, A. A.; Dheyaa, R. Mohammed; Ghazali, M. I.

2016-10-01

The effects of highly-ordered rough surface - riblets, applied onto the surface of a NACA 0026 airfoil, are investigated experimentally using wind tunnel. The riblets are arranged in directionally converging - diverging pattern with dimensions of height, h = 1 mm, pitch or spacing, s = 1 mm, yaw angle α = 0o and 10o The airfoil with external geometry of 500 mm span, 600 mm chord and 156 mm thickness has been built using mostly woods and aluminium. Turbulence quantities are collected using hotwire anemometry. Hotwire measurements show that flows past converging and diverging pattern inherit similar patterns in the near-wall region for both mean velocity and turbulence intensities profiles. The mean velocity profiles in logarithmic regions for both flows past converging and diverging riblet pattern are lower than that with yaw angle α = 0o. Converging riblets cause the boundary layer to thicken and the flow with yaw angle α = 0o produces the thinnest boundary layer. Both the converging and diverging riblets cause pronounced outer peaks in the turbulence intensities profiles. Most importantly, flows past converging and diverging pattern experience 30% skin friction reductions. Higher order statistics show that riblet surfaces produce similar effects due to adverse pressure gradient. It is concluded that a small strip of different ordered roughness features applied at a leading edge of an airfoil can change the turbulence characteristics dramatically.

Use of Navier-Stokes methods for the calculation of high-speed nozzle flow fields

NASA Technical Reports Server (NTRS)

Georgiadis, Nicholas J.; Yoder, Dennis A.

1994-01-01

Flows through three reference nozzles have been calculated to determine the capabilities and limitations of the widely used Navier-Stokes solver, PARC. The nozzles examined have similar dominant flow characteristics as those considered for supersonic transport programs. Flows from an inverted velocity profile (IVP) nozzle, an under expanded nozzle, and an ejector nozzle were examined. PARC calculations were obtained with its standard algebraic turbulence model, Thomas, and the two-equation turbulence model, Chien k-epsilon. The Thomas model was run with the default coefficient of mixing set at both 0.09 and a larger value of 0.13 to improve the mixing prediction. Calculations using the default value substantially underpredicted the mixing for all three flows. The calculations obtained with the higher mixing coefficient better predicted mixing in the IVP and underexpanded nozzle flows but adversely affected PARC's convergence characteristics for the IVP nozzle case. The ejector nozzle case did not converge with the Thomas model and the higher mixing coefficient. The Chien k-epsilon results were in better agreement with the experimental data overall than were those of the Thomas run with the default mixing coefficient, but the default boundary conditions for k and epsilon underestimated the levels of mixing near the nozzle exits.

Vortex breakdown simulation

NASA Technical Reports Server (NTRS)

Hafez, M.; Ahmad, J.; Kuruvila, G.; Salas, M. D.

1987-01-01

In this paper, steady, axisymmetric inviscid, and viscous (laminar) swirling flows representing vortex breakdown phenomena are simulated using a stream function-vorticity-circulation formulation and two numerical methods. The first is based on an inverse iteration, where a norm of the solution is prescribed and the swirling parameter is calculated as a part of the output. The second is based on direct Newton iterations, where the linearized equations, for all the unknowns, are solved simultaneously by an efficient banded Gaussian elimination procedure. Several numerical solutions for inviscid and viscous flows are demonstrated, followed by a discussion of the results. Some improvements on previous work have been achieved: first order upwind differences are replaced by second order schemes, line relaxation procedure (with linear convergence rate) is replaced by Newton's iterations (which converge quadratically), and Reynolds numbers are extended from 200 up to 1000.

Real-time three-dimensional color doppler evaluation of the flow convergence zone for quantification of mitral regurgitation: Validation experimental animal study and initial clinical experience

NASA Technical Reports Server (NTRS)

Sitges, Marta; Jones, Michael; Shiota, Takahiro; Qin, Jian Xin; Tsujino, Hiroyuki; Bauer, Fabrice; Kim, Yong Jin; Agler, Deborah A.; Cardon, Lisa A.; Zetts, Arthur D.;

Fast dynamos with finite resistivity in steady flows with stagnation points

NASA Technical Reports Server (NTRS)

Lau, Yun-Tung; Finn, John M.

1993-01-01

Results are presented of a kinematic fast dynamo problem for two classes of steady incompressible flows: the ABC flow and the spatially aperiodic flow of Lau and Finn (1992). The numerical method used to find the solutions is described, together with convergence studies with respect to the time step and the number of points N of the spatial grid. It is shown that the growth rate and frequency can be extrapolated to N = infinity. Results are presented indicating that fast kinematic dynamos can exist in both these flows and that chaotic flow is a necessary condition. It was found that, for the ABC flow with A = B = C, there are two dynamo modes: an oscillating mode and a purely growing mode.

Variational Methods in Design Optimization and Sensitivity Analysis for Two-Dimensional Euler Equations

NASA Technical Reports Server (NTRS)

Ibrahim, A. H.; Tiwari, S. N.; Smith, R. E.

1997-01-01

Variational methods (VM) sensitivity analysis employed to derive the costate (adjoint) equations, the transversality conditions, and the functional sensitivity derivatives. In the derivation of the sensitivity equations, the variational methods use the generalized calculus of variations, in which the variable boundary is considered as the design function. The converged solution of the state equations together with the converged solution of the costate equations are integrated along the domain boundary to uniquely determine the functional sensitivity derivatives with respect to the design function. The application of the variational methods to aerodynamic shape optimization problems is demonstrated for internal flow problems at supersonic Mach number range. The study shows, that while maintaining the accuracy of the functional sensitivity derivatives within the reasonable range for engineering prediction purposes, the variational methods show a substantial gain in computational efficiency, i.e., computer time and memory, when compared with the finite difference sensitivity analysis.

Fast immersed interface Poisson solver for 3D unbounded problems around arbitrary geometries

NASA Astrophysics Data System (ADS)

Gillis, T.; Winckelmans, G.; Chatelain, P.

2018-02-01

We present a fast and efficient Fourier-based solver for the Poisson problem around an arbitrary geometry in an unbounded 3D domain. This solver merges two rewarding approaches, the lattice Green's function method and the immersed interface method, using the Sherman-Morrison-Woodbury decomposition formula. The method is intended to be second order up to the boundary. This is verified on two potential flow benchmarks. We also further analyse the iterative process and the convergence behavior of the proposed algorithm. The method is applicable to a wide range of problems involving a Poisson equation around inner bodies, which goes well beyond the present validation on potential flows.

DOE Office of Scientific and Technical Information (OSTI.GOV)

Zhang, Yijian; Hong, Mingyi; Dall'Anese, Emiliano

This paper considers power distribution systems featuring renewable energy sources (RESs), and develops a distributed optimization method to steer the RES output powers to solutions of AC optimal power flow (OPF) problems. The design of the proposed method leverages suitable linear approximations of the AC-power flow equations, and is based on the Alternating Direction Method of Multipliers (ADMM). Convergence of the RES-inverter output powers to solutions of the OPF problem is established under suitable conditions on the stepsize as well as mismatches between the commanded setpoints and actual RES output powers. In a broad sense, the methods and results proposedmore » here are also applicable to other distributed optimization problem setups with ADMM and inexact dual updates.« less

Internal-Film Cooling of Rocket Nozzles

NASA Technical Reports Server (NTRS)

Sloop, J L; Kinney, George R

1948-01-01

Experiments were conducted with 1000-pound-thrust rocket engine to determine feasibility of cooling convergent-divergent nozzle by internal film of water introduced at nozzle entrance. Water flow of 3 percent of propellant flow reduced heat flow into nozzle to 55 percent of uncooled heat flow. Introduction of water by porous ring before nozzle resulted in more uniform coverage of nozzle than water introduced by single arrangement of 36 jets directed along nozzle wall. Water flow through porous ring of 3.5 percent of propellant flow stabilized wall temperature in convergent section but did not adequately cool throat or divergent sections.

Algorithms for the Euler and Navier-Stokes equations for supercomputers

NASA Technical Reports Server (NTRS)

Turkel, E.

1985-01-01

The steady state Euler and Navier-Stokes equations are considered for both compressible and incompressible flow. Methods are found for accelerating the convergence to a steady state. This acceleration is based on preconditioning the system so that it is no longer time consistent. In order that the acceleration technique be scheme-independent, this preconditioning is done at the differential equation level. Applications are presented for very slow flows and also for the incompressible equations.

Implicit flux-split schemes for the Euler equations

NASA Technical Reports Server (NTRS)

Thomas, J. L.; Walters, R. W.; Van Leer, B.

1985-01-01

Recent progress in the development of implicit algorithms for the Euler equations using the flux-vector splitting method is described. Comparisons of the relative efficiency of relaxation and spatially-split approximately factored methods on a vector processor for two-dimensional flows are made. For transonic flows, the higher convergence rate per iteration of the Gauss-Seidel relaxation algorithms, which are only partially vectorizable, is amply compensated for by the faster computational rate per iteration of the approximately factored algorithm. For supersonic flows, the fully-upwind line-relaxation method is more efficient since the numerical domain of dependence is more closely matched to the physical domain of dependence. A hybrid three-dimensional algorithm using relaxation in one coordinate direction and approximate factorization in the cross-flow plane is developed and applied to a forebody shape at supersonic speeds and a swept, tapered wing at transonic speeds.

Simulation of confined magnetohydrodynamic flows with Dirichlet boundary conditions using a pseudo-spectral method with volume penalization

DOE Office of Scientific and Technical Information (OSTI.GOV)

Morales, Jorge A.; Leroy, Matthieu; Bos, Wouter J.T.

A volume penalization approach to simulate magnetohydrodynamic (MHD) flows in confined domains is presented. Here the incompressible visco-resistive MHD equations are solved using parallel pseudo-spectral solvers in Cartesian geometries. The volume penalization technique is an immersed boundary method which is characterized by a high flexibility for the geometry of the considered flow. In the present case, it allows to use other than periodic boundary conditions in a Fourier pseudo-spectral approach. The numerical method is validated and its convergence is assessed for two- and three-dimensional hydrodynamic (HD) and MHD flows, by comparing the numerical results with results from literature and analyticalmore » solutions. The test cases considered are two-dimensional Taylor–Couette flow, the z-pinch configuration, three dimensional Orszag–Tang flow, Ohmic-decay in a periodic cylinder, three-dimensional Taylor–Couette flow with and without axial magnetic field and three-dimensional Hartmann-instabilities in a cylinder with an imposed helical magnetic field. Finally, we present a magnetohydrodynamic flow simulation in toroidal geometry with non-symmetric cross section and imposing a helical magnetic field to illustrate the potential of the method.« less

Preconditioning and the limit to the incompressible flow equations

NASA Technical Reports Server (NTRS)

Turkel, E.; Fiterman, A.; Vanleer, B.

1993-01-01

The use of preconditioning methods to accelerate the convergence to a steady state for both the incompressible and compressible fluid dynamic equations are considered. The relation between them for both the continuous problem and the finite difference approximation is also considered. The analysis relies on the inviscid equations. The preconditioning consists of a matrix multiplying the time derivatives. Hence, the steady state of the preconditioned system is the same as the steady state of the original system. For finite difference methods the preconditioning can change and improve the steady state solutions. An application to flow around an airfoil is presented.

Integrated and spectral energy flows of the GLAS GCM

NASA Technical Reports Server (NTRS)

Tennebaum, J.

1981-01-01

Methods to analyze the generation, transport, and dissipation of energy to study geophysical fluid flows are discussed. Energetics analyses are pursued in several directions: (1) the longitudinal and time dependence on the energy flow to the stratosphere was examined as a function of geographical sector; (2) strong and weak energy flows were correlated by medium range forecasts; (3) the one dimensional spectral results (Fourier services around latitude circles) were extended to spherical harmonics over a global domain; (4) the validity of vertical velocities derived from mass convergence was examined for their effect on the conversion of eddy available potential energy to eddy kinetic energy.

Convergence of the flow of a chemically reacting gaseous mixture to incompressible Euler equations in a unbounded domain

NASA Astrophysics Data System (ADS)

Kwon, Young-Sam

2017-12-01

The flow of chemically reacting gaseous mixture is associated with a variety of phenomena and processes. We study the combined quasineutral and inviscid limit from the flow of chemically reacting gaseous mixture governed by Poisson equation to incompressible Euler equations with the ill-prepared initial data in the unbounded domain R^2× T. Furthermore, the convergence rates are obtained.

Study of Particle Rotation Effect in Gas-Solid Flows using Direct Numerical Simulation with a Lattice Boltzmann Method

DOE Office of Scientific and Technical Information (OSTI.GOV)

Kwon, Kyung; Fan, Liang-Shih; Zhou, Qiang

A new and efficient direct numerical method with second-order convergence accuracy was developed for fully resolved simulations of incompressible viscous flows laden with rigid particles. The method combines the state-of-the-art immersed boundary method (IBM), the multi-direct forcing method, and the lattice Boltzmann method (LBM). First, the multi-direct forcing method is adopted in the improved IBM to better approximate the no-slip/no-penetration (ns/np) condition on the surface of particles. Second, a slight retraction of the Lagrangian grid from the surface towards the interior of particles with a fraction of the Eulerian grid spacing helps increase the convergence accuracy of the method. Anmore » over-relaxation technique in the procedure of multi-direct forcing method and the classical fourth order Runge-Kutta scheme in the coupled fluid-particle interaction were applied. The use of the classical fourth order Runge-Kutta scheme helps the overall IB-LBM achieve the second order accuracy and provides more accurate predictions of the translational and rotational motion of particles. The preexistent code with the first-order convergence rate is updated so that the updated new code can resolve the translational and rotational motion of particles with the second-order convergence rate. The updated code has been validated with several benchmark applications. The efficiency of IBM and thus the efficiency of IB-LBM were improved by reducing the number of the Lagragian markers on particles by using a new formula for the number of Lagrangian markers on particle surfaces. The immersed boundary-lattice Boltzmann method (IBLBM) has been shown to predict correctly the angular velocity of a particle. Prior to examining drag force exerted on a cluster of particles, the updated IB-LBM code along with the new formula for the number of Lagrangian markers has been further validated by solving several theoretical problems. Moreover, the unsteadiness of the drag force is examined when a fluid is accelerated from rest by a constant average pressure gradient toward a steady Stokes flow. The simulation results agree well with the theories for the short- and long-time behavior of the drag force. Flows through non-rotational and rotational spheres in simple cubic arrays and random arrays are simulated over the entire range of packing fractions, and both low and moderate particle Reynolds numbers to compare the simulated results with the literature results and develop a new drag force formula, a new lift force formula, and a new torque formula. Random arrays of solid particles in fluids are generated with Monte Carlo procedure and Zinchenko's method to avoid crystallization of solid particles over high solid volume fractions. A new drag force formula was developed with extensive simulated results to be closely applicable to real processes over the entire range of packing fractions and both low and moderate particle Reynolds numbers. The simulation results indicate that the drag force is barely affected by rotational Reynolds numbers. Drag force is basically unchanged as the angle of the rotating axis varies.« less

Two dimensional aerodynamic interference effects on oscillating airfoils with flaps in ventilated subsonic wind tunnels. [computational fluid dynamics

NASA Technical Reports Server (NTRS)

Fromme, J.; Golberg, M.; Werth, J.

1979-01-01

The numerical computation of unsteady airloads acting upon thin airfoils with multiple leading and trailing-edge controls in two-dimensional ventilated subsonic wind tunnels is studied. The foundation of the computational method is strengthened with a new and more powerful mathematical existence and convergence theory for solving Cauchy singular integral equations of the first kind, and the method of convergence acceleration by extrapolation to the limit is introduced to analyze airfoils with flaps. New results are presented for steady and unsteady flow, including the effect of acoustic resonance between ventilated wind-tunnel walls and airfoils with oscillating flaps. The computer program TWODI is available for general use and a complete set of instructions is provided.

Eddy Current Minimizing Flow Plug for Use in Flow Conditioning and Flow Metering

NASA Technical Reports Server (NTRS)

England, John Dwight (Inventor); Kelley, Anthony R. (Inventor)

2015-01-01

An eddy-current-minimizing flow plug has open flow channels formed between the plug's inlet and outlet. Each open flow channel includes (i) a first portion that originates at the inlet face and converges to a location within the plug that is downstream of the inlet, and (ii) a second portion that originates within the plug and diverges to the outlet. The diverging second portion is approximately twice the length of the converging first portion. The plug is devoid of planar surface regions at its inlet and outlet, and in fluid flow planes of the plug that are perpendicular to the given direction of a fluid flowing therethrough.

Newton-like methods for Navier-Stokes solution

NASA Astrophysics Data System (ADS)

Qin, N.; Xu, X.; Richards, B. E.

1992-12-01

The paper reports on Newton-like methods called SFDN-alpha-GMRES and SQN-alpha-GMRES methods that have been devised and proven as powerful schemes for large nonlinear problems typical of viscous compressible Navier-Stokes solutions. They can be applied using a partially converged solution from a conventional explicit or approximate implicit method. Developments have included the efficient parallelization of the schemes on a distributed memory parallel computer. The methods are illustrated using a RISC workstation and a transputer parallel system respectively to solve a hypersonic vortical flow.

Statistical characterization of planar two-dimensional Rayleigh-Taylor mixing layers

NASA Astrophysics Data System (ADS)

Sendersky, Dmitry

2000-10-01

The statistical evolution of a planar, randomly perturbed fluid interface subject to Rayleigh-Taylor instability is explored through numerical simulation in two space dimensions. The data set, generated by the front-tracking code FronTier, is highly resolved and covers a large ensemble of initial perturbations, allowing a more refined analysis of closure issues pertinent to the stochastic modeling of chaotic fluid mixing. We closely approach a two-fold convergence of the mean two-phase flow: convergence of the numerical solution under computational mesh refinement, and statistical convergence under increasing ensemble size. Quantities that appear in the two-phase averaged Euler equations are computed directly and analyzed for numerical and statistical convergence. Bulk averages show a high degree of convergence, while interfacial averages are convergent only in the outer portions of the mixing zone, where there is a coherent array of bubble and spike tips. Comparison with the familiar bubble/spike penetration law h = alphaAgt 2 is complicated by the lack of scale invariance, inability to carry the simulations to late time, the increasing Mach numbers of the bubble/spike tips, and sensitivity to the method of data analysis. Finally, we use the simulation data to analyze some constitutive properties of the mixing process.

Advances and future directions of research on spectral methods

NASA Technical Reports Server (NTRS)

Patera, A. T.

1986-01-01

Recent advances in spectral methods are briefly reviewed and characterized with respect to their convergence and computational complexity. Classical finite element and spectral approaches are then compared, and spectral element (or p-type finite element) approximations are introduced. The method is applied to the full Navier-Stokes equations, and examples are given of the application of the technique to several transitional flows. Future directions of research in the field are outlined.

Safety and Convergence Analysis of Intersecting Aircraft Flows Under Decentralized Collision Avoidance

NASA Astrophysics Data System (ADS)

Dallal, Ahmed H.

Safety is an essential requirement for air traffic management and control systems. Aircraft are not allowed to get closer to each other than a specified safety distance, to avoid any conflicts and collisions between aircraft. Forecast analysis predicts a tremendous increase in the number of flights. Subsequently, automated tools are needed to help air traffic controllers resolve air born conflicts. In this dissertation, we consider the problem of conflict resolution of aircraft flows with the assumption that aircraft are flowing through a fixed specified control volume at a constant speed. In this regard, several centralized and decentralized resolution rules have been proposed for path planning and conflict avoidance. For the case of two intersecting flows, we introduce the concept of conflict touches, and a collaborative decentralized conflict resolution rule is then proposed and analyzed for two intersecting flows. The proposed rule is also able to resolved airborne conflicts that resulted from resolving another conflict via the domino effect. We study the safety conditions under the proposed conflict resolution and collision avoidance rule. Then, we use Lyapunov analysis to analytically prove the convergence of conflict resolution dynamics under the proposed rule. The analysis show that, under the proposed conflict resolution rule, the system of intersecting aircraft flows is guaranteed to converge to safe, conflict free, trajectories within a bounded time. Simulations are provided to verify the analytically derived conclusions and study the convergence of the conflict resolution dynamics at different encounter angles. Simulation results show that lateral deviations taken by aircraft in each flow, to resolve conflicts, are bounded, and aircraft converged to safe and conflict free trajectories, within a finite time.

High order spectral difference lattice Boltzmann method for incompressible hydrodynamics

NASA Astrophysics Data System (ADS)

Li, Weidong

2017-09-01

This work presents a lattice Boltzmann equation (LBE) based high order spectral difference method for incompressible flows. In the present method, the spectral difference (SD) method is adopted to discretize the convection and collision term of the LBE to obtain high order (≥3) accuracy. Because the SD scheme represents the solution as cell local polynomials and the solution polynomials have good tensor-product property, the present spectral difference lattice Boltzmann method (SD-LBM) can be implemented on arbitrary unstructured quadrilateral meshes for effective and efficient treatment of complex geometries. Thanks to only first oder PDEs involved in the LBE, no special techniques, such as hybridizable discontinuous Galerkin method (HDG), local discontinuous Galerkin method (LDG) and so on, are needed to discrete diffusion term, and thus, it simplifies the algorithm and implementation of the high order spectral difference method for simulating viscous flows. The proposed SD-LBM is validated with four incompressible flow benchmarks in two-dimensions: (a) the Poiseuille flow driven by a constant body force; (b) the lid-driven cavity flow without singularity at the two top corners-Burggraf flow; and (c) the unsteady Taylor-Green vortex flow; (d) the Blasius boundary-layer flow past a flat plate. Computational results are compared with analytical solutions of these cases and convergence studies of these cases are also given. The designed accuracy of the proposed SD-LBM is clearly verified.

Impact of a Geometric Correction for Proximal Flow Constraint on the Assessment of Mitral Regurgitation Severity Using the Proximal Flow Convergence Method.

PubMed

Jang, Jeong Yoon; Kang, Joon-Won; Yang, Dong Hyun; Lee, Sahmin; Sun, Byung Joo; Kim, Dae-Hee; Song, Jong-Min; Kang, Duk-Hyun; Song, Jae-Kwan

2018-03-01

Overestimation of the severity of mitral regurgitation (MR) by the proximal isovelocity surface area (PISA) method has been reported. We sought to test whether angle correction (AC) of the constrained flow field is helpful to eliminate overestimation in patients with eccentric MR. In a total of 33 patients with MR due to prolapse or flail mitral valve, both echocardiography and cardiac magnetic resonance image (CMR) were performed to calculate regurgitant volume (RV). In addition to RV by conventional PISA (RV PISA ), convergence angle (α) was measured from 2-dimensional Doppler color flow maps and RV was corrected by multiplying by α/180 (RV AC ). RV measured by CMR (RV CMR ) was used as a gold standard, which was calculated by the difference between total stroke volume measured by planimetry of the short axis slices and aortic stroke volume by phase-contrast image. The correlation between RV CMR and RV by echocardiography was modest [RV CMR vs. RV PISA (r = 0.712, p < 0.001) and RV CMR vs. RV AC (r = 0.766, p < 0.001)]. However, RV PISA showed significant overestimation (RV PISA - RV CMR = 50.6 ± 40.6 mL vs. RV AC - RV CMR = 7.7 ± 23.4 mL, p < 0.001). The overall accuracy of RV PISA for diagnosis of severe MR, defined as RV ≥ 60 mL, was 57.6% (19/33), whereas it increased to 84.8% (28/33) by using RV AC ( p = 0.028). Conventional PISA method tends to provide falsely large RV in patients with eccentric MR and a simple geometric AC of the proximal constraint flow largely eliminates overestimation.

Consistent initial conditions for the Saint-Venant equations in river network modeling

NASA Astrophysics Data System (ADS)

Yu, Cheng-Wei; Liu, Frank; Hodges, Ben R.

2017-09-01

Initial conditions for flows and depths (cross-sectional areas) throughout a river network are required for any time-marching (unsteady) solution of the one-dimensional (1-D) hydrodynamic Saint-Venant equations. For a river network modeled with several Strahler orders of tributaries, comprehensive and consistent synoptic data are typically lacking and synthetic starting conditions are needed. Because of underlying nonlinearity, poorly defined or inconsistent initial conditions can lead to convergence problems and long spin-up times in an unsteady solver. Two new approaches are defined and demonstrated herein for computing flows and cross-sectional areas (or depths). These methods can produce an initial condition data set that is consistent with modeled landscape runoff and river geometry boundary conditions at the initial time. These new methods are (1) the pseudo time-marching method (PTM) that iterates toward a steady-state initial condition using an unsteady Saint-Venant solver and (2) the steady-solution method (SSM) that makes use of graph theory for initial flow rates and solution of a steady-state 1-D momentum equation for the channel cross-sectional areas. The PTM is shown to be adequate for short river reaches but is significantly slower and has occasional non-convergent behavior for large river networks. The SSM approach is shown to provide a rapid solution of consistent initial conditions for both small and large networks, albeit with the requirement that additional code must be written rather than applying an existing unsteady Saint-Venant solver.

A positivity-preserving, implicit defect-correction multigrid method for turbulent combustion

NASA Astrophysics Data System (ADS)

Wasserman, M.; Mor-Yossef, Y.; Greenberg, J. B.

2016-07-01

A novel, robust multigrid method for the simulation of turbulent and chemically reacting flows is developed. A survey of previous attempts at implementing multigrid for the problems at hand indicated extensive use of artificial stabilization to overcome numerical instability arising from non-linearity of turbulence and chemistry model source-terms, small-scale physics of combustion, and loss of positivity. These issues are addressed in the current work. The highly stiff Reynolds-averaged Navier-Stokes (RANS) equations, coupled with turbulence and finite-rate chemical kinetics models, are integrated in time using the unconditionally positive-convergent (UPC) implicit method. The scheme is successfully extended in this work for use with chemical kinetics models, in a fully-coupled multigrid (FC-MG) framework. To tackle the degraded performance of multigrid methods for chemically reacting flows, two major modifications are introduced with respect to the basic, Full Approximation Storage (FAS) approach. First, a novel prolongation operator that is based on logarithmic variables is proposed to prevent loss of positivity due to coarse-grid corrections. Together with the extended UPC implicit scheme, the positivity-preserving prolongation operator guarantees unconditional positivity of turbulence quantities and species mass fractions throughout the multigrid cycle. Second, to improve the coarse-grid-correction obtained in localized regions of high chemical activity, a modified defect correction procedure is devised, and successfully applied for the first time to simulate turbulent, combusting flows. The proposed modifications to the standard multigrid algorithm create a well-rounded and robust numerical method that provides accelerated convergence, while unconditionally preserving the positivity of model equation variables. Numerical simulations of various flows involving premixed combustion demonstrate that the proposed MG method increases the efficiency by a factor of up to eight times with respect to an equivalent single-grid method, and by two times with respect to an artificially-stabilized MG method.

Hillslope-scale experiment demonstrates role of convergence during two-step saturation

USGS Publications Warehouse

Gevaert, A. I.; Teuling, A. J.; Uijlenhoet, R.; DeLong, Stephen B.; Huxman, T. E.; Pangle, L. A.; Breshears, David D.; Chorover, J.; Pelletier, John D.; Saleska, S. R.; Zeng, X.; Troch, Peter A.

2014-01-01

Subsurface flow and storage dynamics at hillslope scale are difficult to ascertain, often in part due to a lack of sufficient high-resolution measurements and an incomplete understanding of boundary conditions, soil properties, and other environmental aspects. A continuous and extreme rainfall experiment on an artificial hillslope at Biosphere 2's Landscape Evolution Observatory (LEO) resulted in saturation excess overland flow and gully erosion in the convergent hillslope area. An array of 496 soil moisture sensors revealed a two-step saturation process. First, the downward movement of the wetting front brought soils to a relatively constant but still unsaturated moisture content. Second, soils were brought to saturated conditions from below in response to rising water tables. Convergent areas responded faster than upslope areas, due to contributions from lateral subsurface flow driven by the topography of the bottom boundary, which is comparable to impermeable bedrock in natural environments. This led to the formation of a groundwater ridge in the convergent area, triggering saturation excess runoff generation. This unique experiment demonstrates, at very high spatial and temporal resolution, the role of convergence on subsurface storage and flow dynamics. The results bring into question the representation of saturation excess overland flow in conceptual rainfall-runoff models and land-surface models, since flow is gravity-driven in many of these models and upper layers cannot become saturated from below. The results also provide a baseline to study the role of the co-evolution of ecological and hydrological processes in determining landscape water dynamics during future experiments in LEO.

CONVERGING SUPERGRANULAR FLOWS AND THE FORMATION OF CORONAL PLUMES

DOE Office of Scientific and Technical Information (OSTI.GOV)

Wang, Y.-M.; Warren, H. P.; Muglach, K., E-mail: yi.wang@nrl.navy.mil, E-mail: harry.warren@nrl.navy.mil, E-mail: karin.muglach@nasa.gov

Earlier studies have suggested that coronal plumes are energized by magnetic reconnection between unipolar flux concentrations and nearby bipoles, even though magnetograms sometimes show very little minority-polarity flux near the footpoints of plumes. Here we use high-resolution extreme-ultraviolet (EUV) images and magnetograms from the Solar Dynamics Observatory (SDO) to clarify the relationship between plume emission and the underlying photospheric field. We find that plumes form where unipolar network elements inside coronal holes converge to form dense clumps, and fade as the clumps disperse again. The converging flows also carry internetwork fields of both polarities. Although the minority-polarity flux is sometimesmore » barely visible in the magnetograms, the corresponding EUV images almost invariably show loop-like features in the core of the plumes, with the fine structure changing on timescales of minutes or less. We conclude that the SDO observations are consistent with a model in which plume emission originates from interchange reconnection in converging flows, with the plume lifetime being determined by the ∼1 day evolutionary timescale of the supergranular network. Furthermore, the presence of large EUV bright points and/or ephemeral regions is not a necessary precondition for the formation of plumes, which can be energized even by the weak, mixed-polarity internetwork fields swept up by converging flows.« less

Flow analysis and design optimization methods for nozzle-afterbody of a hypersonic vehicle

NASA Technical Reports Server (NTRS)

Baysal, O.

1992-01-01

This report summarizes the methods developed for the aerodynamic analysis and the shape optimization of the nozzle-afterbody section of a hypersonic vehicle. Initially, exhaust gases were assumed to be air. Internal-external flows around a single scramjet module were analyzed by solving the 3D Navier-Stokes equations. Then, exhaust gases were simulated by a cold mixture of Freon and Ar. Two different models were used to compute these multispecies flows as they mixed with the hypersonic airflow. Surface and off-surface properties were successfully compared with the experimental data. The Aerodynamic Design Optimization with Sensitivity analysis was then developed. Pre- and postoptimization sensitivity coefficients were derived and used in this quasi-analytical method. These coefficients were also used to predict inexpensively the flow field around a changed shape when the flow field of an unchanged shape was given. Starting with totally arbitrary initial afterbody shapes, independent computations were converged to the same optimum shape, which rendered the maximum axial thrust.

Flow analysis and design optimization methods for nozzle afterbody of a hypersonic vehicle

NASA Technical Reports Server (NTRS)

Baysal, Oktay

1991-01-01

This report summarizes the methods developed for the aerodynamic analysis and the shape optimization of the nozzle-afterbody section of a hypersonic vehicle. Initially, exhaust gases were assumed to be air. Internal-external flows around a single scramjet module were analyzed by solving the three dimensional Navier-Stokes equations. Then, exhaust gases were simulated by a cold mixture of Freon and Argon. Two different models were used to compute these multispecies flows as they mixed with the hypersonic airflow. Surface and off-surface properties were successfully compared with the experimental data. In the second phase of this project, the Aerodynamic Design Optimization with Sensitivity analysis (ADOS) was developed. Pre and post optimization sensitivity coefficients were derived and used in this quasi-analytical method. These coefficients were also used to predict inexpensively the flow field around a changed shape when the flow field of an unchanged shape was given. Starting with totally arbitrary initial afterbody shapes, independent computations were converged to the same optimum shape, which rendered the maximum axial thrust.

Grid convergence errors in hemodynamic solution of patient-specific cerebral aneurysms.

PubMed

Hodis, Simona; Uthamaraj, Susheil; Smith, Andrea L; Dennis, Kendall D; Kallmes, David F; Dragomir-Daescu, Dan

2012-11-15

Computational fluid dynamics (CFD) has become a cutting-edge tool for investigating hemodynamic dysfunctions in the body. It has the potential to help physicians quantify in more detail the phenomena difficult to capture with in vivo imaging techniques. CFD simulations in anatomically realistic geometries pose challenges in generating accurate solutions due to the grid distortion that may occur when the grid is aligned with complex geometries. In addition, results obtained with computational methods should be trusted only after the solution has been verified on multiple high-quality grids. The objective of this study was to present a comprehensive solution verification of the intra-aneurysmal flow results obtained on different morphologies of patient-specific cerebral aneurysms. We chose five patient-specific brain aneurysm models with different dome morphologies and estimated the grid convergence errors for each model. The grid convergence errors were estimated with respect to an extrapolated solution based on the Richardson extrapolation method, which accounts for the degree of grid refinement. For four of the five models, calculated velocity, pressure, and wall shear stress values at six different spatial locations converged monotonically, with maximum uncertainty magnitudes ranging from 12% to 16% on the finest grids. Due to the geometric complexity of the fifth model, the grid convergence errors showed oscillatory behavior; therefore, each patient-specific model required its own grid convergence study to establish the accuracy of the analysis. Copyright © 2012 Elsevier Ltd. All rights reserved.

Accurate, meshless methods for magnetohydrodynamics

NASA Astrophysics Data System (ADS)

Hopkins, Philip F.; Raives, Matthias J.

2016-01-01

Recently, we explored new meshless finite-volume Lagrangian methods for hydrodynamics: the `meshless finite mass' (MFM) and `meshless finite volume' (MFV) methods; these capture advantages of both smoothed particle hydrodynamics (SPH) and adaptive mesh refinement (AMR) schemes. We extend these to include ideal magnetohydrodynamics (MHD). The MHD equations are second-order consistent and conservative. We augment these with a divergence-cleaning scheme, which maintains nabla \\cdot B≈ 0. We implement these in the code GIZMO, together with state-of-the-art SPH MHD. We consider a large test suite, and show that on all problems the new methods are competitive with AMR using constrained transport (CT) to ensure nabla \\cdot B=0. They correctly capture the growth/structure of the magnetorotational instability, MHD turbulence, and launching of magnetic jets, in some cases converging more rapidly than state-of-the-art AMR. Compared to SPH, the MFM/MFV methods exhibit convergence at fixed neighbour number, sharp shock-capturing, and dramatically reduced noise, divergence errors, and diffusion. Still, `modern' SPH can handle most test problems, at the cost of larger kernels and `by hand' adjustment of artificial diffusion. Compared to non-moving meshes, the new methods exhibit enhanced `grid noise' but reduced advection errors and diffusion, easily include self-gravity, and feature velocity-independent errors and superior angular momentum conservation. They converge more slowly on some problems (smooth, slow-moving flows), but more rapidly on others (involving advection/rotation). In all cases, we show divergence control beyond the Powell 8-wave approach is necessary, or all methods can converge to unphysical answers even at high resolution.

An approximate theoretical method for modeling the static thrust performance of non-axisymmetric two-dimensional convergent-divergent nozzles. M.S. Thesis - George Washington Univ.

NASA Technical Reports Server (NTRS)

Hunter, Craig A.

1995-01-01

An analytical/numerical method has been developed to predict the static thrust performance of non-axisymmetric, two-dimensional convergent-divergent exhaust nozzles. Thermodynamic nozzle performance effects due to over- and underexpansion are modeled using one-dimensional compressible flow theory. Boundary layer development and skin friction losses are calculated using an approximate integral momentum method based on the classic karman-Polhausen solution. Angularity effects are included with these two models in a computational Nozzle Performance Analysis Code, NPAC. In four different case studies, results from NPAC are compared to experimental data obtained from subscale nozzle testing to demonstrate the capabilities and limitations of the NPAC method. In several cases, the NPAC prediction matched experimental gross thrust efficiency data to within 0.1 percent at a design NPR, and to within 0.5 percent at off-design conditions.

Comparison of viscous-shock-layer solutions by time-asymptotic and steady-state methods. [flow distribution around a Jupiter entry probe

NASA Technical Reports Server (NTRS)

Gupta, R. N.; Moss, J. N.; Simmonds, A. L.

1982-01-01

Two flow-field codes employing the time- and space-marching numerical techniques were evaluated. Both methods were used to analyze the flow field around a massively blown Jupiter entry probe under perfect-gas conditions. In order to obtain a direct point-by-point comparison, the computations were made by using identical grids and turbulence models. For the same degree of accuracy, the space-marching scheme takes much less time as compared to the time-marching method and would appear to provide accurate results for the problems with nonequilibrium chemistry, free from the effect of local differences in time on the final solution which is inherent in time-marching methods. With the time-marching method, however, the solutions are obtainable for the realistic entry probe shapes with massive or uniform surface blowing rates; whereas, with the space-marching technique, it is difficult to obtain converged solutions for such flow conditions. The choice of the numerical method is, therefore, problem dependent. Both methods give equally good results for the cases where results are compared with experimental data.

Local Helioseismology of Emerging Active Regions: A Case Study

NASA Astrophysics Data System (ADS)

Kosovichev, Alexander G.; Zhao, Junwei; Ilonidis, Stathis

2018-04-01

Local helioseismology provides a unique opportunity to investigate the subsurface structure and dynamics of active regions and their effect on the large-scale flows and global circulation of the Sun. We use measurements of plasma flows in the upper convection zone, provided by the Time-Distance Helioseismology Pipeline developed for analysis of solar oscillation data obtained by Helioseismic and Magnetic Imager (HMI) on Solar Dynamics Observatory (SDO), to investigate the subsurface dynamics of emerging active region NOAA 11726. The active region emergence was detected in deep layers of the convection zone about 12 hours before the first bipolar magnetic structure appeared on the surface, and 2 days before the emergence of most of the magnetic flux. The speed of emergence determined by tracking the flow divergence with depth is about 1.4 km/s, very close to the emergence speed in the deep layers. As the emerging magnetic flux becomes concentrated in sunspots local converging flows are observed beneath the forming sunspots. These flows are most prominent in the depth range 1-3 Mm, and remain converging after the formation process is completed. On the larger scale converging flows around active region appear as a diversion of the zonal shearing flows towards the active region, accompanied by formation of a large-scale vortex structure. This process occurs when a substantial amount of the magnetic flux emerged on the surface, and the converging flow pattern remains stable during the following evolution of the active region. The Carrington synoptic flow maps show that the large-scale subsurface inflows are typical for active regions. In the deeper layers (10-13 Mm) the flows become diverging, and surprisingly strong beneath some active regions. In addition, the synoptic maps reveal a complex evolving pattern of large-scale flows on the scale much larger than supergranulation

Influence of the elastic deformation of a foam on its mobility in channels of linearly varying width.

PubMed

Dollet, Benjamin; Jones, Siân A; Méheust, Yves; Cantat, Isabelle

2014-08-01

We study foam flow in an elementary model porous medium consisting of a convergent and a divergent channel positioned side by side and possessing a fixed joint porosity. Configurations of converging or diverging channels are ubiquitous at the pore scale in porous media, as all channels linking pores possess a converging and diverging part. The resulting flow kinematics imposes asymmetric bubble deformations in the two channels, which modulate foam-wall friction and strongly impact the flux distribution. We measure, as well as quantitatively predict, the ratio of the fluxes in the two channels as a function of the channel widths by modeling pressure drops of both viscous and capillary origins. This study reveals the crucial importance of boundary-induced bubble deformation on the mobility of a flowing foam, resulting in particular in flow irreversibility.

Experimental investigation of shock-cell noise reduction for dual-stream nozzles in simulated flight comprehensive data report. Volume 2: Laser velocimeter data, static pressures and shadowgraph photos

NASA Technical Reports Server (NTRS)

Yamamoto, K.; Janardan, B. A.; Brausch, J. F.; Hoerst, D. J.; Price, A. O.

1984-01-01

Parameters which contribute to supersonic jet shock noise were investigated for the purpose of determining means to reduce such noise generation to acceptable levels. Six dual-stream test nozzles with varying flow passage and plug closure designs were evaluated under simulated flight conditions in an anechoic chamber. All nozzles had combined convergent-divergent or convergent flow passages. Mean velocity and turbulence velocity measurements of 25 selected flow conditions were performed employing a laser Doppler velocimeter. Static pressure measurements were made to define the actual convergence-divergence condition. Test point definition, tabulation of aerodynamic test conditions, velocity histograms, and shadowgraph photographs are presented. Flow visualization through shadowgraph photography can contribute to the development of an analytical prediction model for shock noise from coannular plug nozzles.

Analytic Approximate Solutions to the Boundary Layer Flow Equation over a Stretching Wall with Partial Slip at the Boundary.

PubMed

Ene, Remus-Daniel; Marinca, Vasile; Marinca, Bogdan

2016-01-01

Analytic approximate solutions using Optimal Homotopy Perturbation Method (OHPM) are given for steady boundary layer flow over a nonlinearly stretching wall in presence of partial slip at the boundary. The governing equations are reduced to nonlinear ordinary differential equation by means of similarity transformations. Some examples are considered and the effects of different parameters are shown. OHPM is a very efficient procedure, ensuring a very rapid convergence of the solutions after only two iterations.

Navier-Stokes computations for circulation control airfoils

NASA Technical Reports Server (NTRS)

Pulliam, Thomas H.; Jespersen, Dennis C.; Barth, Timothy J.

1987-01-01

Navier-Stokes computations of subsonic to transonic flow past airfoils with augmented lift due to rearward jet blowing over a curved trailing edge are presented. The approach uses a spiral grid topology. Solutions are obtained using a Navier-Stokes code which employs an implicit finite difference method, an algebraic turbulence model, and developments which improve stability, convergence, and accuracy. Results are compared against experiments for no jet blowing and moderate jet pressures and demonstrate the capability to compute these complicated flows.

Navier-Stokes computations for circulation controlled airfoils

NASA Technical Reports Server (NTRS)

Pulliam, T. H.; Jesperen, D. C.; Barth, T. J.

1986-01-01

Navier-Stokes computations of subsonic to transonic flow past airfoils with augmented lift due to rearward jet blowing over a curved trailing edge are presented. The approach uses a spiral grid topology. Solutions are obtained using a Navier-Stokes code which employs an implicit finite difference method, an algebraic turbulence model, and developments which improve stability, convergence, and accuracy. Results are compared against experiments for no jet blowing and moderate jet pressures and demonstrate the capability to compute these complicated flows.

Analytic Approximate Solutions to the Boundary Layer Flow Equation over a Stretching Wall with Partial Slip at the Boundary

PubMed Central

Ene, Remus-Daniel; Marinca, Vasile; Marinca, Bogdan

2016-01-01

Analytic approximate solutions using Optimal Homotopy Perturbation Method (OHPM) are given for steady boundary layer flow over a nonlinearly stretching wall in presence of partial slip at the boundary. The governing equations are reduced to nonlinear ordinary differential equation by means of similarity transformations. Some examples are considered and the effects of different parameters are shown. OHPM is a very efficient procedure, ensuring a very rapid convergence of the solutions after only two iterations. PMID:27031232

Primary and secondary battery consumption trends in Sweden 1996–2013: Method development and detailed accounting by battery type

DOE Office of Scientific and Technical Information (OSTI.GOV)

Patrício, João, E-mail: joao.patricio@chalmers.se; Kalmykova, Yuliya; Berg, Per E.O.

2015-05-15

Highlights: • Developed MFA method was validated by the national statistics. • Exponential increase of EEE sales leads to increase in integrated battery consumption. • Digital convergence is likely to be a cause for primary batteries consumption decline. • Factors for estimation of integrated batteries in EE are provided. • Sweden reached the collection rates defined by European Union. - Abstract: In this article, a new method based on Material Flow Accounting is proposed to study detailed material flows in battery consumption that can be replicated for other countries. The method uses regularly available statistics on import, industrial production andmore » export of batteries and battery-containing electric and electronic equipment (EEE). To promote method use by other scholars with no access to such data, several empirically results and their trends over time, for different types of batteries occurrence among the EEE types are provided. The information provided by the method can be used to: identify drivers of battery consumption; study the dynamic behavior of battery flows – due to technology development, policies, consumers behavior and infrastructures. The method is exemplified by the study of battery flows in Sweden for years 1996–2013. The batteries were accounted, both in units and weight, as primary and secondary batteries; loose and integrated; by electrochemical composition and share of battery use between different types of EEE. Results show that, despite a fivefold increase in the consumption of rechargeable batteries, they account for only about 14% of total use of portable batteries. Recent increase in digital convergence has resulted in a sharp decline in the consumption of primary batteries, which has now stabilized at a fairly low level. Conversely, the consumption of integrated batteries has increased sharply. In 2013, 61% of the total weight of batteries sold in Sweden was collected, and for the particular case of alkaline manganese dioxide batteries, the value achieved 74%.« less

Calculation of viscous effects on transonic flow for oscillating airfoils and comparisons with experiment

NASA Technical Reports Server (NTRS)

Howlett, James T.; Bland, Samuel R.

1987-01-01

A method is described for calculating unsteady transonic flow with viscous interaction by coupling a steady integral boundary-layer code with an unsteady, transonic, inviscid small-disturbance computer code in a quasi-steady fashion. Explicit coupling of the equations together with viscous -inviscid iterations at each time step yield converged solutions with computer times about double those required to obtain inviscid solutions. The accuracy and range of applicability of the method are investigated by applying it to four AGARD standard airfoils. The first-harmonic components of both the unsteady pressure distributions and the lift and moment coefficients have been calculated. Comparisons with inviscid calcualtions and experimental data are presented. The results demonstrate that accurate solutions for transonic flows with viscous effects can be obtained for flows involving moderate-strength shock waves.

Computational investigations and grid refinement study of 3D transient flow in a cylindrical tank using OpenFOAM

NASA Astrophysics Data System (ADS)

Mohd Sakri, F.; Mat Ali, M. S.; Sheikh Salim, S. A. Z.

2016-10-01

The study of physic fluid for a liquid draining inside a tank is easily accessible using numerical simulation. However, numerical simulation is expensive when the liquid draining involves the multi-phase problem. Since an accurate numerical simulation can be obtained if a proper method for error estimation is accomplished, this paper provides systematic assessment of error estimation due to grid convergence error using OpenFOAM. OpenFOAM is an open source CFD-toolbox and it is well-known among the researchers and institutions because of its free applications and ready to use. In this study, three types of grid resolution are used: coarse, medium and fine grids. Grid Convergence Index (GCI) is applied to estimate the error due to the grid sensitivity. A monotonic convergence condition is obtained in this study that shows the grid convergence error has been progressively reduced. The fine grid has the GCI value below 1%. The extrapolated value from Richardson Extrapolation is in the range of the GCI obtained.

A 1D-2D coupled SPH-SWE model applied to open channel flow simulations in complicated geometries

NASA Astrophysics Data System (ADS)

Chang, Kao-Hua; Sheu, Tony Wen-Hann; Chang, Tsang-Jung

2018-05-01

In this study, a one- and two-dimensional (1D-2D) coupled model is developed to solve the shallow water equations (SWEs). The solutions are obtained using a Lagrangian meshless method called smoothed particle hydrodynamics (SPH) to simulate shallow water flows in converging, diverging and curved channels. A buffer zone is introduced to exchange information between the 1D and 2D SPH-SWE models. Interpolated water discharge values and water surface levels at the internal boundaries are prescribed as the inflow/outflow boundary conditions in the two SPH-SWE models. In addition, instead of using the SPH summation operator, we directly solve the continuity equation by introducing a diffusive term to suppress oscillations in the predicted water depth. The performance of the two approaches in calculating the water depth is comprehensively compared through a case study of a straight channel. Additionally, three benchmark cases involving converging, diverging and curved channels are adopted to demonstrate the ability of the proposed 1D and 2D coupled SPH-SWE model through comparisons with measured data and predicted mesh-based numerical results. The proposed model provides satisfactory accuracy and guaranteed convergence.

A numerical investigation of the boundary layer flow of an Eyring-Powell fluid over a stretching sheet via rational Chebyshev functions

NASA Astrophysics Data System (ADS)

Parand, Kourosh; Mahdi Moayeri, Mohammad; Latifi, Sobhan; Delkhosh, Mehdi

2017-07-01

In this paper, a spectral method based on the four kinds of rational Chebyshev functions is proposed to approximate the solution of the boundary layer flow of an Eyring-Powell fluid over a stretching sheet. First, by using the quasilinearization method (QLM), the model which is a nonlinear ordinary differential equation is converted to a sequence of linear ordinary differential equations (ODEs). By applying the proposed method on the ODEs in each iteration, the equations are converted to a system of linear algebraic equations. The results indicate the high accuracy and convergence of our method. Moreover, the effects of the Eyring-Powell fluid material parameters are discussed.

A level-set method for two-phase flows with moving contact line and insoluble surfactant

NASA Astrophysics Data System (ADS)

Xu, Jian-Jun; Ren, Weiqing

2014-04-01

A level-set method for two-phase flows with moving contact line and insoluble surfactant is presented. The mathematical model consists of the Navier-Stokes equation for the flow field, a convection-diffusion equation for the surfactant concentration, together with the Navier boundary condition and a condition for the dynamic contact angle derived by Ren et al. (2010) [37]. The numerical method is based on the level-set continuum surface force method for two-phase flows with surfactant developed by Xu et al. (2012) [54] with some cautious treatment for the boundary conditions. The numerical method consists of three components: a flow solver for the velocity field, a solver for the surfactant concentration, and a solver for the level-set function. In the flow solver, the surface force is dealt with using the continuum surface force model. The unbalanced Young stress at the moving contact line is incorporated into the Navier boundary condition. A convergence study of the numerical method and a parametric study are presented. The influence of surfactant on the dynamics of the moving contact line is illustrated using examples. The capability of the level-set method to handle complex geometries is demonstrated by simulating a pendant drop detaching from a wall under gravity.

Numerical method for predicting flow characteristics and performance of nonaxisymmetric nozzles. Part 2: Applications

NASA Technical Reports Server (NTRS)

Thomas, P. D.

1980-01-01

A computer implemented numerical method for predicting the flow in and about an isolated three dimensional jet exhaust nozzle is summarized. The approach is based on an implicit numerical method to solve the unsteady Navier-Stokes equations in a boundary conforming curvilinear coordinate system. Recent improvements to the original numerical algorithm are summarized. Equations are given for evaluating nozzle thrust and discharge coefficient in terms of computed flowfield data. The final formulation of models that are used to simulate flow turbulence effect is presented. Results are presented from numerical experiments to explore the effect of various quantities on the rate of convergence to steady state and on the final flowfield solution. Detailed flowfield predictions for several two and three dimensional nozzle configurations are presented and compared with wind tunnel experimental data.

A PDF projection method: A pressure algorithm for stand-alone transported PDFs

NASA Astrophysics Data System (ADS)

Ghorbani, Asghar; Steinhilber, Gerd; Markus, Detlev; Maas, Ulrich

2015-03-01

In this paper, a new formulation of the projection approach is introduced for stand-alone probability density function (PDF) methods. The method is suitable for applications in low-Mach number transient turbulent reacting flows. The method is based on a fractional step method in which first the advection-diffusion-reaction equations are modelled and solved within a particle-based PDF method to predict an intermediate velocity field. Then the mean velocity field is projected onto a space where the continuity for the mean velocity is satisfied. In this approach, a Poisson equation is solved on the Eulerian grid to obtain the mean pressure field. Then the mean pressure is interpolated at the location of each stochastic Lagrangian particle. The formulation of the Poisson equation avoids the time derivatives of the density (due to convection) as well as second-order spatial derivatives. This in turn eliminates the major sources of instability in the presence of stochastic noise that are inherent in particle-based PDF methods. The convergence of the algorithm (in the non-turbulent case) is investigated first by the method of manufactured solutions. Then the algorithm is applied to a one-dimensional turbulent premixed flame in order to assess the accuracy and convergence of the method in the case of turbulent combustion. As a part of this work, we also apply the algorithm to a more realistic flow, namely a transient turbulent reacting jet, in order to assess the performance of the method.

Dynamic Supersonic Base Store Ejection Simulation Using Beggar

DTIC Science & Technology

2008-12-01

selected convergence tolerance. Beggar accomplishes this is by using the symmetric Gauss - Seidel relaxation scheme implemented as follows [26]: [ ln+1,m...scheme (Section 2.3.3). To compute a time accurate solution to an unsteady flow problem, Beggar ap- plies Newtons Method to Eq. 2.15. The full method ...3.6. Separation Distance (x/D) . . . . . . . . . . . . . . . . . . . . 46 4.1. Drag Coefficient of Static Solutions Compared to Dynamic Solu- tions

Unsteady Flow Simulation: A Numerical Challenge

DTIC Science & Technology

2003-03-01

drive to convergence the numerical unsteady term. The time marching procedure is based on the approximate implicit Newton method for systems of non...computed through analytical derivatives of S. The linear system stemming from equation (3) is solved at each integration step by the same iterative method...significant reduction of memory usage, thanks to the reduced dimensions of the linear system matrix during the implicit marching of the solution. The

A Discontinuous Petrov-Galerkin Methodology for Adaptive Solutions to the Incompressible Navier-Stokes Equations

DOE Office of Scientific and Technical Information (OSTI.GOV)

Roberts, Nathan V.; Demkowiz, Leszek; Moser, Robert

2015-11-15

The discontinuous Petrov-Galerkin methodology with optimal test functions (DPG) of Demkowicz and Gopalakrishnan [18, 20] guarantees the optimality of the solution in an energy norm, and provides several features facilitating adaptive schemes. Whereas Bubnov-Galerkin methods use identical trial and test spaces, Petrov-Galerkin methods allow these function spaces to differ. In DPG, test functions are computed on the fly and are chosen to realize the supremum in the inf-sup condition; the method is equivalent to a minimum residual method. For well-posed problems with sufficiently regular solutions, DPG can be shown to converge at optimal rates—the inf-sup constants governing the convergence aremore » mesh-independent, and of the same order as those governing the continuous problem [48]. DPG also provides an accurate mechanism for measuring the error, and this can be used to drive adaptive mesh refinements. We employ DPG to solve the steady incompressible Navier-Stokes equations in two dimensions, building on previous work on the Stokes equations, and focusing particularly on the usefulness of the approach for automatic adaptivity starting from a coarse mesh. We apply our approach to a manufactured solution due to Kovasznay as well as the lid-driven cavity flow, backward-facing step, and flow past a cylinder problems.« less

Convergence issues in domain decomposition parallel computation of hovering rotor

NASA Astrophysics Data System (ADS)

Xiao, Zhongyun; Liu, Gang; Mou, Bin; Jiang, Xiong

2018-05-01

Implicit LU-SGS time integration algorithm has been widely used in parallel computation in spite of its lack of information from adjacent domains. When applied to parallel computation of hovering rotor flows in a rotating frame, it brings about convergence issues. To remedy the problem, three LU factorization-based implicit schemes (consisting of LU-SGS, DP-LUR and HLU-SGS) are investigated comparatively. A test case of pure grid rotation is designed to verify these algorithms, which show that LU-SGS algorithm introduces errors on boundary cells. When partition boundaries are circumferential, errors arise in proportion to grid speed, accumulating along with the rotation, and leading to computational failure in the end. Meanwhile, DP-LUR and HLU-SGS methods show good convergence owing to boundary treatment which are desirable in domain decomposition parallel computations.

Finite element modeling of mass transport in high-Péclet cardiovascular flows

NASA Astrophysics Data System (ADS)

Hansen, Kirk; Arzani, Amirhossein; Shadden, Shawn

2016-11-01

Mass transport plays an important role in many important cardiovascular processes, including thrombus formation and atherosclerosis. These mass transport problems are characterized by Péclet numbers of up to 108, leading to several numerical difficulties. The presence of thin near-wall concentration boundary layers requires very fine mesh resolution in these regions, while large concentration gradients within the flow cause numerical stabilization issues. In this work, we will discuss some guidelines for solving mass transport problems in cardiovascular flows using a stabilized Galerkin finite element method. First, we perform mesh convergence studies in a series of idealized and patient-specific geometries to determine the required near-wall mesh resolution for these types of problems, using both first- and second-order tetrahedral finite elements. Second, we investigate the use of several boundary condition types at outflow boundaries where backflow during some parts of the cardiac cycle can lead to convergence issues. Finally, we evaluate the effect of reducing Péclet number by increasing mass diffusivity as has been proposed by some researchers. This work was supported by the NSF GRFP and NSF Career Award #1354541.

Numerical convergence improvements for porflow unsaturated flow simulations

DOE Office of Scientific and Technical Information (OSTI.GOV)

Flach, Greg

2017-08-14

Section 3.6 of SRNL (2016) discusses various PORFLOW code improvements to increase modeling efficiency, in preparation for the next E-Area Performance Assessment (WSRC 2008) revision. This memorandum documents interaction with Analytic & Computational Research, Inc. (http://www.acricfd.com/default.htm) to improve numerical convergence efficiency using PORFLOW version 6.42 for unsaturated flow simulations.

Multigrid schemes for viscous hypersonic flows

NASA Technical Reports Server (NTRS)

Swanson, R. C.; Radespiel, R.

1993-01-01

Several multigrid schemes are considered for the numerical computation of viscous hypersonic flows. For each scheme, the basic solution algorithm employs upwind spatial discretization with explicit multistage time stepping. Two-level versions of the various multigrid algorithms are applied to the two-dimensional advection equation, and Fourier analysis is used to determine their damping properties. The capabilities of the multigrid methods are assessed by solving two different hypersonic flow problems. Some new multigrid schemes, based on semicoarsening strategies, are shown to be quite effective in relieving the stiffness caused by the high-aspect-ratio cells required to resolve high Reynolds number flows. These schemes exhibit good convergence rates for Reynolds numbers up to 200 x 10(exp 6).

Stable and Spectrally Accurate Schemes for the Navier-Stokes Equations

DOE Office of Scientific and Technical Information (OSTI.GOV)

Jia, Jun; Liu, Jie

2011-01-01

In this paper, we present an accurate, efficient and stable numerical method for the incompressible Navier-Stokes equations (NSEs). The method is based on (1) an equivalent pressure Poisson equation formulation of the NSE with proper pressure boundary conditions, which facilitates the design of high-order and stable numerical methods, and (2) the Krylov deferred correction (KDC) accelerated method of lines transpose (mbox MoL{sup T}), which is very stable, efficient, and of arbitrary order in time. Numerical tests with known exact solutions in three dimensions show that the new method is spectrally accurate in time, and a numerical order of convergence 9more » was observed. Two-dimensional computational results of flow past a cylinder and flow in a bifurcated tube are also reported.« less

The Voronoi Implicit Interface Method for computing multiphase physics.

PubMed

Saye, Robert I; Sethian, James A

2011-12-06

We introduce a numerical framework, the Voronoi Implicit Interface Method for tracking multiple interacting and evolving regions (phases) whose motion is determined by complex physics (fluids, mechanics, elasticity, etc.), intricate jump conditions, internal constraints, and boundary conditions. The method works in two and three dimensions, handles tens of thousands of interfaces and separate phases, and easily and automatically handles multiple junctions, triple points, and quadruple points in two dimensions, as well as triple lines, etc., in higher dimensions. Topological changes occur naturally, with no surgery required. The method is first-order accurate at junction points/lines, and of arbitrarily high-order accuracy away from such degeneracies. The method uses a single function to describe all phases simultaneously, represented on a fixed Eulerian mesh. We test the method's accuracy through convergence tests, and demonstrate its applications to geometric flows, accurate prediction of von Neumann's law for multiphase curvature flow, and robustness under complex fluid flow with surface tension and large shearing forces.

Comparison of NACA 0012 Laminar Flow Solutions: Structured and Unstructured Grid Methods

NASA Technical Reports Server (NTRS)

Swanson, R. C.; Langer, S.

2016-01-01

In this paper we consider the solution of the compressible Navier-Stokes equations for a class of laminar airfoil flows. The principal objective of this paper is to demonstrate that members of this class of laminar flows have steady-state solutions. These laminar airfoil flow cases are often used to evaluate accuracy, stability and convergence of numerical solution algorithms for the Navier-Stokes equations. In recent years, such flows have also been used as test cases for high-order numerical schemes. While generally consistent steady-state solutions have been obtained for these flows using higher order schemes, a number of results have been published with various solutions, including unsteady ones. We demonstrate with two different numerical methods and a range of meshes with a maximum density that exceeds 8 × 106 grid points that steady-state solutions are obtained. Furthermore, numerical evidence is presented that even when solving the equations with an unsteady algorithm, one obtains steady-state solutions.

A robust, finite element model for hydrostatic surface water flows

USGS Publications Warehouse

Walters, R.A.; Casulli, V.

1998-01-01

A finite element scheme is introduced for the 2-dimensional shallow water equations using semi-implicit methods in time. A semi-Lagrangian method is used to approximate the effects of advection. A wave equation is formed at the discrete level such that the equations decouple into an equation for surface elevation and a momentum equation for the horizontal velocity. The convergence rates and relative computational efficiency are examined with the use of three test cases representing various degrees of difficulty. A test with a polar-quadrant grid investigates the response to local grid-scale forcing and the presence of spurious modes, a channel test case establishes convergence rates, and a field-scale test case examines problems with highly irregular grids.A finite element scheme is introduced for the 2-dimensional shallow water equations using semi-implicit methods in time. A semi-Lagrangian method is used to approximate the effects of advection. A wave equation is formed at the discrete level such that the equations decouple into an equation for surface elevation and a momentum equation for the horizontal velocity. The convergence rates and relative computational efficiency are examined with the use of three test cases representing various degrees of difficulty. A test with a polar-quadrant grid investigates the response to local grid-scale forcing and the presence of spurious modes, a channel test case establishes convergence rates, and a field-scale test case examines problems with highly irregular grids.

On improving the iterative convergence properties of an implicit approximate-factorization finite difference algorithm. [considering transonic flow

NASA Technical Reports Server (NTRS)

Desideri, J. A.; Steger, J. L.; Tannehill, J. C.

1978-01-01

The iterative convergence properties of an approximate-factorization implicit finite-difference algorithm are analyzed both theoretically and numerically. Modifications to the base algorithm were made to remove the inconsistency in the original implementation of artificial dissipation. In this way, the steady-state solution became independent of the time-step, and much larger time-steps can be used stably. To accelerate the iterative convergence, large time-steps and a cyclic sequence of time-steps were used. For a model transonic flow problem governed by the Euler equations, convergence was achieved with 10 times fewer time-steps using the modified differencing scheme. A particular form of instability due to variable coefficients is also analyzed.

Fast evolution of image manifolds and application to filtering and segmentation in 3D medical images.

PubMed

Deschamps, Thomas; Malladi, Ravi; Ravve, Igor

2004-01-01

In many instances, numerical integration of space-scale PDEs is the most time consuming operation of image processing. This is because the scale step is limited by conditional stability of explicit schemes. In this work, we introduce the unconditionally stable semi-implicit linearized difference scheme that is fashioned after additive operator split (AOS) [1], [2] for Beltrami and the subjective surface computation. The Beltrami flow [3], [4], [5] is one of the most effective denoising algorithms in image processing. For gray-level images, we show that the flow equation can be arranged in an advection-diffusion form, revealing the edge-enhancing properties of this flow. This also suggests the application of AOS method for faster convergence. The subjective surface [6] deals with constructing a perceptually meaningful interpretation from partial image data by mimicking the human visual system. However, initialization of the surface is critical for the final result and its main drawbacks are very slow convergence and the huge number of iterations required. In this paper, we first show that the governing equation for the subjective surface flow can be rearranged in an AOS implementation, providing a near real-time solution to the shape completion problem in 2D and 3D. Then, we devise a new initialization paradigm where we first "condition" the viewpoint surface using the Fast-Marching algorithm. We compare the original method with our new algorithm on several examples of real 3D medical images, thus revealing the improvement achieved.

A numerical solution for the diffusion equation in hydrogeologic systems

USGS Publications Warehouse

Ishii, A.L.; Healy, R.W.; Striegl, Robert G.

1989-01-01

The documentation of a computer code for the numerical solution of the linear diffusion equation in one or two dimensions in Cartesian or cylindrical coordinates is presented. Applications of the program include molecular diffusion, heat conduction, and fluid flow in confined systems. The flow media may be anisotropic and heterogeneous. The model is formulated by replacing the continuous linear diffusion equation by discrete finite-difference approximations at each node in a block-centered grid. The resulting matrix equation is solved by the method of preconditioned conjugate gradients. The conjugate gradient method does not require the estimation of iteration parameters and is guaranteed convergent in the absence of rounding error. The matrixes are preconditioned to decrease the steps to convergence. The model allows the specification of any number of boundary conditions for any number of stress periods, and the output of a summary table for selected nodes showing flux and the concentration of the flux quantity for each time step. The model is written in a modular format for ease of modification. The model was verified by comparison of numerical and analytical solutions for cases of molecular diffusion, two-dimensional heat transfer, and axisymmetric radial saturated fluid flow. Application of the model to a hypothetical two-dimensional field situation of gas diffusion in the unsaturated zone is demonstrated. The input and output files are included as a check on program installation. The definition of variables, input requirements, flow chart, and program listing are included in the attachments. (USGS)

Unsteady two dimensional airloads acting on oscillating thin airfoils in subsonic ventilated wind tunnels

NASA Technical Reports Server (NTRS)

Fromme, J.; Golberg, M.

1978-01-01

The numerical calculation of unsteady two dimensional airloads which act upon thin airfoils in subsonic ventilated wind tunnels was studied. Neglecting certain quadrature errors, Bland's collocation method is rigorously proved to converge to the mathematically exact solution of Bland's integral equation, and a three way equivalence was established between collocation, Galerkin's method and least squares whenever the collocation points are chosen to be the nodes of the quadrature rule used for Galerkin's method. A computer program displayed convergence with respect to the number of pressure basis functions employed, and agreement with known special cases was demonstrated. Results are obtained for the combined effects of wind tunnel wall ventilation and wind tunnel depth to airfoil chord ratio, and for acoustic resonance between the airfoil and wind tunnel walls. A boundary condition is proposed for permeable walls through which mass flow rate is proportional to pressure jump.

Numerical study of spherical Taylor-Couette flow

NASA Technical Reports Server (NTRS)

Yang, R.-J.

1989-01-01

A new technique to simulate Taylor vortices in a spherical gap between a rotating inner sphere and a stationary outer one has been developed and tested. Paths leading to zero-, one-, and two-vortex flows are designed heuristically. Fictitious symmetric boundaries near the equator are imposed, and the choice of the location of the fictitious boundaries is determined by either one- or two-vortex flow being stimulated. The imposition of one or two fictitious boundaries during the initial calculation generates the state suitable for one-or two-vortex flow to exist. After removing the fictitious boundaries, the flow settles down into its own attractor. Using this method, the three steady flow modes can be simulated by using a half domain. The technique can converge to desired flows very fast, and its results show excellent agreement with experimental ones.

Development of parallel algorithms for electrical power management in space applications

NASA Technical Reports Server (NTRS)

Berry, Frederick C.

1989-01-01

The application of parallel techniques for electrical power system analysis is discussed. The Newton-Raphson method of load flow analysis was used along with the decomposition-coordination technique to perform load flow analysis. The decomposition-coordination technique enables tasks to be performed in parallel by partitioning the electrical power system into independent local problems. Each independent local problem represents a portion of the total electrical power system on which a loan flow analysis can be performed. The load flow analysis is performed on these partitioned elements by using the Newton-Raphson load flow method. These independent local problems will produce results for voltage and power which can then be passed to the coordinator portion of the solution procedure. The coordinator problem uses the results of the local problems to determine if any correction is needed on the local problems. The coordinator problem is also solved by an iterative method much like the local problem. The iterative method for the coordination problem will also be the Newton-Raphson method. Therefore, each iteration at the coordination level will result in new values for the local problems. The local problems will have to be solved again along with the coordinator problem until some convergence conditions are met.

A quasi-Lagrangian finite element method for the Navier-Stokes equations in a time-dependent domain

NASA Astrophysics Data System (ADS)

Lozovskiy, Alexander; Olshanskii, Maxim A.; Vassilevski, Yuri V.

2018-05-01

The paper develops a finite element method for the Navier-Stokes equations of incompressible viscous fluid in a time-dependent domain. The method builds on a quasi-Lagrangian formulation of the problem. The paper provides stability and convergence analysis of the fully discrete (finite-difference in time and finite-element in space) method. The analysis does not assume any CFL time-step restriction, it rather needs mild conditions of the form $\\Delta t\\le C$, where $C$ depends only on problem data, and $h^{2m_u+2}\\le c\\,\\Delta t$, $m_u$ is polynomial degree of velocity finite element space. Both conditions result from a numerical treatment of practically important non-homogeneous boundary conditions. The theoretically predicted convergence rate is confirmed by a set of numerical experiments. Further we apply the method to simulate a flow in a simplified model of the left ventricle of a human heart, where the ventricle wall dynamics is reconstructed from a sequence of contrast enhanced Computed Tomography images.

Global Education Inc.: New Policy Networks and the Neoliberal Imaginary

ERIC Educational Resources Information Center

Ball, Stephen J.

2012-01-01

Do private and philanthropic solutions to the problems of education signal the end of state education in its "welfare" form? Education policy is being reformed and re-worked on a global scale. Policies are flowing and converging to produce a singular vision of "best practice" based on the methods and tenets of the "neo-liberal imaginary".…

Convergence acceleration of viscous flow computations

NASA Technical Reports Server (NTRS)

Johnson, G. M.

1982-01-01

A multiple-grid convergence acceleration technique introduced for application to the solution of the Euler equations by means of Lax-Wendroff algorithms is extended to treat compressible viscous flow. Computational results are presented for the solution of the thin-layer version of the Navier-Stokes equations using the explicit MacCormack algorithm, accelerated by a convective coarse-grid scheme. Extensions and generalizations are mentioned.

Calculation of laminar heating rates on three-dimensional configurations using the axisymmetric analogue

NASA Technical Reports Server (NTRS)

Hamilton, H. H., II

1980-01-01

A theoretical method was developed for computing approximate laminar heating rates on three dimensional configurations at angle of attack. The method is based on the axisymmetric analogue which is used to reduce the three dimensional boundary layer equations along surface streamlines to an equivalent axisymmetric form by using the metric coefficient which describes streamline divergence (or convergence). The method was coupled with a three dimensional inviscid flow field program for computing surface streamline paths, metric coefficients, and boundary layer edge conditions.

An artificial viscosity method for the design of supercritical airfoils

NASA Technical Reports Server (NTRS)

Mcfadden, G. B.

1979-01-01

A numerical technique is presented for the design of two-dimensional supercritical wing sections with low wave drag. The method is a design mode of the analysis code H which gives excellent agreement with experimental results and is widely used in the aircraft industry. Topics covered include the partial differential equations of transonic flow, the computational procedure and results; the design procedure; a convergence theorem; and description of the code.

Intensification and refraction of acoustical signals in partially choked converging ducts

NASA Technical Reports Server (NTRS)

Nayfeh, A. H.

1980-01-01

A computer code based on the wave-envelope technique is used to perform detailed numerical calculations for the intensification and refraction of sound in converging hard walled and lined circular ducts carrying high mean Mach number flows. The results show that converging ducts produce substantial refractions toward the duct center for waves propagating against near choked flows. As expected, the magnitude of the refraction decreases as the real part of the admittance increases. The pressure wave pattern is that of interference among the different modes, and hence the variation of the magnitude of pressure refraction with frequency is not monotonic.

Generalized conjugate-gradient methods for the Navier-Stokes equations

NASA Technical Reports Server (NTRS)

Ajmani, Kumud; Ng, Wing-Fai; Liou, Meng-Sing

1991-01-01

A generalized conjugate-gradient method is used to solve the two-dimensional, compressible Navier-Stokes equations of fluid flow. The equations are discretized with an implicit, upwind finite-volume formulation. Preconditioning techniques are incorporated into the new solver to accelerate convergence of the overall iterative method. The superiority of the new solver is demonstrated by comparisons with a conventional line Gauss-Siedel Relaxation solver. Computational test results for transonic flow (trailing edge flow in a transonic turbine cascade) and hypersonic flow (M = 6.0 shock-on-shock phenoena on a cylindrical leading edge) are presented. When applied to the transonic cascade case, the new solver is 4.4 times faster in terms of number of iterations and 3.1 times faster in terms of CPU time than the Relaxation solver. For the hypersonic shock case, the new solver is 3.0 times faster in terms of number of iterations and 2.2 times faster in terms of CPU time than the Relaxation solver.

Some calculations of transonic potential flow for the NACA 64A006 airfoil with oscillating flap

NASA Technical Reports Server (NTRS)

Bennett, R. M.; Bland, S. R.

1978-01-01

A method for calculating the transonic flow over steady and oscillating airfoils was developed by Isogai. It solves the full potential equation with a semi-implicit, time-marching, finite difference technique. Steady flow solutions are obtained from time asymptotic solutions for a steady airfoil. Corresponding oscillatory solutions are obtained by initiating an oscillation and marching in time for several cycles until a converged periodic solution is achieved. In this paper the method is described in general terms, and results are compared with experimental data for both steady flow and for oscillations at several values of reduced frequency. Good agreement for static pressures is shown for subcritical speeds, with increasing deviation as Mach number is increased into the supercritical speed range. Fair agreement with experiment was obtained at high reduced frequencies with larger deviations at low reduced frequencies.

Developing and utilizing an Euler computational method for predicting the airframe/propulsion effects for an aft-mounted turboprop transport. Volume 1: Theory document

NASA Technical Reports Server (NTRS)

Chen, H. C.; Yu, N. Y.

1991-01-01

An Euler flow solver was developed for predicting the airframe/propulsion integration effects for an aft-mounted turboprop transport. This solver employs a highly efficient multigrid scheme, with a successive mesh-refinement procedure to accelerate the convergence of the solution. A new dissipation model was also implemented to render solutions that are grid insensitive. The propeller power effects are simulated by the actuator disk concept. An embedded flow solution method was developed for predicting the detailed flow characteristics in the local vicinity of an aft-mounted propfan engine in the presence of a flow field induced by a complete aircraft. Results from test case analysis are presented. A user's guide for execution of computer programs, including format of various input files, sample job decks, and sample input files, is provided in an accompanying volume.

Dynamic ADMM for Real-Time Optimal Power Flow

DOE Office of Scientific and Technical Information (OSTI.GOV)

Dall-Anese, Emiliano; Zhang, Yijian; Hong, Mingyi

This paper considers distribution networks featuring distributed energy resources (DERs), and develops a dynamic optimization method to maximize given operational objectives in real time while adhering to relevant network constraints. The design of the dynamic algorithm is based on suitable linearization of the AC power flow equations, and it leverages the so-called alternating direction method of multipliers (ADMM). The steps of the ADMM, however, are suitably modified to accommodate appropriate measurements from the distribution network and the DERs. With the aid of these measurements, the resultant algorithm can enforce given operational constraints in spite of inaccuracies in the representation ofmore » the AC power flows, and it avoids ubiquitous metering to gather the state of noncontrollable resources. Optimality and convergence of the proposed algorithm are established in terms of tracking of the solution of a convex surrogate of the AC optimal power flow problem.« less

Dynamic ADMM for Real-Time Optimal Power Flow: Preprint

DOE Office of Scientific and Technical Information (OSTI.GOV)

Dall-Anese, Emiliano; Zhang, Yijian; Hong, Mingyi

This paper considers distribution networks featuring distributed energy resources (DERs), and develops a dynamic optimization method to maximize given operational objectives in real time while adhering to relevant network constraints. The design of the dynamic algorithm is based on suitable linearizations of the AC power flow equations, and it leverages the so-called alternating direction method of multipliers (ADMM). The steps of the ADMM, however, are suitably modified to accommodate appropriate measurements from the distribution network and the DERs. With the aid of these measurements, the resultant algorithm can enforce given operational constraints in spite of inaccuracies in the representation ofmore » the AC power flows, and it avoids ubiquitous metering to gather the state of non-controllable resources. Optimality and convergence of the propose algorithm are established in terms of tracking of the solution of a convex surrogate of the AC optimal power flow problem.« less

Methods of computing steady-state voltage stability margins of power systems

DOEpatents

Chow, Joe Hong; Ghiocel, Scott Gordon

2018-03-20

In steady-state voltage stability analysis, as load increases toward a maximum, conventional Newton-Raphson power flow Jacobian matrix becomes increasingly ill-conditioned so power flow fails to converge before reaching maximum loading. A method to directly eliminate this singularity reformulates the power flow problem by introducing an AQ bus with specified bus angle and reactive power consumption of a load bus. For steady-state voltage stability analysis, the angle separation between the swing bus and AQ bus can be varied to control power transfer to the load, rather than specifying the load power itself. For an AQ bus, the power flow formulation is only made up of a reactive power equation, thus reducing the size of the Jacobian matrix by one. This reduced Jacobian matrix is nonsingular at the critical voltage point, eliminating a major difficulty in voltage stability analysis for power system operations.

Finite analytic numerical solution of heat transfer and flow past a square channel cavity

NASA Technical Reports Server (NTRS)

Chen, C.-J.; Obasih, K.

1982-01-01

A numerical solution of flow and heat transfer characteristics is obtained by the finite analytic method for a two dimensional laminar channel flow over a two-dimensional square cavity. The finite analytic method utilizes the local analytic solution in a small element of the problem region to form the algebraic equation relating an interior nodal value with its surrounding nodal values. Stable and rapidly converged solutions were obtained for Reynolds numbers ranging to 1000 and Prandtl number to 10. Streamfunction, vorticity and temperature profiles are solved. Local and mean Nusselt number are given. It is found that the separation streamlines between the cavity and channel flow are concave into the cavity at low Reynolds number and convex at high Reynolds number (Re greater than 100) and for square cavity the mean Nusselt number may be approximately correlated with Peclet number as Nu(m) = 0.365 Pe exp 0.2.

On transonic flow past a wave-shaped wall

NASA Technical Reports Server (NTRS)

Kaplan, Carl

1953-01-01

This report is an extension of a previous investigation (described in NACA rep. 1069) concerned with the solution of the nonlinear differential equation for transonic flow past a wavy wall. In the present work several new notions are introduced which permit the solution of the recursion formulas arising from the method of integration in series. In addition, a novel numerical tests of convergence, applied to the power series (in transonic similarity parameter) representing the local Mach number distribution at the boundary, indicates that smooth symmetrical potential flow past the wavy wall is no longer possible once the critical value of the stream Mach number has been exceeded.

Flow of nanofluid by nonlinear stretching velocity

NASA Astrophysics Data System (ADS)

Hayat, Tasawar; Rashid, Madiha; Alsaedi, Ahmed; Ahmad, Bashir

2018-03-01

Main objective in this article is to model and analyze the nanofluid flow induced by curved surface with nonlinear stretching velocity. Nanofluid comprises water and silver. Governing problem is solved by using homotopy analysis method (HAM). Induced magnetic field for low magnetic Reynolds number is not entertained. Development of convergent series solutions for velocity and skin friction coefficient is successfully made. Pressure in the boundary layer flow by curved stretching surface cannot be ignored. It is found that magnitude of power-law index parameter increases for pressure distibutions. Magnitude of radius of curvature reduces for pressure field while opposite trend can be observed for velocity.

Application of color Doppler flow mapping to calculate orifice area of St Jude mitral valve

NASA Technical Reports Server (NTRS)

Leung, D. Y.; Wong, J.; Rodriguez, L.; Pu, M.; Vandervoort, P. M.; Thomas, J. D.

1998-01-01

BACKGROUND: The effective orifice area (EOA) of a prosthetic valve is superior to transvalvular gradients as a measure of valve function, but measurement of mitral prosthesis EOA has not been reliable. METHODS AND RESULTS: In vitro flow across St Jude valves was calculated by hemispheric proximal isovelocity surface area (PISA) and segment-of-spheroid (SOS) methods. For steady and pulsatile conditions, PISA and SOS flows correlated with true flow, but SOS and not PISA underestimated flow. These principles were then used intraoperatively to calculate cardiac output and EOA of newly implanted St Jude mitral valves in 36 patients. Cardiac output by PISA agreed closely with thermodilution (r=0.91, Delta=-0.05+/-0.55 L/min), but SOS underestimated it (r=0.82, Delta=-1.33+/-0.73 L/min). Doppler EOAs correlated with Gorlin equation estimates (r=0.75 for PISA and r=0.68 for SOS, P<0.001) but were smaller than corresponding in vitro EOA estimates. CONCLUSIONS: Proximal flow convergence methods can calculate forward flow and estimate EOA of St Jude mitral valves, which may improve noninvasive assessment of prosthetic mitral valve obstruction.

An exploratory study of a finite difference method for calculating unsteady transonic potential flow

NASA Technical Reports Server (NTRS)

Bennett, R. M.; Bland, S. R.

1979-01-01

A method for calculating transonic flow over steady and oscillating airfoils was developed by Isogai. The full potential equation is solved with a semi-implicit, time-marching, finite difference technique. Steady flow solutions are obtained from time asymptotic solutions for a steady airfoil. Corresponding oscillatory solutions are obtained by initiating an oscillation and marching in time for several cycles until a converged periodic solution is achieved. The method is described in general terms and results for the case of an airfoil with an oscillating flap are presented for Mach numbers 0.500 and 0.875. Although satisfactory results are obtained for some reduced frequencies, it is found that the numerical technique generates spurious oscillations in the indicial response functions and in the variation of the aerodynamic coefficients with reduced frequency. These oscillations are examined with a dynamic data reduction method to evaluate their effects and trends with reduced frequency and Mach number. Further development of the numerical method is needed to eliminate these oscillations.

The Voronoi Implicit Interface Method for computing multiphase physics

PubMed Central

Saye, Robert I.; Sethian, James A.

2011-01-01

We introduce a numerical framework, the Voronoi Implicit Interface Method for tracking multiple interacting and evolving regions (phases) whose motion is determined by complex physics (fluids, mechanics, elasticity, etc.), intricate jump conditions, internal constraints, and boundary conditions. The method works in two and three dimensions, handles tens of thousands of interfaces and separate phases, and easily and automatically handles multiple junctions, triple points, and quadruple points in two dimensions, as well as triple lines, etc., in higher dimensions. Topological changes occur naturally, with no surgery required. The method is first-order accurate at junction points/lines, and of arbitrarily high-order accuracy away from such degeneracies. The method uses a single function to describe all phases simultaneously, represented on a fixed Eulerian mesh. We test the method’s accuracy through convergence tests, and demonstrate its applications to geometric flows, accurate prediction of von Neumann’s law for multiphase curvature flow, and robustness under complex fluid flow with surface tension and large shearing forces. PMID:22106269

The Voronoi Implicit Interface Method for computing multiphase physics

DOE PAGES

Saye, Robert I.; Sethian, James A.

2011-11-21

In this paper, we introduce a numerical framework, the Voronoi Implicit Interface Method for tracking multiple interacting and evolving regions (phases) whose motion is determined by complex physics (fluids, mechanics, elasticity, etc.), intricate jump conditions, internal constraints, and boundary conditions. The method works in two and three dimensions, handles tens of thousands of interfaces and separate phases, and easily and automatically handles multiple junctions, triple points, and quadruple points in two dimensions, as well as triple lines, etc., in higher dimensions. Topological changes occur naturally, with no surgery required. The method is first-order accurate at junction points/lines, and of arbitrarilymore » high-order accuracy away from such degeneracies. The method uses a single function to describe all phases simultaneously, represented on a fixed Eulerian mesh. Finally, we test the method’s accuracy through convergence tests, and demonstrate its applications to geometric flows, accurate prediction of von Neumann’s law for multiphase curvature flow, and robustness under complex fluid flow with surface tension and large shearing forces.« less

A locally conservative stabilized continuous Galerkin finite element method for two-phase flow in poroelastic subsurfaces

NASA Astrophysics Data System (ADS)

Deng, Q.; Ginting, V.; McCaskill, B.; Torsu, P.

2017-10-01

We study the application of a stabilized continuous Galerkin finite element method (CGFEM) in the simulation of multiphase flow in poroelastic subsurfaces. The system involves a nonlinear coupling between the fluid pressure, subsurface's deformation, and the fluid phase saturation, and as such, we represent this coupling through an iterative procedure. Spatial discretization of the poroelastic system employs the standard linear finite element in combination with a numerical diffusion term to maintain stability of the algebraic system. Furthermore, direct calculation of the normal velocities from pressure and deformation does not entail a locally conservative field. To alleviate this drawback, we propose an element based post-processing technique through which local conservation can be established. The performance of the method is validated through several examples illustrating the convergence of the method, the effectivity of the stabilization term, and the ability to achieve locally conservative normal velocities. Finally, the efficacy of the method is demonstrated through simulations of realistic multiphase flow in poroelastic subsurfaces.

Long-time uncertainty propagation using generalized polynomial chaos and flow map composition

DOE Office of Scientific and Technical Information (OSTI.GOV)

Luchtenburg, Dirk M., E-mail: dluchten@cooper.edu; Brunton, Steven L.; Rowley, Clarence W.

2014-10-01

We present an efficient and accurate method for long-time uncertainty propagation in dynamical systems. Uncertain initial conditions and parameters are both addressed. The method approximates the intermediate short-time flow maps by spectral polynomial bases, as in the generalized polynomial chaos (gPC) method, and uses flow map composition to construct the long-time flow map. In contrast to the gPC method, this approach has spectral error convergence for both short and long integration times. The short-time flow map is characterized by small stretching and folding of the associated trajectories and hence can be well represented by a relatively low-degree basis. The compositionmore » of these low-degree polynomial bases then accurately describes the uncertainty behavior for long integration times. The key to the method is that the degree of the resulting polynomial approximation increases exponentially in the number of time intervals, while the number of polynomial coefficients either remains constant (for an autonomous system) or increases linearly in the number of time intervals (for a non-autonomous system). The findings are illustrated on several numerical examples including a nonlinear ordinary differential equation (ODE) with an uncertain initial condition, a linear ODE with an uncertain model parameter, and a two-dimensional, non-autonomous double gyre flow.« less

New discretization and solution techniques for incompressible viscous flow problems

NASA Technical Reports Server (NTRS)

Gunzburger, M. D.; Nicolaides, R. A.; Liu, C. H.

1983-01-01

Several topics arising in the finite element solution of the incompressible Navier-Stokes equations are considered. Specifically, the question of choosing finite element velocity/pressure spaces is addressed, particularly from the viewpoint of achieving stable discretizations leading to convergent pressure approximations. The role of artificial viscosity in viscous flow calculations is studied, emphasizing work by several researchers for the anisotropic case. The last section treats the problem of solving the nonlinear systems of equations which arise from the discretization. Time marching methods and classical iterative techniques, as well as some modifications are mentioned.

Prandtl-Meyer flow tables for parahydrogen at total temperatures from 30K to 290K and for nitrogen at total temperatures from 100K to 300K at total pressures from 1 ATM to 10 ATM

NASA Technical Reports Server (NTRS)

Haut, R. C.; Adcock, J. B.

1976-01-01

The dependency of Mach number on the Prandtl-Meyer function was numerically determined by iterating the Prandtl-Meyer function and applying the Muller method to converge on the Mach number for flows in cryogenic parahydrogen and nitrogen at various total pressures and total temperatures. The results are compared with the ideal diatomic gas values and are presented in tabular form.

Gas levitator having fixed levitation node for containerless processing

NASA Technical Reports Server (NTRS)

Berge, L. H.; Oran, W. A.; Theiss, M. (Inventor)

1981-01-01

A method and apparatus is disclosed for levitating a specimen of material in a containerless environment at a stable nodal position independent of gravity. An elongated levitation tube has a contoured interior in the form of convergent section, constriction, and a divergent section in which the levitation node is created. A gas flow control means prevents separation of flow from the interior walls in the region of a specimen. The apparatus provides for levitating and heating the specimen simultaneously by combustion of a suitable gas mixture combined with an inert gas.

Computation of three-dimensional three-phase flow of carbon dioxide using a high-order WENO scheme

NASA Astrophysics Data System (ADS)

Gjennestad, Magnus Aa.; Gruber, Andrea; Lervåg, Karl Yngve; Johansen, Øyvind; Ervik, Åsmund; Hammer, Morten; Munkejord, Svend Tollak

2017-11-01

We have developed a high-order numerical method for the 3D simulation of viscous and inviscid multiphase flow described by a homogeneous equilibrium model and a general equation of state. Here we focus on single-phase, two-phase (gas-liquid or gas-solid) and three-phase (gas-liquid-solid) flow of CO2 whose thermodynamic properties are calculated using the Span-Wagner reference equation of state. The governing equations are spatially discretized on a uniform Cartesian grid using the finite-volume method with a fifth-order weighted essentially non-oscillatory (WENO) scheme and the robust first-order centered (FORCE) flux. The solution is integrated in time using a third-order strong-stability-preserving Runge-Kutta method. We demonstrate close to fifth-order convergence for advection-diffusion and for smooth single- and two-phase flows. Quantitative agreement with experimental data is obtained for a direct numerical simulation of an air jet flowing from a rectangular nozzle. Quantitative agreement is also obtained for the shape and dimensions of the barrel shock in two highly underexpanded CO2 jets.

Interaction of strong converging shock wave with SF6 gas bubble

NASA Astrophysics Data System (ADS)

Liang, Yu; Zhai, ZhiGang; Luo, XiSheng

2018-06-01

Interaction of a strong converging shock wave with an SF6 gas bubble is studied, focusing on the effects of shock intensity and shock shape on interface evolution. Experimentally, the converging shock wave is generated by shock dynamics theory and the gas bubble is created by soap film technique. The post-shock flow field is captured by a schlieren photography combined with a high-speed video camera. Besides, a three-dimensional program is adopted to provide more details of flow field. After the strong converging shock wave impact, a wide and pronged outward jet, which differs from that in planar shock or weak converging shock condition, is derived from the downstream interface pole. This specific phenomenon is considered to be closely associated with shock intensity and shock curvature. Disturbed by the gas bubble, the converging shocks approaching the convergence center have polygonal shapes, and the relationship between shock intensity and shock radius verifies the applicability of polygonal converging shock theory. Subsequently, the motion of upstream point is discussed, and a modified nonlinear theory considering rarefaction wave and high amplitude effects is proposed. In addition, the effects of shock shape on interface morphology and interface scales are elucidated. These results indicate that the shape as well as shock strength plays an important role in interface evolution.

Darcy-Forchheimer Three-Dimensional Flow of Williamson Nanofluid over a Convectively Heated Nonlinear Stretching Surface

NASA Astrophysics Data System (ADS)

Hayat, Tasawar; Aziz, Arsalan; Muhammad, Taseer; Alsaedi, Ahmed

2017-09-01

The present study elaborates three-dimensional flow of Williamson nanoliquid over a nonlinear stretchable surface. Fluid flow obeys Darcy-Forchheimer porous medium. A bidirectional nonlinear stretching surface generates the flow. Convective surface condition of heat transfer is taken into consideration. Further the zero nanoparticles mass flux condition is imposed at the boundary. Effects of thermophoresis and Brownian diffusion are considered. Assumption of boundary layer has been employed in the problem formulation. Convergent series solutions for the nonlinear governing system are established through the optimal homotopy analysis method (OHAM). Graphs have been sketched in order to analyze that how the velocity, temperature and concentration distributions are affected by distinct emerging flow parameters. Skin friction coefficients and local Nusselt number are also computed and discussed.

Comparison of experimental surface pressures with theoretical predictions on twin two-dimensional convergent-divergent nozzles

NASA Technical Reports Server (NTRS)

Carlson, J. R.; Pendergraft, O. C., Jr.; Burley, J. R., II

1986-01-01

A three-dimensional subsonic aerodynamic panel code (VSAERO) was used to predict the effects of upper and lower external nozzle flap geometry on the external afterbody/nozzle pressure coefficient distributions and external nozzle drag of nonaxisymmetric convergent-divergent exhaust nozzles having parallel external sidewalls installed on a generic twin-engine high performance aircraft model. Nozzle static pressure coefficient distributions along the upper and lower surfaces near the model centerline and near the outer edges (corner) of the two surfaces were calculated, and nozzle drag was predicted using these surface pressure distributions. A comparison between the theoretical predictions and experimental wind tunnel data is made to evaluate the utility of the code in calculating the flow about these types of non-axisymmetric afterbody configurations. For free-stream Mach numbers of 0.60 and 0.90, the conditions where the flows were attached on the boattails yielded the best comparison between the theoretical predictions and the experimental data. For the Boattail terminal angles of greater than 15 deg., the experimental data for M = 0.60 and 0.90 indicated areas of separated flow, so the theoretical predictions failed to match the experimental data. Even though calculations of regions of separated flows are within the capabilities of the theoretical method, acceptable solutions were not obtained.

Wavelets solution of MHD 3-D fluid flow in the presence of slip and thermal radiation effects

NASA Astrophysics Data System (ADS)

Usman, M.; Zubair, T.; Hamid, M.; Haq, Rizwan Ul; Wang, Wei

2018-02-01

This article is devoted to analyze the magnetic field, slip, and thermal radiations effects on generalized three-dimensional flow, heat, and mass transfer in a channel of lower stretching wall. We supposed two various lateral direction rates for the lower stretching surface of the wall while the upper wall of the channel is subjected to constant injection. Moreover, influence of thermal slip on the temperature profile beside the viscous dissipation and Joule heating is also taken into account. The governing set of partial differential equations of the heat transfer and flow are transformed to nonlinear set of ordinary differential equations (ODEs) by using the compatible similarity transformations. The obtained nonlinear ODE set tackled by means of a new wavelet algorithm. The outcomes obtained via modified Chebyshev wavelet method are compared with Runge-Kutta (order-4). The worthy comparison, error, and convergence analysis shows an excellent agreement. Additionally, the graphical representation for various physical parameters including the skin friction coefficient, velocity, the temperature gradient, and the temperature profiles are plotted and discussed. It is observed that for a fixed value of velocity slip parameter a suitable selection of stretching ratio parameter can be helpful in hastening the heat transfer rate and in reducing the viscous drag over the stretching sheet. Finally, the convergence analysis is performed which endorsing that this proposed method is well efficient.

A Newton-Krylov method with an approximate analytical Jacobian for implicit solution of Navier-Stokes equations on staggered overset-curvilinear grids with immersed boundaries.

PubMed

Asgharzadeh, Hafez; Borazjani, Iman

2017-02-15

The explicit and semi-implicit schemes in flow simulations involving complex geometries and moving boundaries suffer from time-step size restriction and low convergence rates. Implicit schemes can be used to overcome these restrictions, but implementing them to solve the Navier-Stokes equations is not straightforward due to their non-linearity. Among the implicit schemes for nonlinear equations, Newton-based techniques are preferred over fixed-point techniques because of their high convergence rate but each Newton iteration is more expensive than a fixed-point iteration. Krylov subspace methods are one of the most advanced iterative methods that can be combined with Newton methods, i.e., Newton-Krylov Methods (NKMs) to solve non-linear systems of equations. The success of NKMs vastly depends on the scheme for forming the Jacobian, e.g., automatic differentiation is very expensive, and matrix-free methods without a preconditioner slow down as the mesh is refined. A novel, computationally inexpensive analytical Jacobian for NKM is developed to solve unsteady incompressible Navier-Stokes momentum equations on staggered overset-curvilinear grids with immersed boundaries. Moreover, the analytical Jacobian is used to form preconditioner for matrix-free method in order to improve its performance. The NKM with the analytical Jacobian was validated and verified against Taylor-Green vortex, inline oscillations of a cylinder in a fluid initially at rest, and pulsatile flow in a 90 degree bend. The capability of the method in handling complex geometries with multiple overset grids and immersed boundaries is shown by simulating an intracranial aneurysm. It was shown that the NKM with an analytical Jacobian is 1.17 to 14.77 times faster than the fixed-point Runge-Kutta method, and 1.74 to 152.3 times (excluding an intensively stretched grid) faster than automatic differentiation depending on the grid (size) and the flow problem. In addition, it was shown that using only the diagonal of the Jacobian further improves the performance by 42 - 74% compared to the full Jacobian. The NKM with an analytical Jacobian showed better performance than the fixed point Runge-Kutta because it converged with higher time steps and in approximately 30% less iterations even when the grid was stretched and the Reynold number was increased. In fact, stretching the grid decreased the performance of all methods, but the fixed-point Runge-Kutta performance decreased 4.57 and 2.26 times more than NKM with a diagonal Jacobian when the stretching factor was increased, respectively. The NKM with a diagonal analytical Jacobian and matrix-free method with an analytical preconditioner are the fastest methods and the superiority of one to another depends on the flow problem. Furthermore, the implemented methods are fully parallelized with parallel efficiency of 80-90% on the problems tested. The NKM with the analytical Jacobian can guide building preconditioners for other techniques to improve their performance in the future.

A Newton–Krylov method with an approximate analytical Jacobian for implicit solution of Navier–Stokes equations on staggered overset-curvilinear grids with immersed boundaries

PubMed Central

Asgharzadeh, Hafez; Borazjani, Iman

2016-01-01

The explicit and semi-implicit schemes in flow simulations involving complex geometries and moving boundaries suffer from time-step size restriction and low convergence rates. Implicit schemes can be used to overcome these restrictions, but implementing them to solve the Navier-Stokes equations is not straightforward due to their non-linearity. Among the implicit schemes for nonlinear equations, Newton-based techniques are preferred over fixed-point techniques because of their high convergence rate but each Newton iteration is more expensive than a fixed-point iteration. Krylov subspace methods are one of the most advanced iterative methods that can be combined with Newton methods, i.e., Newton-Krylov Methods (NKMs) to solve non-linear systems of equations. The success of NKMs vastly depends on the scheme for forming the Jacobian, e.g., automatic differentiation is very expensive, and matrix-free methods without a preconditioner slow down as the mesh is refined. A novel, computationally inexpensive analytical Jacobian for NKM is developed to solve unsteady incompressible Navier-Stokes momentum equations on staggered overset-curvilinear grids with immersed boundaries. Moreover, the analytical Jacobian is used to form preconditioner for matrix-free method in order to improve its performance. The NKM with the analytical Jacobian was validated and verified against Taylor-Green vortex, inline oscillations of a cylinder in a fluid initially at rest, and pulsatile flow in a 90 degree bend. The capability of the method in handling complex geometries with multiple overset grids and immersed boundaries is shown by simulating an intracranial aneurysm. It was shown that the NKM with an analytical Jacobian is 1.17 to 14.77 times faster than the fixed-point Runge-Kutta method, and 1.74 to 152.3 times (excluding an intensively stretched grid) faster than automatic differentiation depending on the grid (size) and the flow problem. In addition, it was shown that using only the diagonal of the Jacobian further improves the performance by 42 – 74% compared to the full Jacobian. The NKM with an analytical Jacobian showed better performance than the fixed point Runge-Kutta because it converged with higher time steps and in approximately 30% less iterations even when the grid was stretched and the Reynold number was increased. In fact, stretching the grid decreased the performance of all methods, but the fixed-point Runge-Kutta performance decreased 4.57 and 2.26 times more than NKM with a diagonal Jacobian when the stretching factor was increased, respectively. The NKM with a diagonal analytical Jacobian and matrix-free method with an analytical preconditioner are the fastest methods and the superiority of one to another depends on the flow problem. Furthermore, the implemented methods are fully parallelized with parallel efficiency of 80–90% on the problems tested. The NKM with the analytical Jacobian can guide building preconditioners for other techniques to improve their performance in the future. PMID:28042172

A Newton-Krylov method with an approximate analytical Jacobian for implicit solution of Navier-Stokes equations on staggered overset-curvilinear grids with immersed boundaries

NASA Astrophysics Data System (ADS)

Asgharzadeh, Hafez; Borazjani, Iman

2017-02-01

The explicit and semi-implicit schemes in flow simulations involving complex geometries and moving boundaries suffer from time-step size restriction and low convergence rates. Implicit schemes can be used to overcome these restrictions, but implementing them to solve the Navier-Stokes equations is not straightforward due to their non-linearity. Among the implicit schemes for non-linear equations, Newton-based techniques are preferred over fixed-point techniques because of their high convergence rate but each Newton iteration is more expensive than a fixed-point iteration. Krylov subspace methods are one of the most advanced iterative methods that can be combined with Newton methods, i.e., Newton-Krylov Methods (NKMs) to solve non-linear systems of equations. The success of NKMs vastly depends on the scheme for forming the Jacobian, e.g., automatic differentiation is very expensive, and matrix-free methods without a preconditioner slow down as the mesh is refined. A novel, computationally inexpensive analytical Jacobian for NKM is developed to solve unsteady incompressible Navier-Stokes momentum equations on staggered overset-curvilinear grids with immersed boundaries. Moreover, the analytical Jacobian is used to form a preconditioner for matrix-free method in order to improve its performance. The NKM with the analytical Jacobian was validated and verified against Taylor-Green vortex, inline oscillations of a cylinder in a fluid initially at rest, and pulsatile flow in a 90 degree bend. The capability of the method in handling complex geometries with multiple overset grids and immersed boundaries is shown by simulating an intracranial aneurysm. It was shown that the NKM with an analytical Jacobian is 1.17 to 14.77 times faster than the fixed-point Runge-Kutta method, and 1.74 to 152.3 times (excluding an intensively stretched grid) faster than automatic differentiation depending on the grid (size) and the flow problem. In addition, it was shown that using only the diagonal of the Jacobian further improves the performance by 42-74% compared to the full Jacobian. The NKM with an analytical Jacobian showed better performance than the fixed point Runge-Kutta because it converged with higher time steps and in approximately 30% less iterations even when the grid was stretched and the Reynold number was increased. In fact, stretching the grid decreased the performance of all methods, but the fixed-point Runge-Kutta performance decreased 4.57 and 2.26 times more than NKM with a diagonal and full Jacobian, respectivley, when the stretching factor was increased. The NKM with a diagonal analytical Jacobian and matrix-free method with an analytical preconditioner are the fastest methods and the superiority of one to another depends on the flow problem. Furthermore, the implemented methods are fully parallelized with parallel efficiency of 80-90% on the problems tested. The NKM with the analytical Jacobian can guide building preconditioners for other techniques to improve their performance in the future.

Method for transition prediction in high-speed boundary layers, phase 2

NASA Astrophysics Data System (ADS)

Herbert, T.; Stuckert, G. K.; Lin, N.

1993-09-01

The parabolized stability equations (PSE) are a new and more reliable approach to analyzing the stability of streamwise varying flows such as boundary layers. This approach has been previously validated for idealized incompressible flows. Here, the PSE are formulated for highly compressible flows in general curvilinear coordinates to permit the analysis of high-speed boundary-layer flows over fairly general bodies. Vigorous numerical studies are carried out to study convergence and accuracy of the linear-stability code LSH and the linear/nonlinear PSE code PSH. Physical interfaces are set up to analyze the M = 8 boundary layer over a blunt cone calculated by using a thin-layer Navier Stokes (TNLS) code and the flow over a sharp cone at angle of attack calculated using the AFWAL parabolized Navier-Stokes (PNS) code. While stability and transition studies at high speeds are far from routine, the method developed here is the best tool available to research the physical processes in high-speed boundary layers.

Numerical methods for multi-scale modeling of non-Newtonian flows

NASA Astrophysics Data System (ADS)

Symeonidis, Vasileios

This work presents numerical methods for the simulation of Non-Newtonian fluids in the continuum as well as the mesoscopic level. The former is achieved with Direct Numerical Simulation (DNS) spectral h/p methods, while the latter employs the Dissipative Particle Dynamics (DPD) technique. Physical results are also presented as a motivation for a clear understanding of the underlying numerical approaches. The macroscopic simulations employ two non-Newtonian models, namely the Reiner-Ravlin (RR) and the viscoelastic FENE-P model. (1) A spectral viscosity method defined by two parameters ε, M is used to stabilize the FENE-P conformation tensor c. Convergence studies are presented for different combinations of these parameters. Two boundary conditions for the tensor c are also investigated. (2) Agreement is achieved with other works for Stokes flow of a two-dimensional cylinder in a channel. Comparison of the axial normal stress and drag coefficient on the cylinder is presented. Further, similar results from unsteady two- and three-dimensional turbulent flows past a flat plate in a channel are shown. (3) The RR problem is formulated for nearly incompressible flows, with the introduction of a mathematically equivalent tensor formulation. A spectral viscosity method and polynomial over-integration are studied. Convergence studies, including a three-dimensional channel flow with a parallel slot, investigate numerical problems arising from elemental boundaries and sharp corners. (4) The round hole pressure problem is presented for Newtonian and RR fluids in geometries with different hole sizes. Comparison with experimental data is made for the Newtonian case. The flaw in the experimental assumptions of undisturbed pressure opposite the hole is revealed, while good agreement with the data is shown. The Higashitani-Pritchard kinematical theory for RR, fluids is recovered for round holes and an approximate formula for the RR Stokes hole pressure is presented. The mesoscopic simulations assume bead-spring representations of polymer chains and investigate different integrating schemes of the DPD equations and different intra-polymer force combinations. (1) A novel family of time-staggered integrators is presented, taking advantage of the time-scale disparity between polymer-solvent and solvent-solvent interactions. Convergence tests for relaxation parameters for the velocity-Verlet and Lowe's schemes are presented. (2) Wormlike chains simulating lambda- DNA molecules subject to constant shear are studied, and direct comparison with Brownian Dynamics and experimental results is made. The effect of the number of beads per chain is examined through the extension autocorrelation function. (3) The Schmidt number (Sc) for each numerical scheme is investigated and the dependence on the scheme's parameters is shown. Re-visiting the wormlike chain problem under shear, we recover a better agreement with the experimental data through proper adjustment of Sc.

Progress with multigrid schemes for hypersonic flow problems

NASA Technical Reports Server (NTRS)

Radespiel, R.; Swanson, R. C.

1991-01-01

Several multigrid schemes are considered for the numerical computation of viscous hypersonic flows. For each scheme, the basic solution algorithm uses upwind spatial discretization with explicit multistage time stepping. Two level versions of the various multigrid algorithms are applied to the two dimensional advection equation, and Fourier analysis is used to determine their damping properties. The capabilities of the multigrid methods are assessed by solving three different hypersonic flow problems. Some new multigrid schemes based on semicoarsening strategies are shown to be quite effective in relieving the stiffness caused by the high aspect ratio cells required to resolve high Reynolds number flows. These schemes exhibit good convergence rates for Reynolds numbers up to 200 x 10(exp 6) and Mach numbers up to 25.

Semi-implicit iterative methods for low Mach number turbulent reacting flows: Operator splitting versus approximate factorization

NASA Astrophysics Data System (ADS)

MacArt, Jonathan F.; Mueller, Michael E.

2016-12-01

Two formally second-order accurate, semi-implicit, iterative methods for the solution of scalar transport-reaction equations are developed for Direct Numerical Simulation (DNS) of low Mach number turbulent reacting flows. The first is a monolithic scheme based on a linearly implicit midpoint method utilizing an approximately factorized exact Jacobian of the transport and reaction operators. The second is an operator splitting scheme based on the Strang splitting approach. The accuracy properties of these schemes, as well as their stability, cost, and the effect of chemical mechanism size on relative performance, are assessed in two one-dimensional test configurations comprising an unsteady premixed flame and an unsteady nonpremixed ignition, which have substantially different Damköhler numbers and relative stiffness of transport to chemistry. All schemes demonstrate their formal order of accuracy in the fully-coupled convergence tests. Compared to a (non-)factorized scheme with a diagonal approximation to the chemical Jacobian, the monolithic, factorized scheme using the exact chemical Jacobian is shown to be both more stable and more economical. This is due to an improved convergence rate of the iterative procedure, and the difference between the two schemes in convergence rate grows as the time step increases. The stability properties of the Strang splitting scheme are demonstrated to outpace those of Lie splitting and monolithic schemes in simulations at high Damköhler number; however, in this regime, the monolithic scheme using the approximately factorized exact Jacobian is found to be the most economical at practical CFL numbers. The performance of the schemes is further evaluated in a simulation of a three-dimensional, spatially evolving, turbulent nonpremixed planar jet flame.

An Upwind Multigrid Algorithm for Calculating Flows on Unstructured Grids

NASA Technical Reports Server (NTRS)

Bonhaus, Daryl L.

1993-01-01

An algorithm is described that calculates inviscid, laminar, and turbulent flows on triangular meshes with an upwind discretization. A brief description of the base solver and the multigrid implementation is given, followed by results that consist mainly of convergence rates for inviscid and viscous flows over a NACA four-digit airfoil section. The results show that multigrid does accelerate convergence when the same relaxation parameters that yield good single-grid performance are used; however, larger gains in performance can be realized by doing less work in the relaxation scheme.

Estimating the vibration level of an L-shaped beam using power flow techniques

NASA Technical Reports Server (NTRS)

Cuschieri, J. M.; Mccollum, M.; Rassineux, J. L.; Gilbert, T.

1986-01-01

The response of one component of an L-shaped beam, with point force excitation on the other component, is estimated using the power flow method. The transmitted power from the source component to the receiver component is expressed in terms of the transfer and input mobilities at the excitation point and the joint. The response is estimated both in narrow frequency bands, using the exact geometry of the beams, and as a frequency averaged response using infinite beam models. The results using this power flow technique are compared to the results obtained using finite element analysis (FEA) of the L-shaped beam for the low frequency response and to results obtained using statistical energy analysis (SEA) for the high frequencies. The agreement between the FEA results and the power flow method results at low frequencies is very good. SEA results are in terms of frequency averaged levels and these are in perfect agreement with the results obtained using the infinite beam models in the power flow method. The narrow frequency band results from the power flow method also converge to the SEA results at high frequencies. The advantage of the power flow method is that detail of the response can be retained while reducing computation time, which will allow the narrow frequency band analysis of the response to be extended to higher frequencies.

Nearfield Summary and Statistical Analysis of the Second AIAA Sonic Boom Prediction Workshop

NASA Technical Reports Server (NTRS)

Park, Michael A.; Nemec, Marian

2017-01-01

A summary is provided for the Second AIAA Sonic Boom Workshop held 8-9 January 2017 in conjunction with AIAA SciTech 2017. The workshop used three required models of increasing complexity: an axisymmetric body, a wing body, and a complete configuration with flow-through nacelle. An optional complete configuration with propulsion boundary conditions is also provided. These models are designed with similar nearfield signatures to isolate geometry and shock/expansion interaction effects. Eleven international participant groups submitted nearfield signatures with forces, pitching moment, and iterative convergence norms. Statistics and grid convergence of these nearfield signatures are presented. These submissions are propagated to the ground, and noise levels are computed. This allows the grid convergence and the statistical distribution of a noise level to be computed. While progress is documented since the first workshop, improvement to the analysis methods for a possible subsequent workshop are provided. The complete configuration with flow-through nacelle showed the most dramatic improvement between the two workshops. The current workshop cases are more relevant to vehicles with lower loudness and have the potential for lower annoyance than the first workshop cases. The models for this workshop with quieter ground noise levels than the first workshop exposed weaknesses in analysis, particularly in convective discretization.

Multigrid Relaxation of a Factorizable, Conservative Discretization of the Compressible Flow Equations

NASA Technical Reports Server (NTRS)

Roberts, Thomas W.; Sidilkover, David; Thomas, J. L.

2000-01-01

The second-order factorizable discretization of the compressible Euler equations developed by Sidilkover is extended to conservation form on general curvilinear body-fitted grids. The discrete equations are solved by symmetric collective Gauss-Seidel relaxation and FAS multigrid. Solutions for flow in a channel with Mach numbers ranging from 0.0001 to a supercritical Mach number are shown, demonstrating uniform convergence rates and no loss of accuracy in the incompressible limit. A solution for the flow around the leading edge of a semi-infinite parabolic body demonstrates that the scheme maintains rapid convergence for a flow containing a stagnation point.

Vortex methods for separated flows

NASA Technical Reports Server (NTRS)

Spalart, Philippe R.

1988-01-01

The numerical solution of the Euler or Navier-Stokes equations by Lagrangian vortex methods is discussed. The mathematical background is presented in an elementary fashion and includes the relationship with traditional point-vortex studies, the convergence to smooth solutions of the Euler equations, and the essential differences between two- and three-dimensional cases. The difficulties in extending the method to viscous or compressible flows are explained. The overlap with the excellent review articles available is kept to a minimum and more emphasis is placed on the area of expertise, namely two-dimensional flows around bluff bodies. When solid walls are present, complete mathematical models are not available and a more heuristic attitude must be adopted. The imposition of inviscid and viscous boundary conditions without conformal mappings or image vortices and the creation of vorticity along solid walls are examined in detail. Methods for boundary-layer treatment and the question of the Kutta condition are discussed. Practical aspects and tips helpful in creating a method that really works are explained. The topics include the robustness of the method and the assessment of accuracy, vortex-core profiles, timemarching schemes, numerical dissipation, and efficient programming. Calculations of flows past streamlined or bluff bodies are used as examples when appropriate.

Transient electrophoretic motion of a charged particle through a converging-diverging microchannel: effect of direct current-dielectrophoretic force.

PubMed

Ai, Ye; Joo, Sang W; Jiang, Yingtao; Xuan, Xiangchun; Qian, Shizhi

2009-07-01

Transient electrophoretic motion of a charged particle through a converging-diverging microchannel is studied by solving the coupled system of the Navier-Stokes equations for fluid flow and the Laplace equation for electrical field with an arbitrary Lagrangian-Eulerian finite-element method. A spatially non-uniform electric field is induced in the converging-diverging section, which gives rise to a direct current dielectrophoretic (DEP) force in addition to the electrostatic force acting on the charged particle. As a sequence, the symmetry of the particle velocity and trajectory with respect to the throat is broken. We demonstrate that the predicted particle trajectory shifts due to DEP show quantitative agreements with the existing experimental data. Although converging-diverging microchannels can be used for super fast electrophoresis due to the enhancement of the local electric field, it is shown that large particles may be blocked due to the induced DEP force, which thus must be taken into account in the study of electrophoresis in microfluidic devices where non-uniform electric fields are present.

Phase retrieval via incremental truncated amplitude flow algorithm

NASA Astrophysics Data System (ADS)

Zhang, Quanbing; Wang, Zhifa; Wang, Linjie; Cheng, Shichao

2017-10-01

This paper considers the phase retrieval problem of recovering the unknown signal from the given quadratic measurements. A phase retrieval algorithm based on Incremental Truncated Amplitude Flow (ITAF) which combines the ITWF algorithm and the TAF algorithm is proposed. The proposed ITAF algorithm enhances the initialization by performing both of the truncation methods used in ITWF and TAF respectively, and improves the performance in the gradient stage by applying the incremental method proposed in ITWF to the loop stage of TAF. Moreover, the original sampling vector and measurements are preprocessed before initialization according to the variance of the sensing matrix. Simulation experiments verified the feasibility and validity of the proposed ITAF algorithm. The experimental results show that it can obtain higher success rate and faster convergence speed compared with other algorithms. Especially, for the noiseless random Gaussian signals, ITAF can recover any real-valued signal accurately from the magnitude measurements whose number is about 2.5 times of the signal length, which is close to the theoretic limit (about 2 times of the signal length). And it usually converges to the optimal solution within 20 iterations which is much less than the state-of-the-art algorithms.

Performance Analysis and Design Synthesis (PADS) computer program. Volume 2: Program description, part 2

NASA Technical Reports Server (NTRS)

1972-01-01

The QL module of the Performance Analysis and Design Synthesis (PADS) computer program is described. Execution of this module is initiated when and if subroutine PADSI calls subroutine GROPE. Subroutine GROPE controls the high level logical flow of the QL module. The purpose of the module is to determine a trajectory that satisfies the necessary variational conditions for optimal performance. The module achieves this by solving a nonlinear multi-point boundary value problem. The numerical method employed is described. It is an iterative technique that converges quadratically when it does converge. The three basic steps of the module are: (1) initialization, (2) iteration, and (3) culmination. For Volume 1 see N73-13199.

Understanding CO2 decomposition by thermal plasma with supersonic expansion quench

NASA Astrophysics Data System (ADS)

Tao, YANG; Jun, SHEN; Tangchun, RAN; Jiao, LI; Pan, CHEN; Yongxiang, YIN

2018-04-01

CO2 pyrolysis by thermal plasma was investigated, and a high conversion rate of 33% and energy efficiency of 17% were obtained. The high performance benefited from a novel quenching method, which synergizes the converging nozzle and cooling tube. To understand the synergy effect, a computational fluid dynamics simulation was carried out. A quick quenching rate of 107 K s‑1 could be expected when the pyrolysis gas temperature decreased from more than 3000 to 1000 K. According to the simulation results, the quenching mechanism was discussed as follows: first, the compressible fluid was adiabatically expanded in the converging nozzle and accelerated to sonic speed, and parts of the heat energy converted to convective kinetic energy; second, the sonic fluid jet into the cooling tube formed a strong eddy, which greatly enhanced the heat transfer between the inverse-flowing fluid and cooling tube. These two mechanisms ensure a quick quenching to prevent the reverse reaction of CO2 pyrolysis gas when it flows out from the thermal plasma reactor.

A high-order multi-zone cut-stencil method for numerical simulations of high-speed flows over complex geometries

NASA Astrophysics Data System (ADS)

Greene, Patrick T.; Eldredge, Jeff D.; Zhong, Xiaolin; Kim, John

2016-07-01

In this paper, we present a method for performing uniformly high-order direct numerical simulations of high-speed flows over arbitrary geometries. The method was developed with the goal of simulating and studying the effects of complex isolated roughness elements on the stability of hypersonic boundary layers. The simulations are carried out on Cartesian grids with the geometries imposed by a third-order cut-stencil method. A fifth-order hybrid weighted essentially non-oscillatory scheme was implemented to capture any steep gradients in the flow created by the geometries and a third-order Runge-Kutta method is used for time advancement. A multi-zone refinement method was also utilized to provide extra resolution at locations with expected complex physics. The combination results in a globally fourth-order scheme in space and third order in time. Results confirming the method's high order of convergence are shown. Two-dimensional and three-dimensional test cases are presented and show good agreement with previous results. A simulation of Mach 3 flow over the logo of the Ubuntu Linux distribution is shown to demonstrate the method's capabilities for handling complex geometries. Results for Mach 6 wall-bounded flow over a three-dimensional cylindrical roughness element are also presented. The results demonstrate that the method is a promising tool for the study of hypersonic roughness-induced transition.

A general multiblock Euler code for propulsion integration. Volume 1: Theory document

NASA Technical Reports Server (NTRS)

Chen, H. C.; Su, T. Y.; Kao, T. J.

1991-01-01

A general multiblock Euler solver was developed for the analysis of flow fields over geometrically complex configurations either in free air or in a wind tunnel. In this approach, the external space around a complex configuration was divided into a number of topologically simple blocks, so that surface-fitted grids and an efficient flow solution algorithm could be easily applied in each block. The computational grid in each block is generated using a combination of algebraic and elliptic methods. A grid generation/flow solver interface program was developed to facilitate the establishment of block-to-block relations and the boundary conditions for each block. The flow solver utilizes a finite volume formulation and an explicit time stepping scheme to solve the Euler equations. A multiblock version of the multigrid method was developed to accelerate the convergence of the calculations. The generality of the method was demonstrated through the analysis of two complex configurations at various flow conditions. Results were compared to available test data. Two accompanying volumes, user manuals for the preparation of multi-block grids (vol. 2) and for the Euler flow solver (vol. 3), provide information on input data format and program execution.

Convergence acceleration of the Proteus computer code with multigrid methods

NASA Technical Reports Server (NTRS)

Demuren, A. O.; Ibraheem, S. O.

1995-01-01

This report presents the results of a study to implement convergence acceleration techniques based on the multigrid concept in the two-dimensional and three-dimensional versions of the Proteus computer code. The first section presents a review of the relevant literature on the implementation of the multigrid methods in computer codes for compressible flow analysis. The next two sections present detailed stability analysis of numerical schemes for solving the Euler and Navier-Stokes equations, based on conventional von Neumann analysis and the bi-grid analysis, respectively. The next section presents details of the computational method used in the Proteus computer code. Finally, the multigrid implementation and applications to several two-dimensional and three-dimensional test problems are presented. The results of the present study show that the multigrid method always leads to a reduction in the number of iterations (or time steps) required for convergence. However, there is an overhead associated with the use of multigrid acceleration. The overhead is higher in 2-D problems than in 3-D problems, thus overall multigrid savings in CPU time are in general better in the latter. Savings of about 40-50 percent are typical in 3-D problems, but they are about 20-30 percent in large 2-D problems. The present multigrid method is applicable to steady-state problems and is therefore ineffective in problems with inherently unstable solutions.

Implicit high-order discontinuous Galerkin method with HWENO type limiters for steady viscous flow simulations

NASA Astrophysics Data System (ADS)

Jiang, Zhen-Hua; Yan, Chao; Yu, Jian

2013-08-01

Two types of implicit algorithms have been improved for high order discontinuous Galerkin (DG) method to solve compressible Navier-Stokes (NS) equations on triangular grids. A block lower-upper symmetric Gauss-Seidel (BLU-SGS) approach is implemented as a nonlinear iterative scheme. And a modified LU-SGS (LLU-SGS) approach is suggested to reduce the memory requirements while retain the good convergence performance of the original LU-SGS approach. Both implicit schemes have the significant advantage that only the diagonal block matrix is stored. The resulting implicit high-order DG methods are applied, in combination with Hermite weighted essentially non-oscillatory (HWENO) limiters, to solve viscous flow problems. Numerical results demonstrate that the present implicit methods are able to achieve significant efficiency improvements over explicit counterparts and for viscous flows with shocks, and the HWENO limiters can be used to achieve the desired essentially non-oscillatory shock transition and the designed high-order accuracy simultaneously.

Moisture convergence using satellite-derived wind fields - A severe local storm case study

NASA Technical Reports Server (NTRS)

Negri, A. J.; Vonder Haar, T. H.

1980-01-01

Five-minute interval 1-km resolution SMS visible channel data were used to derive low-level wind fields by tracking small cumulus clouds on NASA's Atmospheric and Oceanographic Information Processing System. The satellite-derived wind fields were combined with surface mixing ratios to derive horizontal moisture convergence in the prestorm environment of April 24, 1975. Storms began developing in an area extending from southwest Oklahoma to eastern Tennessee 2 h subsequent to the time of the derived fields. The maximum moisture convergence was computed to be 0.0022 g/kg per sec and areas of low-level convergence of moisture were in general indicative of regions of severe storm genesis. The resultant moisture convergence fields derived from two wind sets 20 min apart were spatially consistent and reflected the mesoscale forcing of ensuing storm development. Results are discussed with regard to possible limitations in quantifying the relationship between low-level flow and between low-level flow and satellite-derived cumulus motion in an antecedent storm environment.

A cell-vertex multigrid method for the Navier-Stokes equations

NASA Technical Reports Server (NTRS)

Radespiel, R.

1989-01-01

A cell-vertex scheme for the Navier-Stokes equations, which is based on central difference approximations and Runge-Kutta time stepping, is described. Using local time stepping, implicit residual smoothing, a multigrid method, and carefully controlled artificial dissipative terms, very good convergence rates are obtained for a wide range of two- and three-dimensional flows over airfoils and wings. The accuracy of the code is examined by grid refinement studies and comparison with experimental data. For an accurate prediction of turbulent flows with strong separations, a modified version of the nonequilibrium turbulence model of Johnson and King is introduced, which is well suited for an implementation into three-dimensional Navier-Stokes codes. It is shown that the solutions for three-dimensional flows with strong separations can be dramatically improved, when a nonequilibrium model of turbulence is used.

Optimal Power Flow Pursuit

DOE Office of Scientific and Technical Information (OSTI.GOV)

Dall'Anese, Emiliano; Simonetto, Andrea

This paper considers distribution networks featuring inverter-interfaced distributed energy resources, and develops distributed feedback controllers that continuously drive the inverter output powers to solutions of AC optimal power flow (OPF) problems. Particularly, the controllers update the power setpoints based on voltage measurements as well as given (time-varying) OPF targets, and entail elementary operations implementable onto low-cost microcontrollers that accompany power-electronics interfaces of gateways and inverters. The design of the control framework is based on suitable linear approximations of the AC power-flow equations as well as Lagrangian regularization methods. Convergence and OPF-target tracking capabilities of the controllers are analytically established. Overall,more » the proposed method allows to bypass traditional hierarchical setups where feedback control and optimization operate at distinct time scales, and to enable real-time optimization of distribution systems.« less

Network Simulation solution of free convective flow from a vertical cone with combined effect of non- uniform surface heat flux and heat generation or absorption

NASA Astrophysics Data System (ADS)

Immanuel, Y.; Pullepu, Bapuji; Sambath, P.

2018-04-01

A two dimensional mathematical model is formulated for the transitive laminar free convective, incompressible viscous fluid flow over vertical cone with variable surface heat flux combined with the effects of heat generation and absorption is considered . using a powerful computational method based on thermoelectric analogy called Network Simulation Method (NSM0, the solutions of governing nondimensionl coupled, unsteady and nonlinear partial differential conservation equations of the flow that are obtained. The numerical technique is always stable and convergent which establish high efficiency and accuracy by employing network simulator computer code Pspice. The effects of velocity and temperature profiles have been analyzed for various factors, namely Prandtl number Pr, heat flux power law exponent n and heat generation/absorption parameter Δ are analyzed graphically.

Lubricated immersed boundary method in two dimensions

NASA Astrophysics Data System (ADS)

Fai, Thomas G.; Rycroft, Chris H.

2018-03-01

Many biological examples of fluid-structure interaction, including the transit of red blood cells through the narrow slits in the spleen and the intracellular trafficking of vesicles into dendritic spines, involve the near-contact of elastic structures separated by thin layers of fluid. Motivated by such problems, we introduce an immersed boundary method that uses elements of lubrication theory to resolve thin fluid layers between immersed boundaries. We demonstrate 2nd-order accurate convergence for simple two-dimensional flows with known exact solutions to showcase the increased accuracy of this method compared to the standard immersed boundary method. Motivated by the phenomenon of wall-induced migration, we apply the lubricated immersed boundary method to simulate an elastic vesicle near a wall in shear flow. We also simulate the dynamics of a vesicle traveling through a narrow channel and observe the ability of the lubricated method to capture the vesicle motion on relatively coarse fluid grids.

High speed flow cytometer droplet formation system and method

DOEpatents

Van den Engh, Ger

2000-01-01

A droplet forming flow cytometer system allows high speed processing without the need for high oscillator drive powers through the inclusion of an oscillator or piezoelectric crystal such as within the nozzle volume or otherwise unidirectionally coupled to the sheath fluid. The nozzle container continuously converges so as to amplify unidirectional oscillations which are transmitted as pressure waves through the nozzle volume to the nozzle exit so as to form droplets from the fluid jet. The oscillator is directionally isolated so as to avoid moving the entire nozzle container so as to create only pressure waves within the sheath fluid. A variation in substance concentration is achieved through a movable substance introduction port which is positioned within a convergence zone to vary the relative concentration of substance to sheath fluid while still maintaining optimal laminar flow conditions. This variation may be automatically controlled through a sensor and controller configuration. A replaceable tip design is also provided whereby the ceramic nozzle tip is positioned within an edge insert in the nozzle body so as to smoothly transition from nozzle body to nozzle tip. The nozzle tip is sealed against its outer surface to the nozzle body so it may be removable for cleaning or replacement.

Some effects of oscillation waveform and amplitude on unsteady turbulent shear flows

NASA Technical Reports Server (NTRS)

Agarwal, Naval K.; Simpson, Roger L.; Shivaprasad, B. G.

1992-01-01

Some physical features of several unsteady separating turbulent boundary layers are presented for practical Reynolds numbers and reduced frequencies such as for helicopter and turbomachinery flows. The effects of unsteadiness amplitude and waveform are examined for flows along the floor of a converging and diverging wind tunnel test section. At the end of the converging portion, the mean skin friction coefficient normalized on the mean dynamic pressure is independent of the waveform and amplitude within low experimental uncertainties. In the detaching and detached portions of the flow, wall values of the fraction of time that the flow moves downstream of gamma sub pu, which is a separated flow state variable, shows that oscillation waveform and amplitude strongly influence the detached flow behavior. Distributions of gamma sub pu during a cycle indicate hysteresis within the detached flow and the effects of the higher harmonics of pressure gradient and velocity.

Three-Dimensional Navier-Stokes Method with Two-Equation Turbulence Models for Efficient Numerical Simulation of Hypersonic Flows

NASA Technical Reports Server (NTRS)

Bardina, J. E.

1994-01-01

A new computational efficient 3-D compressible Reynolds-averaged implicit Navier-Stokes method with advanced two equation turbulence models for high speed flows is presented. All convective terms are modeled using an entropy satisfying higher-order Total Variation Diminishing (TVD) scheme based on implicit upwind flux-difference split approximations and arithmetic averaging procedure of primitive variables. This method combines the best features of data management and computational efficiency of space marching procedures with the generality and stability of time dependent Navier-Stokes procedures to solve flows with mixed supersonic and subsonic zones, including streamwise separated flows. Its robust stability derives from a combination of conservative implicit upwind flux-difference splitting with Roe's property U to provide accurate shock capturing capability that non-conservative schemes do not guarantee, alternating symmetric Gauss-Seidel 'method of planes' relaxation procedure coupled with a three-dimensional two-factor diagonal-dominant approximate factorization scheme, TVD flux limiters of higher-order flux differences satisfying realizability, and well-posed characteristic-based implicit boundary-point a'pproximations consistent with the local characteristics domain of dependence. The efficiency of the method is highly increased with Newton Raphson acceleration which allows convergence in essentially one forward sweep for supersonic flows. The method is verified by comparing with experiment and other Navier-Stokes methods. Here, results of adiabatic and cooled flat plate flows, compression corner flow, and 3-D hypersonic shock-wave/turbulent boundary layer interaction flows are presented. The robust 3-D method achieves a better computational efficiency of at least one order of magnitude over the CNS Navier-Stokes code. It provides cost-effective aerodynamic predictions in agreement with experiment, and the capability of predicting complex flow structures in complex geometries with good accuracy.

A grid generation and flow solution method for the Euler equations on unstructured grids

NASA Astrophysics Data System (ADS)

Anderson, W. Kyle

1994-01-01

A grid generation and flow solution algorithm for the Euler equations on unstructured grids is presented. The grid generation scheme utilizes Delaunay triangulation and self-generates the field points for the mesh based on cell aspect ratios and allows for clustering near solid surfaces. The flow solution method is an implicit algorithm in which the linear set of equations arising at each time step is solved using a Gauss Seidel procedure which is completely vectorizable. In addition, a study is conducted to examine the number of subiterations required for good convergence of the overall algorithm. Grid generation results are shown in two dimensions for a National Advisory Committee for Aeronautics (NACA) 0012 airfoil as well as a two-element configuration. Flow solution results are shown for two-dimensional flow over the NACA 0012 airfoil and for a two-element configuration in which the solution has been obtained through an adaptation procedure and compared to an exact solution. Preliminary three-dimensional results are also shown in which subsonic flow over a business jet is computed.

Vectorized schemes for conical potential flow using the artificial density method

NASA Technical Reports Server (NTRS)

Bradley, P. F.; Dwoyer, D. L.; South, J. C., Jr.; Keen, J. M.

1984-01-01

A method is developed to determine solutions to the full-potential equation for steady supersonic conical flow using the artificial density method. Various update schemes used generally for transonic potential solutions are investigated. The schemes are compared for speed and robustness. All versions of the computer code have been vectorized and are currently running on the CYBER-203 computer. The update schemes are vectorized, where possible, either fully (explicit schemes) or partially (implicit schemes). Since each version of the code differs only by the update scheme and elements other than the update scheme are completely vectorizable, comparisons of computational effort and convergence rate among schemes are a measure of the specific scheme's performance. Results are presented for circular and elliptical cones at angle of attack for subcritical and supercritical crossflows.

Numerical simulation and experimental investigation about internal and external flows†

NASA Astrophysics Data System (ADS)

Wang, Tao; Yang, Guowei; Huang, Guojun; Zhou, Liandi

2006-06-01

In this paper, TASCflow3D is used to solve inner and outer 3D viscous incompressible turbulent flow (Re=5.6×106) around axisymmetric body with duct. The governing equation is a RANS equation with standard k ɛ turbulence model. The discrete method used is a finite volume method based on the finite element approach. In this method, the description of geometry is very flexible and at the same time important conservative properties are retained. The multi-block and algebraic multi-grid techniques are used for the convergence acceleration. Agreement between experimental results and calculation is good. It indicates that this novel approach can be used to simulate complex flow such as the interaction between rotor and stator or propulsion systems containing tip clearance and cavitation.

Efficient stabilization and acceleration of numerical simulation of fluid flows by residual recombination

NASA Astrophysics Data System (ADS)

Citro, V.; Luchini, P.; Giannetti, F.; Auteri, F.

2017-09-01

The study of the stability of a dynamical system described by a set of partial differential equations (PDEs) requires the computation of unstable states as the control parameter exceeds its critical threshold. Unfortunately, the discretization of the governing equations, especially for fluid dynamic applications, often leads to very large discrete systems. As a consequence, matrix based methods, like for example the Newton-Raphson algorithm coupled with a direct inversion of the Jacobian matrix, lead to computational costs too large in terms of both memory and execution time. We present a novel iterative algorithm, inspired by Krylov-subspace methods, which is able to compute unstable steady states and/or accelerate the convergence to stable configurations. Our new algorithm is based on the minimization of the residual norm at each iteration step with a projection basis updated at each iteration rather than at periodic restarts like in the classical GMRES method. The algorithm is able to stabilize any dynamical system without increasing the computational time of the original numerical procedure used to solve the governing equations. Moreover, it can be easily inserted into a pre-existing relaxation (integration) procedure with a call to a single black-box subroutine. The procedure is discussed for problems of different sizes, ranging from a small two-dimensional system to a large three-dimensional problem involving the Navier-Stokes equations. We show that the proposed algorithm is able to improve the convergence of existing iterative schemes. In particular, the procedure is applied to the subcritical flow inside a lid-driven cavity. We also discuss the application of Boostconv to compute the unstable steady flow past a fixed circular cylinder (2D) and boundary-layer flow over a hemispherical roughness element (3D) for supercritical values of the Reynolds number. We show that Boostconv can be used effectively with any spatial discretization, be it a finite-difference, finite-volume, finite-element or spectral method.

Finite Element Method Analysis of An Out Flow With Free Surface In Transition Zones

NASA Astrophysics Data System (ADS)

Saoula, R. Iddir S.; Mokhtar, K. Ait

The object of this work is to present this part of the fluid mechanics that relates to out-flows of the fluid to big speeds in transitions. Results usually gotten by the classic processes can only have a qualitative aspect. The method fluently used for the count of these out-flows to big speeds is the one of characteristics, this approach remains interesting so much that doesn't appear within the out-flow of intersections of shock waves, as well as of reflections of these. In the simple geometry case, the method of finite differences satisfying result, But when the complexity of this geometry imposes itself, it is the method of finite elements that is proposed to solve this type of prob- lem, in particular for problems Trans critic. The goal of our work is to analyse free surface flows in channels no prismatic has oblong transverse section in zone of tran- sition. (Convergent, divergent). The basic mathematical model of this study is Saint Venant derivatives partial equations. To solve these equations we use the finite ele- ment method, the element of reference is the triangular element with 6 nodes which are quadratic in speed and linear in height (pressure). Our results and their obtains by others are very close to experimental results.

Self-similar dynamic converging shocks - I. An isothermal gas sphere with self-gravity

NASA Astrophysics Data System (ADS)

Lou, Yu-Qing; Shi, Chun-Hui

2014-07-01

We explore novel self-similar dynamic evolution of converging spherical shocks in a self-gravitating isothermal gas under conceivable astrophysical situations. The construction of such converging shocks involves a time-reversal operation on feasible flow profiles in self-similar expansion with a proper care for the increasing direction of the specific entropy. Pioneered by Guderley since 1942 but without self-gravity so far, self-similar converging shocks are important for implosion processes in aerodynamics, combustion, and inertial fusion. Self-gravity necessarily plays a key role for grossly spherical structures in very broad contexts of astrophysics and cosmology, such as planets, stars, molecular clouds (cores), compact objects, planetary nebulae, supernovae, gamma-ray bursts, supernova remnants, globular clusters, galactic bulges, elliptical galaxies, clusters of galaxies as well as relatively hollow cavity or bubble structures on diverse spatial and temporal scales. Large-scale dynamic flows associated with such quasi-spherical systems (including collapses, accretions, fall-backs, winds and outflows, explosions, etc.) in their initiation, formation, and evolution are likely encounter converging spherical shocks at times. Our formalism lays an important theoretical basis for pertinent astrophysical and cosmological applications of various converging shock solutions and for developing and calibrating numerical codes. As examples, we describe converging shock triggered star formation, supernova explosions, and void collapses.

Numerical Modeling of Fuel Injection into an Accelerating, Turning Flow with a Cavity

NASA Astrophysics Data System (ADS)

Colcord, Ben James

Deliberate continuation of the combustion in the turbine passages of a gas turbine engine has the potential to increase the efficiency and the specific thrust or power of current gas-turbine engines. This concept, known as a turbine-burner, must overcome many challenges before becoming a viable product. One major challenge is the injection, mixing, ignition, and burning of fuel within a short residence time in a turbine passage characterized by large three-dimensional accelerations. One method of increasing the residence time is to inject the fuel into a cavity adjacent to the turbine passage, creating a low-speed zone for mixing and combustion. This situation is simulated numerically, with the turbine passage modeled as a turning, converging channel flow of high-temperature, vitiated air adjacent to a cavity. Both two- and three-dimensional, reacting and non-reacting calculations are performed, examining the effects of channel curvature and convergence, fuel and additional air injection configurations, and inlet conditions. Two-dimensional, non-reacting calculations show that higher aspect ratio cavities improve the fluid interaction between the channel flow and the cavity, and that the cavity dimensions are important for enhancing the mixing. Two-dimensional, reacting calculations show that converging channels improve the combustion efficiency. Channel curvature can be either beneficial or detrimental to combustion efficiency, depending on the location of the cavity and the fuel and air injection configuration. Three-dimensional, reacting calculations show that injecting fuel and air so as to disrupt the natural motion of the cavity stimulates three-dimensional instability and improves the combustion efficiency.

Hydrodynamics beyond Navier-Stokes: exact solution to the lattice Boltzmann hierarchy.

PubMed

Ansumali, S; Karlin, I V; Arcidiacono, S; Abbas, A; Prasianakis, N I

2007-03-23

The exact solution to the hierarchy of nonlinear lattice Boltzmann (LB) kinetic equations in the stationary planar Couette flow is found at nonvanishing Knudsen numbers. A new method of solving LB kinetic equations which combines the method of moments with boundary conditions for populations enables us to derive closed-form solutions for all higher-order moments. A convergence of results suggests that the LB hierarchy with larger velocity sets is the novel way to approximate kinetic theory.

Losses in Channels with Increased External Turbulence

NASA Technical Reports Server (NTRS)

Zaryankin, A. Y.; Soloveva, G. S.

1986-01-01

An approximate method for determining the effect of the level of turbulence on the aerodynamic characteristics of convergent and diffuser channels is examined. A momentum equation for the boundary layer is in the method, introducing external flow turbulence on the basis of experimental values of the coefficient of friction and the form factor. It is found that at significant levels of external turbulence, losses must be considered not only in the boundary layer but also in the central region of the channel.

Efficient Numerical Methods for Nonequilibrium Re-Entry Flows

DTIC Science & Technology

2014-01-14

right-hand side is the only quadratic operation). The number of sub- iterations , kmax, used in this update needs to be chosen for optimal convergence and...Upper Symmetric Gauss - Seidel Method for the Euler and Navier-Stokes Equations,”, AIAA Journal, Vol. 26, No. 9, pp. 1025-1026, Sept. 1988. 11Edwards, J.R...Candler, “The Solution of the Navier-Stokes Equations Using Gauss - Seidel Line Relaxation,” Computers and Fluids, Vol. 17, No. 1, pp. 135-150, 1989

Investigation on Convergence – Divergence Nozzle Shape for Microscale Channel in Harvesting Kinetic Energy

NASA Astrophysics Data System (ADS)

Zakaria, M. S.; Zairi, S.; Misbah, M. N.; Saifizi, M.; Rakawi, Izzudin

2018-03-01

This paper presents performance evaluation of nozzle shapes on microscale channel by employing different types of NACA airfoils profile and conventional profile. The deploying nozzle used are NACA 0012, NACA 0021 and NACA 0024 airfoils while for conventional convergence-divergence nozzle diameter ratio (d2 / d1) in the range from 1/4 to 3/4 are applied. These nozzles are assembled on rectangular cross sectional microscale channel which has designated constant fluid flow velocity at the channel inlet. This study revealed reduction on diameter ratio increased dramatically fluid velocity but further reduction on diameter ratio exposed fluid flow to fluctuate which slightly slowing down the fluid velocity. Nevertheless, curved NACA profiles are favourable for convergence – divergence nozzle in microscale channel as it significantly improved flow characteristics by enhancing fluid velocity and resultant kinetic energy as compared to conventional profile.

Improving Advanced Inverter Control Convergence in Distribution Power Flow

DOE Office of Scientific and Technical Information (OSTI.GOV)

Nagarajan, Adarsh; Palmintier, Bryan; Ding, Fei

Simulation of modern distribution system powerflow increasingly requires capturing the impact of advanced PV inverter voltage regulation on powerflow. With Volt/var control, the inverter adjusts its reactive power flow as a function of the point of common coupling (PCC) voltage. Similarly, Volt/watt control curtails active power production as a function of PCC voltage. However, with larger systems and higher penetrations of PV, this active/reactive power flow itself can cause significant changes to the PCC voltage potentially introducing oscillations that slow the convergence of system simulations. Improper treatment of these advanced inverter functions could potentially lead to incorrect results. This papermore » explores a simple approach to speed such convergence by blending in the previous iteration's reactive power estimate to dampen these oscillations. Results with a single large (5MW) PV system and with multiple 500kW advanced inverters show dramatic improvements using this approach.« less

Experimental and numerical analysis of convergent nozzlex

NASA Astrophysics Data System (ADS)

Srinivas, G.; Rakham, Bhupal

2017-05-01

In this paper the main focus was given to convergent nozzle where both the experimental and numerical calculations were carried out with the support of standardized literature. In the recent years the field of air breathing and non-air breathing engine developments significantly increase its performance. To enhance the performance of both the type of engines the nozzle is the one of the component which will play a vital role, especially selecting the type of nozzle depends upon the vehicle speed requirement and aerodynamic behavior at most important in the field of propulsion. The convergent nozzle flow experimental analysis done using scaled apparatus and the similar setup was arranged artificially in the ANSYS software for doing the flow analysis across the convergent nozzle. The consistent calculation analysis are done based on the public literature survey to validate the experimental and numerical simulation results of convergent nozzle. Using these two experimental and numerical simulation approaches the best fit results will bring up to meet the design requirements. However the comparison also made to meet the reliability of the work on design criteria of convergent nozzle which can entrench in the field of propulsion applications.

Microfluidic converging/diverging channels optimised for homogeneous extensional deformation.

PubMed

Zografos, K; Pimenta, F; Alves, M A; Oliveira, M S N

2016-07-01

In this work, we optimise microfluidic converging/diverging geometries in order to produce constant strain-rates along the centreline of the flow, for performing studies under homogeneous extension. The design is examined for both two-dimensional and three-dimensional flows where the effects of aspect ratio and dimensionless contraction length are investigated. Initially, pressure driven flows of Newtonian fluids under creeping flow conditions are considered, which is a reasonable approximation in microfluidics, and the limits of the applicability of the design in terms of Reynolds numbers are investigated. The optimised geometry is then used for studying the flow of viscoelastic fluids and the practical limitations in terms of Weissenberg number are reported. Furthermore, the optimisation strategy is also applied for electro-osmotic driven flows, where the development of a plug-like velocity profile allows for a wider region of homogeneous extensional deformation in the flow field.

Microfluidic converging/diverging channels optimised for homogeneous extensional deformation

PubMed Central

Zografos, K.; Oliveira, M. S. N.

2016-01-01

In this work, we optimise microfluidic converging/diverging geometries in order to produce constant strain-rates along the centreline of the flow, for performing studies under homogeneous extension. The design is examined for both two-dimensional and three-dimensional flows where the effects of aspect ratio and dimensionless contraction length are investigated. Initially, pressure driven flows of Newtonian fluids under creeping flow conditions are considered, which is a reasonable approximation in microfluidics, and the limits of the applicability of the design in terms of Reynolds numbers are investigated. The optimised geometry is then used for studying the flow of viscoelastic fluids and the practical limitations in terms of Weissenberg number are reported. Furthermore, the optimisation strategy is also applied for electro-osmotic driven flows, where the development of a plug-like velocity profile allows for a wider region of homogeneous extensional deformation in the flow field. PMID:27478523

Mode Propagation in Nonuniform Circular Ducts with Potential Flow

NASA Technical Reports Server (NTRS)

Cho, Y. C.; Ingard, K. U.

1982-01-01

A previously reported closed form solution is expanded to determine effects of isentropic mean flow on mode propagation in a slowly converging-diverging duct, a circular cosh duct. On the assumption of uniform steady fluid density, the mean flow increases the power transmission coefficient. The increase is directly related to the increase of the cutoff ratio at the duct throat. With the negligible transverse gradients of the steady fluid variables, the conversion from one mode to another is negligible, and the power transmission coefficient remains unchanged with the mean flow direction reversed. With a proper choice of frequency parameter, many different modes can be made subject to a single value of the power transmission loss. A systematic method to include the effects of the gradients of the steady fluid variables is also described.

Finite element analysis of low speed viscous and inviscid aerodynamic flows

NASA Technical Reports Server (NTRS)

Baker, A. J.; Manhardt, P. D.

1977-01-01

A weak interaction solution algorithm was established for aerodynamic flow about an isolated airfoil. Finite element numerical methodology was applied to solution of each of differential equations governing potential flow, and viscous and turbulent boundary layer and wake flow downstream of the sharp trailing edge. The algorithm accounts for computed viscous displacement effects on the potential flow. Closure for turbulence was accomplished using both first and second order models. The COMOC finite element fluid mechanics computer program was modified to solve the identified equation systems for two dimensional flows. A numerical program was completed to determine factors affecting solution accuracy, convergence and stability for the combined potential, boundary layer, and parabolic Navier-Stokes equation systems. Good accuracy and convergence are demonstrated. Each solution is obtained within the identical finite element framework of COMOC.

Choice of implicit and explicit operators for the upwind differencing method

NASA Technical Reports Server (NTRS)

Liou, Meng-Sing; Vanleer, Bram

1988-01-01

The flux-vector and flux-difference splittings of Steger-Warming, van Leer and Roe are tested in all possible combinations on the implicit and explicit operators that can be distinguished in implicit relaxation methods for the steady Euler and Navier-Stokes equations. The tests include one-dimensional inviscid nozzle flow, and two-dimensional inviscid and viscous shock reflection. Roe's splitting, as anticipated, is found to uniformly yield the most accurate results. On the other hand, an approximate Roe splitting of the implicit operator (the complete Roe splitting is too complicated for practical use) proves to be the least robust with regard to convergence to the steady state. In this respect, the Steger-Warming splitting is the most robust; it leads to convergence when combined with any of the splittings in the explicit operator, although not necessarily in the most efficient way.

Modeling electrokinetic flows by consistent implicit incompressible smoothed particle hydrodynamics

DOE Office of Scientific and Technical Information (OSTI.GOV)

Pan, Wenxiao; Kim, Kyungjoo; Perego, Mauro

2017-04-01

We present an efficient implicit incompressible smoothed particle hydrodynamics (I2SPH) discretization of Navier-Stokes, Poisson-Boltzmann, and advection-diffusion equations subject to Dirichlet or Robin boundary conditions. It is applied to model various two and three dimensional electrokinetic flows in simple or complex geometries. The I2SPH's accuracy and convergence are examined via comparison with analytical solutions, grid-based numerical solutions, or empirical models. The new method provides a framework to explore broader applications of SPH in microfluidics and complex fluids with charged objects, such as colloids and biomolecules, in arbitrary complex geometries.

The evaluation of the rolling moments induced by wraparound fins

NASA Technical Reports Server (NTRS)

Seginer, A.; Bar-Haim, B.

1983-01-01

A possible reason is suggested for the induced rolling moments occurring on wraparound-fin configurations in subsonic flight at zero angle of attack. The subsonic potential flow over the configuration at zero incidence is solved numerically. The body is simulated by a distribution of sources along its axis, and the fins are described by a vortex-lattice method. It is shown that rolling moments can be induced on the antisymmetric fins by the radial flow generated at the base of the configuration, either over the converging separated wake, or over the diverging plume of a rocket motor.

New discretization and solution techniques for incompressible viscous flow problems

NASA Technical Reports Server (NTRS)

Gunzburger, M. D.; Nicolaides, R. A.; Liu, C. H.

1983-01-01

This paper considers several topics arising in the finite element solution of the incompressible Navier-Stokes equations. Specifically, the question of choosing finite element velocity/pressure spaces is addressed, particularly from the viewpoint of achieving stable discretizations leading to convergent pressure approximations. Following this, the role of artificial viscosity in viscous flow calculations is studied, emphasizing recent work by several researchers for the anisotropic case. The last section treats the problem of solving the nonlinear systems of equations which arise from the discretization. Time marching methods and classical iterative techniques, as well as some recent modifications are mentioned.

Three dimensional radiative flow of magnetite-nanofluid with homogeneous-heterogeneous reactions

NASA Astrophysics Data System (ADS)

Hayat, Tasawar; Rashid, Madiha; Alsaedi, Ahmed

2018-03-01

Present communication deals with the effects of homogeneous-heterogeneous reactions in flow of nanofluid by non-linear stretching sheet. Water based nanofluid containing magnetite nanoparticles is considered. Non-linear radiation and non-uniform heat sink/source effects are examined. Non-linear differential systems are computed by Optimal homotopy analysis method (OHAM). Convergent solutions of nonlinear systems are established. The optimal data of auxiliary variables is obtained. Impact of several non-dimensional parameters for velocity components, temperature and concentration fields are examined. Graphs are plotted for analysis of surface drag force and heat transfer rate.

Inverse Modeling Using Markov Chain Monte Carlo Aided by Adaptive Stochastic Collocation Method with Transformation

NASA Astrophysics Data System (ADS)

Zhang, D.; Liao, Q.

2016-12-01

The Bayesian inference provides a convenient framework to solve statistical inverse problems. In this method, the parameters to be identified are treated as random variables. The prior knowledge, the system nonlinearity, and the measurement errors can be directly incorporated in the posterior probability density function (PDF) of the parameters. The Markov chain Monte Carlo (MCMC) method is a powerful tool to generate samples from the posterior PDF. However, since the MCMC usually requires thousands or even millions of forward simulations, it can be a computationally intensive endeavor, particularly when faced with large-scale flow and transport models. To address this issue, we construct a surrogate system for the model responses in the form of polynomials by the stochastic collocation method. In addition, we employ interpolation based on the nested sparse grids and takes into account the different importance of the parameters, under the condition of high random dimensions in the stochastic space. Furthermore, in case of low regularity such as discontinuous or unsmooth relation between the input parameters and the output responses, we introduce an additional transform process to improve the accuracy of the surrogate model. Once we build the surrogate system, we may evaluate the likelihood with very little computational cost. We analyzed the convergence rate of the forward solution and the surrogate posterior by Kullback-Leibler divergence, which quantifies the difference between probability distributions. The fast convergence of the forward solution implies fast convergence of the surrogate posterior to the true posterior. We also tested the proposed algorithm on water-flooding two-phase flow reservoir examples. The posterior PDF calculated from a very long chain with direct forward simulation is assumed to be accurate. The posterior PDF calculated using the surrogate model is in reasonable agreement with the reference, revealing a great improvement in terms of computational efficiency.

Efficiency trade-offs of steady-state methods using FEM and FDM. [iterative solutions for nonlinear flow equations

NASA Technical Reports Server (NTRS)

Gartling, D. K.; Roache, P. J.

1978-01-01

The efficiency characteristics of finite element and finite difference approximations for the steady-state solution of the Navier-Stokes equations are examined. The finite element method discussed is a standard Galerkin formulation of the incompressible, steady-state Navier-Stokes equations. The finite difference formulation uses simple centered differences that are O(delta x-squared). Operation counts indicate that a rapidly converging Newton-Raphson-Kantorovitch iteration scheme is generally preferable over a Picard method. A split NOS Picard iterative algorithm for the finite difference method was most efficient.

DOE Office of Scientific and Technical Information (OSTI.GOV)

Harding, Samuel F.; Romero-Gomez, Pedro D. J.; Richmond, Marshall C.

Standards provide recommendations for the best practices in the installation of current meters for measuring fluid flow in closed conduits. These include PTC-18 and IEC-41 . Both of these standards refer to the requirements of the ISO Standard 3354 for cases where the velocity distribution is assumed to be regular and the flow steady. Due to the nature of the short converging intakes of Kaplan hydroturbines, these assumptions may be invalid if current meters are intended to be used to characterize turbine flows. In this study, we examine a combination of measurement guidelines from both ISO standards by means ofmore » virtual current meters (VCM) set up over a simulated hydroturbine flow field. To this purpose, a computational fluid dynamics (CFD) model was developed to model the velocity field of a short converging intake of the Ice Harbor Dam on the Snake River, in the State of Washington. The detailed geometry and resulting wake of the submersible traveling screen (STS) at the first gate slot was of particular interest in the development of the CFD model using a detached eddy simulation (DES) turbulence solution. An array of virtual point velocity measurements were extracted from the resulting velocity field to simulate VCM at two virtual measurement (VM) locations at different distances downstream of the STS. The discharge through each bay was calculated from the VM using the graphical integration solution to the velocity-area method. This method of representing practical velocimetry techniques in a numerical flow field has been successfully used in a range of marine and conventional hydropower applications. A sensitivity analysis was performed to observe the effect of the VCM array resolution on the discharge error. The downstream VM section required 11–33% less VCM in the array than the upstream VM location to achieve a given discharge error. In general, more instruments were required to quantify the discharge at high levels of accuracy when the STS was introduced because of the increased spatial variability of the flow velocity.« less

Accurate motion parameter estimation for colonoscopy tracking using a regression method

NASA Astrophysics Data System (ADS)

Liu, Jianfei; Subramanian, Kalpathi R.; Yoo, Terry S.

2010-03-01

Co-located optical and virtual colonoscopy images have the potential to provide important clinical information during routine colonoscopy procedures. In our earlier work, we presented an optical flow based algorithm to compute egomotion from live colonoscopy video, permitting navigation and visualization of the corresponding patient anatomy. In the original algorithm, motion parameters were estimated using the traditional Least Sum of squares(LS) procedure which can be unstable in the context of optical flow vectors with large errors. In the improved algorithm, we use the Least Median of Squares (LMS) method, a robust regression method for motion parameter estimation. Using the LMS method, we iteratively analyze and converge toward the main distribution of the flow vectors, while disregarding outliers. We show through three experiments the improvement in tracking results obtained using the LMS method, in comparison to the LS estimator. The first experiment demonstrates better spatial accuracy in positioning the virtual camera in the sigmoid colon. The second and third experiments demonstrate the robustness of this estimator, resulting in longer tracked sequences: from 300 to 1310 in the ascending colon, and 410 to 1316 in the transverse colon.

Low-Density Nozzle Flow by the Direct Simulation Monte Carlo and Continuum Methods

NASA Technical Reports Server (NTRS)

Chung, Chang-Hong; Kim, Sku C.; Stubbs, Robert M.; Dewitt, Kenneth J.

1994-01-01

Two different approaches, the direct simulation Monte Carlo (DSMC) method based on molecular gasdynamics, and a finite-volume approximation of the Navier-Stokes equations, which are based on continuum gasdynamics, are employed in the analysis of a low-density gas flow in a small converging-diverging nozzle. The fluid experiences various kinds of flow regimes including continuum, slip, transition, and free-molecular. Results from the two numerical methods are compared with Rothe's experimental data, in which density and rotational temperature variations along the centerline and at various locations inside a low-density nozzle were measured by the electron-beam fluorescence technique. The continuum approach showed good agreement with the experimental data as far as density is concerned. The results from the DSMC method showed good agreement with the experimental data, both in the density and the rotational temperature. It is also shown that the simulation parameters, such as the gas/surface interaction model, the energy exchange model between rotational and translational modes, and the viscosity-temperature exponent, have substantial effects on the results of the DSMC method.

Improvements in surface singularity analysis and design methods. [applicable to airfoils

NASA Technical Reports Server (NTRS)

Bristow, D. R.

1979-01-01

The coupling of the combined source vortex distribution of Green's potential flow function with contemporary numerical techniques is shown to provide accurate, efficient, and stable solutions to subsonic inviscid analysis and design problems for multi-element airfoils. The analysis problem is solved by direct calculation of the surface singularity distribution required to satisfy the flow tangency boundary condition. The design or inverse problem is solved by an iteration process. In this process, the geometry and the associated pressure distribution are iterated until the pressure distribution most nearly corresponding to the prescribed design distribution is obtained. Typically, five iteration cycles are required for convergence. A description of the analysis and design method is presented, along with supporting examples.

Transonic airfoil analysis and design in nonuniform flow

NASA Technical Reports Server (NTRS)

Chang, J. F.; Lan, C. E.

1986-01-01

A nonuniform transonic airfoil code is developed for applications in analysis, inverse design and direct optimization involving an airfoil immersed in propfan slipstream. Problems concerning the numerical stability, convergence, divergence and solution oscillations are discussed. The code is validated by comparing with some known results in incompressible flow. A parametric investigation indicates that the airfoil lift-drag ratio can be increased by decreasing the thickness ratio. A better performance can be achieved if the airfoil is located below the slipstream center. Airfoil characteristics designed by the inverse method and a direct optimization are compared. The airfoil designed with the method of direct optimization exhibits better characteristics and achieves a gain of 22 percent in lift-drag ratio with a reduction of 4 percent in thickness.

Estimating zero-g flow rates in open channels having capillary pumping vanes

NASA Astrophysics Data System (ADS)

Srinivasan, Radhakrishnan

2003-02-01

In vane-type surface tension propellant management devices (PMD) commonly used in satellite fuel tanks, the propellant is transported along guiding vanes from a reservoir at the inlet of the device to a sump at the outlet from where it is pumped to the satellite engine. The pressure gradient driving this free-surface flow under zero-gravity (zero-g) conditions is generated by surface tension and is related to the differential curvatures of the propellant-gas interface at the inlet and outlet of the PMD. A new semi-analytical procedure is prescribed for accurately calculating the extremely small fuel flow rates under reasonably idealized conditions. Convergence of the algorithm is demonstrated by detailed numerical calculations. Owing to the substantial cost and the technical hurdles involved in accurately estimating these minuscule flow rates by either direct numerical simulation or by experimental methods which simulate zero-g conditions in the lab, it is expected that the proposed method will be an indispensable tool in the design and operation of satellite fuel tanks.

A Computational Study of a New Dual Throat Fluidic Thrust Vectoring Nozzle Concept

NASA Technical Reports Server (NTRS)

Deere, Karen A.; Berrier, Bobby L.; Flamm, Jeffrey D.; Johnson, Stuart K.

2005-01-01

A computational investigation of a two-dimensional nozzle was completed to assess the use of fluidic injection to manipulate flow separation and cause thrust vectoring of the primary jet thrust. The nozzle was designed with a recessed cavity to enhance the throat shifting method of fluidic thrust vectoring. Several design cycles with the structured-grid, computational fluid dynamics code PAB3D and with experiments in the NASA Langley Research Center Jet Exit Test Facility have been completed to guide the nozzle design and analyze performance. This paper presents computational results on potential design improvements for best experimental configuration tested to date. Nozzle design variables included cavity divergence angle, cavity convergence angle and upstream throat height. Pulsed fluidic injection was also investigated for its ability to decrease mass flow requirements. Internal nozzle performance (wind-off conditions) and thrust vector angles were computed for several configurations over a range of nozzle pressure ratios from 2 to 7, with the fluidic injection flow rate equal to 3 percent of the primary flow rate. Computational results indicate that increasing cavity divergence angle beyond 10 is detrimental to thrust vectoring efficiency, while increasing cavity convergence angle from 20 to 30 improves thrust vectoring efficiency at nozzle pressure ratios greater than 2, albeit at the expense of discharge coefficient. Pulsed injection was no more efficient than steady injection for the Dual Throat Nozzle concept.

Preconditioned conjugate-gradient methods for low-speed flow calculations

NASA Technical Reports Server (NTRS)

Ajmani, Kumud; Ng, Wing-Fai; Liou, Meng-Sing

1993-01-01

An investigation is conducted into the viability of using a generalized Conjugate Gradient-like method as an iterative solver to obtain steady-state solutions of very low-speed fluid flow problems. Low-speed flow at Mach 0.1 over a backward-facing step is chosen as a representative test problem. The unsteady form of the two dimensional, compressible Navier-Stokes equations is integrated in time using discrete time-steps. The Navier-Stokes equations are cast in an implicit, upwind finite-volume, flux split formulation. The new iterative solver is used to solve a linear system of equations at each step of the time-integration. Preconditioning techniques are used with the new solver to enhance the stability and convergence rate of the solver and are found to be critical to the overall success of the solver. A study of various preconditioners reveals that a preconditioner based on the Lower-Upper Successive Symmetric Over-Relaxation iterative scheme is more efficient than a preconditioner based on Incomplete L-U factorizations of the iteration matrix. The performance of the new preconditioned solver is compared with a conventional Line Gauss-Seidel Relaxation (LGSR) solver. Overall speed-up factors of 28 (in terms of global time-steps required to converge to a steady-state solution) and 20 (in terms of total CPU time on one processor of a CRAY-YMP) are found in favor of the new preconditioned solver, when compared with the LGSR solver.

Preconditioned Conjugate Gradient methods for low speed flow calculations

NASA Technical Reports Server (NTRS)

Ajmani, Kumud; Ng, Wing-Fai; Liou, Meng-Sing

1993-01-01

An investigation is conducted into the viability of using a generalized Conjugate Gradient-like method as an iterative solver to obtain steady-state solutions of very low-speed fluid flow problems. Low-speed flow at Mach 0.1 over a backward-facing step is chosen as a representative test problem. The unsteady form of the two dimensional, compressible Navier-Stokes equations are integrated in time using discrete time-steps. The Navier-Stokes equations are cast in an implicit, upwind finite-volume, flux split formulation. The new iterative solver is used to solve a linear system of equations at each step of the time-integration. Preconditioning techniques are used with the new solver to enhance the stability and the convergence rate of the solver and are found to be critical to the overall success of the solver. A study of various preconditioners reveals that a preconditioner based on the lower-upper (L-U)-successive symmetric over-relaxation iterative scheme is more efficient than a preconditioner based on incomplete L-U factorizations of the iteration matrix. The performance of the new preconditioned solver is compared with a conventional line Gauss-Seidel relaxation (LGSR) solver. Overall speed-up factors of 28 (in terms of global time-steps required to converge to a steady-state solution) and 20 (in terms of total CPU time on one processor of a CRAY-YMP) are found in favor of the new preconditioned solver, when compared with the LGSR solver.

PRECONDITIONED CONJUGATE-GRADIENT 2 (PCG2), a computer program for solving ground-water flow equations

USGS Publications Warehouse

Hill, Mary C.

1990-01-01

This report documents PCG2 : a numerical code to be used with the U.S. Geological Survey modular three-dimensional, finite-difference, ground-water flow model . PCG2 uses the preconditioned conjugate-gradient method to solve the equations produced by the model for hydraulic head. Linear or nonlinear flow conditions may be simulated. PCG2 includes two reconditioning options : modified incomplete Cholesky preconditioning, which is efficient on scalar computers; and polynomial preconditioning, which requires less computer storage and, with modifications that depend on the computer used, is most efficient on vector computers . Convergence of the solver is determined using both head-change and residual criteria. Nonlinear problems are solved using Picard iterations. This documentation provides a description of the preconditioned conjugate gradient method and the two preconditioners, detailed instructions for linking PCG2 to the modular model, sample data inputs, a brief description of PCG2, and a FORTRAN listing.

[Doppler echocardiography of tricuspid insufficiency. Methods of quantification].

PubMed

Loubeyre, C; Tribouilloy, C; Adam, M C; Mirode, A; Trojette, F; Lesbre, J P

1994-01-01

Evaluation of tricuspid incompetence has benefitted considerably from the development of Doppler ultrasound. In addition to direct analysis of the valves, which provides information about the mechanism involved, this method is able to provide an accurate evaluation, mainly through use of the Doppler mode. In addition to new criteria being evaluated (mainly the convergence zone of the regurgitant jet), some indices are recognised as good quantitative parameters: extension of the regurgitant jet into the right atrium, anterograde tricuspid flow, laminar nature of the regurgitant flow, analysis of the flow in the supra-hepatic veins, this is only semi-quantitative, since the calculation of the regurgitation fraction from the pulsed Doppler does not seem to be reliable; This accurate semi-quantitative evaluation is made possible by careful and consistent use of all the criteria available. The authors set out to discuss the value of the various evaluation criteria mentioned in the literature and try to define a practical approach.

An Exact Dual Adjoint Solution Method for Turbulent Flows on Unstructured Grids

NASA Technical Reports Server (NTRS)

Nielsen, Eric J.; Lu, James; Park, Michael A.; Darmofal, David L.

2003-01-01

An algorithm for solving the discrete adjoint system based on an unstructured-grid discretization of the Navier-Stokes equations is presented. The method is constructed such that an adjoint solution exactly dual to a direct differentiation approach is recovered at each time step, yielding a convergence rate which is asymptotically equivalent to that of the primal system. The new approach is implemented within a three-dimensional unstructured-grid framework and results are presented for inviscid, laminar, and turbulent flows. Improvements to the baseline solution algorithm, such as line-implicit relaxation and a tight coupling of the turbulence model, are also presented. By storing nearest-neighbor terms in the residual computation, the dual scheme is computationally efficient, while requiring twice the memory of the flow solution. The scheme is expected to have a broad impact on computational problems related to design optimization as well as error estimation and grid adaptation efforts.

Multilevel Monte Carlo for two phase flow and Buckley–Leverett transport in random heterogeneous porous media

DOE Office of Scientific and Technical Information (OSTI.GOV)

Müller, Florian, E-mail: florian.mueller@sam.math.ethz.ch; Jenny, Patrick, E-mail: jenny@ifd.mavt.ethz.ch; Meyer, Daniel W., E-mail: meyerda@ethz.ch

2013-10-01

Monte Carlo (MC) is a well known method for quantifying uncertainty arising for example in subsurface flow problems. Although robust and easy to implement, MC suffers from slow convergence. Extending MC by means of multigrid techniques yields the multilevel Monte Carlo (MLMC) method. MLMC has proven to greatly accelerate MC for several applications including stochastic ordinary differential equations in finance, elliptic stochastic partial differential equations and also hyperbolic problems. In this study, MLMC is combined with a streamline-based solver to assess uncertain two phase flow and Buckley–Leverett transport in random heterogeneous porous media. The performance of MLMC is compared tomore » MC for a two dimensional reservoir with a multi-point Gaussian logarithmic permeability field. The influence of the variance and the correlation length of the logarithmic permeability on the MLMC performance is studied.« less

Computational Study of Fluidic Thrust Vectoring using Separation Control in a Nozzle

NASA Technical Reports Server (NTRS)

Deere, Karen; Berrier, Bobby L.; Flamm, Jeffrey D.; Johnson, Stuart K.

2003-01-01

A computational investigation of a two- dimensional nozzle was completed to assess the use of fluidic injection to manipulate flow separation and cause thrust vectoring of the primary jet thrust. The nozzle was designed with a recessed cavity to enhance the throat shifting method of fluidic thrust vectoring. The structured-grid, computational fluid dynamics code PAB3D was used to guide the design and analyze over 60 configurations. Nozzle design variables included cavity convergence angle, cavity length, fluidic injection angle, upstream minimum height, aft deck angle, and aft deck shape. All simulations were computed with a static freestream Mach number of 0.05. a nozzle pressure ratio of 3.858, and a fluidic injection flow rate equal to 6 percent of the primary flow rate. Results indicate that the recessed cavity enhances the throat shifting method of fluidic thrust vectoring and allows for greater thrust-vector angles without compromising thrust efficiency.

Semi-implicit time integration of atmospheric flows with characteristic-based flux partitioning

DOE Office of Scientific and Technical Information (OSTI.GOV)

Ghosh, Debojyoti; Constantinescu, Emil M.

2016-06-23

Here, this paper presents a characteristic-based flux partitioning for the semi-implicit time integration of atmospheric flows. Nonhydrostatic models require the solution of the compressible Euler equations. The acoustic time scale is significantly faster than the advective scale, yet it is typically not relevant to atmospheric and weather phenomena. The acoustic and advective components of the hyperbolic flux are separated in the characteristic space. High-order, conservative additive Runge-Kutta methods are applied to the partitioned equations so that the acoustic component is integrated in time implicitly with an unconditionally stable method, while the advective component is integrated explicitly. The time step ofmore » the overall algorithm is thus determined by the advective scale. Benchmark flow problems are used to demonstrate the accuracy, stability, and convergence of the proposed algorithm. The computational cost of the partitioned semi-implicit approach is compared with that of explicit time integration.« less

Reformulation of Possio's kernel with application to unsteady wind tunnel interference

NASA Technical Reports Server (NTRS)

Fromme, J. A.; Golberg, M. A.

1980-01-01

An efficient method for computing the Possio kernel has remained elusive up to the present time. In this paper the Possio is reformulated so that it can be computed accurately using existing high precision numerical quadrature techniques. Convergence to the correct values is demonstrated and optimization of the integration procedures is discussed. Since more general kernels such as those associated with unsteady flows in ventilated wind tunnels are analytic perturbations of the Possio free air kernel, a more accurate evaluation of their collocation matrices results with an exponential improvement in convergence. An application to predicting frequency response of an airfoil-trailing edge control system in a wind tunnel compared with that in free air is given showing strong interference effects.

On the convergence of a fully discrete scheme of LES type to physically relevant solutions of the incompressible Navier-Stokes

NASA Astrophysics Data System (ADS)

Berselli, Luigi C.; Spirito, Stefano

2018-06-01

Obtaining reliable numerical simulations of turbulent fluids is a challenging problem in computational fluid mechanics. The large eddy simulation (LES) models are efficient tools to approximate turbulent fluids, and an important step in the validation of these models is the ability to reproduce relevant properties of the flow. In this paper, we consider a fully discrete approximation of the Navier-Stokes-Voigt model by an implicit Euler algorithm (with respect to the time variable) and a Fourier-Galerkin method (in the space variables). We prove the convergence to weak solutions of the incompressible Navier-Stokes equations satisfying the natural local entropy condition, hence selecting the so-called physically relevant solutions.

An Initial Investigation of the Effects of Turbulence Models on the Convergence of the RK/Implicit Scheme

NASA Technical Reports Server (NTRS)

Swanson, R. C.; Rossow, C.-C.

2008-01-01

A three-stage Runge-Kutta (RK) scheme with multigrid and an implicit preconditioner has been shown to be an effective solver for the fluid dynamic equations. This scheme has been applied to both the compressible and essentially incompressible Reynolds-averaged Navier-Stokes (RANS) equations using the algebraic turbulence model of Baldwin and Lomax (BL). In this paper we focus on the convergence of the RK/implicit scheme when the effects of turbulence are represented by either the Spalart-Allmaras model or the Wilcox k-! model, which are frequently used models in practical fluid dynamic applications. Convergence behavior of the scheme with these turbulence models and the BL model are directly compared. For this initial investigation we solve the flow equations and the partial differential equations of the turbulence models indirectly coupled. With this approach we examine the convergence behavior of each system. Both point and line symmetric Gauss-Seidel are considered for approximating the inverse of the implicit operator of the flow solver. To solve the turbulence equations we use a diagonally dominant alternating direction implicit (DDADI) scheme. Computational results are presented for three airfoil flow cases and comparisons are made with experimental data. We demonstrate that the two-dimensional RANS equations and transport-type equations for turbulence modeling can be efficiently solved with an indirectly coupled algorithm that uses the RK/implicit scheme for the flow equations.

A comparative study of Rosenbrock-type and implicit Runge-Kutta time integration for discontinuous Galerkin method for unsteady 3D compressible Navier-Stokes equations

DOE Office of Scientific and Technical Information (OSTI.GOV)

Liu, Xiaodong; Xia, Yidong; Luo, Hong

A comparative study of two classes of third-order implicit time integration schemes is presented for a third-order hierarchical WENO reconstructed discontinuous Galerkin (rDG) method to solve the 3D unsteady compressible Navier-Stokes equations: — 1) the explicit first stage, single diagonally implicit Runge-Kutta (ESDIRK3) scheme, and 2) the Rosenbrock-Wanner (ROW) schemes based on the differential algebraic equations (DAEs) of Index-2. Compared with the ESDIRK3 scheme, a remarkable feature of the ROW schemes is that, they only require one approximate Jacobian matrix calculation every time step, thus considerably reducing the overall computational cost. A variety of test cases, ranging from inviscid flowsmore » to DNS of turbulent flows, are presented to assess the performance of these schemes. Here, numerical experiments demonstrate that the third-order ROW scheme for the DAEs of index-2 can not only achieve the designed formal order of temporal convergence accuracy in a benchmark test, but also require significantly less computing time than its ESDIRK3 counterpart to converge to the same level of discretization errors in all of the flow simulations in this study, indicating that the ROW methods provide an attractive alternative for the higher-order time-accurate integration of the unsteady compressible Navier-Stokes equations.« less

A comparative study of Rosenbrock-type and implicit Runge-Kutta time integration for discontinuous Galerkin method for unsteady 3D compressible Navier-Stokes equations

DOE PAGES

Liu, Xiaodong; Xia, Yidong; Luo, Hong; ...

2016-10-05

A comparative study of two classes of third-order implicit time integration schemes is presented for a third-order hierarchical WENO reconstructed discontinuous Galerkin (rDG) method to solve the 3D unsteady compressible Navier-Stokes equations: — 1) the explicit first stage, single diagonally implicit Runge-Kutta (ESDIRK3) scheme, and 2) the Rosenbrock-Wanner (ROW) schemes based on the differential algebraic equations (DAEs) of Index-2. Compared with the ESDIRK3 scheme, a remarkable feature of the ROW schemes is that, they only require one approximate Jacobian matrix calculation every time step, thus considerably reducing the overall computational cost. A variety of test cases, ranging from inviscid flowsmore » to DNS of turbulent flows, are presented to assess the performance of these schemes. Here, numerical experiments demonstrate that the third-order ROW scheme for the DAEs of index-2 can not only achieve the designed formal order of temporal convergence accuracy in a benchmark test, but also require significantly less computing time than its ESDIRK3 counterpart to converge to the same level of discretization errors in all of the flow simulations in this study, indicating that the ROW methods provide an attractive alternative for the higher-order time-accurate integration of the unsteady compressible Navier-Stokes equations.« less

Precision and accuracy of clinical quantification of myocardial blood flow by dynamic PET: A technical perspective.

PubMed

Moody, Jonathan B; Lee, Benjamin C; Corbett, James R; Ficaro, Edward P; Murthy, Venkatesh L

2015-10-01

A number of exciting advances in PET/CT technology and improvements in methodology have recently converged to enhance the feasibility of routine clinical quantification of myocardial blood flow and flow reserve. Recent promising clinical results are pointing toward an important role for myocardial blood flow in the care of patients. Absolute blood flow quantification can be a powerful clinical tool, but its utility will depend on maintaining precision and accuracy in the face of numerous potential sources of methodological errors. Here we review recent data and highlight the impact of PET instrumentation, image reconstruction, and quantification methods, and we emphasize (82)Rb cardiac PET which currently has the widest clinical application. It will be apparent that more data are needed, particularly in relation to newer PET technologies, as well as clinical standardization of PET protocols and methods. We provide recommendations for the methodological factors considered here. At present, myocardial flow reserve appears to be remarkably robust to various methodological errors; however, with greater attention to and more detailed understanding of these sources of error, the clinical benefits of stress-only blood flow measurement may eventually be more fully realized.

Meshfree and efficient modeling of swimming cells

NASA Astrophysics Data System (ADS)

Gallagher, Meurig T.; Smith, David J.

2018-05-01

Locomotion in Stokes flow is an intensively studied problem because it describes important biological phenomena such as the motility of many species' sperm, bacteria, algae, and protozoa. Numerical computations can be challenging, particularly in three dimensions, due to the presence of moving boundaries and complex geometries; methods which combine ease of implementation and computational efficiency are therefore needed. A recently proposed method to discretize the regularized Stokeslet boundary integral equation without the need for a connected mesh is applied to the inertialess locomotion problem in Stokes flow. The mathematical formulation and key aspects of the computational implementation in matlab® or GNU Octave are described, followed by numerical experiments with biflagellate algae and multiple uniflagellate sperm swimming between no-slip surfaces, for which both swimming trajectories and flow fields are calculated. These computational experiments required minutes of time on modest hardware; an extensible implementation is provided in a GitHub repository. The nearest-neighbor discretization dramatically improves convergence and robustness, a key challenge in extending the regularized Stokeslet method to complicated three-dimensional biological fluid problems.

A comparison of three-dimensional nonequilibrium solution algorithms applied to hypersonic flows with stiff chemical source terms

NASA Technical Reports Server (NTRS)

Palmer, Grant; Venkatapathy, Ethiraj

1993-01-01

Three solution algorithms, explicit underrelaxation, point implicit, and lower upper symmetric Gauss-Seidel (LUSGS), are used to compute nonequilibrium flow around the Apollo 4 return capsule at 62 km altitude. By varying the Mach number, the efficiency and robustness of the solution algorithms were tested for different levels of chemical stiffness. The performance of the solution algorithms degraded as the Mach number and stiffness of the flow increased. At Mach 15, 23, and 30, the LUSGS method produces an eight order of magnitude drop in the L2 norm of the energy residual in 1/3 to 1/2 the Cray C-90 computer time as compared to the point implicit and explicit under-relaxation methods. The explicit under-relaxation algorithm experienced convergence difficulties at Mach 23 and above. At Mach 40 the performance of the LUSGS algorithm deteriorates to the point it is out-performed by the point implicit method. The effects of the viscous terms are investigated. Grid dependency questions are explored.

Finite-difference method Stokes solver (FDMSS) for 3D pore geometries: Software development, validation and case studies

NASA Astrophysics Data System (ADS)

Gerke, Kirill M.; Vasilyev, Roman V.; Khirevich, Siarhei; Collins, Daniel; Karsanina, Marina V.; Sizonenko, Timofey O.; Korost, Dmitry V.; Lamontagne, Sébastien; Mallants, Dirk

2018-05-01

Permeability is one of the fundamental properties of porous media and is required for large-scale Darcian fluid flow and mass transport models. Whilst permeability can be measured directly at a range of scales, there are increasing opportunities to evaluate permeability from pore-scale fluid flow simulations. We introduce the free software Finite-Difference Method Stokes Solver (FDMSS) that solves Stokes equation using a finite-difference method (FDM) directly on voxelized 3D pore geometries (i.e. without meshing). Based on explicit convergence studies, validation on sphere packings with analytically known permeabilities, and comparison against lattice-Boltzmann and other published FDM studies, we conclude that FDMSS provides a computationally efficient and accurate basis for single-phase pore-scale flow simulations. By implementing an efficient parallelization and code optimization scheme, permeability inferences can now be made from 3D images of up to 109 voxels using modern desktop computers. Case studies demonstrate the broad applicability of the FDMSS software for both natural and artificial porous media.

Contaminant transport in wetland flows with bulk degradation and bed absorption

NASA Astrophysics Data System (ADS)

Wang, Ping; Chen, G. Q.

2017-09-01

Ecological degradation and absorption are ubiquitous and exert considerable influence on the contaminant transport in natural and constructed wetland flows. It creates an increased demand on models to accurately characterize the spatial concentration distribution of the transport process. This work extends a method of spatial concentration moments by considering the non-uniform longitudinal solute displacements along the vertical direction, and analytically determines the spatial concentration distribution in the very initial stage since source release with effects of bulk degradation and bed absorption. The present method is demonstrated to bear a more accurate prediction especially in the initial stage through convergence analysis of Hermite polynomials. Results reveal that contaminant cloud shows to be more contracted and reformed by bed absorption with increasing damping factor of wetland flows. Tremendous vertical concentration variation especially in the downstream of the contaminant cloud remains great even at asymptotic large times. Spatial concentration evolution by the extended method other than the mean by previous studies is potential for various implements associated with contaminant transport with strict environmental standards.

Multigrid Strategies for Viscous Flow Solvers on Anisotropic Unstructured Meshes

NASA Technical Reports Server (NTRS)

Movriplis, Dimitri J.

1998-01-01

Unstructured multigrid techniques for relieving the stiffness associated with high-Reynolds number viscous flow simulations on extremely stretched grids are investigated. One approach consists of employing a semi-coarsening or directional-coarsening technique, based on the directions of strong coupling within the mesh, in order to construct more optimal coarse grid levels. An alternate approach is developed which employs directional implicit smoothing with regular fully coarsened multigrid levels. The directional implicit smoothing is obtained by constructing implicit lines in the unstructured mesh based on the directions of strong coupling. Both approaches yield large increases in convergence rates over the traditional explicit full-coarsening multigrid algorithm. However, maximum benefits are achieved by combining the two approaches in a coupled manner into a single algorithm. An order of magnitude increase in convergence rate over the traditional explicit full-coarsening algorithm is demonstrated, and convergence rates for high-Reynolds number viscous flows which are independent of the grid aspect ratio are obtained. Further acceleration is provided by incorporating low-Mach-number preconditioning techniques, and a Newton-GMRES strategy which employs the multigrid scheme as a preconditioner. The compounding effects of these various techniques on speed of convergence is documented through several example test cases.

A high-order semi-explicit discontinuous Galerkin solver for 3D incompressible flow with application to DNS and LES of turbulent channel flow

NASA Astrophysics Data System (ADS)

Krank, Benjamin; Fehn, Niklas; Wall, Wolfgang A.; Kronbichler, Martin

2017-11-01

We present an efficient discontinuous Galerkin scheme for simulation of the incompressible Navier-Stokes equations including laminar and turbulent flow. We consider a semi-explicit high-order velocity-correction method for time integration as well as nodal equal-order discretizations for velocity and pressure. The non-linear convective term is treated explicitly while a linear system is solved for the pressure Poisson equation and the viscous term. The key feature of our solver is a consistent penalty term reducing the local divergence error in order to overcome recently reported instabilities in spatially under-resolved high-Reynolds-number flows as well as small time steps. This penalty method is similar to the grad-div stabilization widely used in continuous finite elements. We further review and compare our method to several other techniques recently proposed in literature to stabilize the method for such flow configurations. The solver is specifically designed for large-scale computations through matrix-free linear solvers including efficient preconditioning strategies and tensor-product elements, which have allowed us to scale this code up to 34.4 billion degrees of freedom and 147,456 CPU cores. We validate our code and demonstrate optimal convergence rates with laminar flows present in a vortex problem and flow past a cylinder and show applicability of our solver to direct numerical simulation as well as implicit large-eddy simulation of turbulent channel flow at Reτ = 180 as well as 590.

Slope instability in complex 3D topography promoted by convergent 3D groundwater flow

NASA Astrophysics Data System (ADS)

Reid, M. E.; Brien, D. L.

2012-12-01

Slope instability in complex topography is generally controlled by the interaction between gravitationally induced stresses, 3D strengths, and 3D pore-fluid pressure fields produced by flowing groundwater. As an example of this complexity, coastal bluffs sculpted by landsliding commonly exhibit a progression of undulating headlands and re-entrants. In this landscape, stresses differ between headlands and re-entrants and 3D groundwater flow varies from vertical rainfall infiltration to lateral groundwater flow on lower permeability layers with subsequent discharge at the curved bluff faces. In plan view, groundwater flow converges in the re-entrant regions. To investigate relative slope instability induced by undulating topography, we couple the USGS 3D limit-equilibrium slope-stability model, SCOOPS, with the USGS 3D groundwater flow model, MODFLOW. By rapidly analyzing the stability of millions of potential failures, the SCOOPS model can determine relative slope stability throughout the 3D domain underlying a digital elevation model (DEM), and it can utilize both fully 3D distributions of pore-water pressure and material strength. The two models are linked by first computing a groundwater-flow field in MODFLOW, and then computing stability in SCOOPS using the pore-pressure field derived from groundwater flow. Using these two models, our analyses of 60m high coastal bluffs in Seattle, Washington showed augmented instability in topographic re-entrants given recharge from a rainy season. Here, increased recharge led to elevated perched water tables with enhanced effects in the re-entrants owing to convergence of groundwater flow. Stability in these areas was reduced about 80% compared to equivalent dry conditions. To further isolate these effects, we examined groundwater flow and stability in hypothetical landscapes composed of uniform and equally spaced, oscillating headlands and re-entrants with differing amplitudes. The landscapes had a constant slope for both headlands and re-entrants to minimize slope effects on stability. Despite these equal slopes, our analyses, given dry conditions, illustrated that the headlands can be 5-7% less stable than the re-entrants, owing to the geometry of the 3D failure mass with the lowest stability. We then simulated groundwater flow in these landscapes; flow was caused by recharge perching on a horizontal low permeability layer with discharge at the bluff faces. By systematically varying recharge, hydraulic conductivity of the material, and conductance at the bluffs, we created different 3D pore-pressure fields. Recharge rates and hydraulic conductivities controlled the height of the water table, whereas bluff conductance influenced the gradient of the water table near the bluff face. Given elevated water tables with steep gradients, bluffs in the re-entrants became unstable where flow converged. Thus, with progressively stronger effects from water flow, overall instability evolved from relatively unstable headlands to more uniform stability to relatively unstable re-entrants. Larger re-entrants led to more 3D flow convergence and greater localized instability. One- or two-dimensional models cannot fully characterize slope instability in complex topography.

An installed nacelle design code using a multiblock Euler solver. Volume 1: Theory document

NASA Technical Reports Server (NTRS)

Chen, H. C.

1992-01-01

An efficient multiblock Euler design code was developed for designing a nacelle installed on geometrically complex airplane configurations. This approach employed a design driver based on a direct iterative surface curvature method developed at LaRC. A general multiblock Euler flow solver was used for computing flow around complex geometries. The flow solver used a finite-volume formulation with explicit time-stepping to solve the Euler Equations. It used a multiblock version of the multigrid method to accelerate the convergence of the calculations. The design driver successively updated the surface geometry to reduce the difference between the computed and target pressure distributions. In the flow solver, the change in surface geometry was simulated by applying surface transpiration boundary conditions to avoid repeated grid generation during design iterations. Smoothness of the designed surface was ensured by alternate application of streamwise and circumferential smoothings. The capability and efficiency of the code was demonstrated through the design of both an isolated nacelle and an installed nacelle at various flow conditions. Information on the execution of the computer program is provided in volume 2.

Viscid/inviscid interaction analysis of thrust augmenting ejectors

NASA Technical Reports Server (NTRS)

Bevilacqua, P. M.; Dejoode, A. D.

1979-01-01

A method was developed for calculating the static performance of thrust augmenting ejectors by matching a viscous solution for the flow through the ejector to an inviscid solution for the flow outside the ejector. A two dimensional analysis utilizing a turbulence kinetic energy model is used to calculate the rate of entrainment by the jets. Vortex panel methods are then used with the requirement that the ejector shroud must be a streamline of the flow induced by the jets to determine the strength of circulation generated around the shroud. In effect, the ejector shroud is considered to be flying in the velocity field of the jets. The solution is converged by iterating between the rate of entrainment and the strength of the circulation. This approach offers the advantage of including external influences on the flow through the ejector. Comparisons with data are presented for an ejector having a single central nozzle and Coanda jet on the walls. The accuracy of the matched solution is found to be especially sensitive to the jet flap effect of the flow just downstream of the ejector exit.

Towards inverse modeling of turbidity currents: The inverse lock-exchange problem

NASA Astrophysics Data System (ADS)

Lesshafft, Lutz; Meiburg, Eckart; Kneller, Ben; Marsden, Alison

2011-04-01

A new approach is introduced for turbidite modeling, leveraging the potential of computational fluid dynamics methods to simulate the flow processes that led to turbidite formation. The practical use of numerical flow simulation for the purpose of turbidite modeling so far is hindered by the need to specify parameters and initial flow conditions that are a priori unknown. The present study proposes a method to determine optimal simulation parameters via an automated optimization process. An iterative procedure matches deposit predictions from successive flow simulations against available localized reference data, as in practice may be obtained from well logs, and aims at convergence towards the best-fit scenario. The final result is a prediction of the entire deposit thickness and local grain size distribution. The optimization strategy is based on a derivative-free, surrogate-based technique. Direct numerical simulations are performed to compute the flow dynamics. A proof of concept is successfully conducted for the simple test case of a two-dimensional lock-exchange turbidity current. The optimization approach is demonstrated to accurately retrieve the initial conditions used in a reference calculation.

Design optimization of axial flow hydraulic turbine runner: Part I - an improved Q3D inverse method

NASA Astrophysics Data System (ADS)

Peng, Guoyi; Cao, Shuliang; Ishizuka, Masaru; Hayama, Shinji

2002-06-01

With the aim of constructing a comprehensive design optimization procedure of axial flow hydraulic turbine, an improved quasi-three-dimensional inverse method has been proposed from the viewpoint of system and a set of rotational flow governing equations as well as a blade geometry design equation has been derived. The computation domain is firstly taken from the inlet of guide vane to the far outlet of runner blade in the inverse method and flows in different regions are solved simultaneously. So the influence of wicket gate parameters on the runner blade design can be considered and the difficulty to define the flow condition at the runner blade inlet is surmounted. As a pre-computation of initial blade design on S2m surface is newly adopted, the iteration of S1 and S2m surfaces has been reduced greatly and the convergence of inverse computation has been improved. The present model has been applied to the inverse computation of a Kaplan turbine runner. Experimental results and the direct flow analysis have proved the validation of inverse computation. Numerical investigations show that a proper enlargement of guide vane distribution diameter is advantageous to improve the performance of axial hydraulic turbine runner. Copyright

PDF approach for compressible turbulent reacting flows

NASA Technical Reports Server (NTRS)

Hsu, A. T.; Tsai, Y.-L. P.; Raju, M. S.

1993-01-01

The objective of the present work is to develop a probability density function (pdf) turbulence model for compressible reacting flows for use with a CFD flow solver. The probability density function of the species mass fraction and enthalpy are obtained by solving a pdf evolution equation using a Monte Carlo scheme. The pdf solution procedure is coupled with a compressible CFD flow solver which provides the velocity and pressure fields. A modeled pdf equation for compressible flows, capable of capturing shock waves and suitable to the present coupling scheme, is proposed and tested. Convergence of the combined finite-volume Monte Carlo solution procedure is discussed, and an averaging procedure is developed to provide smooth Monte-Carlo solutions to ensure convergence. Two supersonic diffusion flames are studied using the proposed pdf model and the results are compared with experimental data; marked improvements over CFD solutions without pdf are observed. Preliminary applications of pdf to 3D flows are also reported.

Blade design and analysis using a modified Euler solver

NASA Technical Reports Server (NTRS)

Leonard, O.; Vandenbraembussche, R. A.

1991-01-01

An iterative method for blade design based on Euler solver and described in an earlier paper is used to design compressor and turbine blades providing shock free transonic flows. The method shows a rapid convergence, and indicates how much the flow is sensitive to small modifications of the blade geometry, that the classical iterative use of analysis methods might not be able to define. The relationship between the required Mach number distribution and the resulting geometry is discussed. Examples show how geometrical constraints imposed upon the blade shape can be respected by using free geometrical parameters or by relaxing the required Mach number distribution. The same code is used both for the design of the required geometry and for the off-design calculations. Examples illustrate the difficulty of designing blade shapes with optimal performance also outside of the design point.

A monolithic homotopy continuation algorithm with application to computational fluid dynamics

NASA Astrophysics Data System (ADS)

Brown, David A.; Zingg, David W.

2016-09-01

A new class of homotopy continuation methods is developed suitable for globalizing quasi-Newton methods for large sparse nonlinear systems of equations. The new continuation methods, described as monolithic homotopy continuation, differ from the classical predictor-corrector algorithm in that the predictor and corrector phases are replaced with a single phase which includes both a predictor and corrector component. Conditional convergence and stability are proved analytically. Using a Laplacian-like operator to construct the homotopy, the new algorithm is shown to be more efficient than the predictor-corrector homotopy continuation algorithm as well as an implementation of the widely-used pseudo-transient continuation algorithm for some inviscid and turbulent, subsonic and transonic external aerodynamic flows over the ONERA M6 wing and the NACA 0012 airfoil using a parallel implicit Newton-Krylov finite-difference flow solver.

Parallel discontinuous Galerkin FEM for computing hyperbolic conservation law on unstructured grids

NASA Astrophysics Data System (ADS)

Ma, Xinrong; Duan, Zhijian

2018-04-01

High-order resolution Discontinuous Galerkin finite element methods (DGFEM) has been known as a good method for solving Euler equations and Navier-Stokes equations on unstructured grid, but it costs too much computational resources. An efficient parallel algorithm was presented for solving the compressible Euler equations. Moreover, the multigrid strategy based on three-stage three-order TVD Runge-Kutta scheme was used in order to improve the computational efficiency of DGFEM and accelerate the convergence of the solution of unsteady compressible Euler equations. In order to make each processor maintain load balancing, the domain decomposition method was employed. Numerical experiment performed for the inviscid transonic flow fluid problems around NACA0012 airfoil and M6 wing. The results indicated that our parallel algorithm can improve acceleration and efficiency significantly, which is suitable for calculating the complex flow fluid.

Method and apparatus for ultrasonic doppler velocimetry using speed of sound and reflection mode pulsed wideband doppler

DOEpatents

Shekarriz, Alireza; Sheen, David M.

2000-01-01

According to the present invention, a method and apparatus rely upon tomographic measurement of the speed of sound and fluid velocity in a pipe. The invention provides a more accurate profile of velocity within flow fields where the speed of sound varies within the cross-section of the pipe. This profile is obtained by reconstruction of the velocity profile from the local speed of sound measurement simultaneously with the flow velocity. The method of the present invention is real-time tomographic ultrasonic Doppler velocimetry utilizing a to plurality of ultrasonic transmission and reflection measurements along two orthogonal sets of parallel acoustic lines-of-sight. The fluid velocity profile and the acoustic velocity profile are determined by iteration between determining a fluid velocity profile and measuring local acoustic velocity until convergence is reached.

Geophysical constraints on geodynamic processes at convergent margins: A global perspective

NASA Astrophysics Data System (ADS)

Artemieva, Irina; Thybo, Hans; Shulgin, Alexey

2016-04-01

Convergent margins, being the boundaries between colliding lithospheric plates, form the most disastrous areas in the world due to intensive, strong seismicity and volcanism. We review global geophysical data in order to illustrate the effects of the plate tectonic processes at convergent margins on the crustal and upper mantle structure, seismicity, and geometry of subducting slab. We present global maps of free-air and Bouguer gravity anomalies, heat flow, seismicity, seismic Vs anomalies in the upper mantle, and plate convergence rate, as well as 20 profiles across different convergent margins. A global analysis of these data for three types of convergent margins, formed by ocean-ocean, ocean-continent, and continent-continent collisions, allows us to recognize the following patterns. (1) Plate convergence rate depends on the type of convergent margins and it is significantly larger when, at least, one of the plates is oceanic. However, the oldest oceanic plate in the Pacific ocean has the smallest convergence rate. (2) The presence of an oceanic plate is, in general, required for generation of high-magnitude (M N 8.0) earthquakes and for generating intermediate and deep seismicity along the convergent margins. When oceanic slabs subduct beneath a continent, a gap in the seismogenic zone exists at depths between ca. 250 km and 500 km. Given that the seismogenic zone terminates at ca. 200 km depth in case of continent-continent collision, we propose oceanic origin of subducting slabs beneath the Zagros, the Pamir, and the Vrancea zone. (3) Dip angle of the subducting slab in continent-ocean collision does not correlate neither with the age of subducting oceanic slab, nor with the convergence rate. For ocean-ocean subduction, clear trends are recognized: steeply dipping slabs are characteristic of young subducting plates and of oceanic plates with high convergence rate, with slab rotation towards a near-vertical dip angle at depths below ca. 500 km at very high convergence rate. (4) Local isostasy is not satisfied at the convergent margins as evidenced by strong free air gravity anomalies of positive and negative signs. However, near-isostatic equilibrium may exist in broad zones of distributed deformation such as Tibet. (5) No systematic patterns are recognized in heat flow data due to strong heterogeneity of measured values which are strongly affected by hydrothermal circulation, magmatic activity, crustal faulting, horizontal heat transfer, and also due to low number of heat flow measurements across many margins. (6) Low upper mantle Vs seismic velocities beneath the convergent margins are restricted to the upper 150 km and may be related to mantle wedge melting which is confined to shallow mantle levels. Artemieva, I.M., Thybo, H., and Shulgin, A., 2015. Geophysical constraints on geodynamic processes at convergent margins: A global perspective. Gondwana Research, http://dx.doi.org/10.1016/j.gr.2015.06.010

Parameter investigation with line-implicit lower-upper symmetric Gauss-Seidel on 3D stretched grids

NASA Astrophysics Data System (ADS)

Otero, Evelyn; Eliasson, Peter

2015-03-01

An implicit lower-upper symmetric Gauss-Seidel (LU-SGS) solver has been implemented as a multigrid smoother combined with a line-implicit method as an acceleration technique for Reynolds-averaged Navier-Stokes (RANS) simulation on stretched meshes. The computational fluid dynamics code concerned is Edge, an edge-based finite volume Navier-Stokes flow solver for structured and unstructured grids. The paper focuses on the investigation of the parameters related to our novel line-implicit LU-SGS solver for convergence acceleration on 3D RANS meshes. The LU-SGS parameters are defined as the Courant-Friedrichs-Lewy number, the left-hand side dissipation, and the convergence of iterative solution of the linear problem arising from the linearisation of the implicit scheme. The influence of these parameters on the overall convergence is presented and default values are defined for maximum convergence acceleration. The optimised settings are applied to 3D RANS computations for comparison with explicit and line-implicit Runge-Kutta smoothing. For most of the cases, a computing time acceleration of the order of 2 is found depending on the mesh type, namely the boundary layer and the magnitude of residual reduction.

Comparison of gravimetric and mantle flow solutions for sub-lithopsheric stress modeling and their combination

NASA Astrophysics Data System (ADS)

Eshagh, Mehdi; Steinberger, Bernhard; Tenzer, Robert; Tassara, Andrés

2018-05-01

Based on Hager and O'Connell's solution to mantle flow equations, the stresses induced by mantle convection are determined using the density and viscosity structure in addition to topographic data and a plate velocity model. The solution to mantle flow equations requires the knowledge of mantle properties that are typically retrieved from seismic information. Large parts of the world are, however, not yet covered sufficiently by seismic surveys. An alternative method of modeling the stress field was introduced by Runcorn. He formulated a direct relation between the stress field and gravity data, while adopting several assumptions, particularly disregarding the toroidal mantle flow component and mantle viscosity variations. A possible way to overcome theoretical deficiencies of Runcorn's theory as well as some practical limitations of applying Hager and O'Connell's theory (in the absence of seismic data) is to combine these two methods. In this study, we apply a least-squares analysis to combine these two methods based on the gravity data inversion constraint on mantle flow equations. In particular, we use vertical gravity gradients from the Gravity field and steady state Ocean Circulation Explorer that are corrected for the gravitational contribution of crustal density heterogeneities prior to applying a localized gravity-gradient inversion. This gravitational contribution is estimated based on combining the Vening Meinesz-Moritz and flexural isostatic theories. Moreover, we treat the non-isostatic effect implicitly by applying a band-limited kernel of the integral equation during the inversion. In numerical studies of modeling, the stress field within the South American continental lithosphere we compare the results obtained after applying Runcorn and Hager and O'Connell's methods as well as their combination. The results show that, according to Hager and O'Connell's (mantle flow) solution, the maximum stress intensity is inferred under the northern Andes. Additional large stress anomalies are detected along the central and southern Andes, while stresses under most of old, stable cratonic formations are much less pronounced or absent. A prevailing stress-vector orientation realistically resembles a convergent mantle flow and downward currents under continental basins that separate Andean Orogeny from the Amazonian Shield and adjacent cratons. Runcorn's (gravimetric) solution, on the other hand, reflects a tectonic response of the lithosphere to mantle flow, with the maximum stress intensity detected along the subduction zone between the Nazca and Altiplano plates and along the convergent tectonic margin between the Altiplano and South American plates. The results also reveal a very close agreement between the results obtained from the combined and Hager and O'Connell's solutions.

Convergence of Newton's method for a single real equation

NASA Technical Reports Server (NTRS)

Campbell, C. W.

1985-01-01

Newton's method for finding the zeroes of a single real function is investigated in some detail. Convergence is generally checked using the Contraction Mapping Theorem which yields sufficient but not necessary conditions for convergence of the general single point iteration method. The resulting convergence intervals are frequently considerably smaller than actual convergence zones. For a specific single point iteration method, such as Newton's method, better estimates of regions of convergence should be possible. A technique is described which, under certain conditions (frequently satisfied by well behaved functions) gives much larger zones where convergence is guaranteed.

WIND: Computer program for calculation of three dimensional potential compressible flow about wind turbine rotor blades

NASA Technical Reports Server (NTRS)

Dulikravich, D. S.

1980-01-01

A computer program is presented which numerically solves an exact, full potential equation (FPE) for three dimensional, steady, inviscid flow through an isolated wind turbine rotor. The program automatically generates a three dimensional, boundary conforming grid and iteratively solves the FPE while fully accounting for both the rotating cascade and Coriolis effects. The numerical techniques incorporated involve rotated, type dependent finite differencing, a finite volume method, artificial viscosity in conservative form, and a successive line overrelaxation combined with the sequential grid refinement procedure to accelerate the iterative convergence rate. Consequently, the WIND program is capable of accurately analyzing incompressible and compressible flows, including those that are locally transonic and terminated by weak shocks. The program can also be used to analyze the flow around isolated aircraft propellers and helicopter rotors in hover as long as the total relative Mach number of the oncoming flow is subsonic.

Computer program for calculating full potential transonic, quasi-three-dimensional flow through a rotating turbomachinery blade row

NASA Technical Reports Server (NTRS)

Farrell, C. A.

1982-01-01

A fast, reliable computer code is described for calculating the flow field about a cascade of arbitrary two dimensional airfoils. The method approximates the three dimensional flow in a turbomachinery blade row by correcting for stream tube convergence and radius change in the throughflow direction. A fully conservative solution of the full potential equation is combined with the finite volume technique on a body-fitted periodic mesh, with an artificial density imposed in the transonic region to insure stability and the capture of shock waves. The instructions required to set up and use the code are included. The name of the code is QSONIC. A numerical example is also given to illustrate the output of the program.

Textbook Multigrid Efficiency for the Steady Euler Equations

NASA Technical Reports Server (NTRS)

Roberts, Thomas W.; Sidilkover, David; Swanson, R. C.

2004-01-01

A fast multigrid solver for the steady incompressible Euler equations is presented. Unlike time-marching schemes, this approach uses relaxation of the steady equations. Application of this method results in a discretization that correctly distinguishes between the advection and elliptic parts of the operator, allowing efficient smoothers to be constructed. Solvers for both unstructured triangular grids and structured quadrilateral grids have been written. Computations for channel flow and flow over a nonlifting airfoil have computed. Using Gauss-Seidel relaxation ordered in the flow direction, textbook multigrid convergence rates of nearly one order-of-magnitude residual reduction per multigrid cycle are achieved, independent of the grid spacing. This approach also may be applied to the compressible Euler equations and the incompressible Navier-Stokes equations.

Radiation effects on the flow of Powell-Eyring fluid past an unsteady inclined stretching sheet with non-uniform heat source/sink.

PubMed

Hayat, Tasawar; Asad, Sadia; Mustafa, Meraj; Alsaedi, Ahmed

2014-01-01

This study investigates the unsteady flow of Powell-Eyring fluid past an inclined stretching sheet. Unsteadiness in the flow is due to the time-dependence of the stretching velocity and wall temperature. Mathematical analysis is performed in the presence of thermal radiation and non-uniform heat source/sink. The relevant boundary layer equations are reduced into self-similar forms by suitable transformations. The analytic solutions are constructed in a series form by homotopy analysis method (HAM). The convergence interval of the auxiliary parameter is obtained. Graphical results displaying the influence of interesting parameters are given. Numerical values of skin friction coefficient and local Nusselt number are computed and analyzed.

Assessment of Preconditioner for a USM3D Hierarchical Adaptive Nonlinear Method (HANIM) (Invited)

NASA Technical Reports Server (NTRS)

Pandya, Mohagna J.; Diskin, Boris; Thomas, James L.; Frink, Neal T.

2016-01-01

Enhancements to the previously reported mixed-element USM3D Hierarchical Adaptive Nonlinear Iteration Method (HANIM) framework have been made to further improve robustness, efficiency, and accuracy of computational fluid dynamic simulations. The key enhancements include a multi-color line-implicit preconditioner, a discretely consistent symmetry boundary condition, and a line-mapping method for the turbulence source term discretization. The USM3D iterative convergence for the turbulent flows is assessed on four configurations. The configurations include a two-dimensional (2D) bump-in-channel, the 2D NACA 0012 airfoil, a three-dimensional (3D) bump-in-channel, and a 3D hemisphere cylinder. The Reynolds Averaged Navier Stokes (RANS) solutions have been obtained using a Spalart-Allmaras turbulence model and families of uniformly refined nested grids. Two types of HANIM solutions using line- and point-implicit preconditioners have been computed. Additional solutions using the point-implicit preconditioner alone (PA) method that broadly represents the baseline solver technology have also been computed. The line-implicit HANIM shows superior iterative convergence in most cases with progressively increasing benefits on finer grids.

An overlapped grid method for multigrid, finite volume/difference flow solvers: MaGGiE

NASA Technical Reports Server (NTRS)

Baysal, Oktay; Lessard, Victor R.

1990-01-01

The objective is to develop a domain decomposition method via overlapping/embedding the component grids, which is to be used by upwind, multi-grid, finite volume solution algorithms. A computer code, given the name MaGGiE (Multi-Geometry Grid Embedder) is developed to meet this objective. MaGGiE takes independently generated component grids as input, and automatically constructs the composite mesh and interpolation data, which can be used by the finite volume solution methods with or without multigrid convergence acceleration. Six demonstrative examples showing various aspects of the overlap technique are presented and discussed. These cases are used for developing the procedure for overlapping grids of different topologies, and to evaluate the grid connection and interpolation data for finite volume calculations on a composite mesh. Time fluxes are transferred between mesh interfaces using a trilinear interpolation procedure. Conservation losses are minimal at the interfaces using this method. The multi-grid solution algorithm, using the coaser grid connections, improves the convergence time history as compared to the solution on composite mesh without multi-gridding.

Solving groundwater flow problems by conjugate-gradient methods and the strongly implicit procedure

USGS Publications Warehouse

Hill, Mary C.

1990-01-01

The performance of the preconditioned conjugate-gradient method with three preconditioners is compared with the strongly implicit procedure (SIP) using a scalar computer. The preconditioners considered are the incomplete Cholesky (ICCG) and the modified incomplete Cholesky (MICCG), which require the same computer storage as SIP as programmed for a problem with a symmetric matrix, and a polynomial preconditioner (POLCG), which requires less computer storage than SIP. Although POLCG is usually used on vector computers, it is included here because of its small storage requirements. In this paper, published comparisons of the solvers are evaluated, all four solvers are compared for the first time, and new test cases are presented to provide a more complete basis by which the solvers can be judged for typical groundwater flow problems. Based on nine test cases, the following conclusions are reached: (1) SIP is actually as efficient as ICCG for some of the published, linear, two-dimensional test cases that were reportedly solved much more efficiently by ICCG; (2) SIP is more efficient than other published comparisons would indicate when common convergence criteria are used; and (3) for problems that are three-dimensional, nonlinear, or both, and for which common convergence criteria are used, SIP is often more efficient than ICCG, and is sometimes more efficient than MICCG.

New echocardiographic windows for quantitative determination of aortic regurgitation volume using color Doppler flow convergence and vena contracta

NASA Technical Reports Server (NTRS)

Shiota, T.; Jones, M.; Agler, D. A.; McDonald, R. W.; Marcella, C. P.; Qin, J. X.; Zetts, A. D.; Greenberg, N. L.; Cardon, L. A.; Sun, J. P.;

New echocardiographic windows for quantitative determination of aortic regurgitation volume using color Doppler flow convergence and vena contracta.

PubMed

Shiota, T; Jones, M; Agler, D A; McDonald, R W; Marcella, C P; Qin, J X; Zetts, A D; Greenberg, N L; Cardon, L A; Sun, J P; Sahn, D J; Thomas, J D

1999-04-01

Color Doppler images of aortic regurgitation (AR) flow acceleration, flow convergence (FC), and the vena contracta (VC) have been reported to be useful for evaluating severity of AR. However, clinical application of these methods has been limited because of the difficulty in clearly imaging the FC and VC. This study aimed to explore new windows for imaging the FC and VC to evaluate AR volumes in patients and to validate this in animals with chronic AR. Forty patients with AR and 17 hemodynamic states in 4 sheep with strictly quantified AR volumes were evaluated. A Toshiba SSH 380A with a 3.75-MHz transducer was used to image the FC and VC. After routine echo Doppler imaging, patients were repositioned in the right lateral decubitus position, and the FC and VC were imaged from high right parasternal windows. In only 15 of the 40 patients was it possible to image clearly and measure accurately the FC and VC from conventional (left decubitus) apical or parasternal views. In contrast, 31 of 40 patients had clearly imaged FC regions and VCs using the new windows. In patients, AR volumes derived from the FC and VC methods combined with continuous velocity agreed well with each other (r = 0.97, mean difference = -7.9 ml +/- 9.9 ml/beat). In chronic animal model studies, AR volumes derived from both the VC and the FC agreed well with the electromagnetically derived AR volumes (r = 0.92, mean difference = -1.3 +/- 4.0 ml/beat). By imaging from high right parasternal windows in the right decubitus position, complementary use of the FC and VC methods can provide clinically valuable information about AR volumes.

New preconditioning strategy for Jacobian-free solvers for variably saturated flows with Richards’ equation

DOE Office of Scientific and Technical Information (OSTI.GOV)

Lipnikov, Konstantin; Moulton, David; Svyatskiy, Daniil

2016-04-29

We develop a new approach for solving the nonlinear Richards’ equation arising in variably saturated flow modeling. The growing complexity of geometric models for simulation of subsurface flows leads to the necessity of using unstructured meshes and advanced discretization methods. Typically, a numerical solution is obtained by first discretizing PDEs and then solving the resulting system of nonlinear discrete equations with a Newton-Raphson-type method. Efficiency and robustness of the existing solvers rely on many factors, including an empiric quality control of intermediate iterates, complexity of the employed discretization method and a customized preconditioner. We propose and analyze a new preconditioningmore » strategy that is based on a stable discretization of the continuum Jacobian. We will show with numerical experiments for challenging problems in subsurface hydrology that this new preconditioner improves convergence of the existing Jacobian-free solvers 3-20 times. Furthermore, we show that the Picard method with this preconditioner becomes a more efficient nonlinear solver than a few widely used Jacobian-free solvers.« less

Finite volume multigrid method of the planar contraction flow of a viscoelastic fluid

NASA Astrophysics Data System (ADS)

Moatssime, H. Al; Esselaoui, D.; Hakim, A.; Raghay, S.

2001-08-01

This paper reports on a numerical algorithm for the steady flow of viscoelastic fluid. The conservative and constitutive equations are solved using the finite volume method (FVM) with a hybrid scheme for the velocities and first-order upwind approximation for the viscoelastic stress. A non-uniform staggered grid system is used. The iterative SIMPLE algorithm is employed to relax the coupled momentum and continuity equations. The non-linear algebraic equations over the flow domain are solved iteratively by the symmetrical coupled Gauss-Seidel (SCGS) method. In both, the full approximation storage (FAS) multigrid algorithm is used. An Oldroyd-B fluid model was selected for the calculation. Results are reported for planar 4:1 abrupt contraction at various Weissenberg numbers. The solutions are found to be stable and smooth. The solutions show that at high Weissenberg number the domain must be long enough. The convergence of the method has been verified with grid refinement. All the calculations have been performed on a PC equipped with a Pentium III processor at 550 MHz. Copyright

Nested sparse grid collocation method with delay and transformation for subsurface flow and transport problems

NASA Astrophysics Data System (ADS)

Liao, Qinzhuo; Zhang, Dongxiao; Tchelepi, Hamdi

2017-06-01

In numerical modeling of subsurface flow and transport problems, formation properties may not be deterministically characterized, which leads to uncertainty in simulation results. In this study, we propose a sparse grid collocation method, which adopts nested quadrature rules with delay and transformation to quantify the uncertainty of model solutions. We show that the nested Kronrod-Patterson-Hermite quadrature is more efficient than the unnested Gauss-Hermite quadrature. We compare the convergence rates of various quadrature rules including the domain truncation and domain mapping approaches. To further improve accuracy and efficiency, we present a delayed process in selecting quadrature nodes and a transformed process for approximating unsmooth or discontinuous solutions. The proposed method is tested by an analytical function and in one-dimensional single-phase and two-phase flow problems with different spatial variances and correlation lengths. An additional example is given to demonstrate its applicability to three-dimensional black-oil models. It is found from these examples that the proposed method provides a promising approach for obtaining satisfactory estimation of the solution statistics and is much more efficient than the Monte-Carlo simulations.

Flow in a porous nozzle with massive wall injection

NASA Technical Reports Server (NTRS)

Kinney, R. B.

1973-01-01

An analytical and experimental investigation has been conducted to determine the effect of massive wall injection on the flow characteristics in a nozzle. The experiments were performed on a water table with a porous-nozzle test section. This had 45 deg and 15 deg half angles of convergence and divergence, respectively, throat radius of 2.5 inches, and throat width of 3 inches. The hydraulic analogy was employed to qualitatively extend the results to a compressible gas flow through the nozzle. An analysis of the water table flow was made using a one-dimensional flow assumption in the continuity and momentum equations. An analysis of a compressible flow in a nozzle was made in a manner analogous to that for the water flow. It is shown that the effect of blowing is to move the sonic position downstream of the geometric throat. Similar results were determined for the incompressible water table flow. Limited photographic results are presented for an injection of air, CO2, and Freon-12 into a main-stream air flow in a convergent-divergent nozzle. Schlieren photographs were used to visualize the flow.

A kernel function method for computing steady and oscillatory supersonic aerodynamics with interference.

NASA Technical Reports Server (NTRS)

Cunningham, A. M., Jr.

1973-01-01

The method presented uses a collocation technique with the nonplanar kernel function to solve supersonic lifting surface problems with and without interference. A set of pressure functions are developed based on conical flow theory solutions which account for discontinuities in the supersonic pressure distributions. These functions permit faster solution convergence than is possible with conventional supersonic pressure functions. An improper integral of a 3/2 power singularity along the Mach hyperbola of the nonplanar supersonic kernel function is described and treated. The method is compared with other theories and experiment for a variety of cases.

Efficient spectral computation of the stationary states of rotating Bose-Einstein condensates by preconditioned nonlinear conjugate gradient methods

NASA Astrophysics Data System (ADS)

Antoine, Xavier; Levitt, Antoine; Tang, Qinglin

2017-08-01

We propose a preconditioned nonlinear conjugate gradient method coupled with a spectral spatial discretization scheme for computing the ground states (GS) of rotating Bose-Einstein condensates (BEC), modeled by the Gross-Pitaevskii Equation (GPE). We first start by reviewing the classical gradient flow (also known as imaginary time (IMT)) method which considers the problem from the PDE standpoint, leading to numerically solve a dissipative equation. Based on this IMT equation, we analyze the forward Euler (FE), Crank-Nicolson (CN) and the classical backward Euler (BE) schemes for linear problems and recognize classical power iterations, allowing us to derive convergence rates. By considering the alternative point of view of minimization problems, we propose the preconditioned steepest descent (PSD) and conjugate gradient (PCG) methods for the GS computation of the GPE. We investigate the choice of the preconditioner, which plays a key role in the acceleration of the convergence process. The performance of the new algorithms is tested in 1D, 2D and 3D. We conclude that the PCG method outperforms all the previous methods, most particularly for 2D and 3D fast rotating BECs, while being simple to implement.

Application of multi-grid methods for solving the Navier-Stokes equations

NASA Technical Reports Server (NTRS)

Demuren, A. O.

1989-01-01

The application of a class of multi-grid methods to the solution of the Navier-Stokes equations for two-dimensional laminar flow problems is discussed. The methods consist of combining the full approximation scheme-full multi-grid technique (FAS-FMG) with point-, line-, or plane-relaxation routines for solving the Navier-Stokes equations in primitive variables. The performance of the multi-grid methods is compared to that of several single-grid methods. The results show that much faster convergence can be procured through the use of the multi-grid approach than through the various suggestions for improving single-grid methods. The importance of the choice of relaxation scheme for the multi-grid method is illustrated.

Application of multi-grid methods for solving the Navier-Stokes equations

NASA Technical Reports Server (NTRS)

Demuren, A. O.

1989-01-01

This paper presents the application of a class of multi-grid methods to the solution of the Navier-Stokes equations for two-dimensional laminar flow problems. The methods consists of combining the full approximation scheme-full multi-grid technique (FAS-FMG) with point-, line- or plane-relaxation routines for solving the Navier-Stokes equations in primitive variables. The performance of the multi-grid methods is compared to those of several single-grid methods. The results show that much faster convergence can be procured through the use of the multi-grid approach than through the various suggestions for improving single-grid methods. The importance of the choice of relaxation scheme for the multi-grid method is illustrated.

Analysis of uncertainties and convergence of the statistical quantities in turbulent wall-bounded flows by means of a physically based criterion

NASA Astrophysics Data System (ADS)

Andrade, João Rodrigo; Martins, Ramon Silva; Thompson, Roney Leon; Mompean, Gilmar; da Silveira Neto, Aristeu

2018-04-01

The present paper provides an analysis of the statistical uncertainties associated with direct numerical simulation (DNS) results and experimental data for turbulent channel and pipe flows, showing a new physically based quantification of these errors, to improve the determination of the statistical deviations between DNSs and experiments. The analysis is carried out using a recently proposed criterion by Thompson et al. ["A methodology to evaluate statistical errors in DNS data of plane channel flows," Comput. Fluids 130, 1-7 (2016)] for fully turbulent plane channel flows, where the mean velocity error is estimated by considering the Reynolds stress tensor, and using the balance of the mean force equation. It also presents how the residual error evolves in time for a DNS of a plane channel flow, and the influence of the Reynolds number on its convergence rate. The root mean square of the residual error is shown in order to capture a single quantitative value of the error associated with the dimensionless averaging time. The evolution in time of the error norm is compared with the final error provided by DNS data of similar Reynolds numbers available in the literature. A direct consequence of this approach is that it was possible to compare different numerical results and experimental data, providing an improved understanding of the convergence of the statistical quantities in turbulent wall-bounded flows.

Smoothed Particle Hydrodynamics: A consistent model for interfacial multiphase fluid flow simulations

NASA Astrophysics Data System (ADS)

Krimi, Abdelkader; Rezoug, Mehdi; Khelladi, Sofiane; Nogueira, Xesús; Deligant, Michael; Ramírez, Luis

2018-04-01

In this work, a consistent Smoothed Particle Hydrodynamics (SPH) model to deal with interfacial multiphase fluid flows simulation is proposed. A modification to the Continuum Stress Surface formulation (CSS) [1] to enhance the stability near the fluid interface is developed in the framework of the SPH method. A non-conservative first-order consistency operator is used to compute the divergence of stress surface tensor. This formulation benefits of all the advantages of the one proposed by Adami et al. [2] and, in addition, it can be applied to more than two phases fluid flow simulations. Moreover, the generalized wall boundary conditions [3] are modified in order to be well adapted to multiphase fluid flows with different density and viscosity. In order to allow the application of this technique to wall-bounded multiphase flows, a modification of generalized wall boundary conditions is presented here for using the SPH method. In this work we also present a particle redistribution strategy as an extension of the damping technique presented in [3] to smooth the initial transient phase of gravitational multiphase fluid flow simulations. Several computational tests are investigated to show the accuracy, convergence and applicability of the proposed SPH interfacial multiphase model.

A high order accurate finite element algorithm for high Reynolds number flow prediction

NASA Technical Reports Server (NTRS)

Baker, A. J.

1978-01-01

A Galerkin-weighted residuals formulation is employed to establish an implicit finite element solution algorithm for generally nonlinear initial-boundary value problems. Solution accuracy, and convergence rate with discretization refinement, are quantized in several error norms, by a systematic study of numerical solutions to several nonlinear parabolic and a hyperbolic partial differential equation characteristic of the equations governing fluid flows. Solutions are generated using selective linear, quadratic and cubic basis functions. Richardson extrapolation is employed to generate a higher-order accurate solution to facilitate isolation of truncation error in all norms. Extension of the mathematical theory underlying accuracy and convergence concepts for linear elliptic equations is predicted for equations characteristic of laminar and turbulent fluid flows at nonmodest Reynolds number. The nondiagonal initial-value matrix structure introduced by the finite element theory is determined intrinsic to improved solution accuracy and convergence. A factored Jacobian iteration algorithm is derived and evaluated to yield a consequential reduction in both computer storage and execution CPU requirements while retaining solution accuracy.

Weighted interior penalty discretization of fully nonlinear and weakly dispersive free surface shallow water flows

NASA Astrophysics Data System (ADS)

Di Pietro, Daniele A.; Marche, Fabien

2018-02-01

In this paper, we further investigate the use of a fully discontinuous Finite Element discrete formulation for the study of shallow water free surface flows in the fully nonlinear and weakly dispersive flow regime. We consider a decoupling strategy in which we approximate the solutions of the classical shallow water equations supplemented with a source term globally accounting for the non-hydrostatic effects. This source term can be computed through the resolution of elliptic second-order linear sub-problems, which only involve second order partial derivatives in space. We then introduce an associated Symmetric Weighted Internal Penalty discrete bilinear form, allowing to deal with the discontinuous nature of the elliptic problem's coefficients in a stable and consistent way. Similar discrete formulations are also introduced for several recent optimized fully nonlinear and weakly dispersive models. These formulations are validated again several benchmarks involving h-convergence, p-convergence and comparisons with experimental data, showing optimal convergence properties.

Modeling and Numerical Challenges in Eulerian-Lagrangian Computations of Shock-driven Multiphase Flows

NASA Astrophysics Data System (ADS)

Diggs, Angela; Balachandar, Sivaramakrishnan

2015-06-01

The present work addresses the numerical methods required for particle-gas and particle-particle interactions in Eulerian-Lagrangian simulations of multiphase flow. Local volume fraction as seen by each particle is the quantity of foremost importance in modeling and evaluating such interactions. We consider a general multiphase flow with a distribution of particles inside a fluid flow discretized on an Eulerian grid. Particle volume fraction is needed both as a Lagrangian quantity associated with each particle and also as an Eulerian quantity associated with the flow. In Eulerian Projection (EP) methods, the volume fraction is first obtained within each cell as an Eulerian quantity and then interpolated to each particle. In Lagrangian Projection (LP) methods, the particle volume fraction is obtained at each particle and then projected onto the Eulerian grid. Traditionally, EP methods are used in multiphase flow, but sub-grid resolution can be obtained through use of LP methods. By evaluating the total error and its components we compare the performance of EP and LP methods. The standard von Neumann error analysis technique has been adapted for rigorous evaluation of rate of convergence. The methods presented can be extended to obtain accurate field representations of other Lagrangian quantities. Most importantly, we will show that such careful attention to numerical methodologies is needed in order to capture complex shock interaction with a bed of particles. Supported by U.S. Department of Defense SMART Program and the U.S. Department of Energy PSAAP-II program under Contract No. DE-NA0002378.

Flow of High Internal Phase Ratio Emulsions through Pipes

NASA Astrophysics Data System (ADS)

Kostak, K.; Özsaygı, R.; Gündüz, I.; Yorgancıoǧlu, E.; Tekden, E.; Güzel, O.; Sadıklar, D.; Peker, S.; Helvacı, Ş. Ş.

2015-04-01

The flow behavior of W/O type of HIPRE stabilized by hydrogen bonds with a sugar (sorbitol) in the aqueous phase, was studied. Two groups of experiments were done in this work: The effect of wall shear stresses were investigated in flow through pipes of different diameters. For this end, HIPREs prestirred at constant rate for the same duration were used to obtain similar drop size distributions. Existence and extent of elongational viscosity were used as a probe to elucidate the effect of drop size distribution on the flow behavior: HIPREs prestirred for the same duration at different rates were subjected to flow through converging pipes. The experimental flow curves for flow through small cylindrical pipes indicated four different stages: 1) initial increase in the flow rate at low pressure difference, 2) subsequent decrease in the flow rate due to capillary flow, 3) pressure increase after reaching the minimum flow rate and 4) slip flow after a critical pressure difference. HIPREs with sufficient external liquid phase in the plateau borders can elongate during passage through converging pipes. In the absence of liquid stored in the plateau borders, the drops rupture during extension and slip flow takes place without elongation.

Convergent evolution and divergent selection: lizards at the White Sands ecotone.

PubMed

Rosenblum, Erica Bree

2006-01-01

Ecological transition zones, where organismal phenotypes result from a delicate balance between selection and migration, highlight the interplay of local adaptation and gene flow. Here, I study the response of an entire species assemblage to natural selection across a common ecotone. Three lizard species, distributed along a dramatic environmental gradient in substrate color, display convergent adaptation of blanched coloration on the gypsum dunes of White Sands National Monument. I investigate the role of gene flow in modulating phenotypic response to selection by quantifying color variation and genetic variation across the ecotone. I find species differences in degree of background matching and in genetic connectivity of populations across the ecotone. Differences among species in phenotypic response to selection scale precisely to levels of genetic isolation. Species with higher levels of gene flow across the ecotone exhibit less dramatic responses to selection. Results also reveal a strong signal of ecologically mediated divergence for White Sands lizards. For all species, phenotypic variation is better explained by habitat similarity than genetic similarity. Convergent evolution of blanched coloration at White Sands clearly reflects the action of strong divergent selection; however, adaptive response appears to be modulated by gene flow and demographic history and can be predicted by divergence-with-gene-flow models.

A third-order implicit discontinuous Galerkin method based on a Hermite WENO reconstruction for time-accurate solution of the compressible Navier-Stokes equations

DOE Office of Scientific and Technical Information (OSTI.GOV)

Xia, Yidong; Liu, Xiaodong; Luo, Hong

2015-06-01

Here, a space and time third-order discontinuous Galerkin method based on a Hermite weighted essentially non-oscillatory reconstruction is presented for the unsteady compressible Euler and Navier–Stokes equations. At each time step, a lower-upper symmetric Gauss–Seidel preconditioned generalized minimal residual solver is used to solve the systems of linear equations arising from an explicit first stage, single diagonal coefficient, diagonally implicit Runge–Kutta time integration scheme. The performance of the developed method is assessed through a variety of unsteady flow problems. Numerical results indicate that this method is able to deliver the designed third-order accuracy of convergence in both space and time,more » while requiring remarkably less storage than the standard third-order discontinous Galerkin methods, and less computing time than the lower-order discontinous Galerkin methods to achieve the same level of temporal accuracy for computing unsteady flow problems.« less

Anomalous transport in fracture networks: field scale experiments and modelling

NASA Astrophysics Data System (ADS)

Kang, P. K.; Le Borgne, T.; Bour, O.; Dentz, M.; Juanes, R.

2012-12-01

Anomalous transport is widely observed in different settings and scales of transport through porous and fractured geologic media. A common signature of anomalous transport is the late-time power law tailing in breakthrough curves (BTCs) during tracer tests. Various conceptual models of anomalous transport have been proposed, including multirate mass transfer, continuous time random walk, and stream tube models. Since different conceptual models can produce equally good fits to a single BTC, tracer test interpretation has been plagued with ambiguity. Here, we propose to resolve such ambiguity by analyzing BTCs obtained from both convergent and push-pull flow configurations at two different fracture planes. We conducted field tracer tests in a fractured granite formation close to Ploemeur, France. We observe that BTC tailing depends on the flow configuration and the injection fracture. Specifically the tailing disappears under push-pull geometry, and when we injected at a fracture with high flux (Figure 1). This indicates that for this fractured granite, BTC tailing is controlled by heterogeneous advection and not by matrix diffusion. To explain the change in tailing behavior for different flow configurations, we employ a simple lattice network model with heterogeneous conductivity distribution. The model assigns random conductivities to the fractures and solves the Darcy equation for an incompressible fluid, enforcing mass conservation at fracture intersections. The mass conservation constraint yields a correlated random flow through the fracture system. We investigate whether BTC tailing can be explained by the spatial distribution of preferential flow paths and stagnation zones, which is controlled by the conductivity variance and correlation length. By combining the results from the field tests and numerical modeling, we show that the reversibility of spreading is a key mechanism that needs to be captured. We also demonstrate the dominant role of the injection fracture on the tailing behavior: where we inject makes the difference in the tailing. Blue line is a BTC with injection into a slow velocity zone under convergent flow configuration. The late-time tailing observed for the convergent test diminished for push-pull experiment performed in the same zone(red line). Black line is a BTC with injection into a high velocity zone under convergent flow configuration. Insets: illustration of convergent and push-pull tracer tests using a double packer system.

Development and application of a volume penalization immersed boundary method for the computation of blood flow and shear stresses in cerebral vessels and aneurysms.

PubMed

Mikhal, Julia; Geurts, Bernard J

2013-12-01

A volume-penalizing immersed boundary method is presented for the simulation of laminar incompressible flow inside geometrically complex blood vessels in the human brain. We concentrate on cerebral aneurysms and compute flow in curved brain vessels with and without spherical aneurysm cavities attached. We approximate blood as an incompressible Newtonian fluid and simulate the flow with the use of a skew-symmetric finite-volume discretization and explicit time-stepping. A key element of the immersed boundary method is the so-called masking function. This is a binary function with which we identify at any location in the domain whether it is 'solid' or 'fluid', allowing to represent objects immersed in a Cartesian grid. We compare three definitions of the masking function for geometries that are non-aligned with the grid. In each case a 'staircase' representation is used in which a grid cell is either 'solid' or 'fluid'. Reliable findings are obtained with our immersed boundary method, even at fairly coarse meshes with about 16 grid cells across a velocity profile. The validation of the immersed boundary method is provided on the basis of classical Poiseuille flow in a cylindrical pipe. We obtain first order convergence for the velocity and the shear stress, reflecting the fact that in our approach the solid-fluid interface is localized with an accuracy on the order of a grid cell. Simulations for curved vessels and aneurysms are done for different flow regimes, characterized by different values of the Reynolds number (Re). The validation is performed for laminar flow at Re = 250, while the flow in more complex geometries is studied at Re = 100 and Re = 250, as suggested by physiological conditions pertaining to flow of blood in the circle of Willis.

A two-stage flow-based intrusion detection model for next-generation networks.

PubMed

Umer, Muhammad Fahad; Sher, Muhammad; Bi, Yaxin

2018-01-01

The next-generation network provides state-of-the-art access-independent services over converged mobile and fixed networks. Security in the converged network environment is a major challenge. Traditional packet and protocol-based intrusion detection techniques cannot be used in next-generation networks due to slow throughput, low accuracy and their inability to inspect encrypted payload. An alternative solution for protection of next-generation networks is to use network flow records for detection of malicious activity in the network traffic. The network flow records are independent of access networks and user applications. In this paper, we propose a two-stage flow-based intrusion detection system for next-generation networks. The first stage uses an enhanced unsupervised one-class support vector machine which separates malicious flows from normal network traffic. The second stage uses a self-organizing map which automatically groups malicious flows into different alert clusters. We validated the proposed approach on two flow-based datasets and obtained promising results.

A two-stage flow-based intrusion detection model for next-generation networks

PubMed Central

2018-01-01

The next-generation network provides state-of-the-art access-independent services over converged mobile and fixed networks. Security in the converged network environment is a major challenge. Traditional packet and protocol-based intrusion detection techniques cannot be used in next-generation networks due to slow throughput, low accuracy and their inability to inspect encrypted payload. An alternative solution for protection of next-generation networks is to use network flow records for detection of malicious activity in the network traffic. The network flow records are independent of access networks and user applications. In this paper, we propose a two-stage flow-based intrusion detection system for next-generation networks. The first stage uses an enhanced unsupervised one-class support vector machine which separates malicious flows from normal network traffic. The second stage uses a self-organizing map which automatically groups malicious flows into different alert clusters. We validated the proposed approach on two flow-based datasets and obtained promising results. PMID:29329294

Modeling electrokinetic flows by consistent implicit incompressible smoothed particle hydrodynamics

DOE PAGES

Pan, Wenxiao; Kim, Kyungjoo; Perego, Mauro; ...

2017-01-03

In this paper, we present a consistent implicit incompressible smoothed particle hydrodynamics (I 2SPH) discretization of Navier–Stokes, Poisson–Boltzmann, and advection–diffusion equations subject to Dirichlet or Robin boundary conditions. It is applied to model various two and three dimensional electrokinetic flows in simple or complex geometries. The accuracy and convergence of the consistent I 2SPH are examined via comparison with analytical solutions, grid-based numerical solutions, or empirical models. Lastly, the new method provides a framework to explore broader applications of SPH in microfluidics and complex fluids with charged objects, such as colloids and biomolecules, in arbitrary complex geometries.

Shape functions for velocity interpolation in general hexahedral cells

USGS Publications Warehouse

Naff, R.L.; Russell, T.F.; Wilson, J.D.

2002-01-01

Numerical methods for grids with irregular cells require discrete shape functions to approximate the distribution of quantities across cells. For control-volume mixed finite-element (CVMFE) methods, vector shape functions approximate velocities and vector test functions enforce a discrete form of Darcy's law. In this paper, a new vector shape function is developed for use with irregular, hexahedral cells (trilinear images of cubes). It interpolates velocities and fluxes quadratically, because as shown here, the usual Piola-transformed shape functions, which interpolate linearly, cannot match uniform flow on general hexahedral cells. Truncation-error estimates for the shape function are demonstrated. CVMFE simulations of uniform and non-uniform flow with irregular meshes show first- and second-order convergence of fluxes in the L2 norm in the presence and absence of singularities, respectively.

Texture mapping via optimal mass transport.

PubMed

Dominitz, Ayelet; Tannenbaum, Allen

2010-01-01

In this paper, we present a novel method for texture mapping of closed surfaces. Our method is based on the technique of optimal mass transport (also known as the "earth-mover's metric"). This is a classical problem that concerns determining the optimal way, in the sense of minimal transportation cost, of moving a pile of soil from one site to another. In our context, the resulting mapping is area preserving and minimizes angle distortion in the optimal mass sense. Indeed, we first begin with an angle-preserving mapping (which may greatly distort area) and then correct it using the mass transport procedure derived via a certain gradient flow. In order to obtain fast convergence to the optimal mapping, we incorporate a multiresolution scheme into our flow. We also use ideas from discrete exterior calculus in our computations.

Analysis of experimental shaft seal data for high-performance turbomachines, as for Space Shuttle main engines

NASA Technical Reports Server (NTRS)

Hendricks, R. C.; Braun, M. J.; Mullen, R. L.; Burcham, R. E.; Diamond, W. A.

1985-01-01

High-pressure, high-temperature seal flow (leakage) data for nonrotating and rotating Raleigh-step and convergent-tapered-bore seals were characterized in terms of a normalized flow coefficient. The data for normalized Rayleigh-steip and nonrotating tapered-bore seals were in reasonable agreement with theory, but data for the rotating tapered-bore seals were not. The tapered-bore-seal operational clearances estimated from the flow data were significantly larger than calculated. Although clearances are influenced by wear from conical to cylindrical geometry and errors in clearance corrections, the problem was isolated to the shaft temperature - rotational speed clearance correction. The geometric changes support the use of some conical convergence in any seal. Under these conditions rotation reduced the normalized flow coefficiently by nearly 10 percent.

Analysis of experimental shaft seal data for high-performance turbomachines - As for Space Shuttle main engines

NASA Technical Reports Server (NTRS)

Hendricks, R. C.; Mullen, R. L.; Braun, M. J.; Burcham, R. E.; Diamond, W. A.

1987-01-01

High-pressure, high-temperature seal flow (leakage) data for nonrotating and rotating Raleigh-step and convergent-tapered-bore seals were characterized in terms of a normalized flow coefficient. The data for normalized Rayleigh-step and nonrotating tapered-bore seals were in reasonable agreement with theory, but data for the rotating tapered-bore seals were not. The tapered-bore-seal operational clearances estimated from the flow data were significantly larger than calculated. Although clearances are influenced by wear from conical to cylindrical geometry and errors in clearance corrections, the problem was isolated to the shaft temperature - rotational speed clearance correction. The geometric changes support the use of some conical convergence in any seal. Under these conditions rotation reduced the normalized flow coefficiently by nearly 10 percent.

Three dimensional investigation of the shock train structure in a convergent-divergent nozzle

NASA Astrophysics Data System (ADS)

Mousavi, Seyed Mahmood; Roohi, Ehsan

2014-12-01

Three-dimensional computational fluid dynamics analyses have been employed to study the compressible and turbulent flow of the shock train in a convergent-divergent nozzle. The primary goal is to determine the behavior, location, and number of shocks. In this context, full multi-grid initialization, Reynolds stress turbulence model (RSM), and the grid adaption techniques in the Fluent software are utilized under the 3D investigation. The results showed that RSM solution matches with the experimental data suitably. The effects of applying heat generation sources and changing inlet flow total temperature have been investigated. Our simulations showed that changes in the heat generation rate and total temperature of the intake flow influence on the starting point of shock, shock strength, minimum pressure, as well as the maximum flow Mach number.

Pore geometry effects on intrapore viscous to inertial flows and on effective hydraulic parameters

NASA Astrophysics Data System (ADS)

Chaudhary, Kuldeep; Cardenas, M. Bayani; Deng, Wen; Bennett, Philip C.

2013-02-01

In this article, the effects of different diverging-converging pore geometries were investigated, and the microscale fluid flow and effective hydraulic properties from these pores were compared with that of a pipe from viscous to inertial laminar flow regimes. The flow fields are obtained using computational fluid dynamics, and the comparative analysis is based on a new dimensionless hydraulic shape factor β, which is the "specific surface" scaled by the length of pores. Results from all diverging-converging pores show an inverse pattern in velocity and vorticity distributions relative to the pipe flow. The hydraulic conductivity K of all pores is dependent on and can be predicted from β with a power function with an exponent of 3/2. The differences in K are due to the differences in distribution of local friction drag on the pore walls. At Reynolds number (Re) ˜ 0 flows, viscous eddies are found to exist almost in all pores in different sizes, but not in the pipe. Eddies grow when Re → 1 and leads to the failure of Darcy's law. During non-Darcy or Forchheimer flows, the apparent hydraulic conductivity Ka decreases due to the growth of eddies, which constricts the bulk flow region. At Re > 1, the rate of decrease in Ka increases, and at Re >> 1, it decreases to where the change in Ka ≈ 0, and flows once again exhibits a Darcy-type relationship. The degree of nonlinearity during non-Darcy flow decreases for pores with increasing β. The nonlinear flow behavior becomes weaker as β increases to its maximum value in the pipe, which shows no nonlinearity in the flow; in essence, Darcy's law stays valid in the pipe at all laminar flow conditions. The diverging-converging geometry in pores plays a critical role in modifying the intrapore fluid flow, implying that this property should be incorporated in effective larger-scale models, e.g., pore-network models.

A numerical approach for simulating fluid structure interaction of flexible thin shells undergoing arbitrarily large deformations in complex domains

DOE Office of Scientific and Technical Information (OSTI.GOV)

Gilmanov, Anvar, E-mail: agilmano@umn.edu; Le, Trung Bao, E-mail: lebao002@umn.edu; Sotiropoulos, Fotis, E-mail: fotis@umn.edu

We present a new numerical methodology for simulating fluid–structure interaction (FSI) problems involving thin flexible bodies in an incompressible fluid. The FSI algorithm uses the Dirichlet–Neumann partitioning technique. The curvilinear immersed boundary method (CURVIB) is coupled with a rotation-free finite element (FE) model for thin shells enabling the efficient simulation of FSI problems with arbitrarily large deformation. Turbulent flow problems are handled using large-eddy simulation with the dynamic Smagorinsky model in conjunction with a wall model to reconstruct boundary conditions near immersed boundaries. The CURVIB and FE solvers are coupled together on the flexible solid–fluid interfaces where the structural nodalmore » positions, displacements, velocities and loads are calculated and exchanged between the two solvers. Loose and strong coupling FSI schemes are employed enhanced by the Aitken acceleration technique to ensure robust coupling and fast convergence especially for low mass ratio problems. The coupled CURVIB-FE-FSI method is validated by applying it to simulate two FSI problems involving thin flexible structures: 1) vortex-induced vibrations of a cantilever mounted in the wake of a square cylinder at different mass ratios and at low Reynolds number; and 2) the more challenging high Reynolds number problem involving the oscillation of an inverted elastic flag. For both cases the computed results are in excellent agreement with previous numerical simulations and/or experiential measurements. Grid convergence tests/studies are carried out for both the cantilever and inverted flag problems, which show that the CURVIB-FE-FSI method provides their convergence. Finally, the capability of the new methodology in simulations of complex cardiovascular flows is demonstrated by applying it to simulate the FSI of a tri-leaflet, prosthetic heart valve in an anatomic aorta and under physiologic pulsatile conditions.« less

Sound source localization method in an environment with flow based on Amiet-IMACS

NASA Astrophysics Data System (ADS)

Wei, Long; Li, Min; Qin, Sheng; Fu, Qiang; Yang, Debin

2017-05-01

A sound source localization method is proposed to localize and analyze the sound source in an environment with airflow. It combines the improved mapping of acoustic correlated sources (IMACS) method and Amiet's method, and is called Amiet-IMACS. It can localize uncorrelated and correlated sound sources with airflow. To implement this approach, Amiet's method is used to correct the sound propagation path in 3D, which improves the accuracy of the array manifold matrix and decreases the position error of the localized source. Then, the mapping of acoustic correlated sources (MACS) method, which is as a high-resolution sound source localization algorithm, is improved by self-adjusting the constraint parameter at each irritation process to increase convergence speed. A sound source localization experiment using a pair of loud speakers in an anechoic wind tunnel under different flow speeds is conducted. The experiment exhibits the advantage of Amiet-IMACS in localizing a more accurate sound source position compared with implementing IMACS alone in an environment with flow. Moreover, the aerodynamic noise produced by a NASA EPPLER 862 STRUT airfoil model in airflow with a velocity of 80 m/s is localized using the proposed method, which further proves its effectiveness in a flow environment. Finally, the relationship between the source position of this airfoil model and its frequency, along with its generation mechanism, is determined and interpreted.

Practical Aerodynamic Design Optimization Based on the Navier-Stokes Equations and a Discrete Adjoint Method

NASA Technical Reports Server (NTRS)

Grossman, Bernard

1999-01-01

The technical details are summarized below: Compressible and incompressible versions of a three-dimensional unstructured mesh Reynolds-averaged Navier-Stokes flow solver have been differentiated and resulting derivatives have been verified by comparisons with finite differences and a complex-variable approach. In this implementation, the turbulence model is fully coupled with the flow equations in order to achieve this consistency. The accuracy demonstrated in the current work represents the first time that such an approach has been successfully implemented. The accuracy of a number of simplifying approximations to the linearizations of the residual have been examined. A first-order approximation to the dependent variables in both the adjoint and design equations has been investigated. The effects of a "frozen" eddy viscosity and the ramifications of neglecting some mesh sensitivity terms were also examined. It has been found that none of the approximations yielded derivatives of acceptable accuracy and were often of incorrect sign. However, numerical experiments indicate that an incomplete convergence of the adjoint system often yield sufficiently accurate derivatives, thereby significantly lowering the time required for computing sensitivity information. The convergence rate of the adjoint solver relative to the flow solver has been examined. Inviscid adjoint solutions typically require one to four times the cost of a flow solution, while for turbulent adjoint computations, this ratio can reach as high as eight to ten. Numerical experiments have shown that the adjoint solver can stall before converging the solution to machine accuracy, particularly for viscous cases. A possible remedy for this phenomenon would be to include the complete higher-order linearization in the preconditioning step, or to employ a simple form of mesh sequencing to obtain better approximations to the solution through the use of coarser meshes. . An efficient surface parameterization based on a free-form deformation technique has been utilized and the resulting codes have been integrated with an optimization package. Lastly, sample optimizations have been shown for inviscid and turbulent flow over an ONERA M6 wing. Drag reductions have been demonstrated by reducing shock strengths across the span of the wing.

Minimal gain marching schemes: searching for unstable steady-states with unsteady solvers

NASA Astrophysics Data System (ADS)

de S. Teixeira, Renan; S. de B. Alves, Leonardo

2017-12-01

Reference solutions are important in several applications. They are used as base states in linear stability analyses as well as initial conditions and reference states for sponge zones in numerical simulations, just to name a few examples. Their accuracy is also paramount in both fields, leading to more reliable analyses and efficient simulations, respectively. Hence, steady-states usually make the best reference solutions. Unfortunately, standard marching schemes utilized for accurate unsteady simulations almost never reach steady-states of unstable flows. Steady governing equations could be solved instead, by employing Newton-type methods often coupled with continuation techniques. However, such iterative approaches do require large computational resources and very good initial guesses to converge. These difficulties motivated the development of a technique known as selective frequency damping (SFD) (Åkervik et al. in Phys Fluids 18(6):068102, 2006). It adds a source term to the unsteady governing equations that filters out the unstable frequencies, allowing a steady-state to be reached. This approach does not require a good initial condition and works well for self-excited flows, where a single nonzero excitation frequency is selected by either absolute or global instability mechanisms. On the other hand, it seems unable to damp stationary disturbances. Furthermore, flows with a broad unstable frequency spectrum might require the use of multiple filters, which delays convergence significantly. Both scenarios appear in convectively, absolutely or globally unstable flows. An alternative approach is proposed in the present paper. It modifies the coefficients of a marching scheme in such a way that makes the absolute value of its linear gain smaller than one within the required unstable frequency spectra, allowing the respective disturbance amplitudes to decay given enough time. These ideas are applied here to implicit multi-step schemes. A few chosen test cases shows that they enable convergence toward solutions that are unstable to stationary and oscillatory disturbances, with either a single or multiple frequency content. Finally, comparisons with SFD are also performed, showing significant reduction in computer cost for complex flows by using the implicit multi-step MGM schemes.

Recent Advances in Laplace Transform Analytic Element Method (LT-AEM) Theory and Application to Transient Groundwater Flow

NASA Astrophysics Data System (ADS)

Kuhlman, K. L.; Neuman, S. P.

2006-12-01

Furman and Neuman (2003) proposed a Laplace Transform Analytic Element Method (LT-AEM) for transient groundwater flow. LT-AEM applies the traditionally steady-state AEM to the Laplace transformed groundwater flow equation, and back-transforms the resulting solution to the time domain using a Fourier Series numerical inverse Laplace transform method (de Hoog, et.al., 1982). We have extended the method so it can compute hydraulic head and flow velocity distributions due to any two-dimensional combination and arrangement of point, line, circular and elliptical area sinks and sources, nested circular or elliptical regions having different hydraulic properties, and areas of specified head, flux or initial condition. The strengths of all sinks and sources, and the specified head and flux values, can all vary in both space and time in an independent and arbitrary fashion. Initial conditions may vary from one area element to another. A solution is obtained by matching heads and normal fluxes along the boundary of each element. The effect which each element has on the total flow is expressed in terms of generalized Fourier series which converge rapidly (<20 terms) in most cases. As there are more matching points than unknown Fourier terms, the matching is accomplished in Laplace space using least-squares. The method is illustrated by calculating the resulting transient head and flow velocities due to an arrangement of elements in both finite and infinite domains. The 2D LT-AEM elements already developed and implemented are currently being extended to solve the 3D groundwater flow equation.

Galilean-invariant preconditioned central-moment lattice Boltzmann method without cubic velocity errors for efficient steady flow simulations

NASA Astrophysics Data System (ADS)

Hajabdollahi, Farzaneh; Premnath, Kannan N.

2018-05-01

Lattice Boltzmann (LB) models used for the computation of fluid flows represented by the Navier-Stokes (NS) equations on standard lattices can lead to non-Galilean-invariant (GI) viscous stress involving cubic velocity errors. This arises from the dependence of their third-order diagonal moments on the first-order moments for standard lattices, and strategies have recently been introduced to restore Galilean invariance without such errors using a modified collision operator involving corrections to either the relaxation times or the moment equilibria. Convergence acceleration in the simulation of steady flows can be achieved by solving the preconditioned NS equations, which contain a preconditioning parameter that can be used to tune the effective sound speed, and thereby alleviating the numerical stiffness. In the present paper, we present a GI formulation of the preconditioned cascaded central-moment LB method used to solve the preconditioned NS equations, which is free of cubic velocity errors on a standard lattice, for steady flows. A Chapman-Enskog analysis reveals the structure of the spurious non-GI defect terms and it is demonstrated that the anisotropy of the resulting viscous stress is dependent on the preconditioning parameter, in addition to the fluid velocity. It is shown that partial correction to eliminate the cubic velocity defects is achieved by scaling the cubic velocity terms in the off-diagonal third-order moment equilibria with the square of the preconditioning parameter. Furthermore, we develop additional corrections based on the extended moment equilibria involving gradient terms with coefficients dependent locally on the fluid velocity and the preconditioning parameter. Such parameter dependent corrections eliminate the remaining truncation errors arising from the degeneracy of the diagonal third-order moments and fully restore Galilean invariance without cubic defects for the preconditioned LB scheme on a standard lattice. Several conclusions are drawn from the analysis of the structure of the non-GI errors and the associated corrections, with particular emphasis on their dependence on the preconditioning parameter. The GI preconditioned central-moment LB method is validated for a number of complex flow benchmark problems and its effectiveness to achieve convergence acceleration and improvement in accuracy is demonstrated.

DOE Office of Scientific and Technical Information (OSTI.GOV)

Romero, Casildo A.

Crenulative turbulence is a nonlinear extension of the Bell-Plesset instability, usually observed in a converging system in which there is a nonhomogeneous response of stress to strain and/or strain rate. In general, crenelation occurs in any circumstance in which the mean flow streamlines converge the material more strongly than the compressibility can accommodate. Elements of the material slip past each other, resulting in local fluctuations in velocity from that of the mean flow, producing a type of turbulence that is more kinematic than inertial. For a homogeneous material, crenelation occurs at the atomic or molecular scale. With nonhomogeneous stress responsemore » at larger scales, the crenulative process can also occur at those larger scales. The results are manifested by a decrease in the rate of dissipation to heat, and by the configurationally-irreversible mixing of nonhomogeneities across any mean-flow-transported interface. We obtain a mathematical description of the crenulative process by means of Reynolds decomposition of the appropriate variables, and the derivation of transport equations for the second-order moments that arise in the mean-flow momentum and energy equations. The theory is illustrated by application to the spherical convergence of an incompressible fluid with nonhomogeneous distribution of kinematic viscosity.« less

Three-dimensional computational fluid dynamics modeling of particle uptake by an occupational air sampler using manually-scaled and adaptive grids

PubMed Central

Landázuri, Andrea C.; Sáez, A. Eduardo; Anthony, T. Renée

2016-01-01

This work presents fluid flow and particle trajectory simulation studies to determine the aspiration efficiency of a horizontally oriented occupational air sampler using computational fluid dynamics (CFD). Grid adaption and manual scaling of the grids were applied to two sampler prototypes based on a 37-mm cassette. The standard k–ε model was used to simulate the turbulent air flow and a second order streamline-upwind discretization scheme was used to stabilize convective terms of the Navier–Stokes equations. Successively scaled grids for each configuration were created manually and by means of grid adaption using the velocity gradient in the main flow direction. Solutions were verified to assess iterative convergence, grid independence and monotonic convergence. Particle aspiration efficiencies determined for both prototype samplers were undistinguishable, indicating that the porous filter does not play a noticeable role in particle aspiration. Results conclude that grid adaption is a powerful tool that allows to refine specific regions that require lots of detail and therefore better resolve flow detail. It was verified that adaptive grids provided a higher number of locations with monotonic convergence than the manual grids and required the least computational effort. PMID:26949268

Flow in a discrete slotted nozzle with massive injection. [water table tests

NASA Technical Reports Server (NTRS)

Perkins, H. C.

1974-01-01

An experimental investigation has been conducted to determine the effect of massive wall injection on the flow characteristics in a slotted nozzle. Some of the experiments were performed on a water table with a slotted-nozzle test section. This has 45 deg and 15 deg half angles of convergence and divergence, respectively, throat radius of 2.5 inches, and throat width of 3 inches. The hydraulic analogy was employed to qualitatively extend the results to a compressible gas flow through the nozzle. Experimental results from the water table include contours of constant Froude and Mach number with and without injection. Photographic results are also presented for the injection through slots of CO2 and Freon-12 into a main-stream air flow in a convergent-divergent nozzle in a wind tunnel. Schlieren photographs were used to visualize the flow, and qualititative agreement between the results from the gas tunnel and water table is good.

Computational technique and performance of Transient Inundation Model for Rivers--2 Dimensional (TRIM2RD) : a depth-averaged two-dimensional flow model

USGS Publications Warehouse

Fulford, Janice M.

2003-01-01

A numerical computer model, Transient Inundation Model for Rivers -- 2 Dimensional (TrimR2D), that solves the two-dimensional depth-averaged flow equations is documented and discussed. The model uses a semi-implicit, semi-Lagrangian finite-difference method. It is a variant of the Trim model and has been used successfully in estuarine environments such as San Francisco Bay. The abilities of the model are documented for three scenarios: uniform depth flows, laboratory dam-break flows, and large-scale riverine flows. The model can start computations from a ?dry? bed and converge to accurate solutions. Inflows are expressed as source terms, which limits the use of the model to sufficiently long reaches where the flow reaches equilibrium with the channel. The data sets used by the investigation demonstrate that the model accurately propagates flood waves through long river reaches and simulates dam breaks with abrupt water-surface changes.

DOE Office of Scientific and Technical Information (OSTI.GOV)

Potomkin, Mykhailo; Kaiser, Andreas; Berlyand, Leonid

We consider active particles swimming in a convergent fluid flow in a trapezoid nozzle with no-slip walls. We use mathematical modeling to analyze trajectories of these particles inside the nozzle. By extensive Monte Carlo simulations, we show that trajectories are strongly affected by the background fluid flow and geometry of the nozzle leading to wall accumulation and upstream motion (rheotaxis). In particular, we describe the non-trivial focusing of active rods depending on physical and geometrical parameters. It is also established that the convergent component of the background flow leads to stability of both downstream and upstream swimming at the centerline.more » The stability of downstream swimming enhances focusing, and the stability of upstream swimming enables rheotaxis in the bulk.« less

A far-field non-reflecting boundary condition for two-dimensional wake flows

NASA Technical Reports Server (NTRS)

Danowitz, Jeffrey S.; Abarbanel, Saul A.; Turkel, Eli

1995-01-01

Far-field boundary conditions for external flow problems have been developed based upon long-wave perturbations of linearized flow equations about a steady state far field solution. The boundary improves convergence to steady state in single-grid temporal integration schemes using both regular-time-stepping and local-time-stepping. The far-field boundary may be near the trailing edge of the body which significantly reduces the number of grid points, and therefore the computational time, in the numerical calculation. In addition the solution produced is smoother in the far-field than when using extrapolation conditions. The boundary condition maintains the convergence rate to steady state in schemes utilizing multigrid acceleration.

Implementation of Preconditioned Dual-Time Procedures in OVERFLOW

NASA Technical Reports Server (NTRS)

Pandya, Shishir A.; Venkateswaran, Sankaran; Pulliam, Thomas H.; Kwak, Dochan (Technical Monitor)

2003-01-01

Preconditioning methods have become the method of choice for the solution of flowfields involving the simultaneous presence of low Mach and transonic regions. It is well known that these methods are important for insuring accurate numerical discretization as well as convergence efficiency over various operating conditions such as low Mach number, low Reynolds number and high Strouhal numbers. For unsteady problems, the preconditioning is introduced within a dual-time framework wherein the physical time-derivatives are used to march the unsteady equations and the preconditioned time-derivatives are used for purposes of numerical discretization and iterative solution. In this paper, we describe the implementation of the preconditioned dual-time methodology in the OVERFLOW code. To demonstrate the performance of the method, we employ both simple and practical unsteady flowfields, including vortex propagation in a low Mach number flow, flowfield of an impulsively started plate (Stokes' first problem) arid a cylindrical jet in a low Mach number crossflow with ground effect. All the results demonstrate that the preconditioning algorithm is responsible for improvements to both numerical accuracy and convergence efficiency and, thereby, enables low Mach number unsteady computations to be performed at a fraction of the cost of traditional time-marching methods.

Flow of ultra-hot Precambrian orogens and the making of crustal layering in Phanerozoic orogenic plateaux

NASA Astrophysics Data System (ADS)

Chardon, Dominique; Gapais, Denis; Cagnard, Florence; Jayananda, Mudlappa; Peucat, Jean-Jacques

2010-05-01

Reassessment of structural / metamorphic properties of ultra-hot Precambrian orogens and shortening of model weak lithospheres support a syn-convergence flow mode on an orogen scale, with a large component of horizontal finite elongation parallel to the orogen. This orogen-scale flow mode combines distributed shortening, gravity-driven flow, lateral escape, and three-dimensional mass redistribution of buried supracrustal rocks, magmas and migmatites in a thick fluid lower crust. This combination preserves a nearly flat surface and Moho. The upper crust maintains a nearly constant thickness by real-time erosion and near-field clastic sedimentation and by ablation at its base by burial of pop-downs into the lower crust. Steady state regime of these orogens is allowed by activation of an attachment layer that maintains kinematic compatibility between the thin and dominantly plastic upper crust and a thick "water bed" of lower crust. Because very thin lithospheres of orogenic plateaux and Precambrian hot orogens have similar thermomechanical structures, bulk orogenic flow comparable to that governing Precambrian hot orogens should actually operate through today's orogenic plateaux as well. Thus, syn-convergence flow fabrics documented on exposed crustal sections of ancient hot orogens that have not undergone collapse may be used to infer the nature of flow fabrics that are imaged by geophysical techniques beneath orogenic plateaux. We provide a detailed geological perspective on syn-convergence crustal flow in relation to magma emplacement and partial melting on a wide oblique crustal transition of the Neoarchean ultra-hot orogen of Southern India. We document sub-horizontal bulk longitudinal flow of the partially molten lower crust over a protracted period of 60 Ma. Bulk flow results from the interplay of (1) pervasive longitudinal transtensional flow of the partially molten crust, (2) longitudinal coaxial flow on flat fabrics in early plutons, (3) distributed, orogen-normal shortening, (4) emplacement of late prolate shape plutons in the direction of flow, and (5) late, conjugate strike-slip shearing. The macroscopic- to regional scale tectonoplutonic pattern produced by longitudinal flow forms a flat composite anisotropy throughout the lower crust. In the light of GPS data, these results suggest that bulk longitudinal flow accounts for observed deformation of the Tibetan plateau as well as for its seismic structure. This flow mode may be preferred to lateral, east-directed channel flow because it combines both lateral gravity-driven thinning and distributed, orogen-normal shortening of the crust. These results further suggest that lower crustal seismic reflectivity in orogenic belts may not necessarily images fabrics produced by extensional tectonics, as commonly thought, but crustal layering produced by syn-convergence lateral flow.

Three-Dimensional Navier-Stokes Calculations Using the Modified Space-Time CESE Method

NASA Technical Reports Server (NTRS)

Chang, Chau-lyan

2007-01-01

The space-time conservation element solution element (CESE) method is modified to address the robustness issues of high-aspect-ratio, viscous, near-wall meshes. In this new approach, the dependent variable gradients are evaluated using element edges and the corresponding neighboring solution elements while keeping the original flux integration procedure intact. As such, the excellent flux conservation property is retained and the new edge-based gradients evaluation significantly improves the robustness for high-aspect ratio meshes frequently encountered in three-dimensional, Navier-Stokes calculations. The order of accuracy of the proposed method is demonstrated for oblique acoustic wave propagation, shock-wave interaction, and hypersonic flows over a blunt body. The confirmed second-order convergence along with the enhanced robustness in handling hypersonic blunt body flow calculations makes the proposed approach a very competitive CFD framework for 3D Navier-Stokes simulations.

An improved weakly compressible SPH method for simulating free surface flows of viscous and viscoelastic fluids

NASA Astrophysics Data System (ADS)

Xu, Xiaoyang; Deng, Xiao-Long

2016-04-01

In this paper, an improved weakly compressible smoothed particle hydrodynamics (SPH) method is proposed to simulate transient free surface flows of viscous and viscoelastic fluids. The improved SPH algorithm includes the implementation of (i) the mixed symmetric correction of kernel gradient to improve the accuracy and stability of traditional SPH method and (ii) the Rusanov flux in the continuity equation for improving the computation of pressure distributions in the dynamics of liquids. To assess the effectiveness of the improved SPH algorithm, a number of numerical examples including the stretching of an initially circular water drop, dam breaking flow against a vertical wall, the impact of viscous and viscoelastic fluid drop with a rigid wall, and the extrudate swell of viscoelastic fluid have been presented and compared with available numerical and experimental data in literature. The convergent behavior of the improved SPH algorithm has also been studied by using different number of particles. All numerical results demonstrate that the improved SPH algorithm proposed here is capable of modeling free surface flows of viscous and viscoelastic fluids accurately and stably, and even more important, also computing an accurate and little oscillatory pressure field.

The effects of sampling location and turbulence on discharge estimates in short converging turbine intakes

DOE Office of Scientific and Technical Information (OSTI.GOV)

Romero-Gomez, P.; Harding, S. F.; Richmond, M. C.

2017-01-01

Standards provide recommendations for best practices when installing current meters to measure fluid flow in closed conduits. A central guideline requires the velocity distribution to be regular and the flow steady. Because of the nature of the short converging intakes typical of low-head hydroturbines, these assumptions may be invalid if current meters are intended to be used to estimate discharge. Usual concerns are (1) the effects of the number of devices, (2) the sampling location and (3) the high turbulence caused by blockage from submersible traveling screens usually deployed for safe downstream fish passage. These three effects were examined inmore » the present study by using 3D simulated flow fields in both steady-state and transient modes. In the process of describing an application at an existing hydroturbine intake at Ice Harbor Dam, the present work outlined the methods involved, which combined computational fluid dynamics, laboratory measurements in physical models of the hydroturbine, and current meter performance evaluations in experimental settings. The main conclusions in this specific application were that a steady-state flow field sufficed to determine the adequate number of meters and their location, and that both the transverse velocity and turbulence intensity had a small impact on estimate errors. However, while it may not be possible to extrapolate these findings to other field conditions and measuring devices, the study laid out a path to conduct similar assessments in other applications.« less

Fluid dynamic aspects of jet noise generation. [noise measurement of jet blast effects from supersonic jet flow in convergent-divergent nozzles

NASA Technical Reports Server (NTRS)

Barra, V.; Panunzio, S.

1976-01-01

Jet engine noise generation and noise propagation was investigated by studying supersonic nozzle flow of various nozzle configurations in an experimental test facility. The experimental facility was constructed to provide a coaxial axisymmetric jet flow of unheated air. In the test setup, an inner primary flow exhausted from a 7 in. exit diameter convergent--divergent nozzle at Mach 2, while a secondary flow had a 10 in. outside diameter and was sonic at the exit. The large dimensions of the jets permitted probes to be placed inside the jet core without significantly disturbing the flow. Static pressure fluctuations were measured for the flows. The nozzles were designed for shock free (balanced) flow at Mach 2. Data processing techniques and experimental procedures were developed in order to study induced disturbances at the edge of the supersonic flows, and the propagation of those disturbances throughout the flows. Equipment used (specifications are given) to record acoustic levels (far field noise) is described. Results and conclusions are presented and discussed. Diagrams of the jet flow fields are included along with photographs of the test stand.

Magnetohydrodynamic Flow by a Stretching Cylinder with Newtonian Heating and Homogeneous-Heterogeneous Reactions

PubMed Central

Hayat, T.; Hussain, Zakir; Alsaedi, A.; Farooq, M.

2016-01-01

This article examines the effects of homogeneous-heterogeneous reactions and Newtonian heating in magnetohydrodynamic (MHD) flow of Powell-Eyring fluid by a stretching cylinder. The nonlinear partial differential equations of momentum, energy and concentration are reduced to the nonlinear ordinary differential equations. Convergent solutions of momentum, energy and reaction equations are developed by using homotopy analysis method (HAM). This method is very efficient for development of series solutions of highly nonlinear differential equations. It does not depend on any small or large parameter like the other methods i. e., perturbation method, δ—perturbation expansion method etc. We get more accurate result as we increase the order of approximations. Effects of different parameters on the velocity, temperature and concentration distributions are sketched and discussed. Comparison of present study with the previous published work is also made in the limiting sense. Numerical values of skin friction coefficient and Nusselt number are also computed and analyzed. It is noticed that the flow accelerates for large values of Powell-Eyring fluid parameter. Further temperature profile decreases and concentration profile increases when Powell-Eyring fluid parameter enhances. Concentration distribution is decreasing function of homogeneous reaction parameter while opposite influence of heterogeneous reaction parameter appears. PMID:27280883

Magnetohydrodynamic Flow by a Stretching Cylinder with Newtonian Heating and Homogeneous-Heterogeneous Reactions.

PubMed

Hayat, T; Hussain, Zakir; Alsaedi, A; Farooq, M

2016-01-01

This article examines the effects of homogeneous-heterogeneous reactions and Newtonian heating in magnetohydrodynamic (MHD) flow of Powell-Eyring fluid by a stretching cylinder. The nonlinear partial differential equations of momentum, energy and concentration are reduced to the nonlinear ordinary differential equations. Convergent solutions of momentum, energy and reaction equations are developed by using homotopy analysis method (HAM). This method is very efficient for development of series solutions of highly nonlinear differential equations. It does not depend on any small or large parameter like the other methods i. e., perturbation method, δ-perturbation expansion method etc. We get more accurate result as we increase the order of approximations. Effects of different parameters on the velocity, temperature and concentration distributions are sketched and discussed. Comparison of present study with the previous published work is also made in the limiting sense. Numerical values of skin friction coefficient and Nusselt number are also computed and analyzed. It is noticed that the flow accelerates for large values of Powell-Eyring fluid parameter. Further temperature profile decreases and concentration profile increases when Powell-Eyring fluid parameter enhances. Concentration distribution is decreasing function of homogeneous reaction parameter while opposite influence of heterogeneous reaction parameter appears.

Total synthesis of feglymycin based on a linear/convergent hybrid approach using micro-flow amide bond formation

NASA Astrophysics Data System (ADS)

Fuse, Shinichiro; Mifune, Yuto; Nakamura, Hiroyuki; Tanaka, Hiroshi

2016-11-01

Feglymycin is a naturally occurring, anti-HIV and antimicrobial 13-mer peptide that includes highly racemizable 3,5-dihydroxyphenylglycines (Dpgs). Here we describe the total synthesis of feglymycin based on a linear/convergent hybrid approach. Our originally developed micro-flow amide bond formation enabled highly racemizable peptide chain elongation based on a linear approach that was previously considered impossible. Our developed approach will enable the practical preparation of biologically active oligopeptides that contain highly racemizable amino acids, which are attractive drug candidates.

A monolithic mass tracking formulation for bubbles in incompressible flow

NASA Astrophysics Data System (ADS)

Aanjaneya, Mridul; Patkar, Saket; Fedkiw, Ronald

2013-08-01

We devise a novel method for treating bubbles in incompressible flow that relies on the conservative advection of bubble mass and an associated equation of state in order to determine pressure boundary conditions inside each bubble. We show that executing this algorithm in a traditional manner leads to stability issues similar to those seen for partitioned methods for solid-fluid coupling. Therefore, we reformulate the problem monolithically. This is accomplished by first proposing a new fully monolithic approach to coupling incompressible flow to fully nonlinear compressible flow including the effects of shocks and rarefactions, and then subsequently making a number of simplifying assumptions on the air flow removing not only the nonlinearities but also the spatial variations of both the density and the pressure. The resulting algorithm is quite robust, has been shown to converge to known solutions for test problems, and has been shown to be quite effective on more realistic problems including those with multiple bubbles, merging and pinching, etc. Notably, this approach departs from a standard two-phase incompressible flow model where the air flow preserves its volume despite potentially large forces and pressure differentials in the surrounding incompressible fluid that should change its volume. Our bubbles readily change volume according to an isothermal equation of state.

An Improved Treatment of External Boundary for Three-Dimensional Flow Computations

NASA Technical Reports Server (NTRS)

Tsynkov, Semyon V.; Vatsa, Veer N.

1997-01-01

We present an innovative numerical approach for setting highly accurate nonlocal boundary conditions at the external computational boundaries when calculating three-dimensional compressible viscous flows over finite bodies. The approach is based on application of the difference potentials method by V. S. Ryaben'kii and extends our previous technique developed for the two-dimensional case. The new boundary conditions methodology has been successfully combined with the NASA-developed code TLNS3D and used for the analysis of wing-shaped configurations in subsonic and transonic flow regimes. As demonstrated by the computational experiments, the improved external boundary conditions allow one to greatly reduce the size of the computational domain while still maintaining high accuracy of the numerical solution. Moreover, they may provide for a noticeable speedup of convergence of the multigrid iterations.

Implicit and Multigrid Method for Ideal Multigrid Convergence: Direct Numerical Simulation of Separated Flow Around NACA 0012 Airfoil

NASA Technical Reports Server (NTRS)

Liu, Chao-Qun; Shan, H.; Jiang, L.

1999-01-01

Numerical investigation of flow separation over a NACA 0012 airfoil at large angles of attack has been carried out. The numerical calculation is performed by solving the full Navier-Stokes equations in generalized curvilinear coordinates. The second-order LU-SGS implicit scheme is applied for time integration. This scheme requires no tridiagonal inversion and is capable of being completely vectorized, provided the corresponding Jacobian matrices are properly selected. A fourth-order centered compact scheme is used for spatial derivatives. In order to reduce numerical oscillation, a sixth-order implicit filter is employed. Non-reflecting boundary conditions are imposed at the far-field and outlet boundaries to avoid possible non-physical wave reflection. Complex flow separation and vortex shedding phenomenon have been observed and discussed.

Comments regarding two upwind methods for solving two-dimensional external flows using unstructured grids

NASA Technical Reports Server (NTRS)

Kleb, W. L.

1994-01-01

Steady flow over the leading portion of a multicomponent airfoil section is studied using computational fluid dynamics (CFD) employing an unstructured grid. To simplify the problem, only the inviscid terms are retained from the Reynolds-averaged Navier-Stokes equations - leaving the Euler equations. The algorithm is derived using the finite-volume approach, incorporating explicit time-marching of the unsteady Euler equations to a time-asymptotic, steady-state solution. The inviscid fluxes are obtained through either of two approximate Riemann solvers: Roe's flux difference splitting or van Leer's flux vector splitting. Results are presented which contrast the solutions given by the two flux functions as a function of Mach number and grid resolution. Additional information is presented concerning code verification techniques, flow recirculation regions, convergence histories, and computational resources.

Data assimilation in integrated hydrological modelling in the presence of observation bias

NASA Astrophysics Data System (ADS)

Rasmussen, J.; Madsen, H.; Jensen, K. H.; Refsgaard, J. C.

2015-08-01

The use of bias-aware Kalman filters for estimating and correcting observation bias in groundwater head observations is evaluated using both synthetic and real observations. In the synthetic test, groundwater head observations with a constant bias and unbiased stream discharge observations are assimilated in a catchment scale integrated hydrological model with the aim of updating stream discharge and groundwater head, as well as several model parameters relating to both stream flow and groundwater modeling. The Colored Noise Kalman filter (ColKF) and the Separate bias Kalman filter (SepKF) are tested and evaluated for correcting the observation biases. The study found that both methods were able to estimate most of the biases and that using any of the two bias estimation methods resulted in significant improvements over using a bias-unaware Kalman Filter. While the convergence of the ColKF was significantly faster than the convergence of the SepKF, a much larger ensemble size was required as the estimation of biases would otherwise fail. Real observations of groundwater head and stream discharge were also assimilated, resulting in improved stream flow modeling in terms of an increased Nash-Sutcliffe coefficient while no clear improvement in groundwater head modeling was observed. Both the ColKF and the SepKF tended to underestimate the biases, which resulted in drifting model behavior and sub-optimal parameter estimation, but both methods provided better state updating and parameter estimation than using a bias-unaware filter.

Development of an explicit multiblock/multigrid flow solver for viscous flows in complex geometries

NASA Technical Reports Server (NTRS)

Steinthorsson, E.; Liou, M. S.; Povinelli, L. A.

1993-01-01

A new computer program is being developed for doing accurate simulations of compressible viscous flows in complex geometries. The code employs the full compressible Navier-Stokes equations. The eddy viscosity model of Baldwin and Lomax is used to model the effects of turbulence on the flow. A cell centered finite volume discretization is used for all terms in the governing equations. The Advection Upwind Splitting Method (AUSM) is used to compute the inviscid fluxes, while central differencing is used for the diffusive fluxes. A four-stage Runge-Kutta time integration scheme is used to march solutions to steady state, while convergence is enhanced by a multigrid scheme, local time-stepping, and implicit residual smoothing. To enable simulations of flows in complex geometries, the code uses composite structured grid systems where all grid lines are continuous at block boundaries (multiblock grids). Example results shown are a flow in a linear cascade, a flow around a circular pin extending between the main walls in a high aspect-ratio channel, and a flow of air in a radial turbine coolant passage.

Development of an explicit multiblock/multigrid flow solver for viscous flows in complex geometries

NASA Technical Reports Server (NTRS)

Steinthorsson, E.; Liou, M.-S.; Povinelli, L. A.

1993-01-01

A new computer program is being developed for doing accurate simulations of compressible viscous flows in complex geometries. The code employs the full compressible Navier-Stokes equations. The eddy viscosity model of Baldwin and Lomax is used to model the effects of turbulence on the flow. A cell centered finite volume discretization is used for all terms in the governing equations. The Advection Upwind Splitting Method (AUSM) is used to compute the inviscid fluxes, while central differencing is used for the diffusive fluxes. A four-stage Runge-Kutta time integration scheme is used to march solutions to steady state, while convergence is enhanced by a multigrid scheme, local time-stepping and implicit residual smoothing. To enable simulations of flows in complex geometries, the code uses composite structured grid systems where all grid lines are continuous at block boundaries (multiblock grids). Example results are shown a flow in a linear cascade, a flow around a circular pin extending between the main walls in a high aspect-ratio channel, and a flow of air in a radial turbine coolant passage.

An experimental study of a self-confined flow with ring-vorticity distribution. Ph.D. Thesis. Final Report

NASA Technical Reports Server (NTRS)

Lin, K. M.; Moore, F. K.

1976-01-01

A new form of self-confined flow was investigated in which a recirculation zone forms away from any solid boundary. An inviscid flow analysis indicated that in a purely meridional axisymmetric flow a stationary, spherical, self-confined region should occur in the center of a streamlined divergent-convergent enlargement zone. The spherical confinement region would be at rest and at constant pressure. Experimental investigations were carried out in a specially built test apparatus to establish the desired confined flow. The streamlined divergent-convergent interior shape of the test section was fabricated according to the theoretical calculation for a particular streamline. The required inlet vorticity distribution was generated by producing a velocity profile with a shaped gauze screen in the straight pipe upstream of the test section. Fluid speed and turbulence intensity were measured with a constant-temperature hot-wire anemometer system. The measured results indicated a very orderly and stable flow field.

Nondestructive method and apparatus for imaging grains in curved surfaces of polycrystalline articles

DOEpatents

Carpenter, Donald A.

1995-01-01

A nondestructive method, and associated apparatus, are provided for determining the grain flow of the grains in a convex curved, textured polycrystalline surface. The convex, curved surface of a polycrystalline article is aligned in a horizontal x-ray diffractometer and a monochromatic, converging x-ray beam is directed onto the curved surface of the polycrystalline article so that the converging x-ray beam is diffracted by crystallographic planes of the grains in the polycrystalline article. The diffracted x-ray beam is caused to pass through a set of horizontal, parallel slits to limit the height of the beam and thereafter. The linear intensity of the diffracted x-ray is measured, using a linear position sensitive proportional counter, as a function of position in a direction orthogonal to the counter so as to generate two dimensional data. An image of the grains in the curved surface of the polycrystalline article is provided based on the two-dimensional data.

Nondestructive method and apparatus for imaging grains in curved surfaces of polycrystalline articles

DOEpatents

Carpenter, D.A.

1995-05-23

A nondestructive method, and associated apparatus, are provided for determining the grain flow of the grains in a convex curved, textured polycrystalline surface. The convex, curved surface of a polycrystalline article is aligned in a horizontal x-ray diffractometer and a monochromatic, converging x-ray beam is directed onto the curved surface of the polycrystalline article so that the converging x-ray beam is diffracted by crystallographic planes of the grains in the polycrystalline article. The diffracted x-ray beam is caused to pass through a set of horizontal, parallel slits to limit the height of the beam and thereafter. The linear intensity of the diffracted x-ray is measured, using a linear position sensitive proportional counter, as a function of position in a direction orthogonal to the counter so as to generate two dimensional data. An image of the grains in the curved surface of the polycrystalline article is provided based on the two-dimensional data. 7 Figs.

Full dimensional computer simulations to study pulsatile blood flow in vessels, aortic arch and bifurcated veins: Investigation of blood viscosity and turbulent effects.

PubMed

Sultanov, Renat A; Guster, Dennis

2009-01-01

We report computational results of blood flow through a model of the human aortic arch and a vessel of actual diameter and length. A realistic pulsatile flow is used in all simulations. Calculations for bifurcation type vessels are also carried out and presented. Different mathematical methods for numerical solution of the fluid dynamics equations have been considered. The non-Newtonian behaviour of the human blood is investigated together with turbulence effects. A detailed time-dependent mathematical convergence test has been carried out. The results of computer simulations of the blood flow in vessels of three different geometries are presented: for pressure, strain rate and velocity component distributions we found significant disagreements between our results obtained with realistic non-Newtonian treatment of human blood and the widely used method in the literature: a simple Newtonian approximation. A significant increase of the strain rate and, as a result, the wall shear stress distribution, is found in the region of the aortic arch. Turbulent effects are found to be important, particularly in the case of bifurcation vessels.

Identification of spatially-localized initial conditions via sparse PCA

NASA Astrophysics Data System (ADS)

Dwivedi, Anubhav; Jovanovic, Mihailo

2017-11-01

Principal Component Analysis involves maximization of a quadratic form subject to a quadratic constraint on the initial flow perturbations and it is routinely used to identify the most energetic flow structures. For general flow configurations, principal components can be efficiently computed via power iteration of the forward and adjoint governing equations. However, the resulting flow structures typically have a large spatial support leading to a question of physical realizability. To obtain spatially-localized structures, we modify the quadratic constraint on the initial condition to include a convex combination with an additional regularization term which promotes sparsity in the physical domain. We formulate this constrained optimization problem as a nonlinear eigenvalue problem and employ an inverse power-iteration-based method to solve it. The resulting solution is guaranteed to converge to a nonlinear eigenvector which becomes increasingly localized as our emphasis on sparsity increases. We use several fluids examples to demonstrate that our method indeed identifies the most energetic initial perturbations that are spatially compact. This work was supported by Office of Naval Research through Grant Number N00014-15-1-2522.

Procedures for Computing Transonic Flows for Control of Adaptive Wind Tunnels. Ph.D. Thesis - Technische Univ., Berlin, Mar. 1986

NASA Technical Reports Server (NTRS)

Rebstock, Rainer

1987-01-01

Numerical methods are developed for control of three dimensional adaptive test sections. The physical properties of the design problem occurring in the external field computation are analyzed, and a design procedure suited for solution of the problem is worked out. To do this, the desired wall shape is determined by stepwise modification of an initial contour. The necessary changes in geometry are determined with the aid of a panel procedure, or, with incident flow near the sonic range, with a transonic small perturbation (TSP) procedure. The designed wall shape, together with the wall deflections set during the tunnel run, are the input to a newly derived one-step formula which immediately yields the adapted wall contour. This is particularly important since the classical iterative adaptation scheme is shown to converge poorly for 3D flows. Experimental results obtained in the adaptive test section with eight flexible walls are presented to demonstrate the potential of the procedure. Finally, a method is described to minimize wall interference in 3D flows by adapting only the top and bottom wind tunnel walls.

Double stratification effects in chemically reactive squeezed Sutterby fluid flow with thermal radiation and mixed convection

NASA Astrophysics Data System (ADS)

Ahmad, S.; Farooq, M.; Javed, M.; Anjum, Aisha

2018-03-01

A current analysis is carried out to study theoretically the mixed convection characteristics in squeezing flow of Sutterby fluid in squeezed channel. The constitutive equation of Sutterby model is utilized to characterize the rheology of squeezing phenomenon. Flow characteristics are explored with dual stratification. In flowing fluid which contains heat and mass transport, the first order chemical reaction and radiative heat flux affect the transport phenomenon. The systems of non-linear governing equations have been modulating which then solved by mean of convergent approach (Homotopy Analysis Method). The graphs are reported and illustrated for emerging parameters. Through graphical explanations, drag force, rate of heat and mass transport are conversed for different pertinent parameters. It is found that heat and mass transport rate decays with dominant double stratified parameters and chemical reaction parameter. The present two-dimensional examination is applicable in some of the engineering processes and industrial fluid mechanics.

Parallel closure theory for toroidally confined plasmas

NASA Astrophysics Data System (ADS)

Ji, Jeong-Young; Held, Eric D.

2017-10-01

We solve a system of general moment equations to obtain parallel closures for electrons and ions in an axisymmetric toroidal magnetic field. Magnetic field gradient terms are kept and treated using the Fourier series method. Assuming lowest order density (pressure) and temperature to be flux labels, the parallel heat flow, friction, and viscosity are expressed in terms of radial gradients of the lowest-order temperature and pressure, parallel gradients of temperature and parallel flow, and the relative electron-ion parallel flow velocity. Convergence of closure quantities is demonstrated as the number of moments and Fourier modes are increased. Properties of the moment equations in the collisionless limit are also discussed. Combining closures with fluid equations parallel mass flow and electric current are also obtained. Work in collaboration with the PSI Center and supported by the U.S. DOE under Grant Nos. DE-SC0014033, DE-SC0016256, and DE-FG02-04ER54746.

Rarefied gas flow through two-dimensional nozzles

NASA Technical Reports Server (NTRS)

De Witt, Kenneth J.; Jeng, Duen-Ren; Keith, Theo G., Jr.; Chung, Chan-Hong

1989-01-01

A kinetic theory analysis is made of the flow of a rarefied gas from one reservoir to another through two-dimensional nozzles with arbitrary curvature. The Boltzmann equation simplified by a model collision integral is solved by means of finite-difference approximations with the discrete ordinate method. The physical space is transformed by a general grid generation technique and the velocity space is transformed to a polar coordinate system. A numerical code is developed which can be applied to any two-dimensional passage of complicated geometry for the flow regimes from free-molecular to slip. Numerical values of flow quantities can be calculated for the entire physical space including both inside the nozzle and in the outside plume. Predictions are made for the case of parallel slots and compared with existing literature data. Also, results for the cases of convergent or divergent slots and two-dimensional nozzles with arbitrary curvature at arbitrary knudsen number are presented.

High-order shock-fitted detonation propagation in high explosives

NASA Astrophysics Data System (ADS)

Romick, Christopher M.; Aslam, Tariq D.

2017-03-01

A highly accurate numerical shock and material interface fitting scheme composed of fifth-order spatial and third- or fifth-order temporal discretizations is applied to the two-dimensional reactive Euler equations in both slab and axisymmetric geometries. High rates of convergence are not typically possible with shock-capturing methods as the Taylor series analysis breaks down in the vicinity of discontinuities. Furthermore, for typical high explosive (HE) simulations, the effects of material interfaces at the charge boundary can also cause significant computational errors. Fitting a computational boundary to both the shock front and material interface (i.e. streamline) alleviates the computational errors associated with captured shocks and thus opens up the possibility of high rates of convergence for multi-dimensional shock and detonation flows. Several verification tests, including a Sedov blast wave, a Zel'dovich-von Neumann-Döring (ZND) detonation wave, and Taylor-Maccoll supersonic flow over a cone, are utilized to demonstrate high rates of convergence to nontrivial shock and reaction flows. Comparisons to previously published shock-capturing multi-dimensional detonations in a polytropic fluid with a constant adiabatic exponent (PF-CAE) are made, demonstrating significantly lower computational error for the present shock and material interface fitting method. For an error on the order of 10 m /s, which is similar to that observed in experiments, shock-fitting offers a computational savings on the order of 1000. In addition, the behavior of the detonation phase speed is examined for several slab widths to evaluate the detonation performance of PBX 9501 while utilizing the Wescott-Stewart-Davis (WSD) model, which is commonly used in HE modeling. It is found that the thickness effect curve resulting from this equation of state and reaction model using published values is dramatically more steep than observed in recent experiments. Utilizing the present fitting strategy, in conjunction with a nonlinear optimizer, a new set of reaction rate parameters improves the correlation of the model to experimental results. Finally, this new model is tested against two dimensional slabs as a validation test.

Comparison of Nonequilibrium Solution Algorithms Applied to Chemically Stiff Hypersonic Flows

NASA Technical Reports Server (NTRS)

Palmer, Grant; Venkatapathy, Ethiraj

1995-01-01

Three solution algorithms, explicit under-relaxation, point implicit, and lower-upper symmetric Gauss-Seidel, are used to compute nonequilibrium flow around the Apollo 4 return capsule at the 62-km altitude point in its descent trajectory. By varying the Mach number, the efficiency and robustness of the solution algorithms were tested for different levels of chemical stiffness.The performance of the solution algorithms degraded as the Mach number and stiffness of the flow increased. At Mach 15 and 30, the lower-upper symmetric Gauss-Seidel method produces an eight order of magnitude drop in the energy residual in one-third to one-half the Cray C-90 computer time as compared to the point implicit and explicit under-relaxation methods. The explicit under-relaxation algorithm experienced convergence difficulties at Mach 30 and above. At Mach 40 the performance of the lower-upper symmetric Gauss-Seidel algorithm deteriorates to the point that it is out performed by the point implicit method. The effects of the viscous terms are investigated. Grid dependency questions are explored.

Effects of mesh style and grid convergence on particle deposition in bifurcating airway models with comparisons to experimental data.

PubMed

Longest, P Worth; Vinchurkar, Samir

2007-04-01

A number of research studies have employed a wide variety of mesh styles and levels of grid convergence to assess velocity fields and particle deposition patterns in models of branching biological systems. Generating structured meshes based on hexahedral elements requires significant time and effort; however, these meshes are often associated with high quality solutions. Unstructured meshes that employ tetrahedral elements can be constructed much faster but may increase levels of numerical diffusion, especially in tubular flow systems with a primary flow direction. The objective of this study is to better establish the effects of mesh generation techniques and grid convergence on velocity fields and particle deposition patterns in bifurcating respiratory models. In order to achieve this objective, four widely used mesh styles including structured hexahedral, unstructured tetrahedral, flow adaptive tetrahedral, and hybrid grids have been considered for two respiratory airway configurations. Initial particle conditions tested are based on the inlet velocity profile or the local inlet mass flow rate. Accuracy of the simulations has been assessed by comparisons to experimental in vitro data available in the literature for the steady-state velocity field in a single bifurcation model as well as the local particle deposition fraction in a double bifurcation model. Quantitative grid convergence was assessed based on a grid convergence index (GCI), which accounts for the degree of grid refinement. The hexahedral mesh was observed to have GCI values that were an order of magnitude below the unstructured tetrahedral mesh values for all resolutions considered. Moreover, the hexahedral mesh style provided GCI values of approximately 1% and reduced run times by a factor of 3. Based on comparisons to empirical data, it was shown that inlet particle seedings should be consistent with the local inlet mass flow rate. Furthermore, the mesh style was found to have an observable effect on cumulative particle depositions with the hexahedral solution most closely matching empirical results. Future studies are needed to assess other mesh generation options including various forms of the hybrid configuration and unstructured hexahedral meshes.

Numerical Simulation of Dynamic Contact Angles and Contact Lines in Multiphase Flows using Level Set Method

NASA Astrophysics Data System (ADS)

Pendota, Premchand

Many physical phenomena and industrial applications involve multiphase fluid flows and hence it is of high importance to be able to simulate various aspects of these flows accurately. The Dynamic Contact Angles (DCA) and the contact lines at the wall boundaries are a couple of such important aspects. In the past few decades, many mathematical models were developed for predicting the contact angles of the inter-face with the wall boundary under various flow conditions. These models are used to incorporate the physics of DCA and contact line motion in numerical simulations using various interface capturing/tracking techniques. In the current thesis, a simple approach to incorporate the static and dynamic contact angle boundary conditions using the level set method is developed and implemented in multiphase CFD codes, LIT (Level set Interface Tracking) (Herrmann (2008)) and NGA (flow solver) (Desjardins et al (2008)). Various DCA models and associated boundary conditions are reviewed. In addition, numerical aspects such as the occurrence of a stress singularity at the contact lines and grid convergence of macroscopic interface shape are dealt with in the context of the level set approach.

Validation of a RANS transition model using a high-order weighted compact nonlinear scheme

NASA Astrophysics Data System (ADS)

Tu, GuoHua; Deng, XiaoGang; Mao, MeiLiang

2013-04-01

A modified transition model is given based on the shear stress transport (SST) turbulence model and an intermittency transport equation. The energy gradient term in the original model is replaced by flow strain rate to saving computational costs. The model employs local variables only, and then it can be conveniently implemented in modern computational fluid dynamics codes. The fifth-order weighted compact nonlinear scheme and the fourth-order staggered scheme are applied to discrete the governing equations for the purpose of minimizing discretization errors, so as to mitigate the confusion between numerical errors and transition model errors. The high-order package is compared with a second-order TVD method on simulating the transitional flow of a flat plate. Numerical results indicate that the high-order package give better grid convergence property than that of the second-order method. Validation of the transition model is performed for transitional flows ranging from low speed to hypersonic speed.

Assessment of computational prediction of tail buffeting

NASA Technical Reports Server (NTRS)

Edwards, John W.

1990-01-01

Assessments of the viability of computational methods and the computer resource requirements for the prediction of tail buffeting are made. Issues involved in the use of Euler and Navier-Stokes equations in modeling vortex-dominated and buffet flows are discussed and the requirement for sufficient grid density to allow accurate, converged calculations is stressed. Areas in need of basic fluid dynamics research are highlighted: vorticity convection, vortex breakdown, dynamic turbulence modeling for free shear layers, unsteady flow separation for moderately swept, rounded leading-edge wings, vortex flows about wings at high subsonic speeds. An estimate of the computer run time for a buffeting response calculation for a full span F-15 aircraft indicates that an improvement in computer and/or algorithm efficiency of three orders of magnitude is needed to enable routine use of such methods. Attention is also drawn to significant uncertainties in the estimates, in particular with regard to nonlinearities contained within the modeling and the question of the repeatability or randomness of buffeting response.

The solution of three-variable duct-flow equations

NASA Technical Reports Server (NTRS)

Stuart, A. R.; Hetherington, R.

1974-01-01

This paper establishes a numerical method for the solution of three-variable problems and is applied here to rotational flows through ducts of various cross sections. An iterative scheme is developed, the main feature of which is the addition of a duplicate variable to the forward component of velocity. Two forward components of velocity result from integrating two sets of first order ordinary differential equations for the streamline curvatures, in intersecting directions across the duct. Two pseudo-continuity equations are introduced with source/sink terms, whose strengths are dependent on the difference between the forward components of velocity. When convergence is obtained, the two forward components of velocity are identical, the source/sink terms are zero, and the original equations are satisfied. A computer program solves the exact equations and boundary conditions numerically. The method is economical and compares successfully with experiments on bent ducts of circular and rectangular cross section where secondary flows are caused by gradients of total pressure upstream.

Computations of Internal and External Axisymmetric Nozzle Aerodynamics at Transonic Speeds

NASA Technical Reports Server (NTRS)

Dalbello, Teryn; Georgiadis, Nicholas; Yoder, Dennis; Keith, Theo

2003-01-01

Computational Fluid Dynamics (CFD) analyses of axisymmetric circular-arc boattail nozzles have been completed in support of NASA's Next Generation Launch Technology Program to investigate the effects of high-speed nozzle geometries on the nozzle internal flow and the surrounding boattail regions. These computations span the very difficult transonic flight regime, with shock-induced separations and strong adverse pressure gradients. External afterbody and internal nozzle pressure distributions computed with the Wind code are compared with experimental data. A range of turbulence models were examined in Wind, including an Explicit Algebraic Stress model (EASM). Computations on two nozzle geometries have been completed at freestream Mach numbers ranging from 0.6 to 0.9, driven by nozzle pressure ratios (NPR) ranging from 2.9 to 5. Results obtained on converging-only geometry indicate reasonable agreement to experimental data, with the EASM and Shear Stress Transport (SST) turbulence models providing the best agreement. Calculations completed on a converging-diverging geometry involving large-scale internal flow separation did not converge to a true steady-state solution when run with variable timestepping (steady-state). Calculations obtained using constant timestepping (time-accurate) indicate less variations in flow properties compared with steady-state solutions. This failure to converge to a steady-state solution was found to be the result of difficulties in using variable time-stepping with large-scale separations present in the flow. Nevertheless, time-averaged boattail surface pressure coefficient and internal nozzle pressures show fairly good agreement with experimental data. The SST turbulence model demonstrates the best over-all agreement with experimental data.

A distributed approach to the OPF problem

NASA Astrophysics Data System (ADS)

Erseghe, Tomaso

2015-12-01

This paper presents a distributed approach to optimal power flow (OPF) in an electrical network, suitable for application in a future smart grid scenario where access to resource and control is decentralized. The non-convex OPF problem is solved by an augmented Lagrangian method, similar to the widely known ADMM algorithm, with the key distinction that penalty parameters are constantly increased. A (weak) assumption on local solver reliability is required to always ensure convergence. A certificate of convergence to a local optimum is available in the case of bounded penalty parameters. For moderate sized networks (up to 300 nodes, and even in the presence of a severe partition of the network), the approach guarantees a performance very close to the optimum, with an appreciably fast convergence speed. The generality of the approach makes it applicable to any (convex or non-convex) distributed optimization problem in networked form. In the comparison with the literature, mostly focused on convex SDP approximations, the chosen approach guarantees adherence to the reference problem, and it also requires a smaller local computational complexity effort.

Floating shock fitting via Lagrangian adaptive meshes

NASA Technical Reports Server (NTRS)

Vanrosendale, John

1995-01-01

In recent work we have formulated a new approach to compressible flow simulation, combining the advantages of shock-fitting and shock-capturing. Using a cell-centered on Roe scheme discretization on unstructured meshes, we warp the mesh while marching to steady state, so that mesh edges align with shocks and other discontinuities. This new algorithm, the Shock-fitting Lagrangian Adaptive Method (SLAM), is, in effect, a reliable shock-capturing algorithm which yields shock-fitted accuracy at convergence.

A Monte Carlo Code for Relativistic Radiation Transport Around Kerr Black Holes

NASA Technical Reports Server (NTRS)

Schnittman, Jeremy David; Krolik, Julian H.

2013-01-01

We present a new code for radiation transport around Kerr black holes, including arbitrary emission and absorption mechanisms, as well as electron scattering and polarization. The code is particularly useful for analyzing accretion flows made up of optically thick disks and optically thin coronae. We give a detailed description of the methods employed in the code and also present results from a number of numerical tests to assess its accuracy and convergence.

A non-hydrostatic flat-bottom ocean model entirely based on Fourier expansion

NASA Astrophysics Data System (ADS)

Wirth, A.

2005-01-01

We show how to implement free-slip and no-slip boundary conditions in a three dimensional Boussinesq flat-bottom ocean model based on Fourier expansion. Our method is inspired by the immersed or virtual boundary technique in which the effect of boundaries on the flow field is modeled by a virtual force field. Our method, however, explicitly depletes the velocity on the boundary induced by the pressure, while at the same time respecting the incompressibility of the flow field. Spurious spatial oscillations remain at a negligible level in the simulated flow field when using our technique and no filtering of the flow field is necessary. We furthermore show that by using the method presented here the residual velocities at the boundaries are easily reduced to a negligible value. This stands in contradistinction to previous calculations using the immersed or virtual boundary technique. The efficiency is demonstrated by simulating a Rayleigh impulsive flow, for which the time evolution of the simulated flow is compared to an analytic solution, and a three dimensional Boussinesq simulation of ocean convection. The second instance is taken form a well studied oceanographic context: A free slip boundary condition is applied on the upper surface, the modeled sea surface, and a no-slip boundary condition to the lower boundary, the modeled ocean floor. Convergence properties of the method are investigated by solving a two dimensional stationary problem at different spatial resolutions. The work presented here is restricted to a flat ocean floor. Extensions of our method to ocean models with a realistic topography are discussed.

Choice of boundary condition for lattice-Boltzmann simulation of moderate-Reynolds-number flow in complex domains.

PubMed

Nash, Rupert W; Carver, Hywel B; Bernabeu, Miguel O; Hetherington, James; Groen, Derek; Krüger, Timm; Coveney, Peter V

2014-02-01

Modeling blood flow in larger vessels using lattice-Boltzmann methods comes with a challenging set of constraints: a complex geometry with walls and inlets and outlets at arbitrary orientations with respect to the lattice, intermediate Reynolds (Re) number, and unsteady flow. Simple bounce-back is one of the most commonly used, simplest, and most computationally efficient boundary conditions, but many others have been proposed. We implement three other methods applicable to complex geometries [Guo, Zheng, and Shi, Phys. Fluids 14, 2007 (2002); Bouzidi, Firdaouss, and Lallemand, Phys. Fluids 13, 3452 (2001); Junk and Yang, Phys. Rev. E 72, 066701 (2005)] in our open-source application hemelb. We use these to simulate Poiseuille and Womersley flows in a cylindrical pipe with an arbitrary orientation at physiologically relevant Re number (1-300) and Womersley (4-12) numbers and steady flow in a curved pipe at relevant Dean number (100-200) and compare the accuracy to analytical solutions. We find that both the Bouzidi-Firdaouss-Lallemand (BFL) and Guo-Zheng-Shi (GZS) methods give second-order convergence in space while simple bounce-back degrades to first order. The BFL method appears to perform better than GZS in unsteady flows and is significantly less computationally expensive. The Junk-Yang method shows poor stability at larger Re number and so cannot be recommended here. The choice of collision operator (lattice Bhatnagar-Gross-Krook vs multiple relaxation time) and velocity set (D3Q15 vs D3Q19 vs D3Q27) does not significantly affect the accuracy in the problems studied.

2D Inviscid and Viscous Inverse Design Using Continuous Adjoint and Lax-Wendroff Formulation

NASA Astrophysics Data System (ADS)

Proctor, Camron Lisle

The continuous adjoint (CA) technique for optimization and/or inverse-design of aerodynamic components has seen nearly 30 years of documented success in academia. The benefits of using CA versus a direct sensitivity analysis are shown repeatedly in the literature. However, the use of CA in industry is relatively unheard-of. The sparseness of industry contributions to the field may be attributed to the tediousness of the derivation and/or to the difficulties in implementation due to the lack of well-documented adjoint numerical methods. The focus of this work has been to thoroughly document the techniques required to build a two-dimensional CA inverse-design tool. To this end, this work begins with a short background on computational fluid dynamics (CFD) and the use of optimization tools in conjunction with CFD tools to solve aerodynamic optimization problems. A thorough derivation of the continuous adjoint equations and the accompanying gradient calculations for inviscid and viscous constraining equations follows the introduction. Next, the numerical techniques used for solving the partial differential equations (PDEs) governing the flow equations and the adjoint equations are described. Numerical techniques for the supplementary equations are discussed briefly. Subsequently, a verification of the efficacy of the inverse design tool, for the inviscid adjoint equations as well as possible numerical implementation pitfalls are discussed. The NACA0012 airfoil is used as an initial airfoil and surface pressure distribution and the NACA16009 is used as the desired pressure and vice versa. Using a Savitsky-Golay gradient filter, convergence (defined as a cost function<1E-5) is reached in approximately 220 design iteration using 121 design variables. The inverse-design using inviscid adjoint equations results are followed by the discussion of the viscous inverse design results and techniques used to further the convergence of the optimizer. The relationship between limiting step-size and convergence in a line-search optimization is shown to slightly decrease the final cost function at significant computational cost. A gradient damping technique is presented and shown to increase the convergence rate for the optimization in viscous problems, at a negligible increase in computational cost, but is insufficient to converge the solution. Systematically including adjacent surface vertices in the perturbation of a design variable, also a surface vertex, is shown to affect the convergence capability of the viscous optimizer. Finally, a comparison of using inviscid adjoint equations, as opposed to viscous adjoint equations, on viscous flow is presented, and the inviscid adjoint paired with viscous flow is found to reduce the cost function further than the viscous adjoint for the presented problem.

Plasma motion in the Venus ionosphere: Transition to supersonic flow

DOE Office of Scientific and Technical Information (OSTI.GOV)

Whitten, R.C.; Barnes, A.; McCormick, P.T.

1991-07-01

A remarkable feature of the ionosphere of Venus is the presence of nightward supersonic flows at high altitude near the terminator. In general the steady flow of an ideal gas admits a subsonic-supersonic transition only in the presence of special conditions, such as a convergence of the flow followed by divergence, or external forces. In this paper, the authors show that the relatively high pressure dayside plasma wells up slowly, and at high altitude it is accelerated horizontally through a relatively constricted region near the terminator toward the low-density nightside. In effect, the plasma flows through a nozzle that ismore » first converging, then diverging, permitting the transition to supersonic flow. Analysis of results from previously published models of the plasma flow in the upper ionosphere of Venus shows how such a nozzle is formed. The model plasma does indeed accelerate to supersonic speeds, reaching sonic speed just behind the terminator. The computed speeds prove to be close to those observed by the Pioneer Venus orbiter, and the ion transport rates are sufficient to produce and maintain the nightside ionosphere.« less

A block iterative finite element algorithm for numerical solution of the steady-state, compressible Navier-Stokes equations

NASA Technical Reports Server (NTRS)

Cooke, C. H.

1976-01-01

An iterative method for numerically solving the time independent Navier-Stokes equations for viscous compressible flows is presented. The method is based upon partial application of the Gauss-Seidel principle in block form to the systems of nonlinear algebraic equations which arise in construction of finite element (Galerkin) models approximating solutions of fluid dynamic problems. The C deg-cubic element on triangles is employed for function approximation. Computational results for a free shear flow at Re = 1,000 indicate significant achievement of economy in iterative convergence rate over finite element and finite difference models which employ the customary time dependent equations and asymptotic time marching procedure to steady solution. Numerical results are in excellent agreement with those obtained for the same test problem employing time marching finite element and finite difference solution techniques.

Interference method for obtaining the potential flow past an arbitrary cascade of airfoils

NASA Technical Reports Server (NTRS)

Katzoff, S; Finn, Robert S; Laurence, James C

1947-01-01

A procedure is presented for obtaining the pressure distribution on an arbitrary airfoil section in cascade in a two-dimensional, incompressible, and nonviscous flow. The method considers directly the influence on a given airfoil of the rest of the cascade and evaluates this interference by an iterative process, which appeared to converge rapidly in the cases tried (about unit solidity, stagger angles of 0 degree and 45 degrees). Two variations of the basic interference calculations are described. One, which is accurate enough for most purposes, involves the substitution of sources, sinks, and vortices for the interfering airfoils; the other, which may be desirable for the final approximation, involves a contour integration. The computations are simplified by the use of a chart presented by Betz in a related paper. Illustrated examples are included.

Recent Improvements in Aerodynamic Design Optimization on Unstructured Meshes

NASA Technical Reports Server (NTRS)

Nielsen, Eric J.; Anderson, W. Kyle

2000-01-01

Recent improvements in an unstructured-grid method for large-scale aerodynamic design are presented. Previous work had shown such computations to be prohibitively long in a sequential processing environment. Also, robust adjoint solutions and mesh movement procedures were difficult to realize, particularly for viscous flows. To overcome these limiting factors, a set of design codes based on a discrete adjoint method is extended to a multiprocessor environment using a shared memory approach. A nearly linear speedup is demonstrated, and the consistency of the linearizations is shown to remain valid. The full linearization of the residual is used to precondition the adjoint system, and a significantly improved convergence rate is obtained. A new mesh movement algorithm is implemented and several advantages over an existing technique are presented. Several design cases are shown for turbulent flows in two and three dimensions.

Drag reduction by herringbone riblet texture in direct numerical simulations of turbulent channel flow

NASA Astrophysics Data System (ADS)

Benschop, H. O. G.; Breugem, W.-P.

2017-08-01

A bird-feather-inspired herringbone riblet texture was investigated for turbulent drag reduction. The texture consists of blade riblets in a converging/diverging or herringbone pattern with spanwise wavelength Λf. The aim is to quantify the drag change for this texture as compared to a smooth wall and to study the underlying mechanisms. To that purpose, direct numerical simulations of turbulent flow in a channel with height Lz were performed. The Fukagata-Iwamoto-Kasagi identity for drag decomposition was extended to textured walls and was used to study the drag change mechanisms. For Λf/Lz ≳ O(10), the herringbone texture behaves similarly to a conventional parallel-riblet texture in yaw: the suppression of turbulent advective transport results in a slight drag reduction of 2%. For Λf/Lz ≲ O(1), the drag increases strongly with a maximum of 73%. This is attributed to enhanced mean and turbulent advection, which results from the strong secondary flow that forms over regions of riblet convergence/divergence. Hence, the employment of convergent/divergent riblets in the texture seems to be detrimental to turbulent drag reduction.

An efficient fully-implicit multislope MUSCL method for multiphase flow with gravity in discrete fractured media

NASA Astrophysics Data System (ADS)

Jiang, Jiamin; Younis, Rami M.

2017-06-01

The first-order methods commonly employed in reservoir simulation for computing the convective fluxes introduce excessive numerical diffusion leading to severe smoothing of displacement fronts. We present a fully-implicit cell-centered finite-volume (CCFV) framework that can achieve second-order spatial accuracy on smooth solutions, while at the same time maintain robustness and nonlinear convergence performance. A novel multislope MUSCL method is proposed to construct the required values at edge centroids in a straightforward and effective way by taking advantage of the triangular mesh geometry. In contrast to the monoslope methods in which a unique limited gradient is used, the multislope concept constructs specific scalar slopes for the interpolations on each edge of a given element. Through the edge centroids, the numerical diffusion caused by mesh skewness is reduced, and optimal second order accuracy can be achieved. Moreover, an improved smooth flux-limiter is introduced to ensure monotonicity on non-uniform meshes. The flux-limiter provides high accuracy without degrading nonlinear convergence performance. The CCFV framework is adapted to accommodate a lower-dimensional discrete fracture-matrix (DFM) model. Several numerical tests with discrete fractured system are carried out to demonstrate the efficiency and robustness of the numerical model.

Globalized Newton-Krylov-Schwarz Algorithms and Software for Parallel Implicit CFD

NASA Technical Reports Server (NTRS)

Gropp, W. D.; Keyes, D. E.; McInnes, L. C.; Tidriri, M. D.

1998-01-01

Implicit solution methods are important in applications modeled by PDEs with disparate temporal and spatial scales. Because such applications require high resolution with reasonable turnaround, "routine" parallelization is essential. The pseudo-transient matrix-free Newton-Krylov-Schwarz (Psi-NKS) algorithmic framework is presented as an answer. We show that, for the classical problem of three-dimensional transonic Euler flow about an M6 wing, Psi-NKS can simultaneously deliver: globalized, asymptotically rapid convergence through adaptive pseudo- transient continuation and Newton's method-, reasonable parallelizability for an implicit method through deferred synchronization and favorable communication-to-computation scaling in the Krylov linear solver; and high per- processor performance through attention to distributed memory and cache locality, especially through the Schwarz preconditioner. Two discouraging features of Psi-NKS methods are their sensitivity to the coding of the underlying PDE discretization and the large number of parameters that must be selected to govern convergence. We therefore distill several recommendations from our experience and from our reading of the literature on various algorithmic components of Psi-NKS, and we describe a freely available, MPI-based portable parallel software implementation of the solver employed here.

A parallel offline CFD and closed-form approximation strategy for computationally efficient analysis of complex fluid flows

NASA Astrophysics Data System (ADS)

Allphin, Devin

Computational fluid dynamics (CFD) solution approximations for complex fluid flow problems have become a common and powerful engineering analysis technique. These tools, though qualitatively useful, remain limited in practice by their underlying inverse relationship between simulation accuracy and overall computational expense. While a great volume of research has focused on remedying these issues inherent to CFD, one traditionally overlooked area of resource reduction for engineering analysis concerns the basic definition and determination of functional relationships for the studied fluid flow variables. This artificial relationship-building technique, called meta-modeling or surrogate/offline approximation, uses design of experiments (DOE) theory to efficiently approximate non-physical coupling between the variables of interest in a fluid flow analysis problem. By mathematically approximating these variables, DOE methods can effectively reduce the required quantity of CFD simulations, freeing computational resources for other analytical focuses. An idealized interpretation of a fluid flow problem can also be employed to create suitably accurate approximations of fluid flow variables for the purposes of engineering analysis. When used in parallel with a meta-modeling approximation, a closed-form approximation can provide useful feedback concerning proper construction, suitability, or even necessity of an offline approximation tool. It also provides a short-circuit pathway for further reducing the overall computational demands of a fluid flow analysis, again freeing resources for otherwise unsuitable resource expenditures. To validate these inferences, a design optimization problem was presented requiring the inexpensive estimation of aerodynamic forces applied to a valve operating on a simulated piston-cylinder heat engine. The determination of these forces was to be found using parallel surrogate and exact approximation methods, thus evidencing the comparative benefits of this technique. For the offline approximation, latin hypercube sampling (LHS) was used for design space filling across four (4) independent design variable degrees of freedom (DOF). Flow solutions at the mapped test sites were converged using STAR-CCM+ with aerodynamic forces from the CFD models then functionally approximated using Kriging interpolation. For the closed-form approximation, the problem was interpreted as an ideal 2-D converging-diverging (C-D) nozzle, where aerodynamic forces were directly mapped by application of the Euler equation solutions for isentropic compression/expansion. A cost-weighting procedure was finally established for creating model-selective discretionary logic, with a synthesized parallel simulation resource summary provided.

On the Singular Incompressible Limit of Inviscid Compressible Fluids

NASA Astrophysics Data System (ADS)

Secchi, P.

We consider the Euler equations of barotropic inviscid compressible fluids in a bounded domain. It is well known that, as the Mach number goes to zero, the compressible flows approximate the solution of the equations of motion of inviscid, incompressible fluids. In this paper we discuss, for the boundary case, the different kinds of convergence under various assumptions on the data, in particular the weak convergence in the case of uniformly bounded initial data and the strong convergence in the norm of the data space.

Weighted least squares phase unwrapping based on the wavelet transform

NASA Astrophysics Data System (ADS)

Chen, Jiafeng; Chen, Haiqin; Yang, Zhengang; Ren, Haixia

2007-01-01

The weighted least squares phase unwrapping algorithm is a robust and accurate method to solve phase unwrapping problem. This method usually leads to a large sparse linear equation system. Gauss-Seidel relaxation iterative method is usually used to solve this large linear equation. However, this method is not practical due to its extremely slow convergence. The multigrid method is an efficient algorithm to improve convergence rate. However, this method needs an additional weight restriction operator which is very complicated. For this reason, the multiresolution analysis method based on the wavelet transform is proposed. By applying the wavelet transform, the original system is decomposed into its coarse and fine resolution levels and an equivalent equation system with better convergence condition can be obtained. Fast convergence in separate coarse resolution levels speeds up the overall system convergence rate. The simulated experiment shows that the proposed method converges faster and provides better result than the multigrid method.

Optimization of polymer electrolyte membrane fuel cell flow channels using a genetic algorithm

NASA Astrophysics Data System (ADS)

Catlin, Glenn; Advani, Suresh G.; Prasad, Ajay K.

The design of the flow channels in PEM fuel cells directly impacts the transport of reactant gases to the electrodes and affects cell performance. This paper presents results from a study to optimize the geometry of the flow channels in a PEM fuel cell. The optimization process implements a genetic algorithm to rapidly converge on the channel geometry that provides the highest net power output from the cell. In addition, this work implements a method for the automatic generation of parameterized channel domains that are evaluated for performance using a commercial computational fluid dynamics package from ANSYS. The software package includes GAMBIT as the solid modeling and meshing software, the solver FLUENT, and a PEMFC Add-on Module capable of modeling the relevant physical and electrochemical mechanisms that describe PEM fuel cell operation. The result of the optimization process is a set of optimal channel geometry values for the single-serpentine channel configuration. The performance of the optimal geometry is contrasted with a sub-optimal one by comparing contour plots of current density, oxygen and hydrogen concentration. In addition, the role of convective bypass in bringing fresh reactant to the catalyst layer is examined in detail. The convergence to the optimal geometry is confirmed by a bracketing study which compares the performance of the best individual to those of its neighbors with adjacent parameter values.

Bus-based park-and-ride system: a stochastic model on multimodal network with congestion pricing schemes

NASA Astrophysics Data System (ADS)

Liu, Zhiyuan; Meng, Qiang

2014-05-01

This paper focuses on modelling the network flow equilibrium problem on a multimodal transport network with bus-based park-and-ride (P&R) system and congestion pricing charges. The multimodal network has three travel modes: auto mode, transit mode and P&R mode. A continuously distributed value-of-time is assumed to convert toll charges and transit fares to time unit, and the users' route choice behaviour is assumed to follow the probit-based stochastic user equilibrium principle with elastic demand. These two assumptions have caused randomness to the users' generalised travel times on the multimodal network. A comprehensive network framework is first defined for the flow equilibrium problem with consideration of interactions between auto flows and transit (bus) flows. Then, a fixed-point model with unique solution is proposed for the equilibrium flows, which can be solved by a convergent cost averaging method. Finally, the proposed methodology is tested by a network example.

Three-dimensional multigrid algorithms for the flux-split Euler equations

NASA Technical Reports Server (NTRS)

Anderson, W. Kyle; Thomas, James L.; Whitfield, David L.

1988-01-01

The Full Approximation Scheme (FAS) multigrid method is applied to several implicit flux-split algorithms for solving the three-dimensional Euler equations in a body fitted coordinate system. Each of the splitting algorithms uses a variation of approximate factorization and is implemented in a finite volume formulation. The algorithms are all vectorizable with little or no scalar computation required. The flux vectors are split into upwind components using both the splittings of Steger-Warming and Van Leer. The stability and smoothing rate of each of the schemes are examined using a Fourier analysis of the complete system of equations. Results are presented for three-dimensional subsonic, transonic, and supersonic flows which demonstrate substantially improved convergence rates with the multigrid algorithm. The influence of using both a V-cycle and a W-cycle on the convergence is examined.

bhlight: General Relativistic Radiation Magnetohydrodynamics with Monte Carlo Transport

DOE PAGES

Ryan, Benjamin R; Dolence, Joshua C.; Gammie, Charles F.

2015-06-25

We present bhlight, a numerical scheme for solving the equations of general relativistic radiation magnetohydrodynamics using a direct Monte Carlo solution of the frequency-dependent radiative transport equation. bhlight is designed to evolve black hole accretion flows at intermediate accretion rate, in the regime between the classical radiatively efficient disk and the radiatively inefficient accretion flow (RIAF), in which global radiative effects play a sub-dominant but non-negligible role in disk dynamics. We describe the governing equations, numerical method, idiosyncrasies of our implementation, and a suite of test and convergence results. We also describe example applications to radiative Bondi accretion and tomore » a slowly accreting Kerr black hole in axisymmetry.« less

Asynchronous, macrotasked relaxation strategies for the solution of viscous, hypersonic flows

NASA Technical Reports Server (NTRS)

Gnoffo, Peter A.

1991-01-01

A point-implicit, asynchronous macrotasked relaxation of the steady, thin-layer, Navier-Stokes equations is presented. The method employs multidirectional, single-level storage Gauss-Seidel relaxation sweeps, which effectively communicate perturbations across the entire domain in 2n sweeps, where n is the dimension of the domain. In order to enhance convergence the application of relaxation factors to specific components of the Jacobian is examined using a stability analysis of the advection and diffusion equations. Attention is also given to the complications associated with asynchronous multitasking. Solutions are generated for hypersonic flows over blunt bodies in two and three dimensions with chemical reactions, utilizing single-tasked and multitasked relaxation strategies.

Spectral/ hp element methods: Recent developments, applications, and perspectives

NASA Astrophysics Data System (ADS)

Xu, Hui; Cantwell, Chris D.; Monteserin, Carlos; Eskilsson, Claes; Engsig-Karup, Allan P.; Sherwin, Spencer J.

2018-02-01

The spectral/ hp element method combines the geometric flexibility of the classical h-type finite element technique with the desirable numerical properties of spectral methods, employing high-degree piecewise polynomial basis functions on coarse finite element-type meshes. The spatial approximation is based upon orthogonal polynomials, such as Legendre or Chebychev polynomials, modified to accommodate a C 0 - continuous expansion. Computationally and theoretically, by increasing the polynomial order p, high-precision solutions and fast convergence can be obtained and, in particular, under certain regularity assumptions an exponential reduction in approximation error between numerical and exact solutions can be achieved. This method has now been applied in many simulation studies of both fundamental and practical engineering flows. This paper briefly describes the formulation of the spectral/ hp element method and provides an overview of its application to computational fluid dynamics. In particular, it focuses on the use of the spectral/ hp element method in transitional flows and ocean engineering. Finally, some of the major challenges to be overcome in order to use the spectral/ hp element method in more complex science and engineering applications are discussed.

Newton's method applied to finite-difference approximations for the steady-state compressible Navier-Stokes equations

NASA Technical Reports Server (NTRS)

Bailey, Harry E.; Beam, Richard M.

1991-01-01

Finite-difference approximations for steady-state compressible Navier-Stokes equations, whose two spatial dimensions are written in generalized curvilinear coordinates and strong conservation-law form, are presently solved by means of Newton's method in order to obtain a lifting-airfoil flow field under subsonic and transonnic conditions. In addition to ascertaining the computational requirements of an initial guess ensuring convergence and the degree of computational efficiency obtainable via the approximate Newton method's freezing of the Jacobian matrices, attention is given to the need for auxiliary methods assessing the temporal stability of steady-state solutions. It is demonstrated that nonunique solutions of the finite-difference equations are obtainable by Newton's method in conjunction with a continuation method.

Magnetized Converging Flows toward the Hot Core in the Intermediate/High-mass Star-forming Region NGC 6334 V

DOE Office of Scientific and Technical Information (OSTI.GOV)

Juárez, Carmen; Girart, Josep M.; Zamora-Avilés, Manuel

We present Submillimeter Array (SMA) observations at 345 GHz toward the intermediate/high-mass cluster-forming region NGC 6334 V. From the dust emission we spatially resolve three dense condensations, the brightest one presenting the typical chemistry of a hot core. The magnetic field (derived from the dust polarized emission) shows a bimodal converging pattern toward the hot core. The molecular emission traces two filamentary structures at two different velocities, separated by 2 km s{sup −1}, converging to the hot core and following the magnetic field distribution. We compare the velocity field and the magnetic field derived from the SMA observations with magnetohydrodynamicmore » simulations of star-forming regions dominated by gravity. This comparison allows us to show how the gas falls in from the larger-scale extended dense core (∼0.1 pc) of NGC 6334 V toward the higher-density hot core region (∼0.02 pc) through two distinctive converging flows dragging the magnetic field, whose strength seems to have been overcome by gravity.« less

Use of instantaneous streamflow measurements to improve regression estimates of index flow for the summer month of lowest streamflow in Michigan

USGS Publications Warehouse

Holtschlag, David J.

2011-01-01

In Michigan, index flow Q50 is a streamflow characteristic defined as the minimum of median flows for July, August, and September. The state of Michigan uses index flow estimates to help regulate large (greater than 100,000 gallons per day) water withdrawals to prevent adverse effects on characteristic fish populations. At sites where long-term streamgages are located, index flows are computed directly from continuous streamflow records as GageQ50. In an earlier study, a multiple-regression equation was developed to estimate index flows IndxQ50 at ungaged sites. The index equation explains about 94 percent of the variability of index flows at 147 (index) streamgages by use of six explanatory variables describing soil type, aquifer transmissivity, land cover, and precipitation characteristics. This report extends the results of the previous study, by use of Monte Carlo simulations, to evaluate alternative flow estimators, DiscQ50, IntgQ50, SiteQ50, and AugmQ50. The Monte Carlo simulations treated each of the available index streamgages, in turn, as a miscellaneous site where streamflow conditions are described by one or more instantaneous measurements of flow. In the simulations, instantaneous flows were approximated by daily mean flows at the corresponding site. All estimators use information that can be obtained from instantaneous flow measurements and contemporaneous daily mean flow data from nearby long-term streamgages. The efficacy of these estimators was evaluated over a set of measurement intensities in which the number of simulated instantaneous flow measurements ranged from 1 to 100 at a site. The discrete measurement estimator DiscQ50 is based on a simple linear regression developed between information on daily mean flows at five or more streamgages near the miscellaneous site and their corresponding GageQ50 index flows. The regression relation then was used to compute a DiscQ50 estimate at the miscellaneous site by use of the simulated instantaneous flow measurement. This process was repeated to develop a set of DiscQ50 estimates for all simulated instantaneous measurements, a weighted DiscQ50 estimate was formed from this set. Results indicated that the expected value of this weighted estimate was more precise than the IndxQ50 estimate for all measurement intensities evaluated. The integrated index-flow estimator, IntgQ50, was formed by computing a weighted average of the index estimate IndxQ50 and the DiscQ50 estimate. Results indicated that the IntgQ50 estimator was more precise than the DiscQ50 estimator at low measurement intensities of one to two measurements. At greater measurement intensities, the precision of the IntgQ50 estimator converges to the DiscQ50 estimator. Neither the DiscQ50 nor the IntgQ50 estimators provided site-specific estimates. In particular, although expected values of DiscQ50 and IntgQ50 estimates converge with increasing measurement intensity, they do not necessarily converge to the site-specific value of Q50. The site estimator of flow, SiteQ50, was developed to facilitate this convergence at higher measurement intensities. This is accomplished by use of the median of simulated instantaneous flow values for each measurement intensity level. A weighted estimate of the median and information associated with the IntgQ50 estimate was used to form the SiteQ50 estimate. Initial simulations indicate that the SiteQ50 estimator generally has greater precision than the IntgQ50 estimator at measurement intensities greater than 3, however, additional analysis is needed to identify streamflow conditions under which instantaneous measurements will produce estimates that generally converge to the index flows. A preliminary augmented index regression equation was developed, which contains the index regression estimate and two additional variables associated with base-flow recession characteristics. When these recession variables were estimated as the medians of recession parameters compute

GENENG: A program for calculating design and off-design performance for turbojet and turbofan engines

NASA Technical Reports Server (NTRS)

Koenig, R. W.; Fishbach, L. H.

1972-01-01

A computer program entitled GENENG employs component performance maps to perform analytical, steady state, engine cycle calculations. Through a scaling procedure, each of the component maps can be used to represent a family of maps (different design values of pressure ratios, efficiency, weight flow, etc.) Either convergent or convergent-divergent nozzles may be used. Included is a complete FORTRAN 4 listing of the program. Sample results and input explanations are shown for one-spool and two-spool turbojets and two-spool separate- and mixed-flow turbofans operating at design and off-design conditions.

Converging flow and anisotropy cause large-scale folding in Greenland's ice sheet.

PubMed

Bons, Paul D; Jansen, Daniela; Mundel, Felicitas; Bauer, Catherine C; Binder, Tobias; Eisen, Olaf; Jessell, Mark W; Llorens, Maria-Gema; Steinbach, Florian; Steinhage, Daniel; Weikusat, Ilka

2016-04-29

The increasing catalogue of high-quality ice-penetrating radar data provides a unique insight in the internal layering architecture of the Greenland ice sheet. The stratigraphy, an indicator of past deformation, highlights irregularities in ice flow and reveals large perturbations without obvious links to bedrock shape. In this work, to establish a new conceptual model for the formation process, we analysed the radar data at the onset of the Petermann Glacier, North Greenland, and created a three-dimensional model of several distinct stratigraphic layers. We demonstrate that the dominant structures are cylindrical folds sub-parallel to the ice flow. By numerical modelling, we show that these folds can be formed by lateral compression of mechanically anisotropic ice, while a general viscosity contrast between layers would not lead to folding for the same boundary conditions. We conclude that the folds primarily form by converging flow as the mechanically anisotropic ice is channelled towards the glacier.

Converging flow and anisotropy cause large-scale folding in Greenland's ice sheet

NASA Astrophysics Data System (ADS)

Bons, Paul D.; Jansen, Daniela; Mundel, Felicitas; Bauer, Catherine C.; Binder, Tobias; Eisen, Olaf; Jessell, Mark W.; Llorens, Maria-Gema; Steinbach, Florian; Steinhage, Daniel; Weikusat, Ilka

2016-04-01

The increasing catalogue of high-quality ice-penetrating radar data provides a unique insight in the internal layering architecture of the Greenland ice sheet. The stratigraphy, an indicator of past deformation, highlights irregularities in ice flow and reveals large perturbations without obvious links to bedrock shape. In this work, to establish a new conceptual model for the formation process, we analysed the radar data at the onset of the Petermann Glacier, North Greenland, and created a three-dimensional model of several distinct stratigraphic layers. We demonstrate that the dominant structures are cylindrical folds sub-parallel to the ice flow. By numerical modelling, we show that these folds can be formed by lateral compression of mechanically anisotropic ice, while a general viscosity contrast between layers would not lead to folding for the same boundary conditions. We conclude that the folds primarily form by converging flow as the mechanically anisotropic ice is channelled towards the glacier.

Release of dissolved nitrogen from water during depressurization

NASA Technical Reports Server (NTRS)

Simoneau, R. J.

1978-01-01

Experiments were run to study depressurization of water containing various concentrations of dissolved nitrogen gas, the primary case being room temperature water saturated with nitrogen at 4 MPa. In a static depressurization experiment, water with very high nitrogen content was depressurized at rates from 0.09 to 0.50 MPa per second and photographed with high speed movies. The pictures showed that the bubble population at a given pressure increased strongly with decreasing depressurization rate. Flow experiments were performed in an axisymmetric converging-diverging nozzle and in a two-dimensional converging nozzle with glass sidewalls. Depressurization gradients were roughly 500 to 1200 MPa per second. Both nozzles exhibited choked flow behavior even at nitrogen concentration levels as low as 4 percent of saturated. The flow rates were independent of concentration level and could be computed as incompressible water flow based on the difference between stagnation and throat pressures; however, the throat pressures were significantly different between the two nozzles.

Contribution of the Recent AUSM Schemes to the Overflow Code: Implementation and Validation

NASA Technical Reports Server (NTRS)

Liou, Meng-Sing; Buning, Pieter G.

2000-01-01

We shall present results of a recent collaborative effort between the authors attempting to implement the numerical flux scheme, AUSM+ and its new developments, into a widely used NASA code, OVERFLOW. This paper is intended to give a thorough and systematic documentation about the solutions of default test cases using the AUSNI+ scheme. Hence we will address various aspects of numerical solutions, such as accuracy, convergence rate, and effects of turbulence models, over a variety of geometries, speed regimes. We will briefly describe the numerical schemes employed in the calculations, including the capability of solving for low-speed flows and multiphase flows by employing the concept of numerical speed of sound. As a bonus, this low Mach number formulations also enhances convergence to steady solutions for flows even at transonic speed. Calculations for complex 3D turbulent flows were performed with several turbulence models and the results display excellent agreements with measured data.

Fundamental investigation of ARC interruption in gas flows

NASA Astrophysics Data System (ADS)

Benenson, D. M.; Frind, G.; Kinsinger, R. E.; Nagamatsu, H. T.; Noeske, H. O.; Sheer, R. E., Jr.

1980-07-01

Thermal recovery in gas blast interrupters is discussed. The thermal recovery process was investigated with physical and aerodynamic methods, typically using reduced size nozzles and short sinusoidal current pulses. Aerodynamic characterization of the cold flow fields in several different nozzle types included measurements of the pressure and flow fields, both steady-state and turbulent components, with special attention given to wakes and shock structures. Special schlieren techniques on DC arcs and high speed photography on arcs in orifice nozzles show that shock heating broadens the arc independent of turbulence effects and produces a poorly recovering downstream arc section. Measured recovery speeds in both orifice and convergent-divergent nozzles agree with predictions of several arc theories assuming turbulent power losses. However, data on post-zero currents and power loss show values much smaller than theoretical predictions. Hydrogen, deuterium, and methane were measured.

Two-phase choked flow of cryogenic fluids in converging-diverging nozzles

NASA Technical Reports Server (NTRS)

Simoneau, R. J.; Hendricks, R. C.

1979-01-01

Data are presented for the two phase choked flow of three cryogenic fluids - nitrogen, methane, and hydrogen - in four converging-diverging nozzles. The data cover a range of inlet stagnation conditions, all single phase, from well below to well above the thermodynamic critical conditions. In almost all cases the nozzle throat conditions were two phase. The results indicate that the choked flow rates were not very sensitive to nozzle geometry. However, the axial pressure profiles, especially the throat pressure and the point of vaporization, were very sensitive to both nozzle geometry and operating conditions. A modified Henry-Fauske model correlated all the choked flow rate data to within + or - 10 percent. Neither the equilibrium model nor the Henry-Fauske model predicted throat pressures well over the whole range of data. Above the thermodynamic critical temperature the homogeneous equilibrium model was preferred for both flow rate and pressure ratio. The data of the three fluids could be normalized by the principle of corresponding states.

A higher-order conservation element solution element method for solving hyperbolic differential equations on unstructured meshes

NASA Astrophysics Data System (ADS)

Bilyeu, David

This dissertation presents an extension of the Conservation Element Solution Element (CESE) method from second- to higher-order accuracy. The new method retains the favorable characteristics of the original second-order CESE scheme, including (i) the use of the space-time integral equation for conservation laws, (ii) a compact mesh stencil, (iii) the scheme will remain stable up to a CFL number of unity, (iv) a fully explicit, time-marching integration scheme, (v) true multidimensionality without using directional splitting, and (vi) the ability to handle two- and three-dimensional geometries by using unstructured meshes. This algorithm has been thoroughly tested in one, two and three spatial dimensions and has been shown to obtain the desired order of accuracy for solving both linear and non-linear hyperbolic partial differential equations. The scheme has also shown its ability to accurately resolve discontinuities in the solutions. Higher order unstructured methods such as the Discontinuous Galerkin (DG) method and the Spectral Volume (SV) methods have been developed for one-, two- and three-dimensional application. Although these schemes have seen extensive development and use, certain drawbacks of these methods have been well documented. For example, the explicit versions of these two methods have very stringent stability criteria. This stability criteria requires that the time step be reduced as the order of the solver increases, for a given simulation on a given mesh. The research presented in this dissertation builds upon the work of Chang, who developed a fourth-order CESE scheme to solve a scalar one-dimensional hyperbolic partial differential equation. The completed research has resulted in two key deliverables. The first is a detailed derivation of a high-order CESE methods on unstructured meshes for solving the conservation laws in two- and three-dimensional spaces. The second is the code implementation of these numerical methods in a computer code. For code development, a one-dimensional solver for the Euler equations was developed. This work is an extension of Chang's work on the fourth-order CESE method for solving a one-dimensional scalar convection equation. A generic formulation for the nth-order CESE method, where n ≥ 4, was derived. Indeed, numerical implementation of the scheme confirmed that the order of convergence was consistent with the order of the scheme. For the two- and three-dimensional solvers, SOLVCON was used as the basic framework for code implementation. A new solver kernel for the fourth-order CESE method has been developed and integrated into the framework provided by SOLVCON. The main part of SOLVCON, which deals with unstructured meshes and parallel computing, remains intact. The SOLVCON code for data transmission between computer nodes for High Performance Computing (HPC). To validate and verify the newly developed high-order CESE algorithms, several one-, two- and three-dimensional simulations where conducted. For the arbitrary order, one-dimensional, CESE solver, three sets of governing equations were selected for simulation: (i) the linear convection equation, (ii) the linear acoustic equations, (iii) the nonlinear Euler equations. All three systems of equations were used to verify the order of convergence through mesh refinement. In addition the Euler equations were used to solve the Shu-Osher and Blastwave problems. These two simulations demonstrated that the new high-order CESE methods can accurately resolve discontinuities in the flow field.For the two-dimensional, fourth-order CESE solver, the Euler equation was employed in four different test cases. The first case was used to verify the order of convergence through mesh refinement. The next three cases demonstrated the ability of the new solver to accurately resolve discontinuities in the flows. This was demonstrated through: (i) the interaction between acoustic waves and an entropy pulse, (ii) supersonic flow over a circular blunt body, (iii) supersonic flow over a guttered wedge. To validate and verify the three-dimensional, fourth-order CESE solver, two different simulations where selected. The first used the linear convection equations to demonstrate fourth-order convergence. The second used the Euler equations to simulate supersonic flow over a spherical body to demonstrate the scheme's ability to accurately resolve shocks. All test cases used are well known benchmark problems and as such, there are multiple sources available to validate the numerical results. Furthermore, the simulations showed that the high-order CESE solver was stable at a CFL number near unity.

Implicit solution of Navier-Stokes equations on staggered curvilinear grids using a Newton-Krylov method with a novel analytical Jacobian.

NASA Astrophysics Data System (ADS)

Borazjani, Iman; Asgharzadeh, Hafez

2015-11-01

Flow simulations involving complex geometries and moving boundaries suffer from time-step size restriction and low convergence rates with explicit and semi-implicit schemes. Implicit schemes can be used to overcome these restrictions. However, implementing implicit solver for nonlinear equations including Navier-Stokes is not straightforward. Newton-Krylov subspace methods (NKMs) are one of the most advanced iterative methods to solve non-linear equations such as implicit descritization of the Navier-Stokes equation. The efficiency of NKMs massively depends on the Jacobian formation method, e.g., automatic differentiation is very expensive, and matrix-free methods slow down as the mesh is refined. Analytical Jacobian is inexpensive method, but derivation of analytical Jacobian for Navier-Stokes equation on staggered grid is challenging. The NKM with a novel analytical Jacobian was developed and validated against Taylor-Green vortex and pulsatile flow in a 90 degree bend. The developed method successfully handled the complex geometries such as an intracranial aneurysm with multiple overset grids, and immersed boundaries. It is shown that the NKM with an analytical Jacobian is 3 to 25 times faster than the fixed-point implicit Runge-Kutta method, and more than 100 times faster than automatic differentiation depending on the grid (size) and the flow problem. The developed methods are fully parallelized with parallel efficiency of 80-90% on the problems tested.

Inflow/Outflow Boundary Conditions with Application to FUN3D

NASA Technical Reports Server (NTRS)

Carlson, Jan-Renee

2011-01-01

Several boundary conditions that allow subsonic and supersonic flow into and out of the computational domain are discussed. These boundary conditions are demonstrated in the FUN3D computational fluid dynamics (CFD) code which solves the three-dimensional Navier-Stokes equations on unstructured computational meshes. The boundary conditions are enforced through determination of the flux contribution at the boundary to the solution residual. The boundary conditions are implemented in an implicit form where the Jacobian contribution of the boundary condition is included and is exact. All of the flows are governed by the calorically perfect gas thermodynamic equations. Three problems are used to assess these boundary conditions. Solution residual convergence to machine zero precision occurred for all cases. The converged solution boundary state is compared with the requested boundary state for several levels of mesh densities. The boundary values converged to the requested boundary condition with approximately second-order accuracy for all of the cases.

Robust large-scale parallel nonlinear solvers for simulations.

DOE Office of Scientific and Technical Information (OSTI.GOV)

Bader, Brett William; Pawlowski, Roger Patrick; Kolda, Tamara Gibson

2005-11-01

This report documents research to develop robust and efficient solution techniques for solving large-scale systems of nonlinear equations. The most widely used method for solving systems of nonlinear equations is Newton's method. While much research has been devoted to augmenting Newton-based solvers (usually with globalization techniques), little has been devoted to exploring the application of different models. Our research has been directed at evaluating techniques using different models than Newton's method: a lower order model, Broyden's method, and a higher order model, the tensor method. We have developed large-scale versions of each of these models and have demonstrated their usemore » in important applications at Sandia. Broyden's method replaces the Jacobian with an approximation, allowing codes that cannot evaluate a Jacobian or have an inaccurate Jacobian to converge to a solution. Limited-memory methods, which have been successful in optimization, allow us to extend this approach to large-scale problems. We compare the robustness and efficiency of Newton's method, modified Newton's method, Jacobian-free Newton-Krylov method, and our limited-memory Broyden method. Comparisons are carried out for large-scale applications of fluid flow simulations and electronic circuit simulations. Results show that, in cases where the Jacobian was inaccurate or could not be computed, Broyden's method converged in some cases where Newton's method failed to converge. We identify conditions where Broyden's method can be more efficient than Newton's method. We also present modifications to a large-scale tensor method, originally proposed by Bouaricha, for greater efficiency, better robustness, and wider applicability. Tensor methods are an alternative to Newton-based methods and are based on computing a step based on a local quadratic model rather than a linear model. The advantage of Bouaricha's method is that it can use any existing linear solver, which makes it simple to write and easily portable. However, the method usually takes twice as long to solve as Newton-GMRES on general problems because it solves two linear systems at each iteration. In this paper, we discuss modifications to Bouaricha's method for a practical implementation, including a special globalization technique and other modifications for greater efficiency. We present numerical results showing computational advantages over Newton-GMRES on some realistic problems. We further discuss a new approach for dealing with singular (or ill-conditioned) matrices. In particular, we modify an algorithm for identifying a turning point so that an increasingly ill-conditioned Jacobian does not prevent convergence.« less

Many particle approximation of the Aw-Rascle-Zhang second order model for vehicular traffic.

PubMed

Francesco, Marco Di; Fagioli, Simone; Rosini, Massimiliano D

2017-02-01

We consider the follow-the-leader approximation of the Aw-Rascle-Zhang (ARZ) model for traffic flow in a multi population formulation. We prove rigorous convergence to weak solutions of the ARZ system in the many particle limit in presence of vacuum. The result is based on uniform BV estimates on the discrete particle velocity. We complement our result with numerical simulations of the particle method compared with some exact solutions to the Riemann problem of the ARZ system.

Isogeometric Collocation: Cost Comparison with Galerkin Methods and Extension to Adaptive Hierarchical NURBS Discretizations (Preprint)

DTIC Science & Technology

2013-02-06

high order and smoothness. Consequently, the use of IGA for col- location suggests itself, since spline functions such as NURBS or T-splines can be...for the development of higher-order accurate time integration schemes due to the convergence of the high modes in the eigenspectrum [46] as well as...flows [19, 20, 49–52]. Due to their maximum smoothness, B-splines exhibit a high resolution power, which allows the representation of a broad range

A PDE Sensitivity Equation Method for Optimal Aerodynamic Design

NASA Technical Reports Server (NTRS)

Borggaard, Jeff; Burns, John

1996-01-01

The use of gradient based optimization algorithms in inverse design is well established as a practical approach to aerodynamic design. A typical procedure uses a simulation scheme to evaluate the objective function (from the approximate states) and its gradient, then passes this information to an optimization algorithm. Once the simulation scheme (CFD flow solver) has been selected and used to provide approximate function evaluations, there are several possible approaches to the problem of computing gradients. One popular method is to differentiate the simulation scheme and compute design sensitivities that are then used to obtain gradients. Although this black-box approach has many advantages in shape optimization problems, one must compute mesh sensitivities in order to compute the design sensitivity. In this paper, we present an alternative approach using the PDE sensitivity equation to develop algorithms for computing gradients. This approach has the advantage that mesh sensitivities need not be computed. Moreover, when it is possible to use the CFD scheme for both the forward problem and the sensitivity equation, then there are computational advantages. An apparent disadvantage of this approach is that it does not always produce consistent derivatives. However, for a proper combination of discretization schemes, one can show asymptotic consistency under mesh refinement, which is often sufficient to guarantee convergence of the optimal design algorithm. In particular, we show that when asymptotically consistent schemes are combined with a trust-region optimization algorithm, the resulting optimal design method converges. We denote this approach as the sensitivity equation method. The sensitivity equation method is presented, convergence results are given and the approach is illustrated on two optimal design problems involving shocks.

A Conjugate Gradient Algorithm with Function Value Information and N-Step Quadratic Convergence for Unconstrained Optimization.

PubMed

Li, Xiangrong; Zhao, Xupei; Duan, Xiabin; Wang, Xiaoliang

2015-01-01

It is generally acknowledged that the conjugate gradient (CG) method achieves global convergence--with at most a linear convergence rate--because CG formulas are generated by linear approximations of the objective functions. The quadratically convergent results are very limited. We introduce a new PRP method in which the restart strategy is also used. Moreover, the method we developed includes not only n-step quadratic convergence but also both the function value information and gradient value information. In this paper, we will show that the new PRP method (with either the Armijo line search or the Wolfe line search) is both linearly and quadratically convergent. The numerical experiments demonstrate that the new PRP algorithm is competitive with the normal CG method.

Preconditioned conjugate gradient methods for the Navier-Stokes equations

NASA Technical Reports Server (NTRS)

Ajmani, Kumud; Ng, Wing-Fai; Liou, Meng-Sing

1994-01-01

A preconditioned Krylov subspace method (GMRES) is used to solve the linear systems of equations formed at each time-integration step of the unsteady, two-dimensional, compressible Navier-Stokes equations of fluid flow. The Navier-Stokes equations are cast in an implicit, upwind finite-volume, flux-split formulation. Several preconditioning techniques are investigated to enhance the efficiency and convergence rate of the implicit solver based on the GMRES algorithm. The superiority of the new solver is established by comparisons with a conventional implicit solver, namely line Gauss-Seidel relaxation (LGSR). Computational test results for low-speed (incompressible flow over a backward-facing step at Mach 0.1), transonic flow (trailing edge flow in a transonic turbine cascade), and hypersonic flow (shock-on-shock interactions on a cylindrical leading edge at Mach 6.0) are presented. For the Mach 0.1 case, overall speedup factors of up to 17 (in terms of time-steps) and 15 (in terms of CPU time on a CRAY-YMP/8) are found in favor of the preconditioned GMRES solver, when compared with the LGSR solver. The corresponding speedup factors for the transonic flow case are 17 and 23, respectively. The hypersonic flow case shows slightly lower speedup factors of 9 and 13, respectively. The study of preconditioners conducted in this research reveals that a new LUSGS-type preconditioner is much more efficient than a conventional incomplete LU-type preconditioner.