Application of a flux-split algorithm to chemically relaxing, hypervelocity blunt-body flows

NASA Technical Reports Server (NTRS)

Balakrishnan, A.

1987-01-01

Viscous, nonequilibrium, hypervelocity flow fields over two axisymmetric configurations are numerically simulated using a factored, implicit, flux-split algorithm. The governing gas-dynamic and species-continuity equations for laminar flow are presented. The gas-dynamics/nonequilibrium-chemistry coupling procedure is developed as part of the solution procedure and is described in detail. Numerical solutions are presented for hypervelocity flows over a hemisphere and over an axisymmetric aeroassisted orbital transfer vehicle using three different chemistry models. The gas models considered are those for an ideal gas, for a frozen gas, and for chemically relaxing air consisting of five species. The calculated results are compared with existing numerical solutions in the literature along the stagnation line of the hemisphere. The effects of free-stream Reynolds number on the nonequilibrium flow field are discussed.

Solitary solutions including spatially localized chaos and their interactions in two-dimensional Kolmogorov flow.

PubMed

Hiruta, Yoshiki; Toh, Sadayoshi

2015-12-01

Two-dimensional Kolmogorov flow in wide periodic boxes is numerically investigated. It is shown that the total flow rate in the direction perpendicular to the force controls the characteristics of the flow, especially the existence of spatially localized solitary solutions such as traveling waves, periodic solutions, and chaotic solutions, which can behave as elementary components of the flow. We propose a procedure to construct approximate solutions consisting of solitary solutions. It is confirmed by direct numerical simulations that these solutions are stable and represent interactions between elementary components such as collisions, coexistence, and collapse of chaos.

Solution of the Average-Passage Equations for the Incompressible Flow through Multiple-Blade-Row Turbomachinery

DTIC Science & Technology

1994-02-01

numerical treatment. An explicit numerical procedure based on Runqe-Kutta time stepping for cell-centered, hexahedral finite volumes is...An explicit numerical procedure based on Runge-Kutta time stepping for cell-centered, hexahedral finite volumes is outlined for the approximate...Discretization 16 3.1 Cell-Centered Finite -Volume Discretization in Space 16 3.2 Artificial Dissipation 17 3.3 Time Integration 21 3.4 Convergence

Global Properties of Fully Convective Accretion Disks from Local Simulations

NASA Astrophysics Data System (ADS)

Bodo, G.; Cattaneo, F.; Mignone, A.; Ponzo, F.; Rossi, P.

2015-08-01

We present an approach to deriving global properties of accretion disks from the knowledge of local solutions derived from numerical simulations based on the shearing box approximation. The approach consists of a two-step procedure. First, a local solution valid for all values of the disk height is constructed by piecing together an interior solution obtained numerically with an analytical exterior radiative solution. The matching is obtained by assuming hydrostatic balance and radiative equilibrium. Although in principle the procedure can be carried out in general, it simplifies considerably when the interior solution is fully convective. In these cases, the construction is analogous to the derivation of the Hayashi tracks for protostars. The second step consists of piecing together the local solutions at different radii to obtain a global solution. Here we use the symmetry of the solutions with respect to the defining dimensionless numbers—in a way similar to the use of homology relations in stellar structure theory—to obtain the scaling properties of the various disk quantities with radius.

Numerical boundary condition procedures and multigrid methods; Proceedings of the Symposium, NASA Ames Research Center, Moffett Field, CA, October 19-22, 1981

NASA Technical Reports Server (NTRS)

1982-01-01

Papers presented in this volume provide an overview of recent work on numerical boundary condition procedures and multigrid methods. The topics discussed include implicit boundary conditions for the solution of the parabolized Navier-Stokes equations for supersonic flows; far field boundary conditions for compressible flows; and influence of boundary approximations and conditions on finite-difference solutions. Papers are also presented on fully implicit shock tracking and on the stability of two-dimensional hyperbolic initial boundary value problems for explicit and implicit schemes.

Staggered solution procedures for multibody dynamics simulation

NASA Technical Reports Server (NTRS)

Park, K. C.; Chiou, J. C.; Downer, J. D.

1990-01-01

The numerical solution procedure for multibody dynamics (MBD) systems is termed a staggered MBD solution procedure that solves the generalized coordinates in a separate module from that for the constraint force. This requires a reformulation of the constraint conditions so that the constraint forces can also be integrated in time. A major advantage of such a partitioned solution procedure is that additional analysis capabilities such as active controller and design optimization modules can be easily interfaced without embedding them into a monolithic program. After introducing the basic equations of motion for MBD system in the second section, Section 3 briefly reviews some constraint handling techniques and introduces the staggered stabilized technique for the solution of the constraint forces as independent variables. The numerical direct time integration of the equations of motion is described in Section 4. As accurate damping treatment is important for the dynamics of space structures, we have employed the central difference method and the mid-point form of the trapezoidal rule since they engender no numerical damping. This is in contrast to the current practice in dynamic simulations of ground vehicles by employing a set of backward difference formulas. First, the equations of motion are partitioned according to the translational and the rotational coordinates. This sets the stage for an efficient treatment of the rotational motions via the singularity-free Euler parameters. The resulting partitioned equations of motion are then integrated via a two-stage explicit stabilized algorithm for updating both the translational coordinates and angular velocities. Once the angular velocities are obtained, the angular orientations are updated via the mid-point implicit formula employing the Euler parameters. When the two algorithms, namely, the two-stage explicit algorithm for the generalized coordinates and the implicit staggered procedure for the constraint Lagrange multipliers, are brought together in a staggered manner, they constitute a staggered explicit-implicit procedure which is summarized in Section 5. Section 6 presents some example problems and discussions concerning several salient features of the staggered MBD solution procedure are offered in Section 7.

Arbitrary Steady-State Solutions with the K-epsilon Model

NASA Technical Reports Server (NTRS)

Rumsey, Christopher L.; Pettersson Reif, B. A.; Gatski, Thomas B.

2006-01-01

Widely-used forms of the K-epsilon turbulence model are shown to yield arbitrary steady-state converged solutions that are highly dependent on numerical considerations such as initial conditions and solution procedure. These solutions contain pseudo-laminar regions of varying size. By applying a nullcline analysis to the equation set, it is possible to clearly demonstrate the reasons for the anomalous behavior. In summary, the degenerate solution acts as a stable fixed point under certain conditions, causing the numerical method to converge there. The analysis also suggests a methodology for preventing the anomalous behavior in steady-state computations.

Numerical techniques for the solution of the compressible Navier-Stokes equations and implementation of turbulence models. [separated turbulent boundary layer flow problems

NASA Technical Reports Server (NTRS)

Baldwin, B. S.; Maccormack, R. W.; Deiwert, G. S.

1975-01-01

The time-splitting explicit numerical method of MacCormack is applied to separated turbulent boundary layer flow problems. Modifications of this basic method are developed to counter difficulties associated with complicated geometry and severe numerical resolution requirements of turbulence model equations. The accuracy of solutions is investigated by comparison with exact solutions for several simple cases. Procedures are developed for modifying the basic method to improve the accuracy. Numerical solutions of high-Reynolds-number separated flows over an airfoil and shock-separated flows over a flat plate are obtained. A simple mixing length model of turbulence is used for the transonic flow past an airfoil. A nonorthogonal mesh of arbitrary configuration facilitates the description of the flow field. For the simpler geometry associated with the flat plate, a rectangular mesh is used, and solutions are obtained based on a two-equation differential model of turbulence.

GLOBAL PROPERTIES OF FULLY CONVECTIVE ACCRETION DISKS FROM LOCAL SIMULATIONS

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

Bodo, G.; Ponzo, F.; Rossi, P.

2015-08-01

We present an approach to deriving global properties of accretion disks from the knowledge of local solutions derived from numerical simulations based on the shearing box approximation. The approach consists of a two-step procedure. First, a local solution valid for all values of the disk height is constructed by piecing together an interior solution obtained numerically with an analytical exterior radiative solution. The matching is obtained by assuming hydrostatic balance and radiative equilibrium. Although in principle the procedure can be carried out in general, it simplifies considerably when the interior solution is fully convective. In these cases, the construction ismore » analogous to the derivation of the Hayashi tracks for protostars. The second step consists of piecing together the local solutions at different radii to obtain a global solution. Here we use the symmetry of the solutions with respect to the defining dimensionless numbers—in a way similar to the use of homology relations in stellar structure theory—to obtain the scaling properties of the various disk quantities with radius.« less

Evaluation of solution procedures for material and/or geometrically nonlinear structural analysis by the direct stiffness method.

NASA Technical Reports Server (NTRS)

Stricklin, J. A.; Haisler, W. E.; Von Riesemann, W. A.

1972-01-01

This paper presents an assessment of the solution procedures available for the analysis of inelastic and/or large deflection structural behavior. A literature survey is given which summarized the contribution of other researchers in the analysis of structural problems exhibiting material nonlinearities and combined geometric-material nonlinearities. Attention is focused at evaluating the available computation and solution techniques. Each of the solution techniques is developed from a common equation of equilibrium in terms of pseudo forces. The solution procedures are applied to circular plates and shells of revolution in an attempt to compare and evaluate each with respect to computational accuracy, economy, and efficiency. Based on the numerical studies, observations and comments are made with regard to the accuracy and economy of each solution technique.

A three-dimensional, compressible, laminar boundary-layer method for general fuselages. Volume 1: Numerical method

NASA Technical Reports Server (NTRS)

Wie, Yong-Sun

1990-01-01

A procedure for calculating 3-D, compressible laminar boundary layer flow on general fuselage shapes is described. The boundary layer solutions can be obtained in either nonorthogonal 'body oriented' coordinates or orthogonal streamline coordinates. The numerical procedure is 'second order' accurate, efficient and independent of the cross flow velocity direction. Numerical results are presented for several test cases, including a sharp cone, an ellipsoid of revolution, and a general aircraft fuselage at angle of attack. Comparisons are made between numerical results obtained using nonorthogonal curvilinear 'body oriented' coordinates and streamline coordinates.

A comparison of numerical methods for the prediction of two-dimensional heat transfer in an electrothermal deicer pad. M.S. Thesis. Final Contractor Report

NASA Technical Reports Server (NTRS)

Wright, William B.

1988-01-01

Transient, numerical simulations of the deicing of composite aircraft components by electrothermal heating have been performed in a 2-D rectangular geometry. Seven numerical schemes and four solution methods were used to find the most efficient numerical procedure for this problem. The phase change in the ice was simulated using the Enthalpy method along with the Method for Assumed States. Numerical solutions illustrating deicer performance for various conditions are presented. Comparisons are made with previous numerical models and with experimental data. The simulation can also be used to solve a variety of other heat conduction problems involving composite bodies.

Refined numerical solution of the transonic flow past a wedge

NASA Technical Reports Server (NTRS)

Liang, S.-M.; Fung, K.-Y.

1985-01-01

A numerical procedure combining the ideas of solving a modified difference equation and of adaptive mesh refinement is introduced. The numerical solution on a fixed grid is improved by using better approximations of the truncation error computed from local subdomain grid refinements. This technique is used to obtain refined solutions of steady, inviscid, transonic flow past a wedge. The effects of truncation error on the pressure distribution, wave drag, sonic line, and shock position are investigated. By comparing the pressure drag on the wedge and wave drag due to the shocks, a supersonic-to-supersonic shock originating from the wedge shoulder is confirmed.

Reduction of numerical diffusion in three-dimensional vortical flows using a coupled Eulerian/Lagrangian solution procedure

NASA Technical Reports Server (NTRS)

Felici, Helene M.; Drela, Mark

1993-01-01

A new approach based on the coupling of an Eulerian and a Lagrangian solver, aimed at reducing the numerical diffusion errors of standard Eulerian time-marching finite-volume solvers, is presented. The approach is applied to the computation of the secondary flow in two bent pipes and the flow around a 3D wing. Using convective point markers the Lagrangian approach provides a correction of the basic Eulerian solution. The Eulerian flow in turn integrates in time the Lagrangian state-vector. A comparison of coarse and fine grid Eulerian solutions makes it possible to identify numerical diffusion. It is shown that the Eulerian/Lagrangian approach is an effective method for reducing numerical diffusion errors.

Global Asymptotic Behavior of Iterative Implicit Schemes

NASA Technical Reports Server (NTRS)

Yee, H. C.; Sweby, P. K.

1994-01-01

The global asymptotic nonlinear behavior of some standard iterative procedures in solving nonlinear systems of algebraic equations arising from four implicit linear multistep methods (LMMs) in discretizing three models of 2 x 2 systems of first-order autonomous nonlinear ordinary differential equations (ODEs) is analyzed using the theory of dynamical systems. The iterative procedures include simple iteration and full and modified Newton iterations. The results are compared with standard Runge-Kutta explicit methods, a noniterative implicit procedure, and the Newton method of solving the steady part of the ODEs. Studies showed that aside from exhibiting spurious asymptotes, all of the four implicit LMMs can change the type and stability of the steady states of the differential equations (DEs). They also exhibit a drastic distortion but less shrinkage of the basin of attraction of the true solution than standard nonLMM explicit methods. The simple iteration procedure exhibits behavior which is similar to standard nonLMM explicit methods except that spurious steady-state numerical solutions cannot occur. The numerical basins of attraction of the noniterative implicit procedure mimic more closely the basins of attraction of the DEs and are more efficient than the three iterative implicit procedures for the four implicit LMMs. Contrary to popular belief, the initial data using the Newton method of solving the steady part of the DEs may not have to be close to the exact steady state for convergence. These results can be used as an explanation for possible causes and cures of slow convergence and nonconvergence of steady-state numerical solutions when using an implicit LMM time-dependent approach in computational fluid dynamics.

The numerical calculation of laminar boundary-layer separation

NASA Technical Reports Server (NTRS)

Klineberg, J. M.; Steger, J. L.

1974-01-01

Iterative finite-difference techniques are developed for integrating the boundary-layer equations, without approximation, through a region of reversed flow. The numerical procedures are used to calculate incompressible laminar separated flows and to investigate the conditions for regular behavior at the point of separation. Regular flows are shown to be characterized by an integrable saddle-type singularity that makes it difficult to obtain numerical solutions which pass continuously into the separated region. The singularity is removed and continuous solutions ensured by specifying the wall shear distribution and computing the pressure gradient as part of the solution. Calculated results are presented for several separated flows and the accuracy of the method is verified. A computer program listing and complete solution case are included.

Finite element analysis of wrinkling membranes

NASA Technical Reports Server (NTRS)

Miller, R. K.; Hedgepeth, J. M.; Weingarten, V. I.; Das, P.; Kahyai, S.

1984-01-01

The development of a nonlinear numerical algorithm for the analysis of stresses and displacements in partly wrinkled flat membranes, and its implementation on the SAP VII finite-element code are described. A comparison of numerical results with exact solutions of two benchmark problems reveals excellent agreement, with good convergence of the required iterative procedure. An exact solution of a problem involving axisymmetric deformations of a partly wrinkled shallow curved membrane is also reported.

hp-Adaptive time integration based on the BDF for viscous flows

NASA Astrophysics Data System (ADS)

Hay, A.; Etienne, S.; Pelletier, D.; Garon, A.

2015-06-01

This paper presents a procedure based on the Backward Differentiation Formulas of order 1 to 5 to obtain efficient time integration of the incompressible Navier-Stokes equations. The adaptive algorithm performs both stepsize and order selections to control respectively the solution accuracy and the computational efficiency of the time integration process. The stepsize selection (h-adaptivity) is based on a local error estimate and an error controller to guarantee that the numerical solution accuracy is within a user prescribed tolerance. The order selection (p-adaptivity) relies on the idea that low-accuracy solutions can be computed efficiently by low order time integrators while accurate solutions require high order time integrators to keep computational time low. The selection is based on a stability test that detects growing numerical noise and deems a method of order p stable if there is no method of lower order that delivers the same solution accuracy for a larger stepsize. Hence, it guarantees both that (1) the used method of integration operates inside of its stability region and (2) the time integration procedure is computationally efficient. The proposed time integration procedure also features a time-step rejection and quarantine mechanisms, a modified Newton method with a predictor and dense output techniques to compute solution at off-step points.

A single-vendor and a single-buyer integrated inventory model with ordering cost reduction dependent on lead time

NASA Astrophysics Data System (ADS)

Vijayashree, M.; Uthayakumar, R.

2017-09-01

Lead time is one of the major limits that affect planning at every stage of the supply chain system. In this paper, we study a continuous review inventory model. This paper investigates the ordering cost reductions are dependent on lead time. This study addressed two-echelon supply chain problem consisting of a single vendor and a single buyer. The main contribution of this study is that the integrated total cost of the single vendor and the single buyer integrated system is analyzed by adopting two different (linear and logarithmic) types ordering cost reductions act dependent on lead time. In both cases, we develop effective solution procedures for finding the optimal solution and then illustrative numerical examples are given to illustrate the results. The solution procedure is to determine the optimal solutions of order quantity, ordering cost, lead time and the number of deliveries from the single vendor and the single buyer in one production run, so that the integrated total cost incurred has the minimum value. Ordering cost reduction is the main aspect of the proposed model. A numerical example is given to validate the model. Numerical example solved by using Matlab software. The mathematical model is solved analytically by minimizing the integrated total cost. Furthermore, the sensitivity analysis is included and the numerical examples are given to illustrate the results. The results obtained in this paper are illustrated with the help of numerical examples. The sensitivity of the proposed model has been checked with respect to the various major parameters of the system. Results reveal that the proposed integrated inventory model is more applicable for the supply chain manufacturing system. For each case, an algorithm procedure of finding the optimal solution is developed. Finally, the graphical representation is presented to illustrate the proposed model and also include the computer flowchart in each model.

Equilibrium paths analysis of materials with rheological properties by using the chaos theory

NASA Astrophysics Data System (ADS)

Bednarek, Paweł; Rządkowski, Jan

2018-01-01

The numerical equilibrium path analysis of the material with random rheological properties by using standard procedures and specialist computer programs was not successful. The proper solution for the analysed heuristic model of the material was obtained on the base of chaos theory elements and neural networks. The paper deals with mathematical reasons of used computer programs and also are elaborated the properties of the attractor used in analysis. There are presented results of conducted numerical analysis both in a numerical and in graphical form for the used procedures.

Constraint treatment techniques and parallel algorithms for multibody dynamic analysis. Ph.D. Thesis

NASA Technical Reports Server (NTRS)

Chiou, Jin-Chern

1990-01-01

Computational procedures for kinematic and dynamic analysis of three-dimensional multibody dynamic (MBD) systems are developed from the differential-algebraic equations (DAE's) viewpoint. Constraint violations during the time integration process are minimized and penalty constraint stabilization techniques and partitioning schemes are developed. The governing equations of motion, a two-stage staggered explicit-implicit numerical algorithm, are treated which takes advantage of a partitioned solution procedure. A robust and parallelizable integration algorithm is developed. This algorithm uses a two-stage staggered central difference algorithm to integrate the translational coordinates and the angular velocities. The angular orientations of bodies in MBD systems are then obtained by using an implicit algorithm via the kinematic relationship between Euler parameters and angular velocities. It is shown that the combination of the present solution procedures yields a computationally more accurate solution. To speed up the computational procedures, parallel implementation of the present constraint treatment techniques, the two-stage staggered explicit-implicit numerical algorithm was efficiently carried out. The DAE's and the constraint treatment techniques were transformed into arrowhead matrices to which Schur complement form was derived. By fully exploiting the sparse matrix structural analysis techniques, a parallel preconditioned conjugate gradient numerical algorithm is used to solve the systems equations written in Schur complement form. A software testbed was designed and implemented in both sequential and parallel computers. This testbed was used to demonstrate the robustness and efficiency of the constraint treatment techniques, the accuracy of the two-stage staggered explicit-implicit numerical algorithm, and the speed up of the Schur-complement-based parallel preconditioned conjugate gradient algorithm on a parallel computer.

Numerical scheme approximating solution and parameters in a beam equation

NASA Astrophysics Data System (ADS)

Ferdinand, Robert R.

2003-12-01

We present a mathematical model which describes vibration in a metallic beam about its equilibrium position. This model takes the form of a nonlinear second-order (in time) and fourth-order (in space) partial differential equation with boundary and initial conditions. A finite-element Galerkin approximation scheme is used to estimate model solution. Infinite-dimensional model parameters are then estimated numerically using an inverse method procedure which involves the minimization of a least-squares cost functional. Numerical results are presented and future work to be done is discussed.

Parametric study of minimum reactor mass in energy-storage dc-to-dc converters

NASA Technical Reports Server (NTRS)

Wong, R. C.; Owen, H. A., Jr.; Wilson, T. G.

1981-01-01

Closed-form analytical solutions for the design equations of a minimum-mass reactor for a two-winding voltage-or-current step-up converter are derived. A quantitative relationship between the three parameters - minimum total reactor mass, maximum output power, and switching frequency - is extracted from these analytical solutions. The validity of the closed-form solution is verified by a numerical minimization procedure. A computer-aided design procedure using commercially available toroidal cores and magnet wires is also used to examine how the results from practical designs follow the predictions of the analytical solutions.

Preconditioning the Helmholtz Equation for Rigid Ducts

NASA Technical Reports Server (NTRS)

Baumeister, Kenneth J.; Kreider, Kevin L.

1998-01-01

An innovative hyperbolic preconditioning technique is developed for the numerical solution of the Helmholtz equation which governs acoustic propagation in ducts. Two pseudo-time parameters are used to produce an explicit iterative finite difference scheme. This scheme eliminates the large matrix storage requirements normally associated with numerical solutions to the Helmholtz equation. The solution procedure is very fast when compared to other transient and steady methods. Optimization and an error analysis of the preconditioning factors are present. For validation, the method is applied to sound propagation in a 2D semi-infinite hard wall duct.

Numerical Hydrodynamics in General Relativity.

PubMed

Font, José A

2000-01-01

The current status of numerical solutions for the equations of ideal general relativistic hydrodynamics is reviewed. Different formulations of the equations are presented, with special mention of conservative and hyperbolic formulations well-adapted to advanced numerical methods. A representative sample of available numerical schemes is discussed and particular emphasis is paid to solution procedures based on schemes exploiting the characteristic structure of the equations through linearized Riemann solvers. A comprehensive summary of relevant astrophysical simulations in strong gravitational fields, including gravitational collapse, accretion onto black holes and evolution of neutron stars, is also presented. Supplementary material is available for this article at 10.12942/lrr-2000-2.

A tutorial solution to scattering of radiation in a thin atmosphere bounded below by a diffusely reflecting, absorbing surface

NASA Technical Reports Server (NTRS)

Buglia, J. J.

1982-01-01

A simple tutorial method, based on a photon tracking procedure, is described to determine the spherical albedo for a thin atmosphere overlying a reflecting surface. This procedure is used to provide a physical structure with which to interpret the more detailed but highly mathematical analyses presented. The final equations are shown to be in good numerical agreement with more exact solutions for thin atmospheres.

Investigation of advanced counterrotation blade configuration concepts for high speed turboprop systems. Task 4: Advanced fan section aerodynamic analysis computer program user's manual

NASA Technical Reports Server (NTRS)

Crook, Andrew J.; Delaney, Robert A.

1992-01-01

The computer program user's manual for the ADPACAPES (Advanced Ducted Propfan Analysis Code-Average Passage Engine Simulation) program is included. The objective of the computer program is development of a three-dimensional Euler/Navier-Stokes flow analysis for fan section/engine geometries containing multiple blade rows and multiple spanwise flow splitters. An existing procedure developed by Dr. J. J. Adamczyk and associates at the NASA Lewis Research Center was modified to accept multiple spanwise splitter geometries and simulate engine core conditions. The numerical solution is based upon a finite volume technique with a four stage Runge-Kutta time marching procedure. Multiple blade row solutions are based upon the average-passage system of equations. The numerical solutions are performed on an H-type grid system, with meshes meeting the requirement of maintaining a common axisymmetric mesh for each blade row grid. The analysis was run on several geometry configurations ranging from one to five blade rows and from one to four radial flow splitters. The efficiency of the solution procedure was shown to be the same as the original analysis.

Numerical modeling of runback water on ice protected aircraft surfaces

NASA Technical Reports Server (NTRS)

Al-Khalil, Kamel M.; Keith, Theo G., Jr.; Dewitt, Kenneth J.

1992-01-01

A numerical simulation for 'running wet' aircraft anti-icing systems is developed. The model includes breakup of the water film, which exists in regions of direct impingement, into individual rivulets. The wetness factor distribution resulting from the film breakup and the rivulet configuration on the surface are predicted in the numerical solution procedure. The solid wall is modeled as a multilayer structure and the anti-icing system used is of the thermal type utilizing hot air and/or electrical heating elements embedded with the layers. Details of the calculation procedure and the methods used are presented.

Automated smoother for the numerical decoupling of dynamics models.

PubMed

Vilela, Marco; Borges, Carlos C H; Vinga, Susana; Vasconcelos, Ana Tereza R; Santos, Helena; Voit, Eberhard O; Almeida, Jonas S

2007-08-21

Structure identification of dynamic models for complex biological systems is the cornerstone of their reverse engineering. Biochemical Systems Theory (BST) offers a particularly convenient solution because its parameters are kinetic-order coefficients which directly identify the topology of the underlying network of processes. We have previously proposed a numerical decoupling procedure that allows the identification of multivariate dynamic models of complex biological processes. While described here within the context of BST, this procedure has a general applicability to signal extraction. Our original implementation relied on artificial neural networks (ANN), which caused slight, undesirable bias during the smoothing of the time courses. As an alternative, we propose here an adaptation of the Whittaker's smoother and demonstrate its role within a robust, fully automated structure identification procedure. In this report we propose a robust, fully automated solution for signal extraction from time series, which is the prerequisite for the efficient reverse engineering of biological systems models. The Whittaker's smoother is reformulated within the context of information theory and extended by the development of adaptive signal segmentation to account for heterogeneous noise structures. The resulting procedure can be used on arbitrary time series with a nonstationary noise process; it is illustrated here with metabolic profiles obtained from in-vivo NMR experiments. The smoothed solution that is free of parametric bias permits differentiation, which is crucial for the numerical decoupling of systems of differential equations. The method is applicable in signal extraction from time series with nonstationary noise structure and can be applied in the numerical decoupling of system of differential equations into algebraic equations, and thus constitutes a rather general tool for the reverse engineering of mechanistic model descriptions from multivariate experimental time series.

Numerical 3+1 General Relativistic Magnetohydrodynamics: A Local Characteristic Approach

NASA Astrophysics Data System (ADS)

Antón, Luis; Zanotti, Olindo; Miralles, Juan A.; Martí, José M.; Ibáñez, José M.; Font, José A.; Pons, José A.

2006-01-01

We present a general procedure to solve numerically the general relativistic magnetohydrodynamics (GRMHD) equations within the framework of the 3+1 formalism. The work reported here extends our previous investigation in general relativistic hydrodynamics (Banyuls et al. 1997) where magnetic fields were not considered. The GRMHD equations are written in conservative form to exploit their hyperbolic character in the solution procedure. All theoretical ingredients necessary to build up high-resolution shock-capturing schemes based on the solution of local Riemann problems (i.e., Godunov-type schemes) are described. In particular, we use a renormalized set of regular eigenvectors of the flux Jacobians of the relativistic MHD equations. In addition, the paper describes a procedure based on the equivalence principle of general relativity that allows the use of Riemann solvers designed for special relativistic MHD in GRMHD. Our formulation and numerical methodology are assessed by performing various test simulations recently considered by different authors. These include magnetized shock tubes, spherical accretion onto a Schwarzschild black hole, equatorial accretion onto a Kerr black hole, and magnetized thick disks accreting onto a black hole and subject to the magnetorotational instability.

An investigation of several numerical procedures for time-asymptotic compressible Navier-Stokes solutions

NASA Technical Reports Server (NTRS)

Rudy, D. H.; Morris, D. J.; Blanchard, D. K.; Cooke, C. H.; Rubin, S. G.

1975-01-01

The status of an investigation of four numerical techniques for the time-dependent compressible Navier-Stokes equations is presented. Results for free shear layer calculations in the Reynolds number range from 1000 to 81000 indicate that a sequential alternating-direction implicit (ADI) finite-difference procedure requires longer computing times to reach steady state than a low-storage hopscotch finite-difference procedure. A finite-element method with cubic approximating functions was found to require excessive computer storage and computation times. A fourth method, an alternating-direction cubic spline technique which is still being tested, is also described.

Solution procedure of dynamical contact problems with friction

NASA Astrophysics Data System (ADS)

Abdelhakim, Lotfi

2017-07-01

Dynamical contact is one of the common research topics because of its wide applications in the engineering field. The main goal of this work is to develop a time-stepping algorithm for dynamic contact problems. We propose a finite element approach for elastodynamics contact problems [1]. Sticking, sliding and frictional contact can be taken into account. Lagrange multipliers are used to enforce non-penetration condition. For the time discretization, we propose a scheme equivalent to the explicit Newmark scheme. Each time step requires solving a nonlinear problem similar to a static friction problem. The nonlinearity of the system of equation needs an iterative solution procedure based on Uzawa's algorithm [2][3]. The applicability of the algorithm is illustrated by selected sample numerical solutions to static and dynamic contact problems. Results obtained with the model have been compared and verified with results from an independent numerical method.

Time-Accurate Solutions of Incompressible Navier-Stokes Equations for Potential Turbopump Applications

NASA Technical Reports Server (NTRS)

Kiris, Cetin; Kwak, Dochan

2001-01-01

Two numerical procedures, one based on artificial compressibility method and the other pressure projection method, are outlined for obtaining time-accurate solutions of the incompressible Navier-Stokes equations. The performance of the two method are compared by obtaining unsteady solutions for the evolution of twin vortices behind a at plate. Calculated results are compared with experimental and other numerical results. For an un- steady ow which requires small physical time step, pressure projection method was found to be computationally efficient since it does not require any subiterations procedure. It was observed that the artificial compressibility method requires a fast convergence scheme at each physical time step in order to satisfy incompressibility condition. This was obtained by using a GMRES-ILU(0) solver in our computations. When a line-relaxation scheme was used, the time accuracy was degraded and time-accurate computations became very expensive.

Constrained Self-adaptive Solutions Procedures for Structure Subject to High Temperature Elastic-plastic Creep Effects

NASA Technical Reports Server (NTRS)

Padovan, J.; Tovichakchaikul, S.

1983-01-01

This paper will develop a new solution strategy which can handle elastic-plastic-creep problems in an inherently stable manner. This is achieved by introducing a new constrained time stepping algorithm which will enable the solution of creep initiated pre/postbuckling behavior where indefinite tangent stiffnesses are encountered. Due to the generality of the scheme, both monotone and cyclic loading histories can be handled. The presentation will give a thorough overview of current solution schemes and their short comings, the development of constrained time stepping algorithms as well as illustrate the results of several numerical experiments which benchmark the new procedure.

System Simulation by Recursive Feedback: Coupling A Set of Stand-Alone Subsystem Simulations

NASA Technical Reports Server (NTRS)

Nixon, Douglas D.; Hanson, John M. (Technical Monitor)

2002-01-01

Recursive feedback is defined and discussed as a framework for development of specific algorithms and procedures that propagate the time-domain solution for a dynamical system simulation consisting of multiple numerically coupled self-contained stand-alone subsystem simulations. A satellite motion example containing three subsystems (other dynamics, attitude dynamics, and aerodynamics) has been defined and constructed using this approach. Conventional solution methods are used in the subsystem simulations. Centralized and distributed versions of coupling structure have been addressed. Numerical results are evaluated by direct comparison with a standard total-system simultaneous-solution approach.

Formulation of a General Technique for Predicting Pneumatic Attenuation Errors in Airborne Pressure Sensing Devices

NASA Technical Reports Server (NTRS)

Whitmore, Stephen A.

1988-01-01

Presented is a mathematical model derived from the Navier-Stokes equations of momentum and continuity, which may be accurately used to predict the behavior of conventionally mounted pneumatic sensing systems subject to arbitrary pressure inputs. Numerical techniques for solving the general model are developed. Both step and frequency response lab tests were performed. These data are compared with solutions of the mathematical model and show excellent agreement. The procedures used to obtain the lab data are described. In-flight step and frequency response data were obtained. Comparisons with numerical solutions of the math model show good agreement. Procedures used to obtain the flight data are described. Difficulties encountered with obtaining the flight data are discussed.

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.

A Numerical Study of Hypersonic Forebody/Inlet Integration Problem

NASA Technical Reports Server (NTRS)

Kumar, Ajay

1991-01-01

A numerical study of hypersonic forebody/inlet integration problem is presented in the form of the view-graphs. The following topics are covered: physical/chemical modeling; solution procedure; flow conditions; mass flow rate at inlet face; heating and skin friction loads; 3-D forebogy/inlet integration model; and sensitivity studies.

Use of Green's functions in the numerical solution of two-point boundary value problems

NASA Technical Reports Server (NTRS)

Gallaher, L. J.; Perlin, I. E.

1974-01-01

This study investigates the use of Green's functions in the numerical solution of the two-point boundary value problem. The first part deals with the role of the Green's function in solving both linear and nonlinear second order ordinary differential equations with boundary conditions and systems of such equations. The second part describes procedures for numerical construction of Green's functions and considers briefly the conditions for their existence. Finally, there is a description of some numerical experiments using nonlinear problems for which the known existence, uniqueness or convergence theorems do not apply. Examples here include some problems in finding rendezvous orbits of the restricted three body system.

A new procedure for calculating contact stresses in gear teeth

NASA Technical Reports Server (NTRS)

Somprakit, Paisan; Huston, Ronald L.

1991-01-01

A numerical procedure for evaluating and monitoring contact stresses in meshing gear teeth is discussed. The procedure is intended to extend the range of applicability and to improve the accuracy of gear contact stress analysis. The procedure is based upon fundamental solution from the theory of elasticity. It is an iterative numerical procedure. The method is believed to have distinct advantages over the classical Hertz method, the finite-element method, and over existing approaches with the boundary element method. Unlike many classical contact stress analyses, friction effects and sliding are included. Slipping and sticking in the contact region are studied. Several examples are discussed. The results are in agreement with classical results. Applications are presented for spur gears.

TURNS - A free-wake Euler/Navier-Stokes numerical method for helicopter rotors

NASA Technical Reports Server (NTRS)

Srinivasan, G. R.; Baeder, J. D.

1993-01-01

Computational capabilities of a numerical procedure, called TURNS (transonic unsteady rotor Navier-Stokes), to calculate the aerodynamics and acoustics (high-speed impulsive noise) out to several rotor diameters are summarized. The procedure makes it possible to obtain the aerodynamics and acoustics information in one single calculation. The vortical wave and its influence, as well as the acoustics, are captured as part of the overall flowfield solution. The accuracy and suitability of the TURNS method is demonstrated through comparisons with experimental data.

Navier-Stokes computation of compressible turbulent flows with a second order closure

NASA Technical Reports Server (NTRS)

Dingus, C.; Kollmann, W.

1991-01-01

The objective was the development of a complete second order closure for wall bounded flows, including all components of the dissipation rate tensor and a numerical solution procedure for the resulting system of equations. The main topics discussed are the closure of the pressure correlations and the viscous destruction terms in the dissipation rate equations and the numerical solution scheme based on a block-tridiagonal solver for the nine equations required for the prediction of plane or axisymmetric flows.

Numerical solution of fluid flow and heat tranfer problems with surface radiation

NASA Technical Reports Server (NTRS)

Ahuja, S.; Bhatia, K.

1995-01-01

This paper presents a numerical scheme, based on the finite element method, to solve strongly coupled fluid flow and heat transfer problems. The surface radiation effect for gray, diffuse and isothermal surfaces is considered. A procedure for obtaining the view factors between the radiating surfaces is discussed. The overall solution strategy is verified by comparing the available results with those obtained using this approach. An analysis of a thermosyphon is undertaken and the effect of considering the surface radiation is clearly explained.

The structure of shock wave in a gas consisting of ideally elastic, rigid spherical molecules

NASA Technical Reports Server (NTRS)

Cheremisin, F. G.

1972-01-01

Principal approaches are examined to the theoretical study of the shock layer structure. The choice of a molecular model is discussed and three procedures are formulated. These include a numerical calculation method, solution of the kinetic relaxation equation, and solution of the Boltzmann equation.

Research in nonlinear structural and solid mechanics

NASA Technical Reports Server (NTRS)

Mccomb, H. G., Jr. (Compiler); Noor, A. K. (Compiler)

1980-01-01

Nonlinear analysis of building structures and numerical solution of nonlinear algebraic equations and Newton's method are discussed. Other topics include: nonlinear interaction problems; solution procedures for nonlinear problems; crash dynamics and advanced nonlinear applications; material characterization, contact problems, and inelastic response; and formulation aspects and special software for nonlinear analysis.

Influence of the Numerical Scheme on the Solution Quality of the SWE for Tsunami Numerical Codes: The Tohoku-Oki, 2011Example.

NASA Astrophysics Data System (ADS)

Reis, C.; Clain, S.; Figueiredo, J.; Baptista, M. A.; Miranda, J. M. A.

2015-12-01

Numerical tools turn to be very important for scenario evaluations of hazardous phenomena such as tsunami. Nevertheless, the predictions highly depends on the numerical tool quality and the design of efficient numerical schemes still receives important attention to provide robust and accurate solutions. In this study we propose a comparative study between the efficiency of two volume finite numerical codes with second-order discretization implemented with different method to solve the non-conservative shallow water equations, the MUSCL (Monotonic Upstream-Centered Scheme for Conservation Laws) and the MOOD methods (Multi-dimensional Optimal Order Detection) which optimize the accuracy of the approximation in function of the solution local smoothness. The MUSCL is based on a priori criteria where the limiting procedure is performed before updated the solution to the next time-step leading to non-necessary accuracy reduction. On the contrary, the new MOOD technique uses a posteriori detectors to prevent the solution from oscillating in the vicinity of the discontinuities. Indeed, a candidate solution is computed and corrections are performed only for the cells where non-physical oscillations are detected. Using a simple one-dimensional analytical benchmark, 'Single wave on a sloping beach', we show that the classical 1D shallow-water system can be accurately solved with the finite volume method equipped with the MOOD technique and provide better approximation with sharper shock and less numerical diffusion. For the code validation, we also use the Tohoku-Oki 2011 tsunami and reproduce two DART records, demonstrating that the quality of the solution may deeply interfere with the scenario one can assess. This work is funded by the Portugal-France research agreement, through the research project GEONUM FCT-ANR/MAT-NAN/0122/2012.Numerical tools turn to be very important for scenario evaluations of hazardous phenomena such as tsunami. Nevertheless, the predictions highly depends on the numerical tool quality and the design of efficient numerical schemes still receives important attention to provide robust and accurate solutions. In this study we propose a comparative study between the efficiency of two volume finite numerical codes with second-order discretization implemented with different method to solve the non-conservative shallow water equations, the MUSCL (Monotonic Upstream-Centered Scheme for Conservation Laws) and the MOOD methods (Multi-dimensional Optimal Order Detection) which optimize the accuracy of the approximation in function of the solution local smoothness. The MUSCL is based on a priori criteria where the limiting procedure is performed before updated the solution to the next time-step leading to non-necessary accuracy reduction. On the contrary, the new MOOD technique uses a posteriori detectors to prevent the solution from oscillating in the vicinity of the discontinuities. Indeed, a candidate solution is computed and corrections are performed only for the cells where non-physical oscillations are detected. Using a simple one-dimensional analytical benchmark, 'Single wave on a sloping beach', we show that the classical 1D shallow-water system can be accurately solved with the finite volume method equipped with the MOOD technique and provide better approximation with sharper shock and less numerical diffusion. For the code validation, we also use the Tohoku-Oki 2011 tsunami and reproduce two DART records, demonstrating that the quality of the solution may deeply interfere with the scenario one can assess. This work is funded by the Portugal-France research agreement, through the research project GEONUM FCT-ANR/MAT-NAN/0122/2012.

A triangular thin shell finite element: Nonlinear analysis. [structural analysis

NASA Technical Reports Server (NTRS)

Thomas, G. R.; Gallagher, R. H.

1975-01-01

Aspects of the formulation of a triangular thin shell finite element which pertain to geometrically nonlinear (small strain, finite displacement) behavior are described. The procedure for solution of the resulting nonlinear algebraic equations combines a one-step incremental (tangent stiffness) approach with one iteration in the Newton-Raphson mode. A method is presented which permits a rational estimation of step size in this procedure. Limit points are calculated by means of a superposition scheme coupled to the incremental side of the solution procedure while bifurcation points are calculated through a process of interpolation of the determinants of the tangent-stiffness matrix. Numerical results are obtained for a flat plate and two curved shell problems and are compared with alternative solutions.

An efficient solution procedure for the thermoelastic analysis of truss space structures

NASA Technical Reports Server (NTRS)

Givoli, D.; Rand, O.

1992-01-01

A solution procedure is proposed for the thermal and thermoelastic analysis of truss space structures in periodic motion. In this method, the spatial domain is first descretized using a consistent finite element formulation. Then the resulting semi-discrete equations in time are solved analytically by using Fourier decomposition. Geometrical symmetry is taken advantage of completely. An algorithm is presented for the calculation of heat flux distribution. The method is demonstrated via a numerical example of a cylindrically shaped space structure.

An unsteady Euler scheme for the analysis of ducted propellers

NASA Technical Reports Server (NTRS)

Srivastava, R.

1992-01-01

An efficient unsteady solution procedure has been developed for analyzing inviscid unsteady flow past ducted propeller configurations. This scheme is first order accurate in time and second order accurate in space. The solution procedure has been applied to a ducted propeller consisting of an 8-bladed SR7 propeller with a duct of NACA 0003 airfoil cross section around it, operating in a steady axisymmetric flowfield. The variation of elemental blade loading with radius, compares well with other published numerical results.

Application of Four-Point Newton-EGSOR iteration for the numerical solution of 2D Porous Medium Equations

NASA Astrophysics Data System (ADS)

Chew, J. V. L.; Sulaiman, J.

2017-09-01

Partial differential equations that are used in describing the nonlinear heat and mass transfer phenomena are difficult to be solved. For the case where the exact solution is difficult to be obtained, it is necessary to use a numerical procedure such as the finite difference method to solve a particular partial differential equation. In term of numerical procedure, a particular method can be considered as an efficient method if the method can give an approximate solution within the specified error with the least computational complexity. Throughout this paper, the two-dimensional Porous Medium Equation (2D PME) is discretized by using the implicit finite difference scheme to construct the corresponding approximation equation. Then this approximation equation yields a large-sized and sparse nonlinear system. By using the Newton method to linearize the nonlinear system, this paper deals with the application of the Four-Point Newton-EGSOR (4NEGSOR) iterative method for solving the 2D PMEs. In addition to that, the efficiency of the 4NEGSOR iterative method is studied by solving three examples of the problems. Based on the comparative analysis, the Newton-Gauss-Seidel (NGS) and the Newton-SOR (NSOR) iterative methods are also considered. The numerical findings show that the 4NEGSOR method is superior to the NGS and the NSOR methods in terms of the number of iterations to get the converged solutions, the time of computation and the maximum absolute errors produced by the methods.

Finite difference solutions of heat conduction problems in multi-layered bodies with complex geometries

NASA Technical Reports Server (NTRS)

Masiulaniec, K. C.; Keith, T. G., Jr.; Dewitt, K. J.

1984-01-01

A numerical procedure is presented for analyzing a wide variety of heat conduction problems in multilayered bodies having complex geometry. The method is based on a finite difference solution of the heat conduction equation using a body fitted coordinate system transformation. Solution techniques are described for steady and transient problems with and without internal energy generation. Results are found to compare favorably with several well known solutions.

Atmospheric model development in support of SEASAT. Volume 1: Summary of findings

NASA Technical Reports Server (NTRS)

Kesel, P. G.

1977-01-01

Atmospheric analysis and prediction models of varying (grid) resolution were developed. The models were tested using real observational data for the purpose of assessing the impact of grid resolution on short range numerical weather prediction. The discretionary model procedures were examined so that the computational viability of SEASAT data might be enhanced during the conduct of (future) sensitivity tests. The analysis effort covers: (1) examining the procedures for allowing data to influence the analysis; (2) examining the effects of varying the weights in the analysis procedure; (3) testing and implementing procedures for solving the minimization equation in an optimal way; (4) describing the impact of grid resolution on analysis; and (5) devising and implementing numerous practical solutions to analysis problems, generally.

Enforcing positivity in intrusive PC-UQ methods for reactive ODE systems

DOE PAGES

Najm, Habib N.; Valorani, Mauro

2014-04-12

We explore the relation between the development of a non-negligible probability of negative states and the instability of numerical integration of the intrusive Galerkin ordinary differential equation system describing uncertain chemical ignition. To prevent this instability without resorting to either multi-element local polynomial chaos (PC) methods or increasing the order of the PC representation in time, we propose a procedure aimed at modifying the amplitude of the PC modes to bring the probability of negative state values below a user-defined threshold. This modification can be effectively described as a filtering procedure of the spectral PC coefficients, which is applied on-the-flymore » during the numerical integration when the current value of the probability of negative states exceeds the prescribed threshold. We demonstrate the filtering procedure using a simple model of an ignition process in a batch reactor. This is carried out by comparing different observables and error measures as obtained by non-intrusive Monte Carlo and Gauss-quadrature integration and the filtered intrusive procedure. Lastly, the filtering procedure has been shown to effectively stabilize divergent intrusive solutions, and also to improve the accuracy of stable intrusive solutions which are close to the stability limits.« less

Reconstruction Of The Permittivity Profile Of A Stratified Dielectric Layer

NASA Astrophysics Data System (ADS)

Vogelzang, E.; Ferwerda, H. A.; Yevick, D.

1985-03-01

A numerical procedure is given for the reconstruction of the permittivity profile of a dielectric slab on a perfect conductor. Profiles not supporting guided modes are reconstructed from the complex reflection amplitude for TE-polarized, monochromatic plane waves incident from different directions using the Marchenko theory. The contribution of guided modes is incorporated in the reconstruction procedure through the Gelfand-Levitan equations. An advantage of our approach is that a unique solution for the permittivity profile is obtained without the use of complicated regularization techniques. Some illustrative numerical examples are presented.

Numerical solution of the hypersonic viscous-shock-layer equations for laminar, transitional, and turbulent flows of a perfect gas over blunt axially symmetric bodies

NASA Technical Reports Server (NTRS)

Anderson, E. C.; Moss, J. N.

1975-01-01

The viscous shock layer equations applicable to hypersonic laminar, transitional, and turbulent flows of a perfect gas over two-dimensional plane or axially symmetric blunt bodies are presented. The equations are solved by means of an implicit finite difference scheme, and the results are compared with a turbulent boundary layer analysis. The agreement between the two solution procedures is satisfactory for the region of flow where streamline swallowing effects are negligible. For the downstream regions, where streamline swallowing effects are present, the expected differences in the two solution procedures are evident.

Updating QR factorization procedure for solution of linear least squares problem with equality constraints.

PubMed

Zeb, Salman; Yousaf, Muhammad

2017-01-01

In this article, we present a QR updating procedure as a solution approach for linear least squares problem with equality constraints. We reduce the constrained problem to unconstrained linear least squares and partition it into a small subproblem. The QR factorization of the subproblem is calculated and then we apply updating techniques to its upper triangular factor R to obtain its solution. We carry out the error analysis of the proposed algorithm to show that it is backward stable. We also illustrate the implementation and accuracy of the proposed algorithm by providing some numerical experiments with particular emphasis on dense problems.

Stability and bifurcation analysis of oscillators with piecewise-linear characteristics - A general approach

NASA Technical Reports Server (NTRS)

Noah, S. T.; Kim, Y. B.

1991-01-01

A general approach is developed for determining the periodic solutions and their stability of nonlinear oscillators with piecewise-smooth characteristics. A modified harmonic balance/Fourier transform procedure is devised for the analysis. The procedure avoids certain numerical differentiation employed previously in determining the periodic solutions, therefore enhancing the reliability and efficiency of the method. Stability of the solutions is determined via perturbations of their state variables. The method is applied to a forced oscillator interacting with a stop of finite stiffness. Flip and fold bifurcations are found to occur. This led to the identification of parameter ranges in which chaotic response occurred.

A computational procedure for multibody systems including flexible beam dynamics

NASA Technical Reports Server (NTRS)

Downer, J. D.; Park, K. C.; Chiou, J. C.

1990-01-01

A computational procedure suitable for the solution of equations of motions for flexible multibody systems has been developed. A fully nonlinear continuum approach capable of accounting for both finite rotations and large deformations has been used to model a flexible beam component. The beam kinematics are referred directly to an inertial reference frame such that the degrees of freedom embody both the rigid and flexible deformation motions. As such, the beam inertia expression is identical to that of rigid body dynamics. The nonlinear coupling between gross body motion and elastic deformation is contained in the internal force expression. Numerical solution procedures for the integration of spatial kinematic systems can be directily applied to the generalized coordinates of both the rigid and flexible components. An accurate computation of the internal force term which is invariant to rigid motions is incorporated into the general solution procedure.

A numerical method for computing unsteady 2-D boundary layer flows

NASA Technical Reports Server (NTRS)

Krainer, Andreas

1988-01-01

A numerical method for computing unsteady two-dimensional boundary layers in incompressible laminar and turbulent flows is described and applied to a single airfoil changing its incidence angle in time. The solution procedure adopts a first order panel method with a simple wake model to solve for the inviscid part of the flow, and an implicit finite difference method for the viscous part of the flow. Both procedures integrate in time in a step-by-step fashion, in the course of which each step involves the solution of the elliptic Laplace equation and the solution of the parabolic boundary layer equations. The Reynolds shear stress term of the boundary layer equations is modeled by an algebraic eddy viscosity closure. The location of transition is predicted by an empirical data correlation originating from Michel. Since transition and turbulence modeling are key factors in the prediction of viscous flows, their accuracy will be of dominant influence to the overall results.

Numerical modeling and optimization of the Iguassu gas centrifuge

NASA Astrophysics Data System (ADS)

Bogovalov, S. V.; Borman, V. D.; Borisevich, V. D.; Tronin, V. N.; Tronin, I. V.

2017-07-01

The full procedure of the numerical calculation of the optimized parameters of the Iguassu gas centrifuge (GC) is under discussion. The procedure consists of a few steps. On the first step the problem of a hydrodynamical flow of the gas in the rotating rotor of the GC is solved numerically. On the second step the problem of diffusion of the binary mixture of isotopes is solved. The separation power of the gas centrifuge is calculated after that. On the last step the time consuming procedure of optimization of the GC is performed providing us the maximum of the separation power. The optimization is based on the BOBYQA method exploring the results of numerical simulations of the hydrodynamics and diffusion of the mixture of isotopes. Fast convergence of calculations is achieved due to exploring of a direct solver at the solution of the hydrodynamical and diffusion parts of the problem. Optimized separative power and optimal internal parameters of the Iguassu GC with 1 m rotor were calculated using the developed approach. Optimization procedure converges in 45 iterations taking 811 minutes.

Response of a Rotating Propeller to Aerodynamic Excitation

NASA Technical Reports Server (NTRS)

Arnoldi, Walter E.

1949-01-01

The flexural vibration of a rotating propeller blade with clamped shank is analyzed with the object of presenting, in matrix form, equations for the elastic bending moments in forced vibration resulting from aerodynamic forces applied at a fixed multiple of rotational speed. Matrix equations are also derived which define the critical speeds end mode shapes for any excitation order and the relation between critical speed and blade angle. Reference is given to standard works on the numerical solution of matrix equations of the forms derived. The use of a segmented blade as an approximation to a continuous blade provides a simple means for obtaining the matrix solution from the integral equation of equilibrium, so that, in the numerical application of the method presented, the several matrix arrays of the basic physical characteristics of the propeller blade are of simple form, end their simplicity is preserved until, with the solution in sight, numerical manipulations well-known in matrix algebra yield the desired critical speeds and mode shapes frame which the vibration at any operating condition may be synthesized. A close correspondence between the familiar Stodola method and the matrix method is pointed out, indicating that any features of novelty are characteristic not of the analytical procedure but only of the abbreviation, condensation, and efficient organization of the numerical procedure made possible by the use of classical matrix theory.

Numerical calculations of velocity and pressure distribution around oscillating airfoils

NASA Technical Reports Server (NTRS)

Bratanow, T.; Ecer, A.; Kobiske, M.

1974-01-01

An analytical procedure based on the Navier-Stokes equations was developed for analyzing and representing properties of unsteady viscous flow around oscillating obstacles. A variational formulation of the vorticity transport equation was discretized in finite element form and integrated numerically. At each time step of the numerical integration, the velocity field around the obstacle was determined for the instantaneous vorticity distribution from the finite element solution of Poisson's equation. The time-dependent boundary conditions around the oscillating obstacle were introduced as external constraints, using the Lagrangian Multiplier Technique, at each time step of the numerical integration. The procedure was then applied for determining pressures around obstacles oscillating in unsteady flow. The obtained results for a cylinder and an airfoil were illustrated in the form of streamlines and vorticity and pressure distributions.

Rocket injector anomalies study. Volume 1: Description of the mathematical model and solution procedure

NASA Technical Reports Server (NTRS)

Przekwas, A. J.; Singhal, A. K.; Tam, L. T.

1984-01-01

The capability of simulating three dimensional two phase reactive flows with combustion in the liquid fuelled rocket engines is demonstrated. This was accomplished by modifying an existing three dimensional computer program (REFLAN3D) with Eulerian Lagrangian approach to simulate two phase spray flow, evaporation and combustion. The modified code is referred as REFLAN3D-SPRAY. The mathematical formulation of the fluid flow, heat transfer, combustion and two phase flow interaction of the numerical solution procedure, boundary conditions and their treatment are described.

A spectral tau algorithm based on Jacobi operational matrix for numerical solution of time fractional diffusion-wave equations

NASA Astrophysics Data System (ADS)

Bhrawy, A. H.; Doha, E. H.; Baleanu, D.; Ezz-Eldien, S. S.

2015-07-01

In this paper, an efficient and accurate spectral numerical method is presented for solving second-, fourth-order fractional diffusion-wave equations and fractional wave equations with damping. The proposed method is based on Jacobi tau spectral procedure together with the Jacobi operational matrix for fractional integrals, described in the Riemann-Liouville sense. The main characteristic behind this approach is to reduce such problems to those of solving systems of algebraic equations in the unknown expansion coefficients of the sought-for spectral approximations. The validity and effectiveness of the method are demonstrated by solving five numerical examples. Numerical examples are presented in the form of tables and graphs to make comparisons with the results obtained by other methods and with the exact solutions more easier.

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.

A split finite element algorithm for the compressible Navier-Stokes equations

NASA Technical Reports Server (NTRS)

Baker, A. J.

1979-01-01

An accurate and efficient numerical solution algorithm is established for solution of the high Reynolds number limit of the Navier-Stokes equations governing the multidimensional flow of a compressible essentially inviscid fluid. Finite element interpolation theory is used within a dissipative formulation established using Galerkin criteria within the Method of Weighted Residuals. An implicit iterative solution algorithm is developed, employing tensor product bases within a fractional steps integration procedure, that significantly enhances solution economy concurrent with sharply reduced computer hardware demands. The algorithm is evaluated for resolution of steep field gradients and coarse grid accuracy using both linear and quadratic tensor product interpolation bases. Numerical solutions for linear and nonlinear, one, two and three dimensional examples confirm and extend the linearized theoretical analyses, and results are compared to competitive finite difference derived algorithms.

Solution of elliptic PDEs by fast Poisson solvers using a local relaxation factor

NASA Technical Reports Server (NTRS)

Chang, Sin-Chung

1986-01-01

A large class of two- and three-dimensional, nonseparable elliptic partial differential equations (PDEs) is presently solved by means of novel one-step (D'Yakanov-Gunn) and two-step (accelerated one-step) iterative procedures, using a local, discrete Fourier analysis. In addition to being easily implemented and applicable to a variety of boundary conditions, these procedures are found to be computationally efficient on the basis of the results of numerical comparison with other established methods, which lack the present one's: (1) insensitivity to grid cell size and aspect ratio, and (2) ease of convergence rate estimation by means of the coefficient of the PDE being solved. The two-step procedure is numerically demonstrated to outperform the one-step procedure in the case of PDEs with variable coefficients.

On the dynamics of some grid adaption schemes

NASA Technical Reports Server (NTRS)

Sweby, Peter K.; Yee, Helen C.

1994-01-01

The dynamics of a one-parameter family of mesh equidistribution schemes coupled with finite difference discretisations of linear and nonlinear convection-diffusion model equations is studied numerically. It is shown that, when time marched to steady state, the grid adaption not only influences the stability and convergence rate of the overall scheme, but can also introduce spurious dynamics to the numerical solution procedure.

Fluid dynamic modeling of nano-thermite reactions

NASA Astrophysics Data System (ADS)

Martirosyan, Karen S.; Zyskin, Maxim; Jenkins, Charles M.; Yuki Horie, Yasuyuki

2014-03-01

This paper presents a direct numerical method based on gas dynamic equations to predict pressure evolution during the discharge of nanoenergetic materials. The direct numerical method provides for modeling reflections of the shock waves from the reactor walls that generates pressure-time fluctuations. The results of gas pressure prediction are consistent with the experimental evidence and estimates based on the self-similar solution. Artificial viscosity provides sufficient smoothing of shock wave discontinuity for the numerical procedure. The direct numerical method is more computationally demanding and flexible than self-similar solution, in particular it allows study of a shock wave in its early stage of reaction and allows the investigation of "slower" reactions, which may produce weaker shock waves. Moreover, numerical results indicate that peak pressure is not very sensitive to initial density and reaction time, providing that all the material reacts well before the shock wave arrives at the end of the reactor.

Fluid dynamic modeling of nano-thermite reactions

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

Martirosyan, Karen S., E-mail: karen.martirosyan@utb.edu; Zyskin, Maxim; Jenkins, Charles M.

2014-03-14

This paper presents a direct numerical method based on gas dynamic equations to predict pressure evolution during the discharge of nanoenergetic materials. The direct numerical method provides for modeling reflections of the shock waves from the reactor walls that generates pressure-time fluctuations. The results of gas pressure prediction are consistent with the experimental evidence and estimates based on the self-similar solution. Artificial viscosity provides sufficient smoothing of shock wave discontinuity for the numerical procedure. The direct numerical method is more computationally demanding and flexible than self-similar solution, in particular it allows study of a shock wave in its early stagemore » of reaction and allows the investigation of “slower” reactions, which may produce weaker shock waves. Moreover, numerical results indicate that peak pressure is not very sensitive to initial density and reaction time, providing that all the material reacts well before the shock wave arrives at the end of the reactor.« less

Fourth order scheme for wavelet based solution of Black-Scholes equation

NASA Astrophysics Data System (ADS)

Finěk, Václav

2017-12-01

The present paper is devoted to the numerical solution of the Black-Scholes equation for pricing European options. We apply the Crank-Nicolson scheme with Richardson extrapolation for time discretization and Hermite cubic spline wavelets with four vanishing moments for space discretization. This scheme is the fourth order accurate both in time and in space. Computational results indicate that the Crank-Nicolson scheme with Richardson extrapolation significantly decreases the amount of computational work. We also numerically show that optimal convergence rate for the used scheme is obtained without using startup procedure despite the data irregularities in the model.

An upwind space-time conservation element and solution element scheme for solving dusty gas flow model

NASA Astrophysics Data System (ADS)

Rehman, Asad; Ali, Ishtiaq; Qamar, Shamsul

An upwind space-time conservation element and solution element (CE/SE) scheme is extended to numerically approximate the dusty gas flow model. Unlike central CE/SE schemes, the current method uses the upwind procedure to derive the numerical fluxes through the inner boundary of conservation elements. These upwind fluxes are utilized to calculate the gradients of flow variables. For comparison and validation, the central upwind scheme is also applied to solve the same dusty gas flow model. The suggested upwind CE/SE scheme resolves the contact discontinuities more effectively and preserves the positivity of flow variables in low density flows. Several case studies are considered and the results of upwind CE/SE are compared with the solutions of central upwind scheme. The numerical results show better performance of the upwind CE/SE method as compared to the central upwind scheme.

Mass-conservative reconstruction of Galerkin velocity fields for transport simulations

NASA Astrophysics Data System (ADS)

Scudeler, C.; Putti, M.; Paniconi, C.

2016-08-01

Accurate calculation of mass-conservative velocity fields from numerical solutions of Richards' equation is central to reliable surface-subsurface flow and transport modeling, for example in long-term tracer simulations to determine catchment residence time distributions. In this study we assess the performance of a local Larson-Niklasson (LN) post-processing procedure for reconstructing mass-conservative velocities from a linear (P1) Galerkin finite element solution of Richards' equation. This approach, originally proposed for a-posteriori error estimation, modifies the standard finite element velocities by imposing local conservation on element patches. The resulting reconstructed flow field is characterized by continuous fluxes on element edges that can be efficiently used to drive a second order finite volume advective transport model. Through a series of tests of increasing complexity that compare results from the LN scheme to those using velocity fields derived directly from the P1 Galerkin solution, we show that a locally mass-conservative velocity field is necessary to obtain accurate transport results. We also show that the accuracy of the LN reconstruction procedure is comparable to that of the inherently conservative mixed finite element approach, taken as a reference solution, but that the LN scheme has much lower computational costs. The numerical tests examine steady and unsteady, saturated and variably saturated, and homogeneous and heterogeneous cases along with initial and boundary conditions that include dry soil infiltration, alternating solute and water injection, and seepage face outflow. Typical problems that arise with velocities derived from P1 Galerkin solutions include outgoing solute flux from no-flow boundaries, solute entrapment in zones of low hydraulic conductivity, and occurrences of anomalous sources and sinks. In addition to inducing significant mass balance errors, such manifestations often lead to oscillations in concentration values that can moreover cause the numerical solution to explode. These problems do not occur when using LN post-processed velocities.

Diffraction of a shock wave by a compression corner; regular and single Mach reflection

NASA Technical Reports Server (NTRS)

Vijayashankar, V. S.; Kutler, P.; Anderson, D.

1976-01-01

The two dimensional, time dependent Euler equations which govern the flow field resulting from the injection of a planar shock with a compression corner are solved with initial conditions that result in either regular reflection or single Mach reflection of the incident planar shock. The Euler equations which are hyperbolic are transformed to include the self similarity of the problem. A normalization procedure is employed to align the reflected shock and the Mach stem as computational boundaries to implement the shock fitting procedure. A special floating fitting scheme is developed in conjunction with the method of characteristics to fit the slip surface. The reflected shock, the Mach stem, and the slip surface are all treated as harp discontinuities, thus, resulting in a more accurate description of the inviscid flow field. The resulting numerical solutions are compared with available experimental data and existing first-order, shock-capturing numerical solutions.

Accurate modelling of unsteady flows in collapsible tubes.

PubMed

Marchandise, Emilie; Flaud, Patrice

2010-01-01

The context of this paper is the development of a general and efficient numerical haemodynamic tool to help clinicians and researchers in understanding of physiological flow phenomena. We propose an accurate one-dimensional Runge-Kutta discontinuous Galerkin (RK-DG) method coupled with lumped parameter models for the boundary conditions. The suggested model has already been successfully applied to haemodynamics in arteries and is now extended for the flow in collapsible tubes such as veins. The main difference with cardiovascular simulations is that the flow may become supercritical and elastic jumps may appear with the numerical consequence that scheme may not remain monotone if no limiting procedure is introduced. We show that our second-order RK-DG method equipped with an approximate Roe's Riemann solver and a slope-limiting procedure allows us to capture elastic jumps accurately. Moreover, this paper demonstrates that the complex physics associated with such flows is more accurately modelled than with traditional methods such as finite difference methods or finite volumes. We present various benchmark problems that show the flexibility and applicability of the numerical method. Our solutions are compared with analytical solutions when they are available and with solutions obtained using other numerical methods. Finally, to illustrate the clinical interest, we study the emptying process in a calf vein squeezed by contracting skeletal muscle in a normal and pathological subject. We compare our results with experimental simulations and discuss the sensitivity to parameters of our model.

Numerical solution of supersonic three-dimensional free-mixing flows using the parabolic-elliptic Navier-Stokes equations

NASA Technical Reports Server (NTRS)

Hirsh, R. S.

1976-01-01

A numerical method is presented for solving the parabolic-elliptic Navier-Stokes equations. The solution procedure is applied to three-dimensional supersonic laminar jet flow issuing parallel with a supersonic free stream. A coordinate transformation is introduced which maps the boundaries at infinity into a finite computational domain in order to eliminate difficulties associated with the imposition of free-stream boundary conditions. Results are presented for an approximate circular jet, a square jet, varying aspect ratio rectangular jets, and interacting square jets. The solution behavior varies from axisymmetric to nearly two-dimensional in character. For cases where comparisons of the present results with those obtained from shear layer calculations could be made, agreement was good.

Numerical solution of Space Shuttle Orbiter flow field including real gas effects

NASA Technical Reports Server (NTRS)

Prabhu, D. K.; Tannehill, J. C.

1984-01-01

The hypersonic, laminar flow around the Space Shuttle Orbiter has been computed for both an ideal gas (gamma = 1.2) and equilibrium air using a real-gas, parabolized Navier-Stokes code. This code employs a generalized coordinate transformation; hence, it places no restrictions on the orientation of the solution surfaces. The initial solution in the nose region was computed using a 3-D, real-gas, time-dependent Navier-Stokes code. The thermodynamic and transport properties of equilibrium air were obtained from either approximate curve fits or a table look-up procedure. Numerical results are presented for flight conditions corresponding to the STS-3 trajectory. The computed surface pressures and convective heating rates are compared with data from the STS-3 flight.

Preconditioned conjugate residual methods for the solution of spectral equations

NASA Technical Reports Server (NTRS)

Wong, Y. S.; Zang, T. A.; Hussaini, M. Y.

1986-01-01

Conjugate residual methods for the solution of spectral equations are described. An inexact finite-difference operator is introduced as a preconditioner in the iterative procedures. Application of these techniques is limited to problems for which the symmetric part of the coefficient matrix is positive definite. Although the spectral equation is a very ill-conditioned and full matrix problem, the computational effort of the present iterative methods for solving such a system is comparable to that for the sparse matrix equations obtained from the application of either finite-difference or finite-element methods to the same problems. Numerical experiments are shown for a self-adjoint elliptic partial differential equation with Dirichlet boundary conditions, and comparison with other solution procedures for spectral equations is presented.

Recommendations for numerical solution of reinforced-panel and fuselage-ring problems

NASA Technical Reports Server (NTRS)

Hoff, N J; Libby, Paul A

1949-01-01

Procedures are recommended for solving the equations of equilibrium of reinforced panels and isolated fuselage rings as represented by the external loads and the operations table established according to Southwell's method. From the solution of these equations the stress distribution can be easily determined. The method of systematic relaxations, the matrix-calculus method, and several other methods applicable in special cases are discussed. Definite recommendations are made for obtaining the solution of reinforced-panel problems which are generally designated as shear lag problems. The procedures recommended are demonstrated in the analysis of a number of panels. In the case of fuselage rings it is not possible to make definite recommendations for the solution of the equilibrium equations for all rings and loadings. However, suggestions based on the latest experience are made and demonstrated on several rings.

Determination of an Optimal Control Strategy for a Generic Surface Vehicle

DTIC Science & Technology

2014-06-18

paragraphs uses the numerical procedure in MATLAB’s BVP (bvp4c) algorithm using the continuation method. The goal is to find a solution to the set of...solution. Solving the BVP problem using bvp4c requires an initial guess for the solution. Note that the algorithm is very sensitive to the particular...form of the initial guess. The quality of the initial guess is paramount in convergence speed of the BVP algorithm and often determines if the

On Solutions for the Transient Response of Beams

NASA Technical Reports Server (NTRS)

Leonard, Robert W.

1959-01-01

Williams type modal solutions of the elementary and Timoshenko beam equations are presented for the response of several uniform beams to a general applied load. Example computations are shown for a free-free beam subject to various concentrated loads at its center. Discussion includes factors influencing the convergence of modal solutions and factors to be considered in a choice of beam theory. Results obtained by two numerical procedures, the traveling-wave method and Houbolt's method, are also presented and discussed.

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

Numerical Hydrodynamics in General Relativity.

PubMed

Font, José A

2003-01-01

The current status of numerical solutions for the equations of ideal general relativistic hydrodynamics is reviewed. With respect to an earlier version of the article, the present update provides additional information on numerical schemes, and extends the discussion of astrophysical simulations in general relativistic hydrodynamics. Different formulations of the equations are presented, with special mention of conservative and hyperbolic formulations well-adapted to advanced numerical methods. A large sample of available numerical schemes is discussed, paying particular attention to solution procedures based on schemes exploiting the characteristic structure of the equations through linearized Riemann solvers. A comprehensive summary of astrophysical simulations in strong gravitational fields is presented. These include gravitational collapse, accretion onto black holes, and hydrodynamical evolutions of neutron stars. The material contained in these sections highlights the numerical challenges of various representative simulations. It also follows, to some extent, the chronological development of the field, concerning advances on the formulation of the gravitational field and hydrodynamic equations and the numerical methodology designed to solve them. Supplementary material is available for this article at 10.12942/lrr-2003-4.

Modeling of transient heat pipe operation

NASA Technical Reports Server (NTRS)

Colwell, G. T.; Hartley, J. G.

1986-01-01

Mathematical models and associated solution procedures which can be used to design heat pipe cooled structures for use on hypersonic vehicles are being developed. The models should also have the capability to predict off-design performance for a variety of operating conditions. It is expected that the resulting models can be used to predict startup behavior of liquid metal heat pipes to be used in reentry vehicles, hypersonic aircraft, and space nuclear reactors. Work to date related to numerical solutions of governing differential equations for the outer shell and the combination capillary structure and working fluid is summarized. Finite element numerical equations using both implicit, explicit, and combination methods were examined.

Random element method for numerical modeling of diffusional processes

NASA Technical Reports Server (NTRS)

Ghoniem, A. F.; Oppenheim, A. K.

1982-01-01

The random element method is a generalization of the random vortex method that was developed for the numerical modeling of momentum transport processes as expressed in terms of the Navier-Stokes equations. The method is based on the concept that random walk, as exemplified by Brownian motion, is the stochastic manifestation of diffusional processes. The algorithm based on this method is grid-free and does not require the diffusion equation to be discritized over a mesh, it is thus devoid of numerical diffusion associated with finite difference methods. Moreover, the algorithm is self-adaptive in space and explicit in time, resulting in an improved numerical resolution of gradients as well as a simple and efficient computational procedure. The method is applied here to an assortment of problems of diffusion of momentum and energy in one-dimension as well as heat conduction in two-dimensions in order to assess its validity and accuracy. The numerical solutions obtained are found to be in good agreement with exact solution except for a statistical error introduced by using a finite number of elements, the error can be reduced by increasing the number of elements or by using ensemble averaging over a number of solutions.

Numerical analysis of a main crack interactions with micro-defects/inhomogeneities using two-scale generalized/extended finite element method

NASA Astrophysics Data System (ADS)

Malekan, Mohammad; Barros, Felício B.

2017-12-01

Generalized or extended finite element method (G/XFEM) models the crack by enriching functions of partition of unity type with discontinuous functions that represent well the physical behavior of the problem. However, this enrichment functions are not available for all problem types. Thus, one can use numerically-built (global-local) enrichment functions to have a better approximate procedure. This paper investigates the effects of micro-defects/inhomogeneities on a main crack behavior by modeling the micro-defects/inhomogeneities in the local problem using a two-scale G/XFEM. The global-local enrichment functions are influenced by the micro-defects/inhomogeneities from the local problem and thus change the approximate solution of the global problem with the main crack. This approach is presented in detail by solving three different linear elastic fracture mechanics problems for different cases: two plane stress and a Reissner-Mindlin plate problems. The numerical results obtained with the two-scale G/XFEM are compared with the reference solutions from the analytical, numerical solution using standard G/XFEM method and ABAQUS as well, and from the literature.

Numerical solutions of the semiclassical Boltzmann ellipsoidal-statistical kinetic model equation

PubMed Central

Yang, Jaw-Yen; Yan, Chin-Yuan; Huang, Juan-Chen; Li, Zhihui

2014-01-01

Computations of rarefied gas dynamical flows governed by the semiclassical Boltzmann ellipsoidal-statistical (ES) kinetic model equation using an accurate numerical method are presented. The semiclassical ES model was derived through the maximum entropy principle and conserves not only the mass, momentum and energy, but also contains additional higher order moments that differ from the standard quantum distributions. A different decoding procedure to obtain the necessary parameters for determining the ES distribution is also devised. The numerical method in phase space combines the discrete-ordinate method in momentum space and the high-resolution shock capturing method in physical space. Numerical solutions of two-dimensional Riemann problems for two configurations covering various degrees of rarefaction are presented and various contours of the quantities unique to this new model are illustrated. When the relaxation time becomes very small, the main flow features a display similar to that of ideal quantum gas dynamics, and the present solutions are found to be consistent with existing calculations for classical gas. The effect of a parameter that permits an adjustable Prandtl number in the flow is also studied. PMID:25104904

The possible equilibrium shapes of static pendant drops

NASA Astrophysics Data System (ADS)

Sumesh, P. T.; Govindarajan, Rama

2010-10-01

Analytical and numerical studies are carried out on the shapes of two-dimensional and axisymmetric pendant drops hanging under gravity from a solid surface. Drop shapes with both pinned and equilibrium contact angles are obtained naturally from a single boundary condition in the analytical energy optimization procedure. The numerical procedure also yields optimum energy shapes, satisfying Young's equation without the explicit imposition of a boundary condition at the plate. It is shown analytically that a static pendant two-dimensional drop can never be longer than 3.42 times the capillary length. A related finding is that a range of existing solutions for long two-dimensional drops correspond to unphysical drop shapes. Therefore, two-dimensional drops of small volume display only one static solution. In contrast, it is known that axisymmetric drops can display multiple solutions for a given volume. We demonstrate numerically that there is no limit to the height of multiple-lobed Kelvin drops, but the total volume is finite, with the volume of successive lobes forming a convergent series. The stability of such drops is in question, though. Drops of small volume can attain large heights. A bifurcation is found within the one-parameter space of Laplacian shapes, with a range of longer drops displaying a minimum in energy in the investigated space. Axisymmetric Kelvin drops exhibit an infinite number of bifurcations.

Nonlinear earthquake analysis of reinforced concrete frames with fiber and Bernoulli-Euler beam-column element.

PubMed

Karaton, Muhammet

2014-01-01

A beam-column element based on the Euler-Bernoulli beam theory is researched for nonlinear dynamic analysis of reinforced concrete (RC) structural element. Stiffness matrix of this element is obtained by using rigidity method. A solution technique that included nonlinear dynamic substructure procedure is developed for dynamic analyses of RC frames. A predicted-corrected form of the Bossak-α method is applied for dynamic integration scheme. A comparison of experimental data of a RC column element with numerical results, obtained from proposed solution technique, is studied for verification the numerical solutions. Furthermore, nonlinear cyclic analysis results of a portal reinforced concrete frame are achieved for comparing the proposed solution technique with Fibre element, based on flexibility method. However, seismic damage analyses of an 8-story RC frame structure with soft-story are investigated for cases of lumped/distributed mass and load. Damage region, propagation, and intensities according to both approaches are researched.

Finite element procedures for coupled linear analysis of heat transfer, fluid and solid mechanics

NASA Technical Reports Server (NTRS)

Sutjahjo, Edhi; Chamis, Christos C.

1993-01-01

Coupled finite element formulations for fluid mechanics, heat transfer, and solid mechanics are derived from the conservation laws for energy, mass, and momentum. To model the physics of interactions among the participating disciplines, the linearized equations are coupled by combining domain and boundary coupling procedures. Iterative numerical solution strategy is presented to solve the equations, with the partitioning of temporal discretization implemented.

On a perturbed Sparre Andersen risk model with multi-layer dividend strategy

NASA Astrophysics Data System (ADS)

Yang, Hu; Zhang, Zhimin

2009-10-01

In this paper, we consider a perturbed Sparre Andersen risk model, in which the inter-claim times are generalized Erlang(n) distributed. Under the multi-layer dividend strategy, piece-wise integro-differential equations for the discounted penalty functions are derived, and a recursive approach is applied to express the solutions. A numerical example to calculate the ruin probabilities is given to illustrate the solution procedure.

Simulation of a Single-Element Lean-Direct Injection Combustor Using Arbitrary Polyhedral Mesh

NASA Technical Reports Server (NTRS)

Wey, Thomas; Liu, Nan-Suey

2012-01-01

This paper summarizes procedures of generating the arbitrary polyhedral mesh as well as presents sample results from its application to the numerical solution of a single-element LDI combustor using a preliminary version of the new OpenNCC.

CAG12 - A CSCM based procedure for flow of an equilibrium chemically reacting gas

NASA Technical Reports Server (NTRS)

Green, M. J.; Davy, W. C.; Lombard, C. K.

1985-01-01

The Conservative Supra Characteristic Method (CSCM), an implicit upwind Navier-Stokes algorithm, is extended to the numerical simulation of flows in chemical equilibrium. The resulting computer code known as Chemistry and Gasdynamics Implicit - Version 2 (CAG12) is described. First-order accurate results are presented for inviscid and viscous Mach 20 flows of air past a hemisphere-cylinder. The solution procedure captures the bow shock in a chemically reacting gas, a technique that is needed for simulating high altitude, rarefied flows. In an initial effort to validate the code, the inviscid results are compared with published gasdynamic and chemistry solutions and satisfactorily agreement is obtained.

New solutions for steady bubbles in a Hele-Shaw cell

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

Tanveer, S.

1987-03-01

Exact solutions are presented for steadily moving bubbles in a Hele--Shaw cell when the effect of surface tension is neglected. These solutions form a three-parameter family. For specified area, both the speed of the bubble and the distance of its centroid from the channel centerline remain arbitrary when surface tension is ignored. However, numerical evidence suggests that this twofold arbitrariness is removed by the effect of surface tension, i.e., for given bubble area and surface tension, solutions exist only when the bubble velocity and the centroid distance from the channel centerline attain one or more isolated values. From a limitedmore » numerical search, no nonsymmetric solutions could be found; however, a branch of symmetric bubble solutions that was not found in earlier work was found. This branch corresponds to one of the Romero-Vanden-Broeck branch of finger solutions when the bubble size is large. A new procedure for numerical calculations of bubble solutions in the presence of surface tension is presented and is found to work very well for reasonably large bubbles, unlike the previous method of Tanveer (Phys. Fluids 29, 3537 (1986)). The precise power law dependence of bubble velocity on surface tension for small surface tension is explored for bubbles of different area. Agreement is noted with recent analytical results for a finger.« less

Jacobi-Gauss-Lobatto collocation method for the numerical solution of 1+1 nonlinear Schrödinger equations

NASA Astrophysics Data System (ADS)

Doha, E. H.; Bhrawy, A. H.; Abdelkawy, M. A.; Van Gorder, Robert A.

2014-03-01

A Jacobi-Gauss-Lobatto collocation (J-GL-C) method, used in combination with the implicit Runge-Kutta method of fourth order, is proposed as a numerical algorithm for the approximation of solutions to nonlinear Schrödinger equations (NLSE) with initial-boundary data in 1+1 dimensions. Our procedure is implemented in two successive steps. In the first one, the J-GL-C is employed for approximating the functional dependence on the spatial variable, using (N-1) nodes of the Jacobi-Gauss-Lobatto interpolation which depends upon two general Jacobi parameters. The resulting equations together with the two-point boundary conditions induce a system of 2(N-1) first-order ordinary differential equations (ODEs) in time. In the second step, the implicit Runge-Kutta method of fourth order is applied to solve this temporal system. The proposed J-GL-C method, used in combination with the implicit Runge-Kutta method of fourth order, is employed to obtain highly accurate numerical approximations to four types of NLSE, including the attractive and repulsive NLSE and a Gross-Pitaevskii equation with space-periodic potential. The numerical results obtained by this algorithm have been compared with various exact solutions in order to demonstrate the accuracy and efficiency of the proposed method. Indeed, for relatively few nodes used, the absolute error in our numerical solutions is sufficiently small.

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.

An assessment of the adaptive unstructured tetrahedral grid, Euler Flow Solver Code FELISA

NASA Technical Reports Server (NTRS)

Djomehri, M. Jahed; Erickson, Larry L.

1994-01-01

A three-dimensional solution-adaptive Euler flow solver for unstructured tetrahedral meshes is assessed, and the accuracy and efficiency of the method for predicting sonic boom pressure signatures about simple generic models are demonstrated. Comparison of computational and wind tunnel data and enhancement of numerical solutions by means of grid adaptivity are discussed. The mesh generation is based on the advancing front technique. The FELISA code consists of two solvers, the Taylor-Galerkin and the Runge-Kutta-Galerkin schemes, both of which are spacially discretized by the usual Galerkin weighted residual finite-element methods but with different explicit time-marching schemes to steady state. The solution-adaptive grid procedure is based on either remeshing or mesh refinement techniques. An alternative geometry adaptive procedure is also incorporated.

An Assessment of Artificial Compressibility and Pressure Projection Methods for Incompressible Flow Simulations

NASA Technical Reports Server (NTRS)

Kwak, Dochan; Kiris, C.; Smith, Charles A. (Technical Monitor)

1998-01-01

Performance of the two commonly used numerical procedures, one based on artificial compressibility method and the other pressure projection method, are compared. These formulations are selected primarily because they are designed for three-dimensional applications. The computational procedures are compared by obtaining steady state solutions of a wake vortex and unsteady solutions of a curved duct flow. For steady computations, artificial compressibility was very efficient in terms of computing time and robustness. For an unsteady flow which requires small physical time step, pressure projection method was found to be computationally more efficient than an artificial compressibility method. This comparison is intended to give some basis for selecting a method or a flow solution code for large three-dimensional applications where computing resources become a critical issue.

Modification of a method-of-characteristics solute-transport model to incorporate decay and equilibrium-controlled sorption or ion exchange

USGS Publications Warehouse

Goode, D.J.; Konikow, Leonard F.

1989-01-01

The U.S. Geological Survey computer model of two-dimensional solute transport and dispersion in ground water (Konikow and Bredehoeft, 1978) has been modified to incorporate the following types of chemical reactions: (1) first-order irreversible rate-reaction, such as radioactive decay; (2) reversible equilibrium-controlled sorption with linear, Freundlich, or Langmuir isotherms; and (3) reversible equilibrium-controlled ion exchange for monovalent or divalent ions. Numerical procedures are developed to incorporate these processes in the general solution scheme that uses method-of- characteristics with particle tracking for advection and finite-difference methods for dispersion. The first type of reaction is accounted for by an exponential decay term applied directly to the particle concentration. The second and third types of reactions are incorporated through a retardation factor, which is a function of concentration for nonlinear cases. The model is evaluated and verified by comparison with analytical solutions for linear sorption and decay, and by comparison with other numerical solutions for nonlinear sorption and ion exchange.

Plastic zone size and crack tip opening displacement of a Dugdale crack interacting with a coated circular inclusion

NASA Astrophysics Data System (ADS)

Hoh, H. J.; Xiao, Z. M.; Luo, J.

2010-09-01

An analytical investigation on the plastic zone size of a crack near a coated circular inclusion under three different loading conditions of uniaxial tension, uniform tension and pure shear was carried out. Both the crack and coated circular inclusion are embedded in an infinite matrix, with the crack oriented along the radial direction of the inclusion. In the solution procedure, the crack is simulated as a continuous distribution of edge dislocations. With the Dugdale model of small-scale yielding [J. Mech. Phys. Solids 8 (1960) p. 100], two thin strips of yielded plastic zones are introduced at both crack tips. Using the solution for a coated circular inclusion interacting with a single dislocation as the Green's function, the physical problem is formulated into a set of singular integral equations. Using the method of Erdogan and Gupta [Q. J. Appl. Math. 29 (1972) p. 525] and iterative numerical procedures, the singular integral equations are solved numerically for the plastic zone sizes and crack tip opening displacement.

A highly accurate analytical solution for the surface fields of a short vertical wire antenna lying on a multilayer ground

NASA Astrophysics Data System (ADS)

Parise, M.

2018-01-01

A highly accurate analytical solution is derived to the electromagnetic problem of a short vertical wire antenna located on a stratified ground. The derivation consists of three steps. First, the integration path of the integrals describing the fields of the dipole is deformed and wrapped around the pole singularities and the two vertical branch cuts of the integrands located in the upper half of the complex plane. This allows to decompose the radiated field into its three contributions, namely the above-surface ground wave, the lateral wave, and the trapped surface waves. Next, the square root terms responsible for the branch cuts are extracted from the integrands of the branch-cut integrals. Finally, the extracted square roots are replaced with their rational representations according to Newton's square root algorithm, and residue theorem is applied to give explicit expressions, in series form, for the fields. The rigorous integration procedure and the convergence of square root algorithm ensure that the obtained formulas converge to the exact solution. Numerical simulations are performed to show the validity and robustness of the developed formulation, as well as its advantages in terms of time cost over standard numerical integration procedures.

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.

GTA weld penetration and the effects of deviations in machine variables

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

Giedt, W.H.

1987-07-01

Analytical models for predicting the temperature distribution during GTA welding are reviewed with the purpose of developing a procedure for investigating the effects of deviations in machine parameters. The objective was to determine the accuracy required in machine settings to obtain reproducible results. This review revealed a wide range of published values (21 to 90%) for the arc heating efficiency. Low values (21 to 65%) were associated with evaluation of efficiency using constant property conduction models. Values from 75 to 90% were determined from calorimetric type measurements and are applicable for more accurate numerical solution procedures. Although numerical solutions canmore » yield better overall weld zone predictions, calculations are lengthy and complex. In view of this and the indication that acceptable agreement with experimental measurements can be achieved with the moving-point-source solution, it was utilized to investigate the effects of deviations or errors in voltage, current, and travel speed on GTA weld penetration. Variations resulting from welding within current goals for voltage (+-0.1 V), current (+-3.0 A), and travel speed (+-2.0%) were found to be +-2 to 4%, with voltage and current being more influential than travel speed.« less

Numerical investigations of low-density nozzle flow by solving the Boltzmann equation

NASA Technical Reports Server (NTRS)

Deng, Zheng-Tao; Liaw, Goang-Shin; Chou, Lynn Chen

1995-01-01

A two-dimensional finite-difference code to solve the BGK-Boltzmann equation has been developed. The solution procedure consists of three steps: (1) transforming the BGK-Boltzmann equation into two simultaneous partial differential equations by taking moments of the distribution function with respect to the molecular velocity u(sub z), with weighting factors 1 and u(sub z)(sup 2); (2) solving the transformed equations in the physical space based on the time-marching technique and the four-stage Runge-Kutta time integration, for a given discrete-ordinate. The Roe's second-order upwind difference scheme is used to discretize the convective terms and the collision terms are treated as source terms; and (3) using the newly calculated distribution functions at each point in the physical space to calculate the macroscopic flow parameters by the modified Gaussian quadrature formula. Repeating steps 2 and 3, the time-marching procedure stops when the convergent criteria is reached. A low-density nozzle flow field has been calculated by this newly developed code. The BGK Boltzmann solution and experimental data show excellent agreement. It demonstrated that numerical solutions of the BGK-Boltzmann equation are ready to be experimentally validated.

A variational principle for compressible fluid mechanics. Discussion of the one-dimensional theory

NASA Technical Reports Server (NTRS)

Prozan, R. J.

1982-01-01

The second law of thermodynamics is used as a variational statement to derive a numerical procedure to satisfy the governing equations of motion. The procedure, based on numerical experimentation, appears to be stable provided the CFL condition is satisfied. This stability is manifested no matter how severe the gradients (compression or expansion) are in the flow field. For reasons of simplicity only one dimensional inviscid compressible unsteady flow is discussed here; however, the concepts and techniques are not restricted to one dimension nor are they restricted to inviscid non-reacting flow. The solution here is explicit in time. Further study is required to determine the impact of the variational principle on implicit algorithms.

Steady axisymmetric vortex flows with swirl and shear

NASA Astrophysics Data System (ADS)

Elcrat, Alan R.; Fornberg, Bengt; Miller, Kenneth G.

A general procedure is presented for computing axisymmetric swirling vortices which are steady with respect to an inviscid flow that is either uniform at infinity or includes shear. We consider cases both with and without a spherical obstacle. Choices of numerical parameters are given which yield vortex rings with swirl, attached vortices with swirl analogous to spherical vortices found by Moffatt, tubes of vorticity extending to infinity and Beltrami flows. When there is a spherical obstacle we have found multiple solutions for each set of parameters. Flows are found by numerically solving the Bragg-Hawthorne equation using a non-Newton-based iterative procedure which is robust in its dependence on an initial guess.

Four-center bubbled BPS solutions with a Gibbons-Hawking base

NASA Astrophysics Data System (ADS)

Heidmann, Pierre

2017-10-01

We construct four-center bubbled BPS solutions with a Gibbons-Hawking base space. We give a systematic procedure to build scaling solutions: starting from three-supertube configurations and using generalized spectral flows and gauge transformations to extend to solutions with four Gibbons-Hawking centers. This allows us to construct very large families of smooth horizonless solutions that have the same charges and angular momentum as supersymmetric black holes with a macroscopically large horizon area. Our construction reveals that all scaling solutions with four Gibbons Hawking centers have an angular momentum at around 99% of the cosmic censorship bound. We give both an analytical and a numerical explanation for this unexpected feature.

Automated generation of influence functions for planar crack problems

NASA Technical Reports Server (NTRS)

Sire, Robert A.; Harris, David O.; Eason, Ernest D.

1989-01-01

A numerical procedure for the generation of influence functions for Mode I planar problems is described. The resulting influence functions are in a form for convenient evaluation of stress-intensity factors for complex stress distributions. Crack surface displacements are obtained by a least-squares solution of the Williams eigenfunction expansion for displacements in a cracked body. Discrete values of the influence function, evaluated using the crack surface displacements, are curve fit using an assumed functional form. The assumed functional form includes appropriate limit-behavior terms for very deep and very shallow cracks. Continuous representation of the influence function provides a convenient means for evaluating stress-intensity factors for arbitrary stress distributions by numerical integration. The procedure is demonstrated for an edge-cracked strip and a radially cracked disk. Comparisons with available published results demonstrate the accuracy of the procedure.

On Dynamics of Spinning Structures

NASA Technical Reports Server (NTRS)

Gupta, K. K.; Ibrahim, A.

2012-01-01

This paper provides details of developments pertaining to vibration analysis of gyroscopic systems, that involves a finite element structural discretization followed by the solution of the resulting matrix eigenvalue problem by a progressive, accelerated simultaneous iteration technique. Thus Coriolis, centrifugal and geometrical stiffness matrices are derived for shell and line elements, followed by the eigensolution details as well as solution of representative problems that demonstrates the efficacy of the currently developed numerical procedures and tools.

A time-accurate high-resolution TVD scheme for solving the Navier-Stokes equations

NASA Technical Reports Server (NTRS)

Kim, Hyun Dae; Liu, Nan-Suey

1992-01-01

A total variation diminishing (TVD) scheme has been developed and incorporated into an existing time-accurate high-resolution Navier-Stokes code. The accuracy and the robustness of the resulting solution procedure have been assessed by performing many calculations in four different areas: shock tube flows, regular shock reflection, supersonic boundary layer, and shock boundary layer interactions. These numerical results compare well with corresponding exact solutions or experimental data.

Study of viscous flow about airfoils by the integro-differential method

NASA Technical Reports Server (NTRS)

Wu, J. C.; Sampath, S.

1975-01-01

An integro-differential method was used for numerically solving unsteady incompressible viscous flow problems. A computer program was prepared to solve the problem of an impulsively started 9% thick symmetric Joukowski airfoil at an angle of attack of 15 deg and a Reynolds number of 1000. Some of the results obtained for this problem were discussed and compared with related work completed previously. Two numerical procedures were used, an Alternating Direction Implicit (ADI) method and a Successive Line Relaxation (SLR) method. Generally, the ADI solution agrees well with the SLR solution and with previous results are stations away from the trailing edge. At the trailing edge station, the ADI solution differs substantially from previous results, while the vorticity profiles obtained from the SLR method there are in good qualitative agreement with previous results.

Numerical Procedures for Analyzing Dynamical Processes.

DTIC Science & Technology

1992-02-29

different in nature and can be of the third coordinate of the numerically calcu- called crnamic in that information about the dy- lated solution. Such...recover the matrix A by changing coordinates back to the original basis. "The points x, are points on the attractor which are not For example, if we...the attractor contained witun a small distance (of rotate the coordinate axes by 45’, The dynamics Xrer. In this notation. x, and y, are consecutive

Numerical Modelling of Foundation Slabs with use of Schur Complement Method

NASA Astrophysics Data System (ADS)

Koktan, Jiří; Brožovský, Jiří

2017-10-01

The paper discusses numerical modelling of foundation slabs with use of advanced numerical approaches, which are suitable for parallel processing. The solution is based on the Finite Element Method with the slab-type elements. The subsoil is modelled with use of Winklertype contact model (as an alternative a multi-parameter model can be used). The proposed modelling approach uses the Schur Complement method to speed-up the computations of the problem. The method is based on a special division of the analyzed model to several substructures. It adds some complexity to the numerical procedures, especially when subsoil models are used inside the finite element method solution. In other hand, this method makes possible a fast solution of large models but it introduces further problems to the process. Thus, the main aim of this paper is to verify that such method can be successfully used for this type of problem. The most suitable finite elements will be discussed, there will be also discussion related to finite element mesh and limitations of its construction for such problem. The core approaches of the implementation of the Schur Complement Method for this type of the problem will be also presented. The proposed approach was implemented in the form of a computer program, which will be also briefly introduced. There will be also presented results of example computations, which prove the speed-up of the solution - there will be shown important speed-up of solution even in the case of on-parallel processing and the ability of bypass size limitations of numerical models with use of the discussed approach.

A Second Law Based Unstructured Finite Volume Procedure for Generalized Flow Simulation

NASA Technical Reports Server (NTRS)

Majumdar, Alok

1998-01-01

An unstructured finite volume procedure has been developed for steady and transient thermo-fluid dynamic analysis of fluid systems and components. The procedure is applicable for a flow network consisting of pipes and various fittings where flow is assumed to be one dimensional. It can also be used to simulate flow in a component by modeling a multi-dimensional flow using the same numerical scheme. The flow domain is discretized into a number of interconnected control volumes located arbitrarily in space. The conservation equations for each control volume account for the transport of mass, momentum and entropy from the neighboring control volumes. In addition, they also include the sources of each conserved variable and time dependent terms. The source term of entropy equation contains entropy generation due to heat transfer and fluid friction. Thermodynamic properties are computed from the equation of state of a real fluid. The system of equations is solved by a hybrid numerical method which is a combination of simultaneous Newton-Raphson and successive substitution schemes. The paper also describes the application and verification of the procedure by comparing its predictions with the analytical and numerical solution of several benchmark problems.

Numerical algorithm for rigid body position estimation using the quaternion approach

NASA Astrophysics Data System (ADS)

Zigic, Miodrag; Grahovac, Nenad

2017-11-01

This paper deals with rigid body attitude estimation on the basis of the data obtained from an inertial measurement unit mounted on the body. The aim of this work is to present the numerical algorithm, which can be easily applied to the wide class of problems concerning rigid body positioning, arising in aerospace and marine engineering, or in increasingly popular robotic systems and unmanned aerial vehicles. Following the considerations of kinematics of rigid bodies, the relations between accelerations of different points of the body are given. A rotation matrix is formed using the quaternion approach to avoid singularities. We present numerical procedures for determination of the absolute accelerations of the center of mass and of an arbitrary point of the body expressed in the inertial reference frame, as well as its attitude. An application of the algorithm to the example of a heavy symmetrical gyroscope is presented, where input data for the numerical procedure are obtained from the solution of differential equations of motion, instead of using sensor measurements.

The CMC/3DPNS computer program for prediction of three-dimension, subsonic, turbulent aerodynamic juncture region flow. Volume 2: Users' manual

NASA Technical Reports Server (NTRS)

Manhardt, P. D.

1982-01-01

The CMC fluid mechanics program system was developed to transmit the theoretical solution of finite element numerical solution methodology, applied to nonlinear field problems into a versatile computer code for comprehensive flow field analysis. Data procedures for the CMC 3 dimensional Parabolic Navier-Stokes (PNS) algorithm are presented. General data procedures a juncture corner flow standard test case data deck is described. A listing of the data deck and an explanation of grid generation methodology are presented. Tabulations of all commands and variables available to the user are described. These are in alphabetical order with cross reference numbers which refer to storage addresses.

Finite element concepts in computational aerodynamics

NASA Technical Reports Server (NTRS)

Baker, A. J.

1978-01-01

Finite element theory was employed to establish an implicit numerical solution algorithm for the time averaged unsteady Navier-Stokes equations. Both the multidimensional and a time-split form of the algorithm were considered, the latter of particular interest for problem specification on a regular mesh. A Newton matrix iteration procedure is outlined for solving the resultant nonlinear algebraic equation systems. Multidimensional discretization procedures are discussed with emphasis on automated generation of specific nonuniform solution grids and accounting of curved surfaces. The time-split algorithm was evaluated with regards to accuracy and convergence properties for hyperbolic equations on rectangular coordinates. An overall assessment of the viability of the finite element concept for computational aerodynamics is made.

Determination of full piezoelectric complex parameters using gradient-based optimization algorithm

NASA Astrophysics Data System (ADS)

Kiyono, C. Y.; Pérez, N.; Silva, E. C. N.

2016-02-01

At present, numerical techniques allow the precise simulation of mechanical structures, but the results are limited by the knowledge of the material properties. In the case of piezoelectric ceramics, the full model determination in the linear range involves five elastic, three piezoelectric, and two dielectric complex parameters. A successful solution to obtaining piezoceramic properties consists of comparing the experimental measurement of the impedance curve and the results of a numerical model by using the finite element method (FEM). In the present work, a new systematic optimization method is proposed to adjust the full piezoelectric complex parameters in the FEM model. Once implemented, the method only requires the experimental data (impedance modulus and phase data acquired by an impedometer), material density, geometry, and initial values for the properties. This method combines a FEM routine implemented using an 8-noded axisymmetric element with a gradient-based optimization routine based on the method of moving asymptotes (MMA). The main objective of the optimization procedure is minimizing the quadratic difference between the experimental and numerical electrical conductance and resistance curves (to consider resonance and antiresonance frequencies). To assure the convergence of the optimization procedure, this work proposes restarting the optimization loop whenever the procedure ends in an undesired or an unfeasible solution. Two experimental examples using PZ27 and APC850 samples are presented to test the precision of the method and to check the dependency of the frequency range used, respectively.

Wave scattering by an axisymmetric ice floe of varying thickness

NASA Astrophysics Data System (ADS)

Bennetts, Luke G.; Biggs, Nicholas R. T.; Porter, David

2009-04-01

The problem of water wave scattering by a circular ice floe, floating in fluid of finite depth, is formulated and solved numerically. Unlike previous investigations of such situations, here we allow the thickness of the floe (and the fluid depth) to vary axisymmetrically and also incorporate a realistic non-zero draught. A numerical approximation to the solution of this problem is obtained to an arbitrary degree of accuracy by combining a Rayleigh-Ritz approximation of the vertical motion with an appropriate variational principle. This numerical solution procedure builds upon the work of Bennets et al. (2007, J. Fluid Mech., 579, 413-443). As part of the numerical formulation, we utilize a Fourier cosine expansion of the azimuthal motion, resulting in a system of ordinary differential equations to solve in the radial coordinate for each azimuthal mode. The displayed results concentrate on the response of the floe rather than the scattered wave field and show that the effects of introducing the new features of varying floe thickness and a realistic draught are significant.

A Posteriori Finite Element Bounds for Sensitivity Derivatives of Partial-Differential-Equation Outputs. Revised

NASA Technical Reports Server (NTRS)

Lewis, Robert Michael; Patera, Anthony T.; Peraire, Jaume

1998-01-01

We present a Neumann-subproblem a posteriori finite element procedure for the efficient and accurate calculation of rigorous, 'constant-free' upper and lower bounds for sensitivity derivatives of functionals of the solutions of partial differential equations. The design motivation for sensitivity derivative error control is discussed; the a posteriori finite element procedure is described; the asymptotic bounding properties and computational complexity of the method are summarized; and illustrative numerical results are presented.

Numerical CFD Simulation and Test Correlation in a Flight Project Environment

NASA Technical Reports Server (NTRS)

Gupta, K. K.; Lung, S. F.; Ibrahim, A. H.

2015-01-01

This paper presents detailed description of a novel CFD procedure and comparison of its solution results to that obtained by other available CFD codes as well as actual flight and wind tunnel test data pertaining to the GIII aircraft, currently undergoing flight testing at AFRC.

Numerical Procedures for Inlet/Diffuser/Nozzle Flows

NASA Technical Reports Server (NTRS)

Rubin, Stanley G.

1998-01-01

Two primitive variable, pressure based, flux-split, RNS/NS solution procedures for viscous flows are presented. Both methods are uniformly valid across the full Mach number range, Le., from the incompressible limit to high supersonic speeds. The first method is an 'optimized' version of a previously developed global pressure relaxation RNS procedure. Considerable reduction in the number of relatively expensive matrix inversion, and thereby in the computational time, has been achieved with this procedure. CPU times are reduced by a factor of 15 for predominantly elliptic flows (incompressible and low subsonic). The second method is a time-marching, 'linearized' convection RNS/NS procedure. The key to the efficiency of this procedure is the reduction to a single LU inversion at the inflow cross-plane. The remainder of the algorithm simply requires back-substitution with this LU and the corresponding residual vector at any cross-plane location. This method is not time-consistent, but has a convective-type CFL stability limitation. Both formulations are robust and provide accurate solutions for a variety of internal viscous flows to be provided herein.

Numerical simulation of the pollution formed by exhaust jets at the ground running procedure

NASA Astrophysics Data System (ADS)

Korotaeva, T. A.; Turchinovich, A. O.

2016-10-01

The paper presents an approach that is new for aviation-related ecology. The approach allows defining spatial distribution of pollutant concentrations released at engine ground running procedure (GRP) using full gas-dynamic models. For the first time such a task is modeled in three-dimensional approximation in the framework of the numerical solution of the Navier-Stokes equations with taking into account a kinetic model of interaction between the components of engine exhaust and air. The complex pattern of gas-dynamic flow that occurs at the flow around an aircraft with the jet exhausts that interact with each other, air, jet blast deflector (JBD), and surface of the airplane has been studied in the present work. The numerical technique developed for calculating the concentrations of pollutants produced at the GRP stage permits to define level, character, and area of contamination more reliable and increase accuracy in definition of sanitary protection zones.

A quantitative approach to aquifer vulnerability mapping

NASA Astrophysics Data System (ADS)

Connell, L. D.; Daele, Gerd van den

2003-05-01

This paper presents a procedure for calculating the transport to groundwater of surface-released contaminants. The approach is derived from a series of analytical and semi-analytical solutions to the advection-dispersion equation that include root zone and unsaturated water movement effects on the transport process. The steady-state form of these equations provides an efficient means of calculating the maximum concentration at the watertable and therefore has potential for use in vulnerability mapping. A two-layer approach is used in the solutions to represent the unsaturated profile, with the root zone corresponding to the upper layer where evapotranspiration can occur and transport properties can be in contrast to the rest of the profile. A novel transformation is applied to the advection-dispersion equation that considerably simplifies the way in which water movement is represented. To provide a combined flow and transport model an approximate procedure for water movement, using averages of the infiltration and transpiration rates with a novel, simple, quasi-steady state solution, is presented that can be used in conjunction with the solutions to the advection-dispersion equation. This quasi-steady state approximation for water movement allows for layering in the soil profile and root water uptake. Results from the combined quasi-steady state water movement and semi-analytical solute transport procedure compare well with numerical solutions to the coupled unsaturated flow and solute transport equations in a series of hypothetical simulations.

The exact solution of shear-lag problems in flat panels and box beams assumed rigid in the transverse direction

NASA Technical Reports Server (NTRS)

Hildebrand, Francis B

1943-01-01

A mathematical procedure is herein developed for obtaining exact solutions of shear-lag problems in flat panels and box beams: the method is based on the assumption that the amount of stretching of the sheets in the direction perpendicular to the direction of essential normal stresses is negligible. Explicit solutions, including the treatment of cut-outs, are given for several cases and numerical results are presented in graphic and tabular form. The general theory is presented in a from which further solutions can be readily obtained. The extension of the theory to cover certain cases of non-uniform cross section is indicated. Although the solutions are obtained in terms of infinite series, the present developments differ from those previously given in that, in practical cases, the series usually converge so rapidly that sufficient accuracy is afforded by a small number of terms. Comparisons are made in several cases between the present results and the corresponding solutions obtained by approximate procedures devised by Reissner and by Kuhn and Chiarito.

Exact solution of some linear matrix equations using algebraic methods

NASA Technical Reports Server (NTRS)

Djaferis, T. E.; Mitter, S. K.

1977-01-01

A study is done of solution methods for Linear Matrix Equations including Lyapunov's equation, using methods of modern algebra. The emphasis is on the use of finite algebraic procedures which are easily implemented on a digital computer and which lead to an explicit solution to the problem. The action f sub BA is introduced a Basic Lemma is proven. The equation PA + BP = -C as well as the Lyapunov equation are analyzed. Algorithms are given for the solution of the Lyapunov and comment is given on its arithmetic complexity. The equation P - A'PA = Q is studied and numerical examples are given.

Problems Associated with Grid Convergence of Functionals

NASA Technical Reports Server (NTRS)

Salas, Manuel D.; Atkins, Harld L.

2008-01-01

The current use of functionals to evaluate order-of-convergence of a numerical scheme can lead to incorrect values. The problem comes about because of interplay between the errors from the evaluation of the functional, e.g., quadrature error, and from the numerical scheme discretization. Alternative procedures for deducing the order-property of a scheme are presented. The problem is studied within the context of the inviscid supersonic flow over a blunt body; however, the problem and solutions presented are not unique to this example.

On Problems Associated with Grid Convergence of Functionals

NASA Technical Reports Server (NTRS)

Salas, Manuael D.; Atkins, Harold L

2009-01-01

The current use of functionals to evaluate order-of-convergence of a numerical scheme can lead to incorrect values. The problem comes about because of interplay between the errors from the evaluation of the functional, e.g., quadrature error, and from the numerical scheme discretization. Alternative procedures for deducing the order property of a scheme are presented. The problems are studied within the context of the inviscid supersonic flow over a blunt body; however, the problems and solutions presented are not unique to this example.

Nonlinear Earthquake Analysis of Reinforced Concrete Frames with Fiber and Bernoulli-Euler Beam-Column Element

PubMed Central

Karaton, Muhammet

2014-01-01

A beam-column element based on the Euler-Bernoulli beam theory is researched for nonlinear dynamic analysis of reinforced concrete (RC) structural element. Stiffness matrix of this element is obtained by using rigidity method. A solution technique that included nonlinear dynamic substructure procedure is developed for dynamic analyses of RC frames. A predicted-corrected form of the Bossak-α method is applied for dynamic integration scheme. A comparison of experimental data of a RC column element with numerical results, obtained from proposed solution technique, is studied for verification the numerical solutions. Furthermore, nonlinear cyclic analysis results of a portal reinforced concrete frame are achieved for comparing the proposed solution technique with Fibre element, based on flexibility method. However, seismic damage analyses of an 8-story RC frame structure with soft-story are investigated for cases of lumped/distributed mass and load. Damage region, propagation, and intensities according to both approaches are researched. PMID:24578667

A Generalization of the Karush-Kuhn-Tucker Theorem for Approximate Solutions of Mathematical Programming Problems Based on Quadratic Approximation

NASA Astrophysics Data System (ADS)

Voloshinov, V. V.

2018-03-01

In computations related to mathematical programming problems, one often has to consider approximate, rather than exact, solutions satisfying the constraints of the problem and the optimality criterion with a certain error. For determining stopping rules for iterative procedures, in the stability analysis of solutions with respect to errors in the initial data, etc., a justified characteristic of such solutions that is independent of the numerical method used to obtain them is needed. A necessary δ-optimality condition in the smooth mathematical programming problem that generalizes the Karush-Kuhn-Tucker theorem for the case of approximate solutions is obtained. The Lagrange multipliers corresponding to the approximate solution are determined by solving an approximating quadratic programming problem.

Computational procedures for mixed equations with shock waves

NASA Technical Reports Server (NTRS)

Yu, N. J.; Seebass, R.

1974-01-01

This paper discusses the procedures we have developed to treat a canonical problem involving a mixed nonlinear equation with boundary data that imply a discontinuous solution. This equation arises in various physical contexts and is basic to the description of the nonlinear acoustic behavior of a shock wave near a caustic. The numerical scheme developed is of second order, treats discontinuities as such by applying the appropriate jump conditions across them, and eliminates the numerical dissipation and dispersion associated with large gradients. Our results are compared with the results of a first-order scheme and with those of a second-order scheme we have developed. The algorithm used here can easily be generalized to more complicated problems, including transonic flows with imbedded shocks.

Mathematical solution of multilevel fractional programming problem with fuzzy goal programming approach

NASA Astrophysics Data System (ADS)

Lachhwani, Kailash; Poonia, Mahaveer Prasad

2012-08-01

In this paper, we show a procedure for solving multilevel fractional programming problems in a large hierarchical decentralized organization using fuzzy goal programming approach. In the proposed method, the tolerance membership functions for the fuzzily described numerator and denominator part of the objective functions of all levels as well as the control vectors of the higher level decision makers are respectively defined by determining individual optimal solutions of each of the level decision makers. A possible relaxation of the higher level decision is considered for avoiding decision deadlock due to the conflicting nature of objective functions. Then, fuzzy goal programming approach is used for achieving the highest degree of each of the membership goal by minimizing negative deviational variables. We also provide sensitivity analysis with variation of tolerance values on decision vectors to show how the solution is sensitive to the change of tolerance values with the help of a numerical example.

Calculation of afterbody flows with a composite velocity formulation

NASA Technical Reports Server (NTRS)

Swanson, R. C.; Rubin, S. G.; Khosla, P. K.

1983-01-01

A recently developed technique for numerical solution of the Navier-Stokes equations for subsonic, laminar flows is investigated. It is extended here to allow for the computation of transonic and turbulent flows. The basic approach involves a multiplicative composite of the appropriate velocity representations for the inviscid and viscous flow regions. The resulting equations are structured so that far from the surface of the body the momentum equations lead to the Bernoulli equation for the pressure, while the continuity equation reduces to the familiar potential equation. Close to the body surface, the governing equations and solution techniques are characteristic of those describing interacting boundary layers. The velocity components are computed with a coupled strongly implicity procedure. For transonic flows the artificial compressibility method is used to treat supersonic regions. Calculations are made for both laminar and turbulent flows over axisymmetric afterbody configurations. Present results compare favorably with other numerical solutions and/or experimental data.

SIAM Conference on Parallel Processing for Scientific Computing, 4th, Chicago, IL, Dec. 11-13, 1989, Proceedings

NASA Technical Reports Server (NTRS)

Dongarra, Jack (Editor); Messina, Paul (Editor); Sorensen, Danny C. (Editor); Voigt, Robert G. (Editor)

1990-01-01

Attention is given to such topics as an evaluation of block algorithm variants in LAPACK and presents a large-grain parallel sparse system solver, a multiprocessor method for the solution of the generalized Eigenvalue problem on an interval, and a parallel QR algorithm for iterative subspace methods on the CM2. A discussion of numerical methods includes the topics of asynchronous numerical solutions of PDEs on parallel computers, parallel homotopy curve tracking on a hypercube, and solving Navier-Stokes equations on the Cedar Multi-Cluster system. A section on differential equations includes a discussion of a six-color procedure for the parallel solution of elliptic systems using the finite quadtree structure, data parallel algorithms for the finite element method, and domain decomposition methods in aerodynamics. Topics dealing with massively parallel computing include hypercube vs. 2-dimensional meshes and massively parallel computation of conservation laws. Performance and tools are also discussed.

Computational study of engine external aerodynamics as a part of multidisciplinary optimization procedure

NASA Astrophysics Data System (ADS)

Savelyev, Andrey; Anisimov, Kirill; Kazhan, Egor; Kursakov, Innocentiy; Lysenkov, Alexandr

2016-10-01

The paper is devoted to the development of methodology to optimize external aerodynamics of the engine. Optimization procedure is based on numerical solution of the Reynolds-averaged Navier-Stokes equations. As a method of optimization the surrogate based method is used. As a test problem optimal shape design of turbofan nacelle is considered. The results of the first stage, which investigates classic airplane configuration with engine located under the wing, are presented. Described optimization procedure is considered in the context of multidisciplinary optimization of the 3rd generation, developed in the project AGILE.

Bohm-criterion approximation versus optimal matched solution for a cylindrical probe in radial-motion theory

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

Din, Alif

2016-08-15

The theory of positive-ion collection by a probe immersed in a low-pressure plasma was reviewed and extended by Allen et al. [Proc. Phys. Soc. 70, 297 (1957)]. The numerical computations for cylindrical and spherical probes in a sheath region were presented by F. F. Chen [J. Nucl. Energy C 7, 41 (1965)]. Here, in this paper, the sheath and presheath solutions for a cylindrical probe are matched through a numerical matching procedure to yield “matched” potential profile or “M solution.” The solution based on the Bohm criterion approach “B solution” is discussed for this particular problem. The comparison of cylindricalmore » probe characteristics obtained from the correct potential profile (M solution) and the approximated Bohm-criterion approach are different. This raises questions about the correctness of cylindrical probe theories relying only on the Bohm-criterion approach. Also the comparison between theoretical and experimental ion current characteristics shows that in an argon plasma the ions motion towards the probe is almost radial.« less

On the scaling analysis of the solute boundary layer in idealized growth configurations

NASA Astrophysics Data System (ADS)

Garandet, J. P.; Duffar, T.; Favier, J. J.

1990-11-01

A scaling procedure is applied to the equation governing chemical transport in idealized Czochralski and horizontal Bridgman growth experiments. Our purpose is to get a fair estimate of the solute boundary layer in front of the solidification interface. The results are very good in the Czochralski type configuration, the maximum error with respect to the semi-analytical solution of Burton, Prim and Schlichter being of the order of 20%. In the Bridgman type configuration, our predictions compare well with the values of the numerical simulations; however, more data would be needed for a definite conclusion to be drawn.

An efficient technique for higher order fractional differential equation.

PubMed

Ali, Ayyaz; Iqbal, Muhammad Asad; Ul-Hassan, Qazi Mahmood; Ahmad, Jamshad; Mohyud-Din, Syed Tauseef

2016-01-01

In this study, we establish exact solutions of fractional Kawahara equation by using the idea of [Formula: see text]-expansion method. The results of different studies show that the method is very effective and can be used as an alternative for finding exact solutions of nonlinear evolution equations (NLEEs) in mathematical physics. The solitary wave solutions are expressed by the hyperbolic, trigonometric, exponential and rational functions. Graphical representations along with the numerical data reinforce the efficacy of the used procedure. The specified idea is very effective, expedient for fractional PDEs, and could be extended to other physical problems.

Exact solution of some linear matrix equations using algebraic methods

NASA Technical Reports Server (NTRS)

Djaferis, T. E.; Mitter, S. K.

1979-01-01

Algebraic methods are used to construct the exact solution P of the linear matrix equation PA + BP = - C, where A, B, and C are matrices with real entries. The emphasis of this equation is on the use of finite algebraic procedures which are easily implemented on a digital computer and which lead to an explicit solution to the problem. The paper is divided into six sections which include the proof of the basic lemma, the Liapunov equation, and the computer implementation for the rational, integer and modular algorithms. Two numerical examples are given and the entire calculation process is depicted.

Solution methods for one-dimensional viscoelastic problems

NASA Technical Reports Server (NTRS)

Stubstad, John M.; Simitses, George J.

1987-01-01

A recently developed differential methodology for solution of one-dimensional nonlinear viscoelastic problems is presented. Using the example of an eccentrically loaded cantilever beam-column, the results from the differential formulation are compared to results generated using a previously published integral solution technique. It is shown that the results obtained from these distinct methodologies exhibit a surprisingly high degree of correlation with one another. A discussion of the various factors affecting the numerical accuracy and rate of convergence of these two procedures is also included. Finally, the influences of some 'higher order' effects, such as straining along the centroidal axis are discussed.

A Systematic Kernel Function Procedure for Determining Aerodynamic Forces on Oscillating or Steady Finite Wings at Subsonic Speeds

NASA Technical Reports Server (NTRS)

Watkins, Charles E.; Woolston, Donald S.; Cunningham, Herbert J.

1959-01-01

Details are given of a numerical solution of the integral equation which relates oscillatory or steady lift and downwash distributions in subsonic flow. The procedure has been programmed for the IBM 704 electronic data processing machine and yields the pressure distribution and some of its integrated properties for a given Mach number and frequency and for several modes of oscillation in from 3 to 4 minutes, results of several applications are presented.

Vibro-acoustics for Space Station applications

NASA Technical Reports Server (NTRS)

Vaicaitis, R.; Bofilios, D. A.

1986-01-01

An analytical procedure has been developed to study noise generation in a double wall and single wall cylindrical shell due to mechanical point loads. The objective of this study is to develop theoretical procedures for parametetric evaluation of noise generation andd noise transmission for the habitability modules of the proposed Space Station operation. The solutions of the governing acoustic-structural equations are obtained utilizing modal decomposition. The numerical results include modal frequencies, deflection response spectral densities and interior noise sound pressure levels.

Implementation of a block Lanczos algorithm for Eigenproblem solution of gyroscopic systems

NASA Technical Reports Server (NTRS)

Gupta, Kajal K.; Lawson, Charles L.

1987-01-01

The details of implementation of a general numerical procedure developed for the accurate and economical computation of natural frequencies and associated modes of any elastic structure rotating along an arbitrary axis are described. A block version of the Lanczos algorithm is derived for the solution that fully exploits associated matrix sparsity and employs only real numbers in all relevant computations. It is also capable of determining multiple roots and proves to be most efficient when compared to other, similar, exisiting techniques.

On the wing behaviour of the overtones of self-localized modes

NASA Astrophysics Data System (ADS)

Dusi, R.; Wagner, M.

1998-08-01

In this paper the solutions for self-localized modes in a nonlinear chain are investigated. We present a converging iteration procedure, which is based on analytical information of the wings and which takes into account higher overtones of the solitonic oscillations. The accuracy is controlled in a step by step manner by means of a Gaussian error analysis. Our numerical procedure allows for highly accurate solutions, in all anharmonicity regimes, and beyond the rotating-wave approximation (RWA). It is found that the overtone wings change their analytical behaviour at certain critical values of the energy of the self-localized mode: there is a turnover in the exponent of descent. The results are shown for a Fermi-Pasta-Ulam (FPU) chain with quartic anharmonicity.

Stochastic DG Placement for Conservation Voltage Reduction Based on Multiple Replications Procedure

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

Wang, Zhaoyu; Chen, Bokan; Wang, Jianhui

2015-06-01

Conservation voltage reduction (CVR) and distributed-generation (DG) integration are popular strategies implemented by utilities to improve energy efficiency. This paper investigates the interactions between CVR and DG placement to minimize load consumption in distribution networks, while keeping the lowest voltage level within the predefined range. The optimal placement of DG units is formulated as a stochastic optimization problem considering the uncertainty of DG outputs and load consumptions. A sample average approximation algorithm-based technique is developed to solve the formulated problem effectively. A multiple replications procedure is developed to test the stability of the solution and calculate the confidence interval ofmore » the gap between the candidate solution and optimal solution. The proposed method has been applied to the IEEE 37-bus distribution test system with different scenarios. The numerical results indicate that the implementations of CVR and DG, if combined, can achieve significant energy savings.« less

Analytical and numerical analysis of frictional damage in quasi brittle materials

NASA Astrophysics Data System (ADS)

Zhu, Q. Z.; Zhao, L. Y.; Shao, J. F.

2016-07-01

Frictional sliding and crack growth are two main dissipation processes in quasi brittle materials. The frictional sliding along closed cracks is the origin of macroscopic plastic deformation while the crack growth induces a material damage. The main difficulty of modeling is to consider the inherent coupling between these two processes. Various models and associated numerical algorithms have been proposed. But there are so far no analytical solutions even for simple loading paths for the validation of such algorithms. In this paper, we first present a micro-mechanical model taking into account the damage-friction coupling for a large class of quasi brittle materials. The model is formulated by combining a linear homogenization procedure with the Mori-Tanaka scheme and the irreversible thermodynamics framework. As an original contribution, a series of analytical solutions of stress-strain relations are developed for various loading paths. Based on the micro-mechanical model, two numerical integration algorithms are exploited. The first one involves a coupled friction/damage correction scheme, which is consistent with the coupling nature of the constitutive model. The second one contains a friction/damage decoupling scheme with two consecutive steps: the friction correction followed by the damage correction. With the analytical solutions as reference results, the two algorithms are assessed through a series of numerical tests. It is found that the decoupling correction scheme is efficient to guarantee a systematic numerical convergence.

How to Find a Bug in Ten Thousand Lines Transport Solver? Outline of Experiences from AN Advection-Diffusion Code Verification

NASA Astrophysics Data System (ADS)

Zamani, K.; Bombardelli, F.

2011-12-01

Almost all natural phenomena on Earth are highly nonlinear. Even simplifications to the equations describing nature usually end up being nonlinear partial differential equations. Transport (ADR) equation is a pivotal equation in atmospheric sciences and water quality. This nonlinear equation needs to be solved numerically for practical purposes so academicians and engineers thoroughly rely on the assistance of numerical codes. Thus, numerical codes require verification before they are utilized for multiple applications in science and engineering. Model verification is a mathematical procedure whereby a numerical code is checked to assure the governing equation is properly solved as it is described in the design document. CFD verification is not a straightforward and well-defined course. Only a complete test suite can uncover all the limitations and bugs. Results are needed to be assessed to make a distinction between bug-induced-defect and innate limitation of a numerical scheme. As Roache (2009) said, numerical verification is a state-of-the-art procedure. Sometimes novel tricks work out. This study conveys the synopsis of the experiences we gained during a comprehensive verification process which was done for a transport solver. A test suite was designed including unit tests and algorithmic tests. Tests were layered in complexity in several dimensions from simple to complex. Acceptance criteria defined for the desirable capabilities of the transport code such as order of accuracy, mass conservation, handling stiff source term, spurious oscillation, and initial shape preservation. At the begining, mesh convergence study which is the main craft of the verification is performed. To that end, analytical solution of ADR equation gathered. Also a new solution was derived. In the more general cases, lack of analytical solution could be overcome through Richardson Extrapolation and Manufactured Solution. Then, two bugs which were concealed during the mesh convergence study uncovered with the method of false injection and visualization of the results. Symmetry had dual functionality: there was a bug, which was hidden due to the symmetric nature of a test (it was detected afterward utilizing artificial false injection), on the other hand self-symmetry was used to design a new test, and in a case the analytical solution of the ADR equation was unknown. Assisting subroutines designed to check and post-process conservation of mass and oscillatory behavior. Finally, capability of the solver also checked for stiff reaction source term. The above test suite not only was a decent tool of error detection but also it provided a thorough feedback on the ADR solvers limitations. Such information is the crux of any rigorous numerical modeling for a modeler who deals with surface/subsurface pollution transport.

An efficient numerical algorithm for transverse impact problems

NASA Technical Reports Server (NTRS)

Sankar, B. V.; Sun, C. T.

1985-01-01

Transverse impact problems in which the elastic and plastic indentation effects are considered, involve a nonlinear integral equation for the contact force, which, in practice, is usually solved by an iterative scheme with small increments in time. In this paper, a numerical method is proposed wherein the iterations of the nonlinear problem are separated from the structural response computations. This makes the numerical procedures much simpler and also efficient. The proposed method is applied to some impact problems for which solutions are available, and they are found to be in good agreement. The effect of the magnitude of time increment on the results is also discussed.

Numerical simulation of freshwater/seawater interaction in a dual-permeability karst system with conduits: the development of discrete-continuum VDFST-CFP model

NASA Astrophysics Data System (ADS)

Xu, Zexuan; Hu, Bill

2016-04-01

Dual-permeability karst aquifers of porous media and conduit networks with significant different hydrological characteristics are widely distributed in the world. Discrete-continuum numerical models, such as MODFLOW-CFP and CFPv2, have been verified as appropriate approaches to simulate groundwater flow and solute transport in numerical modeling of karst hydrogeology. On the other hand, seawater intrusion associated with fresh groundwater resources contamination has been observed and investigated in numbers of coastal aquifers, especially under conditions of sea level rise. Density-dependent numerical models including SEAWAT are able to quantitatively evaluate the seawater/freshwater interaction processes. A numerical model of variable-density flow and solute transport - conduit flow process (VDFST-CFP) is developed to provide a better description of seawater intrusion and submarine groundwater discharge in a coastal karst aquifer with conduits. The coupling discrete-continuum VDFST-CFP model applies Darcy-Weisbach equation to simulate non-laminar groundwater flow in the conduit system in which is conceptualized and discretized as pipes, while Darcy equation is still used in continuum porous media. Density-dependent groundwater flow and solute transport equations with appropriate density terms in both conduit and porous media systems are derived and numerically solved using standard finite difference method with an implicit iteration procedure. Synthetic horizontal and vertical benchmarks are created to validate the newly developed VDFST-CFP model by comparing with other numerical models such as variable density SEAWAT, couplings of constant density groundwater flow and solute transport MODFLOW/MT3DMS and discrete-continuum CFPv2/UMT3D models. VDFST-CFP model improves the simulation of density dependent seawater/freshwater mixing processes and exchanges between conduit and matrix. Continuum numerical models greatly overestimated the flow rate under turbulent flow condition but discrete-continuum models provide more accurate results. Parameters sensitivities analysis indicates that conduit diameter and friction factor, matrix hydraulic conductivity and porosity are important parameters that significantly affect variable-density flow and solute transport simulation. The pros and cons of model assumptions, conceptual simplifications and numerical techniques in VDFST-CFP are discussed. In general, the development of VDFST-CFP model is an innovation in numerical modeling methodology and could be applied to quantitatively evaluate the seawater/freshwater interaction in coastal karst aquifers. Keywords: Discrete-continuum numerical model; Variable density flow and transport; Coastal karst aquifer; Non-laminar flow

Sequential-Optimization-Based Framework for Robust Modeling and Design of Heterogeneous Catalytic Systems

DOE PAGES

Rangarajan, Srinivas; Maravelias, Christos T.; Mavrikakis, Manos

2017-11-09

Here, we present a general optimization-based framework for (i) ab initio and experimental data driven mechanistic modeling and (ii) optimal catalyst design of heterogeneous catalytic systems. Both cases are formulated as a nonlinear optimization problem that is subject to a mean-field microkinetic model and thermodynamic consistency requirements as constraints, for which we seek sparse solutions through a ridge (L 2 regularization) penalty. The solution procedure involves an iterative sequence of forward simulation of the differential algebraic equations pertaining to the microkinetic model using a numerical tool capable of handling stiff systems, sensitivity calculations using linear algebra, and gradient-based nonlinear optimization.more » A multistart approach is used to explore the solution space, and a hierarchical clustering procedure is implemented for statistically classifying potentially competing solutions. An example of methanol synthesis through hydrogenation of CO and CO 2 on a Cu-based catalyst is used to illustrate the framework. The framework is fast, is robust, and can be used to comprehensively explore the model solution and design space of any heterogeneous catalytic system.« less

Sequential-Optimization-Based Framework for Robust Modeling and Design of Heterogeneous Catalytic Systems

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

Rangarajan, Srinivas; Maravelias, Christos T.; Mavrikakis, Manos

Here, we present a general optimization-based framework for (i) ab initio and experimental data driven mechanistic modeling and (ii) optimal catalyst design of heterogeneous catalytic systems. Both cases are formulated as a nonlinear optimization problem that is subject to a mean-field microkinetic model and thermodynamic consistency requirements as constraints, for which we seek sparse solutions through a ridge (L 2 regularization) penalty. The solution procedure involves an iterative sequence of forward simulation of the differential algebraic equations pertaining to the microkinetic model using a numerical tool capable of handling stiff systems, sensitivity calculations using linear algebra, and gradient-based nonlinear optimization.more » A multistart approach is used to explore the solution space, and a hierarchical clustering procedure is implemented for statistically classifying potentially competing solutions. An example of methanol synthesis through hydrogenation of CO and CO 2 on a Cu-based catalyst is used to illustrate the framework. The framework is fast, is robust, and can be used to comprehensively explore the model solution and design space of any heterogeneous catalytic system.« less

Embedding methods for the steady Euler equations

NASA Technical Reports Server (NTRS)

Chang, S. H.; Johnson, G. M.

1983-01-01

An approach to the numerical solution of the steady Euler equations is to embed the first-order Euler system in a second-order system and then to recapture the original solution by imposing additional boundary conditions. Initial development of this approach and computational experimentation with it were previously based on heuristic physical reasoning. This has led to the construction of a relaxation procedure for the solution of two-dimensional steady flow problems. The theoretical justification for the embedding approach is addressed. It is proven that, with the appropriate choice of embedding operator and additional boundary conditions, the solution to the embedded system is exactly the one to the original Euler equations. Hence, solving the embedded version of the Euler equations will not produce extraneous solutions.

Comparison between two meshless methods based on collocation technique for the numerical solution of four-species tumor growth model

NASA Astrophysics Data System (ADS)

Dehghan, Mehdi; Mohammadi, Vahid

2017-03-01

As is said in [27], the tumor-growth model is the incorporation of nutrient within the mixture as opposed to being modeled with an auxiliary reaction-diffusion equation. The formulation involves systems of highly nonlinear partial differential equations of surface effects through diffuse-interface models [27]. Simulations of this practical model using numerical methods can be applied for evaluating it. The present paper investigates the solution of the tumor growth model with meshless techniques. Meshless methods are applied based on the collocation technique which employ multiquadrics (MQ) radial basis function (RBFs) and generalized moving least squares (GMLS) procedures. The main advantages of these choices come back to the natural behavior of meshless approaches. As well as, a method based on meshless approach can be applied easily for finding the solution of partial differential equations in high-dimension using any distributions of points on regular and irregular domains. The present paper involves a time-dependent system of partial differential equations that describes four-species tumor growth model. To overcome the time variable, two procedures will be used. One of them is a semi-implicit finite difference method based on Crank-Nicolson scheme and another one is based on explicit Runge-Kutta time integration. The first case gives a linear system of algebraic equations which will be solved at each time-step. The second case will be efficient but conditionally stable. The obtained numerical results are reported to confirm the ability of these techniques for solving the two and three-dimensional tumor-growth equations.

Numerical Solution of Incompressible Navier-Stokes Equations Using a Fractional-Step Approach

NASA Technical Reports Server (NTRS)

Kiris, Cetin; Kwak, Dochan

1999-01-01

A fractional step method for the solution of steady and unsteady incompressible Navier-Stokes equations is outlined. The method is based on a finite volume formulation and uses the pressure in the cell center and the mass fluxes across the faces of each cell as dependent variables. Implicit treatment of convective and viscous terms in the momentum equations enables the numerical stability restrictions to be relaxed. The linearization error in the implicit solution of momentum equations is reduced by using three subiterations in order to achieve second order temporal accuracy for time-accurate calculations. In spatial discretizations of the momentum equations, a high-order (3rd and 5th) flux-difference splitting for the convective terms and a second-order central difference for the viscous terms are used. The resulting algebraic equations are solved with a line-relaxation scheme which allows the use of large time step. A four color ZEBRA scheme is employed after the line-relaxation procedure in the solution of the Poisson equation for pressure. This procedure is applied to a Couette flow problem using a distorted computational grid to show that the method minimizes grid effects. Additional benchmark cases include the unsteady laminar flow over a circular cylinder for Reynolds Numbers of 200, and a 3-D, steady, turbulent wingtip vortex wake propagation study. The solution algorithm does a very good job in resolving the vortex core when 5th-order upwind differencing and a modified production term in the Baldwin-Barth one-equation turbulence model are used with adequate grid resolution.

Assessment of a high-resolution central scheme for the solution of the relativistic hydrodynamics equations

NASA Astrophysics Data System (ADS)

Lucas-Serrano, A.; Font, J. A.; Ibáñez, J. M.; Martí, J. M.

2004-12-01

We assess the suitability of a recent high-resolution central scheme developed by \\cite{kurganov} for the solution of the relativistic hydrodynamic equations. The novelty of this approach relies on the absence of Riemann solvers in the solution procedure. The computations we present are performed in one and two spatial dimensions in Minkowski spacetime. Standard numerical experiments such as shock tubes and the relativistic flat-faced step test are performed. As an astrophysical application the article includes two-dimensional simulations of the propagation of relativistic jets using both Cartesian and cylindrical coordinates. The simulations reported clearly show the capabilities of the numerical scheme of yielding satisfactory results, with an accuracy comparable to that obtained by the so-called high-resolution shock-capturing schemes based upon Riemann solvers (Godunov-type schemes), even well inside the ultrarelativistic regime. Such a central scheme can be straightforwardly applied to hyperbolic systems of conservation laws for which the characteristic structure is not explicitly known, or in cases where a numerical computation of the exact solution of the Riemann problem is prohibitively expensive. Finally, we present comparisons with results obtained using various Godunov-type schemes as well as with those obtained using other high-resolution central schemes which have recently been reported in the literature.

A coupled Eulerian/Lagrangian method for the solution of three-dimensional vortical flows

NASA Technical Reports Server (NTRS)

Felici, Helene Marie

1992-01-01

A coupled Eulerian/Lagrangian method is presented for the reduction of numerical diffusion observed in solutions of three-dimensional rotational flows using standard Eulerian finite-volume time-marching procedures. A Lagrangian particle tracking method using particle markers is added to the Eulerian time-marching procedure and provides a correction of the Eulerian solution. In turn, the Eulerian solutions is used to integrate the Lagrangian state-vector along the particles trajectories. The Lagrangian correction technique does not require any a-priori information on the structure or position of the vortical regions. While the Eulerian solution ensures the conservation of mass and sets the pressure field, the particle markers, used as 'accuracy boosters,' take advantage of the accurate convection description of the Lagrangian solution and enhance the vorticity and entropy capturing capabilities of standard Eulerian finite-volume methods. The combined solution procedures is tested in several applications. The convection of a Lamb vortex in a straight channel is used as an unsteady compressible flow preservation test case. The other test cases concern steady incompressible flow calculations and include the preservation of turbulent inlet velocity profile, the swirling flow in a pipe, and the constant stagnation pressure flow and secondary flow calculations in bends. The last application deals with the external flow past a wing with emphasis on the trailing vortex solution. The improvement due to the addition of the Lagrangian correction technique is measured by comparison with analytical solutions when available or with Eulerian solutions on finer grids. The use of the combined Eulerian/Lagrangian scheme results in substantially lower grid resolution requirements than the standard Eulerian scheme for a given solution accuracy.

Singular perturbation solutions of steady-state Poisson-Nernst-Planck systems.

PubMed

Wang, Xiang-Sheng; He, Dongdong; Wylie, Jonathan J; Huang, Huaxiong

2014-02-01

We study the Poisson-Nernst-Planck (PNP) system with an arbitrary number of ion species with arbitrary valences in the absence of fixed charges. Assuming point charges and that the Debye length is small relative to the domain size, we derive an asymptotic formula for the steady-state solution by matching outer and boundary layer solutions. The case of two ionic species has been extensively studied, the uniqueness of the solution has been proved, and an explicit expression for the solution has been obtained. However, the case of three or more ions has received significantly less attention. Previous work has indicated that the solution may be nonunique and that even obtaining numerical solutions is a difficult task since one must solve complicated systems of nonlinear equations. By adopting a methodology that preserves the symmetries of the PNP system, we show that determining the outer solution effectively reduces to solving a single scalar transcendental equation. Due to the simple form of the transcendental equation, it can be solved numerically in a straightforward manner. Our methodology thus provides a standard procedure for solving the PNP system and we illustrate this by solving some practical examples. Despite the fact that for three ions, previous studies have indicated that multiple solutions may exist, we show that all except for one of these solutions are unphysical and thereby prove the existence and uniqueness for the three-ion case.

The development of a mixing layer under the action of weak streamwise vortices

NASA Technical Reports Server (NTRS)

Goldstein, M. E.; Mathew, Joseph

1993-01-01

The action of weak, streamwise vortices on a plane, incompressible, steady mixing layer is examined in the large Reynolds number limit. The outer, inviscid region is bounded by a vortex sheet to which the viscous region is confined. It is shown that the local linear analysis becomes invalid at streamwise distances O(epsilon sup -1), where (epsilon much less than 1) is the crossflow amplitude, and a new nonlinear analysis is constructed for this region. Numerical solutions of the nonlinear problem show that the vortex sheet undergoes an O(1) change in position and that the solution is ultimately terminated by a breakdown in the numerical procedure. The corresponding viscous layer shows downstream thickening, but appears to remain well behaved up to the terminal location.

Modeling of Passive Acoustic Liners from High Fidelity Numerical Simulations

NASA Astrophysics Data System (ADS)

Ferrari, Marcello do Areal Souto

Noise reduction in aviation has been an important focus of study in the last few decades. One common solution is setting up acoustic liners in the internal walls of the engines. However, measurements in the laboratory with liners are expensive and time consuming. The present work proposes a nonlinear physics-based time domain model to predict the acoustic behavior of a given liner in a defined flow condition. The parameters of the model are defined by analysis of accurate numerical solutions of the flow obtained from a high-fidelity numerical code. The length of the cavity is taken into account by using an analytical procedure to account for internal reflections in the interior of the cavity. Vortices and jets originated from internal flow separations are confirmed to be important mechanisms of sound absorption, which defines the overall efficiency of the liner. Numerical simulations at different frequency, geometry and sound pressure level are studied in detail to define the model parameters. Comparisons with high-fidelity numerical simulations show that the proposed model is accurate, robust, and can be used to define a boundary condition simulating a liner in a high-fidelity code.

A new numerical approach for compressible viscous flows

NASA Technical Reports Server (NTRS)

Wu, J. C.; Lekoudis, S. G.

1982-01-01

A numerical approach for computing unsteady compressible viscous flows was developed. This approach offers the capability of confining the region of computation to the viscous region of the flow. The viscous region is defined as the region where the vorticity is nonnegligible and the difference in dilatation between the potential flow and the real flow around the same geometry is also nonnegligible. The method was developed and tested. Also, an application of the procedure to the solution of the steady Navier-Stokes equations for incompressible internal flows is presented.

Finite element analysis and computer graphics visualization of flow around pitching and plunging airfoils

NASA Technical Reports Server (NTRS)

Bratanow, T.; Ecer, A.

1973-01-01

A general computational method for analyzing unsteady flow around pitching and plunging airfoils was developed. The finite element method was applied in developing an efficient numerical procedure for the solution of equations describing the flow around airfoils. The numerical results were employed in conjunction with computer graphics techniques to produce visualization of the flow. The investigation involved mathematical model studies of flow in two phases: (1) analysis of a potential flow formulation and (2) analysis of an incompressible, unsteady, viscous flow from Navier-Stokes equations.

Rapid Inversion of Angular Deflection Data for Certain Axisymmetric Refractive Index Distributions

NASA Technical Reports Server (NTRS)

Rubinstein, R.; Greenberg, P. S.

1994-01-01

Certain functions useful for representing axisymmetric refractive-index distributions are shown to have exact solutions for Abel transformation of the resulting angular deflection data. An advantage of this procedure over direct numerical Abel inversion is that least-squares curve fitting is a smoothing process that reduces the noise sensitivity of the computation

Simulation of a Single-Element Lean-Direct Injection Combustor Using a Polyhedral Mesh Derived from Hanging-Node Elements

NASA Technical Reports Server (NTRS)

Wey, Thomas; Liu, Nan-Suey

2013-01-01

This paper summarizes the procedures of generating a polyhedral mesh derived from hanging-node elements as well as presents sample results from its application to the numerical solution of a single element lean direct injection (LDI) combustor using an open-source version of the National Combustion Code (NCC).

Vibrations and stresses in layered anisotropic cylinders

NASA Technical Reports Server (NTRS)

Mulholland, G. P.; Gupta, B. P.

1976-01-01

An equation describing the radial displacement in a k layered anisotropic cylinder was obtained. The cylinders are initially unstressed but are subjected to either a time dependent normal stress or a displacement at the external boundaries of the laminate. The solution is obtained by utilizing the Vodicka orthogonalization technique. Numerical examples are given to illustrate the procedure.

Numerical investigation of velocity slip and temperature jump effects on unsteady flow over a stretching permeable surface

NASA Astrophysics Data System (ADS)

Hosseini, E.; Loghmani, G. B.; Heydari, M.; Rashidi, M. M.

2017-02-01

In this paper, the boundary layer flow and heat transfer of unsteady flow over a porous accelerating stretching surface in the presence of the velocity slip and temperature jump effects are investigated numerically. A new effective collocation method based on rational Bernstein functions is applied to solve the governing system of nonlinear ordinary differential equations. This method solves the problem on the semi-infinite domain without truncating or transforming it to a finite domain. In addition, the presented method reduces the solution of the problem to the solution of a system of algebraic equations. Graphical and tabular results are presented to investigate the influence of the unsteadiness parameter A , Prandtl number Pr, suction parameter fw, velocity slip parameter γ and thermal slip parameter φ on the velocity and temperature profiles of the fluid. The numerical experiments are reported to show the accuracy and efficiency of the novel proposed computational procedure. Comparisons of present results are made with those obtained by previous works and show excellent agreement.

Fully Nonlinear Modeling and Analysis of Precision Membranes

NASA Technical Reports Server (NTRS)

Pai, P. Frank; Young, Leyland G.

2003-01-01

High precision membranes are used in many current space applications. This paper presents a fully nonlinear membrane theory with forward and inverse analyses of high precision membrane structures. The fully nonlinear membrane theory is derived from Jaumann strains and stresses, exact coordinate transformations, the concept of local relative displacements, and orthogonal virtual rotations. In this theory, energy and Newtonian formulations are fully correlated, and every structural term can be interpreted in terms of vectors. Fully nonlinear ordinary differential equations (ODES) governing the large static deformations of known axisymmetric membranes under known axisymmetric loading (i.e., forward problems) are presented as first-order ODES, and a method for obtaining numerically exact solutions using the multiple shooting procedure is shown. A method for obtaining the undeformed geometry of any axisymmetric membrane with a known inflated geometry and a known internal pressure (i.e., inverse problems) is also derived. Numerical results from forward analysis are verified using results in the literature, and results from inverse analysis are verified using known exact solutions and solutions from the forward analysis. Results show that the membrane theory and the proposed numerical methods for solving nonlinear forward and inverse membrane problems are accurate.

Variational data assimilation problem for the Baltic Sea thermodynamics

NASA Astrophysics Data System (ADS)

Zakharova, Natalia; Agoshkov, Valery; Parmuzin, Eugene

2015-04-01

The most versatile and promising technology for solving problems of monitoring and analysis of the natural environment is a four-dimensional variational data assimilation of observation data. In such problems not only the development and justification of algorithms for numerical solution of variational data assimilation problems but the properties of the optimal solution play an important role. In this work the variational data assimilation problems in the Baltic Sea water area were formulated and studied. Numerical experiments on restoring the ocean heat flux and obtaining solution of the system (temperature, salinity, velocity, and sea surface height) in the Baltic Sea primitive equation hydrodynamics model with assimilation procedure were carried out. In the calculations we used daily sea surface temperature observation from Danish meteorological Institute, prepared on the basis of measurements of the radiometer (AVHRR, AATSR and AMSRE) and spectroradiometer (SEVIRI and MODIS). The spatial resolution of the model grid with respect to the horizontal variables amounted to 0.0625x0.03125 degree. The results of the numerical experiments are presented. This study was supported by the Russian Foundation for Basic Research (project 13-01-00753, project 14-01-31195) and project 14-11-00609 by the Russian Science Foundation. References: 1 E.I. Parmuzin, V.I. Agoshkov, Numerical solution of the variational assimilation problem for sea surface temperature in the model of the Black Sea dynamics. Russ. J. Numer. Anal. Math. Modelling (2012) 27, No.1, 69-94 2 Zakharova N.B., Agoshkov V.I., Parmuzin E.I., The new method of ARGO buoys system observation data interpolation. Russian Journal of Numerical Analysis and Mathematical Modelling. Vol. 28, Issue 1, 2013. 3 Zalesny V.B., Gusev A.V., Chernobay S.Yu., Aps R., Tamsalu R., Kujala P., Rytkönen J. The Bal-tic Sea circulation modelling and assessment of marine pollution, Russ. J. Numer. Analysis and Math. Modelling, 2014, V 29, No. 2, pp. 129-138.

Frictionless contact of aircraft tires

NASA Technical Reports Server (NTRS)

Kim, Kyun O.; Tanner, John A.; Noor, Ahmed K.

1989-01-01

A computational procedure for the solution of frictionless contact problems of spacecraft tires was developed using a two-dimensional laminated anisotropic shell theory incorporating the effects of variations in material and geometric parameters, transverse shear deformation, and geometric nonlinearities to model the nose-gear tire of a space shuttle. Numerical results are presented for the case when the nose-gear tire is subjected to inflation pressure and pressed against a rigid pavement. The results are compared with experimental results obtained at NASA Langley, demonstrating a high accuracy of the model and the effectiveness of the computational procedure.

A novel approach to calibrate the hemodynamic model using functional Magnetic Resonance Imaging (fMRI) measurements.

PubMed

Khoram, Nafiseh; Zayane, Chadia; Djellouli, Rabia; Laleg-Kirati, Taous-Meriem

2016-03-15

The calibration of the hemodynamic model that describes changes in blood flow and blood oxygenation during brain activation is a crucial step for successfully monitoring and possibly predicting brain activity. This in turn has the potential to provide diagnosis and treatment of brain diseases in early stages. We propose an efficient numerical procedure for calibrating the hemodynamic model using some fMRI measurements. The proposed solution methodology is a regularized iterative method equipped with a Kalman filtering-type procedure. The Newton component of the proposed method addresses the nonlinear aspect of the problem. The regularization feature is used to ensure the stability of the algorithm. The Kalman filter procedure is incorporated here to address the noise in the data. Numerical results obtained with synthetic data as well as with real fMRI measurements are presented to illustrate the accuracy, robustness to the noise, and the cost-effectiveness of the proposed method. We present numerical results that clearly demonstrate that the proposed method outperforms the Cubature Kalman Filter (CKF), one of the most prominent existing numerical methods. We have designed an iterative numerical technique, called the TNM-CKF algorithm, for calibrating the mathematical model that describes the single-event related brain response when fMRI measurements are given. The method appears to be highly accurate and effective in reconstructing the BOLD signal even when the measurements are tainted with high noise level (as high as 30%). Published by Elsevier B.V.

High Rayleigh number convection in rectangular enclosures with differentially heated vertical walls and aspect ratios between zero and unity

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

Kassemi, S.A.

1988-04-01

High Rayleigh number convection in a rectangular cavity with insulated horizontal surfaces and differentially heated vertical walls was analyzed for an arbitrary aspect ratio smaller than or equal to unity. Unlike previous analytical studies, a systematic method of solution based on linearization technique and analytical iteration procedure was developed to obtain approximate closed-form solutions for a wide range of aspect ratios. The predicted velocity and temperature fields are shown to be in excellent agreement with available experimental and numerical data.

High Rayleigh number convection in rectangular enclosures with differentially heated vertical walls and aspect ratios between zero and unity

NASA Technical Reports Server (NTRS)

Kassemi, Siavash A.

1988-01-01

High Rayleigh number convection in a rectangular cavity with insulated horizontal surfaces and differentially heated vertical walls was analyzed for an arbitrary aspect ratio smaller than or equal to unity. Unlike previous analytical studies, a systematic method of solution based on linearization technique and analytical iteration procedure was developed to obtain approximate closed-form solutions for a wide range of aspect ratios. The predicted velocity and temperature fields are shown to be in excellent agreement with available experimental and numerical data.

Approaching the investigation of plasma turbulence through a rigorous verification and validation procedure: A practical example

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

Ricci, P., E-mail: paolo.ricci@epfl.ch; Riva, F.; Theiler, C.

In the present work, a Verification and Validation procedure is presented and applied showing, through a practical example, how it can contribute to advancing our physics understanding of plasma turbulence. Bridging the gap between plasma physics and other scientific domains, in particular, the computational fluid dynamics community, a rigorous methodology for the verification of a plasma simulation code is presented, based on the method of manufactured solutions. This methodology assesses that the model equations are correctly solved, within the order of accuracy of the numerical scheme. The technique to carry out a solution verification is described to provide a rigorousmore » estimate of the uncertainty affecting the numerical results. A methodology for plasma turbulence code validation is also discussed, focusing on quantitative assessment of the agreement between experiments and simulations. The Verification and Validation methodology is then applied to the study of plasma turbulence in the basic plasma physics experiment TORPEX [Fasoli et al., Phys. Plasmas 13, 055902 (2006)], considering both two-dimensional and three-dimensional simulations carried out with the GBS code [Ricci et al., Plasma Phys. Controlled Fusion 54, 124047 (2012)]. The validation procedure allows progress in the understanding of the turbulent dynamics in TORPEX, by pinpointing the presence of a turbulent regime transition, due to the competition between the resistive and ideal interchange instabilities.« less

Numerical Investigation of the Interaction of Counterflowing Jets and Supersonic Capsule Flows

NASA Technical Reports Server (NTRS)

Venkatachari, Balaji Shankar; Ito, Yasushi; Cheng, Gary; Chang, Chau-Lyan

2011-01-01

Use of counterflowing jets ejected into supersonic freestreams as a flow control concept to modify the external flowfield has gained renewed interest with regards to potential retropropulsion applications pertinent to entry, descent, and landing investigations. This study describes numerical computations of such a concept for a scaled wind-tunnel capsule model by employing the space-time conservation element solution element viscous flow solver with unstructured meshes. Both steady-state and time-accurate computations are performed for several configurations with different counterflowing jet Mach numbers. Axisymmetric computations exploring the effect of the jet flow rate and jet Mach number on the flow stability, jet interaction with the bow shock and its subsequent impact on the aerodynamic and aerothermal loads on the capsule body are carried out. Similar to previous experimental findings, both long and short penetration modes exist at a windtunnel Mach number of 3.48. It was found that both modes exhibit non-stationary behavior and the former is much more unstable than the latter. It was also found that the unstable long penetration mode only exists in a relatively small range of the jet mass flow rate. Solution-based mesh refinement procedures are used to improve solution accuracy and provide guidelines for a more effective mesh generation procedure for parametric studies. Details of the computed flowfields also serve as a means to broaden the knowledge base for future retropropulsion design studies.

Boundary-fitted curvilinear coordinate systems for solution of partial differential equations on fields containing any number of arbitrary two-dimensional bodies

NASA Technical Reports Server (NTRS)

Thompson, J. F.; Thames, F. C.; Mastin, C. W.

1977-01-01

A method is presented for automatic numerical generation of a general curvilinear coordinate system with coordinate lines coincident with all boundaries of a general multi-connected two-dimensional region containing any number of arbitrarily shaped bodies. No restrictions are placed on the shape of the boundaries, which may even be time-dependent, and the approach is not restricted in principle to two dimensions. With this procedure the numerical solution of a partial differential system may be done on a fixed rectangular field with a square mesh with no interpolation required regardless of the shape of the physical boundaries, regardless of the spacing of the curvilinear coordinate lines in the physical field, and regardless of the movement of the coordinate system in the physical plane. A number of examples of coordinate systems and application thereof to the solution of partial differential equations are given. The FORTRAN computer program and instructions for use are included.

An arbitrary high-order Discontinuous Galerkin method for elastic waves on unstructured meshes - III. Viscoelastic attenuation

NASA Astrophysics Data System (ADS)

Käser, Martin; Dumbser, Michael; de la Puente, Josep; Igel, Heiner

2007-01-01

We present a new numerical method to solve the heterogeneous anelastic, seismic wave equations with arbitrary high order accuracy in space and time on 3-D unstructured tetrahedral meshes. Using the velocity-stress formulation provides a linear hyperbolic system of equations with source terms that is completed by additional equations for the anelastic functions including the strain history of the material. These additional equations result from the rheological model of the generalized Maxwell body and permit the incorporation of realistic attenuation properties of viscoelastic material accounting for the behaviour of elastic solids and viscous fluids. The proposed method combines the Discontinuous Galerkin (DG) finite element (FE) method with the ADER approach using Arbitrary high order DERivatives for flux calculations. The DG approach, in contrast to classical FE methods, uses a piecewise polynomial approximation of the numerical solution which allows for discontinuities at element interfaces. Therefore, the well-established theory of numerical fluxes across element interfaces obtained by the solution of Riemann problems can be applied as in the finite volume framework. The main idea of the ADER time integration approach is a Taylor expansion in time in which all time derivatives are replaced by space derivatives using the so-called Cauchy-Kovalewski procedure which makes extensive use of the governing PDE. Due to the ADER time integration technique the same approximation order in space and time is achieved automatically and the method is a one-step scheme advancing the solution for one time step without intermediate stages. To this end, we introduce a new unrolled recursive algorithm for efficiently computing the Cauchy-Kovalewski procedure by making use of the sparsity of the system matrices. The numerical convergence analysis demonstrates that the new schemes provide very high order accuracy even on unstructured tetrahedral meshes while computational cost and storage space for a desired accuracy can be reduced when applying higher degree approximation polynomials. In addition, we investigate the increase in computing time, when the number of relaxation mechanisms due to the generalized Maxwell body are increased. An application to a well-acknowledged test case and comparisons with analytic and reference solutions, obtained by different well-established numerical methods, confirm the performance of the proposed method. Therefore, the development of the highly accurate ADER-DG approach for tetrahedral meshes including viscoelastic material provides a novel, flexible and efficient numerical technique to approach 3-D wave propagation problems including realistic attenuation and complex geometry.

Analysis of energy states in modulation doped multiquantum well heterostructures

NASA Technical Reports Server (NTRS)

Ji, G.; Henderson, T.; Peng, C. K.; Huang, D.; Morkoc, H.

1990-01-01

A precise and effective numerical procedure to model the band diagram of modulation doped multiquantum well heterostructures is presented. This method is based on a self-consistent iterative solution of the Schroedinger equation and the Poisson equation. It can be used rather easily in any arbitrary modulation-doped structure. In addition to confined energy subbands, the unconfined states can be calculated as well. Examples on realistic device structures are given to demonstrate capabilities of this procedure. The numerical results are in good agreement with experiments. With the aid of this method the transitions involving both the confined and unconfined conduction subbands in a modulation doped AlGaAs/GaAs superlattice, and in a strained layer InGaAs/GaAs superlattice are identified. These results represent the first observation of unconfined transitions in modulation doped multiquantum well structures.

Solution of multi-center molecular integrals of Slater-type orbitals

NASA Technical Reports Server (NTRS)

Tai, H.

1989-01-01

The troublesome multi-center molecular integrals of Slater-type orbitals (STO) in molecular physics calculations can be evaluated by using the Fourier transform and proper coupling of the two center exchange integrals. A numerical integration procedure is then readily rendered to the final expression in which the integrand consists of well known special functions of arguments containing the geometrical arrangement of the nuclear centers and the exponents of the atomic orbitals. A practical procedure was devised for the calculation of a general multi-center molecular integrals coupling arbitrary Slater-type orbitals. Symmetry relations and asymptotic conditions are discussed. Explicit expressions of three-center one-electron nuclear-attraction integrals and four-center two-electron repulsion integrals for STO of principal quantum number n=2 are listed. A few numerical results are given for the purpose of comparison.

Numerical solutions of the Navier-Stokes equations for transonic afterbody flows

NASA Technical Reports Server (NTRS)

Swanson, R. C., Jr.

1980-01-01

The time dependent Navier-Stokes equations in mass averaged variables are solved for transonic flow over axisymmetric boattail plume simulator configurations. Numerical solution of these equations is accomplished with the unsplit explict finite difference algorithm of MacCormack. A grid subcycling procedure and computer code vectorization are used to improve computational efficiency. The two layer algebraic turbulence models of Cebeci-Smith and Baldwin-Lomax are employed for investigating turbulence closure. Two relaxation models based on these baseline models are also considered. Results in the form of surface pressure distribution for three different circular arc boattails at two free stream Mach numbers are compared with experimental data. The pressures in the recirculating flow region for all separated cases are poorly predicted with the baseline turbulence models. Significant improvements in the predictions are usually obtained by using the relaxation models.

Nash equilibrium and multi criterion aerodynamic optimization

NASA Astrophysics Data System (ADS)

Tang, Zhili; Zhang, Lianhe

2016-06-01

Game theory and its particular Nash Equilibrium (NE) are gaining importance in solving Multi Criterion Optimization (MCO) in engineering problems over the past decade. The solution of a MCO problem can be viewed as a NE under the concept of competitive games. This paper surveyed/proposed four efficient algorithms for calculating a NE of a MCO problem. Existence and equivalence of the solution are analyzed and proved in the paper based on fixed point theorem. Specific virtual symmetric Nash game is also presented to set up an optimization strategy for single objective optimization problems. Two numerical examples are presented to verify proposed algorithms. One is mathematical functions' optimization to illustrate detailed numerical procedures of algorithms, the other is aerodynamic drag reduction of civil transport wing fuselage configuration by using virtual game. The successful application validates efficiency of algorithms in solving complex aerodynamic optimization problem.

Design and simulation of a cable-pulley-based transmission for artificial ankle joints

NASA Astrophysics Data System (ADS)

Liu, Huaxin; Ceccarelli, Marco; Huang, Qiang

2016-06-01

In this paper, a mechanical transmission based on cable pulley is proposed for human-like actuation in the artificial ankle joints of human-scale. The anatomy articular characteristics of the human ankle is discussed for proper biomimetic inspiration in designing an accurate, efficient, and robust motion control of artificial ankle joint devices. The design procedure is presented through the inclusion of conceptual considerations and design details for an interactive solution of the transmission system. A mechanical design is elaborated for the ankle joint angular with pitch motion. A multi-body dynamic simulation model is elaborated accordingly and evaluated numerically in the ADAMS environment. Results of the numerical simulations are discussed to evaluate the dynamic performance of the proposed design solution and to investigate the feasibility of the proposed design in future applications for humanoid robots.

Re-Computation of Numerical Results Contained in NACA Report No. 496

NASA Technical Reports Server (NTRS)

Perry, Boyd, III

2015-01-01

An extensive examination of NACA Report No. 496 (NACA 496), "General Theory of Aerodynamic Instability and the Mechanism of Flutter," by Theodore Theodorsen, is described. The examination included checking equations and solution methods and re-computing interim quantities and all numerical examples in NACA 496. The checks revealed that NACA 496 contains computational shortcuts (time- and effort-saving devices for engineers of the time) and clever artifices (employed in its solution methods), but, unfortunately, also contains numerous tripping points (aspects of NACA 496 that have the potential to cause confusion) and some errors. The re-computations were performed employing the methods and procedures described in NACA 496, but using modern computational tools. With some exceptions, the magnitudes and trends of the original results were in fair-to-very-good agreement with the re-computed results. The exceptions included what are speculated to be computational errors in the original in some instances and transcription errors in the original in others. Independent flutter calculations were performed and, in all cases, including those where the original and re-computed results differed significantly, were in excellent agreement with the re-computed results. Appendix A contains NACA 496; Appendix B contains a Matlab(Reistered) program that performs the re-computation of results; Appendix C presents three alternate solution methods, with examples, for the two-degree-of-freedom solution method of NACA 496; Appendix D contains the three-degree-of-freedom solution method (outlined in NACA 496 but never implemented), with examples.

The Motion of a Leaking Oscillator: A Study for the Physics Class

ERIC Educational Resources Information Center

Rodrigues, Hilário; Panza, Nelson; Portes, Dirceu; Soares, Alexandre

2014-01-01

This paper is essentially about the general form of Newton's second law for variable mass problems. We develop a model for describing the motion of the one-dimensional oscillator with a variable mass within the framework of classroom physics. We present a simple numerical procedure for the solution of the equation of motion of the system to…

Procedures for the computation of unsteady transonic flows including viscous effects

NASA Technical Reports Server (NTRS)

Rizzetta, D. P.

1982-01-01

Modifications of the code LTRAN2, developed by Ballhaus and Goorjian, which account for viscous effects in the computation of planar unsteady transonic flows are presented. Two models are considered and their theoretical development and numerical implementation is discussed. Computational examples employing both models are compared with inviscid solutions and with experimental data. Use of the modified code is described.

Semi-implicit and fully implicit shock-capturing methods for hyperbolic conservation laws with stiff source terms

NASA Technical Reports Server (NTRS)

Yee, H. C.; Shinn, J. L.

1986-01-01

Some numerical aspects of finite-difference algorithms for nonlinear multidimensional hyperbolic conservation laws with stiff nonhomogenous (source) terms are discussed. If the stiffness is entirely dominated by the source term, a semi-implicit shock-capturing method is proposed provided that the Jacobian of the soruce terms possesses certain properties. The proposed semi-implicit method can be viewed as a variant of the Bussing and Murman point-implicit scheme with a more appropriate numerical dissipation for the computation of strong shock waves. However, if the stiffness is not solely dominated by the source terms, a fully implicit method would be a better choice. The situation is complicated by problems that are higher than one dimension, and the presence of stiff source terms further complicates the solution procedures for alternating direction implicit (ADI) methods. Several alternatives are discussed. The primary motivation for constructing these schemes was to address thermally and chemically nonequilibrium flows in the hypersonic regime. Due to the unique structure of the eigenvalues and eigenvectors for fluid flows of this type, the computation can be simplified, thus providing a more efficient solution procedure than one might have anticipated.

Numerical Calculations of 3-D High-Lift Flows and Comparison with Experiment

NASA Technical Reports Server (NTRS)

Compton, William B, III

2015-01-01

Solutions were obtained with the Navier-Stokes CFD code TLNS3D to predict the flow about the NASA Trapezoidal Wing, a high-lift wing composed of three elements: the main-wing element, a deployed leading-edge slat, and a deployed trailing-edge flap. Turbulence was modeled by the Spalart-Allmaras one-equation turbulence model. One case with massive separation was repeated using Menter's two-equation SST (Menter's Shear Stress Transport) k-omega turbulence model in an attempt to improve the agreement with experiment. The investigation was conducted at a free stream Mach number of 0.2, and at angles of attack ranging from 10.004 degrees to 34.858 degrees. The Reynolds number based on the mean aerodynamic chord of the wing was 4.3 x 10 (sup 6). Compared to experiment, the numerical procedure predicted the surface pressures very well at angles of attack in the linear range of the lift. However, computed maximum lift was 5% low. Drag was mainly under predicted. The procedure correctly predicted several well-known trends and features of high-lift flows, such as off-body separation. The two turbulence models yielded significantly different solutions for the repeated case.

A new and inexpensive non-bit-for-bit solution reproducibility test based on time step convergence (TSC1.0)

NASA Astrophysics Data System (ADS)

Wan, Hui; Zhang, Kai; Rasch, Philip J.; Singh, Balwinder; Chen, Xingyuan; Edwards, Jim

2017-02-01

A test procedure is proposed for identifying numerically significant solution changes in evolution equations used in atmospheric models. The test issues a fail signal when any code modifications or computing environment changes lead to solution differences that exceed the known time step sensitivity of the reference model. Initial evidence is provided using the Community Atmosphere Model (CAM) version 5.3 that the proposed procedure can be used to distinguish rounding-level solution changes from impacts of compiler optimization or parameter perturbation, which are known to cause substantial differences in the simulated climate. The test is not exhaustive since it does not detect issues associated with diagnostic calculations that do not feedback to the model state variables. Nevertheless, it provides a practical and objective way to assess the significance of solution changes. The short simulation length implies low computational cost. The independence between ensemble members allows for parallel execution of all simulations, thus facilitating fast turnaround. The new method is simple to implement since it does not require any code modifications. We expect that the same methodology can be used for any geophysical model to which the concept of time step convergence is applicable.

Direct computation of stochastic flow in reservoirs with uncertain parameters

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

Dainton, M.P.; Nichols, N.K.; Goldwater, M.H.

1997-01-15

A direct method is presented for determining the uncertainty in reservoir pressure, flow, and net present value (NPV) using the time-dependent, one phase, two- or three-dimensional equations of flow through a porous medium. The uncertainty in the solution is modelled as a probability distribution function and is computed from given statistical data for input parameters such as permeability. The method generates an expansion for the mean of the pressure about a deterministic solution to the system equations using a perturbation to the mean of the input parameters. Hierarchical equations that define approximations to the mean solution at each point andmore » to the field convariance of the pressure are developed and solved numerically. The procedure is then used to find the statistics of the flow and the risked value of the field, defined by the NPV, for a given development scenario. This method involves only one (albeit complicated) solution of the equations and contrasts with the more usual Monte-Carlo approach where many such solutions are required. The procedure is applied easily to other physical systems modelled by linear or nonlinear partial differential equations with uncertain data. 14 refs., 14 figs., 3 tabs.« less

An improved viscid/inviscid interaction procedure for transonic flow over airfoils

NASA Technical Reports Server (NTRS)

Melnik, R. E.; Chow, R. R.; Mead, H. R.; Jameson, A.

1985-01-01

A new interacting boundary layer approach for computing the viscous transonic flow over airfoils is described. The theory includes a complete treatment of viscous interaction effects induced by the wake and accounts for normal pressure gradient effects across the boundary layer near trailing edges. The method is based on systematic expansions of the full Reynolds equation of turbulent flow in the limit of Reynolds numbers, Reynolds infinity. Procedures are developed for incorporating the local trailing edge solution into the numerical solution of the coupled full potential and integral boundary layer equations. Although the theory is strictly applicable to airfoils with cusped or nearly cusped trailing edges and to turbulent boundary layers that remain fully attached to the airfoil surface, the method was successfully applied to more general airfoils and to flows with small separation zones. Comparisons of theoretical solutions with wind tunnel data indicate the present method can accurately predict the section characteristics of airfoils including the absolute levels of drag.

ERS-1 scatterometer calibration and validation activities at ECMWF. B: From radar backscatter characteristics to wind vector solutions

NASA Technical Reports Server (NTRS)

Stoffelen, AD; Anderson, David L. T.; Woiceshyn, Peter M.

1992-01-01

Calibration and validation activities for the ERS-1 scatterometer were carried out at ECMWF (European Center for Medium range Weather Forecast) complementary to the 'Haltenbanken' field campaign off the coast of Norway. At a Numerical Weather Prediction (NWP) center a wealth of verifying data is available both in time and space. This data is used to redefine the wind retrieval procedure given the instrumental characteristics. It was found that a maximum likelihood estimation procedure to obtain the coefficients of a reformulated sigma deg to wind relationship should use radar measurements in logarithmic rather than physical space, and use winds as the wind components rather than wind speed and direction. Doing this, a much more accurate transfer function than the one currently operated by ESA was derived. Sigma deg measurement space shows no signature of a separation in an upwind solution cone and a downwind solution cone. As such signature was anticipated in ESA's wind direction ambiguity removal algorithm, reconsideration of the procedure is necessary. Despite the fact that revisions have to be made in the process of wind retrieval; a grid potential is shown for scatterometry in meteorology and climatology.

Recursive Newton-Euler formulation of manipulator dynamics

NASA Technical Reports Server (NTRS)

Nasser, M. G.

1989-01-01

A recursive Newton-Euler procedure is presented for the formulation and solution of manipulator dynamical equations. The procedure includes rotational and translational joints and a topological tree. This model was verified analytically using a planar two-link manipulator. Also, the model was tested numerically against the Walker-Orin model using the Shuttle Remote Manipulator System data. The hinge accelerations obtained from both models were identical. The computational requirements of the model vary linearly with the number of joints. The computational efficiency of this method exceeds that of Walker-Orin methods. This procedure may be viewed as a considerable generalization of Armstrong's method. A six-by-six formulation is adopted which enhances both the computational efficiency and simplicity of the model.

Development of an efficient procedure for calculating the aerodynamic effects of planform variation

NASA Technical Reports Server (NTRS)

Mercer, J. E.; Geller, E. W.

1981-01-01

Numerical procedures to compute gradients in aerodynamic loading due to planform shape changes using panel method codes were studied. Two procedures were investigated: one computed the aerodynamic perturbation directly; the other computed the aerodynamic loading on the perturbed planform and on the base planform and then differenced these values to obtain the perturbation in loading. It is indicated that computing the perturbed values directly can not be done satisfactorily without proper aerodynamic representation of the pressure singularity at the leading edge of a thin wing. For the alternative procedure, a technique was developed which saves most of the time-consuming computations from a panel method calculation for the base planform. Using this procedure the perturbed loading can be calculated in about one-tenth the time of that for the base solution.

A Solution Method of Scheduling Problem with Worker Allocation by a Genetic Algorithm

NASA Astrophysics Data System (ADS)

Osawa, Akira; Ida, Kenichi

In a scheduling problem with worker allocation (SPWA) proposed by Iima et al, the worker's skill level to each machine is all the same. However, each worker has a different skill level for each machine in the real world. For that reason, we propose a new model of SPWA in which a worker has the different skill level to each machine. To solve the problem, we propose a new GA for SPWA consisting of the following new three procedures, shortening of idle time, modifying infeasible solution to feasible solution, and a new selection method for GA. The effectiveness of the proposed algorithm is clarified by numerical experiments using benchmark problems for job-shop scheduling.

Towards wall functions for the prediction of solute segregation in plane front directional solidification

NASA Astrophysics Data System (ADS)

Chatelain, M.; Rhouzlane, S.; Botton, V.; Albaric, M.; Henry, D.; Millet, S.; Pelletier, D.; Garandet, J. P.

2017-10-01

The present paper focuses on solute segregation occurring in directional solidification processes with sharp solid/liquid interface, like silicon crystal growth. A major difficulty for the simulation of such processes is their inherently multi-scale nature: the impurity segregation problem is controlled at the solute boundary layer scale (micrometers) while the thermal problem is ruled at the crucible scale (meters). The thickness of the solute boundary layer is controlled by the convection regime and requires a specific refinement of the mesh of numerical models. In order to improve numerical simulations, wall functions describing solute boundary layers for convecto-diffusive regimes are derived from a scaling analysis. The aim of these wall functions is to obtain segregation profiles from purely thermo-hydrodynamic simulations, which do not require solute boundary layer refinement at the solid/liquid interface. Regarding industrial applications, various stirring techniques can be used to enhance segregation, leading to fully turbulent flows in the melt. In this context, the scaling analysis is further improved by taking into account the turbulent solute transport. The solute boundary layers predicted by the analytical model are compared to those obtained by transient segregation simulations in a canonical 2D lid driven cavity configuration for validation purposes. Convective regimes ranging from laminar to fully turbulent are considered. Growth rate and molecular diffusivity influences are also investigated. Then, a procedure to predict concentration fields in the solid phase from a hydrodynamic simulation of the solidification process is proposed. This procedure is based on the analytical wall functions and on solute mass conservation. It only uses wall shear-stress profiles at the solidification front as input data. The 2D analytical concentration fields are directly compared to the results of the complete simulation of segregation in the lid driven cavity configuration. Finally, an additional output from the analytical model is also presented. We put in light the correlation between different species convecto-diffusive behaviour; we use it to propose an estimation method for the segregation parameters of various chemical species knowing segregation parameters of one specific species.

Contact stresses in gear teeth: A new method of analysis

NASA Technical Reports Server (NTRS)

Somprakit, Paisan; Huston, Ronald L.; Oswald, Fred B.

1991-01-01

A new, innovative procedure called point load superposition for determining the contact stresses in mating gear teeth. It is believed that this procedure will greatly extend both the range of applicability and the accuracy of gear contact stress analysis. Point load superposition is based upon fundamental solutions from the theory of elasticity. It is an iterative numerical procedure which has distinct advantages over the classical Hertz method, the finite element method, and over existing applications with the boundary element method. Specifically, friction and sliding effects, which are either excluded from or difficult to study with the classical methods, are routinely handled with the new procedure. Presented here are the basic theory and the algorithms. Several examples are given. Results are consistent with those of the classical theories. Applications to spur gears are discussed.

Mr.CAS-A minimalistic (pure) Ruby CAS for fast prototyping and code generation

NASA Astrophysics Data System (ADS)

Ragni, Matteo

There are Computer Algebra System (CAS) systems on the market with complete solutions for manipulation of analytical models. But exporting a model that implements specific algorithms on specific platforms, for target languages or for particular numerical library, is often a rigid procedure that requires manual post-processing. This work presents a Ruby library that exposes core CAS capabilities, i.e. simplification, substitution, evaluation, etc. The library aims at programmers that need to rapidly prototype and generate numerical code for different target languages, while keeping separated mathematical expression from the code generation rules, where best practices for numerical conditioning are implemented. The library is written in pure Ruby language and is compatible with most Ruby interpreters.

Toxicity Minimized Cryoprotectant Addition and Removal Procedures for Adherent Endothelial Cells

PubMed Central

Davidson, Allyson Fry; Glasscock, Cameron; McClanahan, Danielle R.; Benson, James D.; Higgins, Adam Z.

2015-01-01

Ice-free cryopreservation, known as vitrification, is an appealing approach for banking of adherent cells and tissues because it prevents dissociation and morphological damage that may result from ice crystal formation. However, current vitrification methods are often limited by the cytotoxicity of the concentrated cryoprotective agent (CPA) solutions that are required to suppress ice formation. Recently, we described a mathematical strategy for identifying minimally toxic CPA equilibration procedures based on the minimization of a toxicity cost function. Here we provide direct experimental support for the feasibility of these methods when applied to adherent endothelial cells. We first developed a concentration- and temperature-dependent toxicity cost function by exposing the cells to a range of glycerol concentrations at 21°C and 37°C, and fitting the resulting viability data to a first order cell death model. This cost function was then numerically minimized in our state constrained optimization routine to determine addition and removal procedures for 17 molal (mol/kg water) glycerol solutions. Using these predicted optimal procedures, we obtained 81% recovery after exposure to vitrification solutions, as well as successful vitrification with the relatively slow cooling and warming rates of 50°C/min and 130°C/min. In comparison, conventional multistep CPA equilibration procedures resulted in much lower cell yields of about 10%. Our results demonstrate the potential for rational design of minimally toxic vitrification procedures and pave the way for extension of our optimization approach to other adherent cell types as well as more complex systems such as tissues and organs. PMID:26605546

Periodic response of nonlinear systems

NASA Technical Reports Server (NTRS)

Nataraj, C.; Nelson, H. D.

1988-01-01

A procedure is developed to determine approximate periodic solutions of autonomous and non-autonomous systems. The trignometric collocation method (TCM) is formalized to allow for the analysis of relatively small order systems directly in physical coordinates. The TCM is extended to large order systems by utilizing modal analysis in a component mode synthesis strategy. The procedure was coded and verified by several check cases. Numerical results for two small order mechanical systems and one large order rotor dynamic system are presented. The method allows for the possibility of approximating periodic responses for large order forced and self-excited nonlinear systems.

Updates to Simulation of a Single-Element Lean-Direct Injection Combustor Using a Polyhedral Mesh Derived From Hanging-Node Elements

NASA Technical Reports Server (NTRS)

Wey, Changju Thomas; Liu, Nan-Suey

2014-01-01

This paper summarizes the procedures of inserting a thin-layer mesh to existing inviscid polyhedral mesh either with or without hanging-node elements as well as presents sample results from its applications to the numerical solution of a single-element LDI combustor using a releasable edition of the National Combustion Code (NCC).

Updates to Simulation of a Single-Element Lean-Direct Injection Combustor Using a Polyhedral Mesh Derived from Hanging-Node Elements

NASA Technical Reports Server (NTRS)

Wey, Thomas; Liu, Nan-Suey

2014-01-01

This paper summarizes the procedures of inserting a thin-layer mesh to existing inviscid polyhedral mesh either with or without hanging-node elements as well as presents sample results from its applications to the numerical solution of a single-element LDI combustor using a releasable edition of the National Combustion Code (NCC).

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.

Entropy of mixing calculations for compound forming liquid alloys in the hard sphere system

NASA Astrophysics Data System (ADS)

Singh, P.; Khanna, K. N.

1984-06-01

It is shown that the semi-empirical model proposed in a previous paper for the evaluation of the entropy of mixing of simple liquid metals alloys leads to accurate results for compound forming liquid alloys. The procedure is similar to that described for a regular solution. Numerical applications are made to NaGa, KPb and KT1 alloys.

High resolution schemes and the entropy condition

NASA Technical Reports Server (NTRS)

Osher, S.; Chakravarthy, S.

1983-01-01

A systematic procedure for constructing semidiscrete, second order accurate, variation diminishing, five point band width, approximations to scalar conservation laws, is presented. These schemes are constructed to also satisfy a single discrete entropy inequality. Thus, in the convex flux case, convergence is proven to be the unique physically correct solution. For hyperbolic systems of conservation laws, this construction is used formally to extend the first author's first order accurate scheme, and show (under some minor technical hypotheses) that limit solutions satisfy an entropy inequality. Results concerning discrete shocks, a maximum principle, and maximal order of accuracy are obtained. Numerical applications are also presented.

Noniterative three-dimensional grid generation using parabolic partial differential equations

NASA Technical Reports Server (NTRS)

Edwards, T. A.

1985-01-01

A new algorithm for generating three-dimensional grids has been developed and implemented which numerically solves a parabolic partial differential equation (PDE). The solution procedure marches outward in two coordinate directions, and requires inversion of a scalar tridiagonal system in the third. Source terms have been introduced to control the spacing and angle of grid lines near the grid boundaries, and to control the outer boundary point distribution. The method has been found to generate grids about 100 times faster than comparable grids generated via solution of elliptic PDEs, and produces smooth grids for finite-difference flow calculations.

On substructuring algorithms and solution techniques for the numerical approximation of partial differential equations

NASA Technical Reports Server (NTRS)

Gunzburger, M. D.; Nicolaides, R. A.

1986-01-01

Substructuring methods are in common use in mechanics problems where typically the associated linear systems of algebraic equations are positive definite. Here these methods are extended to problems which lead to nonpositive definite, nonsymmetric matrices. The extension is based on an algorithm which carries out the block Gauss elimination procedure without the need for interchanges even when a pivot matrix is singular. Examples are provided wherein the method is used in connection with finite element solutions of the stationary Stokes equations and the Helmholtz equation, and dual methods for second-order elliptic equations.

Numerical solution of modified differential equations based on symmetry preservation.

PubMed

Ozbenli, Ersin; Vedula, Prakash

2017-12-01

In this paper, we propose a method to construct invariant finite-difference schemes for solution of partial differential equations (PDEs) via consideration of modified forms of the underlying PDEs. The invariant schemes, which preserve Lie symmetries, are obtained based on the method of equivariant moving frames. While it is often difficult to construct invariant numerical schemes for PDEs due to complicated symmetry groups associated with cumbersome discrete variable transformations, we note that symmetries associated with more convenient transformations can often be obtained by appropriately modifying the original PDEs. In some cases, modifications to the original PDEs are also found to be useful in order to avoid trivial solutions that might arise from particular selections of moving frames. In our proposed method, modified forms of PDEs can be obtained either by addition of perturbation terms to the original PDEs or through defect correction procedures. These additional terms, whose primary purpose is to enable symmetries with more convenient transformations, are then removed from the system by considering moving frames for which these specific terms go to zero. Further, we explore selection of appropriate moving frames that result in improvement in accuracy of invariant numerical schemes based on modified PDEs. The proposed method is tested using the linear advection equation (in one- and two-dimensions) and the inviscid Burgers' equation. Results obtained for these tests cases indicate that numerical schemes derived from the proposed method perform significantly better than existing schemes not only by virtue of improvement in numerical accuracy but also due to preservation of qualitative properties or symmetries of the underlying differential equations.

A conservative fully implicit algorithm for predicting slug flows

NASA Astrophysics Data System (ADS)

Krasnopolsky, Boris I.; Lukyanov, Alexander A.

2018-02-01

An accurate and predictive modelling of slug flows is required by many industries (e.g., oil and gas, nuclear engineering, chemical engineering) to prevent undesired events potentially leading to serious environmental accidents. For example, the hydrodynamic and terrain-induced slugging leads to unwanted unsteady flow conditions. This demands the development of fast and robust numerical techniques for predicting slug flows. The presented in this paper study proposes a multi-fluid model and its implementation method accounting for phase appearance and disappearance. The numerical modelling of phase appearance and disappearance presents a complex numerical challenge for all multi-component and multi-fluid models. Numerical challenges arise from the singular systems of equations when some phases are absent and from the solution discontinuity when some phases appear or disappear. This paper provides a flexible and robust solution to these issues. A fully implicit formulation described in this work enables to efficiently solve governing fluid flow equations. The proposed numerical method provides a modelling capability of phase appearance and disappearance processes, which is based on switching procedure between various sets of governing equations. These sets of equations are constructed using information about the number of phases present in the computational domain. The proposed scheme does not require an explicit truncation of solutions leading to a conservative scheme for mass and linear momentum. A transient two-fluid model is used to verify and validate the proposed algorithm for conditions of hydrodynamic and terrain-induced slug flow regimes. The developed modelling capabilities allow to predict all the major features of the experimental data, and are in a good quantitative agreement with them.

An axisymmetric analog two-layer convective heating procedure with application to the evaluation of Space Shuttle Orbiter wing leading edge and windward surface heating

NASA Technical Reports Server (NTRS)

Wang, K. C.

1994-01-01

A numerical procedure for predicting the convective heating rate of hypersonic reentry vehicles is described. The procedure, which is based on the axisymmetric analog, consists of obtaining the three-dimensional inviscid flowfield solution; then the surface streamlines and metrics are calculated using the inviscid velocity components on the surface; finally, an axisymmetric boundary layer code or approximate convective heating equations are used to evaluate heating rates. This approach yields heating predictions to general three-dimensional body shapes. The procedure has been applied to the prediction of the wing leading edge heating to the Space Shuttle Orbiter. The numerical results are compared with the results of heat transfer testing (OH66) of an 0.025 scale model of the Space Shuttle Orbiter configuration in the Calspan Hypersonic Shock Tunnel (HST) at Mach 10 and angles of attack of 30 and 40 degrees. Comparisons with STS-5 flight data at Mach 9.15 and angle of attack of 37.4 degrees and STS-2 flight data at Mach 12.86 and angle of attack of 39.7 degrees are also given.

Finite element solution of optimal control problems with inequality constraints

NASA Technical Reports Server (NTRS)

Bless, Robert R.; Hodges, Dewey H.

1990-01-01

A finite-element method based on a weak Hamiltonian form of the necessary conditions is summarized for optimal control problems. Very crude shape functions (so simple that element numerical quadrature is not necessary) can be used to develop an efficient procedure for obtaining candidate solutions (i.e., those which satisfy all the necessary conditions) even for highly nonlinear problems. An extension of the formulation allowing for discontinuities in the states and derivatives of the states is given. A theory that includes control inequality constraints is fully developed. An advanced launch vehicle (ALV) model is presented. The model involves staging and control constraints, thus demonstrating the full power of the weak formulation to date. Numerical results are presented along with total elapsed computer time required to obtain the results. The speed and accuracy in obtaining the results make this method a strong candidate for a real-time guidance algorithm.

Computer model of two-dimensional solute transport and dispersion in ground water

USGS Publications Warehouse

Konikow, Leonard F.; Bredehoeft, J.D.

1978-01-01

This report presents a model that simulates solute transport in flowing ground water. The model is both general and flexible in that it can be applied to a wide range of problem types. It is applicable to one- or two-dimensional problems involving steady-state or transient flow. The model computes changes in concentration over time caused by the processes of convective transport, hydrodynamic dispersion, and mixing (or dilution) from fluid sources. The model assumes that the solute is non-reactive and that gradients of fluid density, viscosity, and temperature do not affect the velocity distribution. However, the aquifer may be heterogeneous and (or) anisotropic. The model couples the ground-water flow equation with the solute-transport equation. The digital computer program uses an alternating-direction implicit procedure to solve a finite-difference approximation to the ground-water flow equation, and it uses the method of characteristics to solve the solute-transport equation. The latter uses a particle- tracking procedure to represent convective transport and a two-step explicit procedure to solve a finite-difference equation that describes the effects of hydrodynamic dispersion, fluid sources and sinks, and divergence of velocity. This explicit procedure has several stability criteria, but the consequent time-step limitations are automatically determined by the program. The report includes a listing of the computer program, which is written in FORTRAN IV and contains about 2,000 lines. The model is based on a rectangular, block-centered, finite difference grid. It allows the specification of any number of injection or withdrawal wells and of spatially varying diffuse recharge or discharge, saturated thickness, transmissivity, boundary conditions, and initial heads and concentrations. The program also permits the designation of up to five nodes as observation points, for which a summary table of head and concentration versus time is printed at the end of the calculations. The data input formats for the model require three data cards and from seven to nine data sets to describe the aquifer properties, boundaries, and stresses. The accuracy of the model was evaluated for two idealized problems for which analytical solutions could be obtained. In the case of one-dimensional flow the agreement was nearly exact, but in the case of plane radial flow a small amount of numerical dispersion occurred. An analysis of several test problems indicates that the error in the mass balance will be generally less than 10 percent. The test problems demonstrated that the accuracy and precision of the numerical solution is sensitive to the initial number of particles placed in each cell and to the size of the time increment, as determined by the stability criteria. Mass balance errors are commonly the greatest during the first several time increments, but tend to decrease and stabilize with time.

Numerical procedures for the calculation of the stresses in monocoques III : calculation of the bending moments in fuselage frames

NASA Technical Reports Server (NTRS)

Hoff, N J; Libby, Paul A; Klein, Bertran

1946-01-01

This report deals with the calculation of the bending moments in and the distortions of fuselage rings upon which known concentrated and distributed loads are acting. In the procedure suggested, the ring is divided into a number of beams each having a constant radius of curvature. The forces and moments caused in the end sections of the beams by individual unit displacements of the end sections are listed in a table designated as the operations table in conformity with Southwell's nomenclature. The operations table and the external loads are equivalent to a set of linear equations. For their solution the following three procedures are presented: 1) Southwell's method of systematic relaxations. This is a step-by-step approximation procedure guided by the physical interpretation of the changes in the values of the unknown. 2) The growing unit procedure in which the individual beams are combined successively into beams of increasing length until finally the entire ring becomes a single beam. In each step of the procedure a set of not more than three simultaneous linear equations is solved. 3) Solution of the entire set of simultaneous equations by the methods of the matrix calculus. In order to demonstrate the manner in which the calculations may be carried out, the following numerical examples are worked out: 1) Curved beam with both its end sections rigidly fixed. The load is a concentrated force. 2) Egg-shape ring with symmetric concentrated loads. 3) Circular ring with antisymmetric concentrated loads and shear flow (torsion of the fuselage). 4) Same with V-braces incorporated in the ring. 5) Egg-shape ring with antisymmetric concentrated loads and shear flow (torsion of the fuselage). 6) Same with V-braces incorporated in the ring. The results of these calculations are checked, whenever possible, by calculations carried out according to known methods of analysis. The agreement is found to be good. The amount of work necessary for the solution of ring problems by the methods described in the present report is practically independent of the degree of redundancy of the structure. For this reason the methods are recommended for use particularly in problems of rings having one or more internal bracing elements.

A new procedure for investigating three-dimensional stress fields in a thin plate with a through-the-thickness crack

NASA Astrophysics Data System (ADS)

Yi, Dake; Wang, TzuChiang

2018-06-01

In the paper, a new procedure is proposed to investigate three-dimensional fracture problems of a thin elastic plate with a long through-the-thickness crack under remote uniform tensile loading. The new procedure includes a new analytical method and high accurate finite element simulations. In the part of theoretical analysis, three-dimensional Maxwell stress functions are employed in order to derive three-dimensional crack tip fields. Based on the theoretical analysis, an equation which can describe the relationship among the three-dimensional J-integral J( z), the stress intensity factor K( z) and the tri-axial stress constraint level T z ( z) is derived first. In the part of finite element simulations, a fine mesh including 153360 elements is constructed to compute the stress field near the crack front, J( z) and T z ( z). Numerical results show that in the plane very close to the free surface, the K field solution is still valid for in-plane stresses. Comparison with the numerical results shows that the analytical results are valid.

A scaling procedure for the response of an isolated system with high modal overlap factor

NASA Astrophysics Data System (ADS)

De Rosa, S.; Franco, F.

2008-10-01

The paper deals with a numerical approach that reduces some physical sizes of the solution domain to compute the dynamic response of an isolated system: it has been named Asymptotical Scaled Modal Analysis (ASMA). The proposed numerical procedure alters the input data needed to obtain the classic modal responses to increase the frequency band of validity of the discrete or continuous coordinates model through the definition of a proper scaling coefficient. It is demonstrated that the computational cost remains acceptable while the frequency range of analysis increases. Moreover, with reference to the flexural vibrations of a rectangular plate, the paper discusses the ASMA vs. the statistical energy analysis and the energy distribution approach. Some insights are also given about the limits of the scaling coefficient. Finally it is shown that the linear dynamic response, predicted with the scaling procedure, has the same quality and characteristics of the statistical energy analysis, but it can be useful when the system cannot be solved appropriately by the standard Statistical Energy Analysis (SEA).

Direct Reconstruction of Two-Dimensional Currents in Thin Films from Magnetic-Field Measurements

NASA Astrophysics Data System (ADS)

Meltzer, Alexander Y.; Levin, Eitan; Zeldov, Eli

2017-12-01

An accurate determination of microscopic transport and magnetization currents is of central importance for the study of the electric properties of low-dimensional materials and interfaces, of superconducting thin films, and of electronic devices. Current distribution is usually derived from the measurement of the perpendicular component of the magnetic field above the surface of the sample, followed by numerical inversion of the Biot-Savart law. The inversion is commonly obtained by deriving the current stream function g , which is then differentiated in order to obtain the current distribution. However, this two-step procedure requires filtering at each step and, as a result, oversmooths the solution. To avoid this oversmoothing, we develop a direct procedure for inversion of the magnetic field that avoids use of the stream function. This approach provides enhanced accuracy of current reconstruction over a wide range of noise levels. We further introduce a reflection procedure that allows for the reconstruction of currents that cross the boundaries of the measurement window. The effectiveness of our approach is demonstrated by several numerical examples.

Navier-Stokes and viscous-inviscid interaction

NASA Technical Reports Server (NTRS)

Steger, Joseph L.; Vandalsem, William R.

1989-01-01

Some considerations toward developing numerical procedures for simulating viscous compressible flows are discussed. Both Navier-Stokes and boundary layer field methods are considered. Because efficient viscous-inviscid interaction methods have been difficult to extend to complex 3-D flow simulations, Navier-Stokes procedures are more frequently being utilized even though they require considerably more work per grid point. It would seem a mistake, however, not to make use of the more efficient approximate methods in those regions in which they are clearly valid. Ideally, a general purpose compressible flow solver that can optionally take advantage of approximate solution methods would suffice, both to improve accuracy and efficiency. Some potentially useful steps toward this goal are described: a generalized 3-D boundary layer formulation and the fortified Navier-Stokes procedure.

Strain-Based Damage Determination Using Finite Element Analysis for Structural Health Management

NASA Technical Reports Server (NTRS)

Hochhalter, Jacob D.; Krishnamurthy, Thiagaraja; Aguilo, Miguel A.

2016-01-01

A damage determination method is presented that relies on in-service strain sensor measurements. The method employs a gradient-based optimization procedure combined with the finite element method for solution to the forward problem. It is demonstrated that strains, measured at a limited number of sensors, can be used to accurately determine the location, size, and orientation of damage. Numerical examples are presented to demonstrate the general procedure. This work is motivated by the need to provide structural health management systems with a real-time damage characterization. The damage cases investigated herein are characteristic of point-source damage, which can attain critical size during flight. The procedure described can be used to provide prognosis tools with the current damage configuration.

Eigenproblem solution by a combined Sturm sequence and inverse iteration technique.

NASA Technical Reports Server (NTRS)

Gupta, K. K.

1973-01-01

Description of an efficient and numerically stable algorithm, along with a complete listing of the associated computer program, developed for the accurate computation of specified roots and associated vectors of the eigenvalue problem Aq = lambda Bq with band symmetric A and B, B being also positive-definite. The desired roots are first isolated by the Sturm sequence procedure; then a special variant of the inverse iteration technique is applied for the individual determination of each root along with its vector. The algorithm fully exploits the banded form of relevant matrices, and the associated program written in FORTRAN V for the JPL UNIVAC 1108 computer proves to be most significantly economical in comparison to similar existing procedures. The program may be conveniently utilized for the efficient solution of practical engineering problems, involving free vibration and buckling analysis of structures. Results of such analyses are presented for representative structures.

Investigation of aerodynamic characteristics of subsonic wings

NASA Technical Reports Server (NTRS)

Dejarnette, F. R.; Frink, N. T.

1979-01-01

An analytical strake design procedure is investigated. A numerical solution to the governing strake design equation is used to generate a series of strakes which are tested in a water tunnel to study their vortex breakdown characteristics. The strakes are scaled for use on a half-scale model of the NASA-LaRC general research fuselage with a 44 degrees trapezoidal wing. An analytical solution to the governing design equation is obtained. The strake design procedure relates the potential-flow leading-edge suction and pressure distributions to vortex stability. Several suction distributions are studied and those which are more triangular and peak near the tip generate strakes that reach higher angles of attack before vortex breakdown occurs at the wing trailing edge. For the same suction distribution, a conical rather than three dimensional pressure specification results in a better strake shape as judged from its vortex breakdown characteristics.

Elastohydrodynamic lubrication of point contacts. Ph.D. Thesis - Leeds Univ.

NASA Technical Reports Server (NTRS)

Hamrock, B. J.

1976-01-01

A procedure for the numerical solution of the complete, isothermal, elastohydrodynamic lubrication problem for point contacts is given. This procedure calls for the simultaneous solution of the elasticity and Reynolds equations. By using this theory the influence of the ellipticity parameter and the dimensionless speed, load, and material parameters on the minimum and central film thicknesses was investigated. Thirty-four different cases were used in obtaining the fully flooded minimum- and central-film-thickness formulas. Lubricant starvation was also studied. From the results it was possible to express the minimum film thickness for a starved condition in terms of the minimum film thickness for a fully flooded condition, the speed parameter, and the inlet distance. Fifteen additional cases plus three fully flooded cases were used in obtaining this formula. Contour plots of pressure and film thickness in and around the contact have been presented for both fully flooded and starved lubrication 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.

HYDRA-II: A hydrothermal analysis computer code: Volume 3, Verification/validation assessments

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

McCann, R.A.; Lowery, P.S.

1987-10-01

HYDRA-II is a hydrothermal computer code capable of three-dimensional analysis of coupled conduction, convection, and thermal radiation problems. This code is especially appropriate for simulating the steady-state performance of spent fuel storage systems. The code has been evaluated for this application for the US Department of Energy's Commercial Spent Fuel Management Program. HYDRA-II provides a finite difference solution in cartesian coordinates to the equations governing the conservation of mass, momentum, and energy. A cylindrical coordinate system may also be used to enclose the cartesian coordinate system. This exterior coordinate system is useful for modeling cylindrical cask bodies. The difference equationsmore » for conservation of momentum are enhanced by the incorporation of directional porosities and permeabilities that aid in modeling solid structures whose dimensions may be smaller than the computational mesh. The equation for conservation of energy permits modeling of orthotropic physical properties and film resistances. Several automated procedures are available to model radiation transfer within enclosures and from fuel rod to fuel rod. The documentation of HYDRA-II is presented in three separate volumes. Volume I - Equations and Numerics describes the basic differential equations, illustrates how the difference equations are formulated, and gives the solution procedures employed. Volume II - User's Manual contains code flow charts, discusses the code structure, provides detailed instructions for preparing an input file, and illustrates the operation of the code by means of a model problem. This volume, Volume III - Verification/Validation Assessments, provides a comparison between the analytical solution and the numerical simulation for problems with a known solution. This volume also documents comparisons between the results of simulations of single- and multiassembly storage systems and actual experimental data. 11 refs., 55 figs., 13 tabs.« less

A new and inexpensive non-bit-for-bit solution reproducibility test based on time step convergence (TSC1.0)

DOE PAGES

Wan, Hui; Zhang, Kai; Rasch, Philip J.; ...

2017-02-03

A test procedure is proposed for identifying numerically significant solution changes in evolution equations used in atmospheric models. The test issues a fail signal when any code modifications or computing environment changes lead to solution differences that exceed the known time step sensitivity of the reference model. Initial evidence is provided using the Community Atmosphere Model (CAM) version 5.3 that the proposed procedure can be used to distinguish rounding-level solution changes from impacts of compiler optimization or parameter perturbation, which are known to cause substantial differences in the simulated climate. The test is not exhaustive since it does not detect issues associatedmore » with diagnostic calculations that do not feedback to the model state variables. Nevertheless, it provides a practical and objective way to assess the significance of solution changes. The short simulation length implies low computational cost. The independence between ensemble members allows for parallel execution of all simulations, thus facilitating fast turnaround. The new method is simple to implement since it does not require any code modifications. We expect that the same methodology can be used for any geophysical model to which the concept of time step  convergence is applicable.« less

Propagation of singularities for linearised hybrid data impedance tomography

NASA Astrophysics Data System (ADS)

Bal, Guillaume; Hoffmann, Kristoffer; Knudsen, Kim

2018-02-01

For a general formulation of linearised hybrid inverse problems in impedance tomography, the qualitative properties of the solutions are analysed. Using an appropriate scalar pseudo-differential formulation, the problems are shown to permit propagating singularities under certain non-elliptic conditions, and the associated directions of propagation are precisely identified relative to the directions in which ellipticity is lost. The same result is found in the setting for the corresponding normal formulation of the scalar pseudo-differential equations. A numerical reconstruction procedure based of the least squares finite element method is derived, and a series of numerical experiments visualise exactly how the loss of ellipticity manifests itself as propagating singularities.

Solving a Multi Objective Transportation Problem(MOTP) Under Fuzziness on Using Interval Numbers

NASA Astrophysics Data System (ADS)

Saraj, Mansour; Mashkoorzadeh, Feryal

2010-09-01

In this paper we present a solution procedure of the Multi Objective Transportation Problem(MOTP) where the coefficients of the objective functions, the source and destination parameters which determined by the decision maker(DM) are symmetric triangular fuzzy numbers. The constraints with interval source and destination parameters have been converted in to deterministic ones. A numerical example is provided to illustrate the approach.

Tension Cutoff and Parameter Identification for the Viscoplastic Cap Model.

DTIC Science & Technology

1983-04-01

computer program "VPDRVR" which employs a Crank-Nicolson time integration scheme and a Newton-Raphson iterative solution procedure. Numerical studies were...parameters was illustrated for triaxial stress and uniaxial strain loading for a well- studied sand material (McCormick Ranch Sand). Lastly, a finite element...viscoplastic tension-cutoff cri- terion and to establish parameter identification techniques with experimental data. Herein lies the impetus of this study

Updates to Simulation of a Single-Element Lean-Direct Injection Combustor Using Arbitary Polyhedral Meshes

NASA Technical Reports Server (NTRS)

Wey, Thomas; Liu, Nan-Suey

2015-01-01

This paper summarizes the procedures of (1) generating control volumes anchored at the nodes of a mesh; and (2) generating staggered control volumes via mesh reconstructions, in terms of either mesh realignment or mesh refinement, as well as presents sample results from their applications to the numerical solution of a single-element LDI combustor using a releasable edition of the National Combustion Code (NCC).

Summation-by-Parts operators with minimal dispersion error for coarse grid flow calculations

NASA Astrophysics Data System (ADS)

Linders, Viktor; Kupiainen, Marco; Nordström, Jan

2017-07-01

We present a procedure for constructing Summation-by-Parts operators with minimal dispersion error both near and far from numerical interfaces. Examples of such operators are constructed and compared with a higher order non-optimised Summation-by-Parts operator. Experiments show that the optimised operators are superior for wave propagation and turbulent flows involving large wavenumbers, long solution times and large ranges of resolution scales.

LSENS: A General Chemical Kinetics and Sensitivity Analysis Code for homogeneous gas-phase reactions. Part 1: Theory and numerical solution procedures

NASA Technical Reports Server (NTRS)

Radhakrishnan, Krishnan

1994-01-01

LSENS, the Lewis General Chemical Kinetics and Sensitivity Analysis Code, has been developed for solving complex, homogeneous, gas-phase chemical kinetics problems and contains sensitivity analysis for a variety of problems, including nonisothermal situations. This report is part 1 of a series of three reference publications that describe LENS, provide a detailed guide to its usage, and present many example problems. Part 1 derives the governing equations and describes the numerical solution procedures for the types of problems that can be solved. The accuracy and efficiency of LSENS are examined by means of various test problems, and comparisons with other methods and codes are presented. LSENS is a flexible, convenient, accurate, and efficient solver for chemical reaction problems such as static system; steady, one-dimensional, inviscid flow; reaction behind incident shock wave, including boundary layer correction; and perfectly stirred (highly backmixed) reactor. In addition, the chemical equilibrium state can be computed for the following assigned states: temperature and pressure, enthalpy and pressure, temperature and volume, and internal energy and volume. For static problems the code computes the sensitivity coefficients of the dependent variables and their temporal derivatives with respect to the initial values of the dependent variables and/or the three rate coefficient parameters of the chemical reactions.

From stochastic processes to numerical methods: A new scheme for solving reaction subdiffusion fractional partial differential equations

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

Angstmann, C.N.; Donnelly, I.C.; Henry, B.I., E-mail: B.Henry@unsw.edu.au

We have introduced a new explicit numerical method, based on a discrete stochastic process, for solving a class of fractional partial differential equations that model reaction subdiffusion. The scheme is derived from the master equations for the evolution of the probability density of a sum of discrete time random walks. We show that the diffusion limit of the master equations recovers the fractional partial differential equation of interest. This limiting procedure guarantees the consistency of the numerical scheme. The positivity of the solution and stability results are simply obtained, provided that the underlying process is well posed. We also showmore » that the method can be applied to standard reaction–diffusion equations. This work highlights the broader applicability of using discrete stochastic processes to provide numerical schemes for partial differential equations, including fractional partial differential equations.« less

Conformal Infinity.

PubMed

Frauendiener, Jörg

2004-01-01

The notion of conformal infinity has a long history within the research in Einstein's theory of gravity. Today, "conformal infinity" is related to almost all other branches of research in general relativity, from quantisation procedures to abstract mathematical issues to numerical applications. This review article attempts to show how this concept gradually and inevitably evolved from physical issues, namely the need to understand gravitational radiation and isolated systems within the theory of gravitation, and how it lends itself very naturally to the solution of radiation problems in numerical relativity. The fundamental concept of null-infinity is introduced. Friedrich's regular conformal field equations are presented and various initial value problems for them are discussed. Finally, it is shown that the conformal field equations provide a very powerful method within numerical relativity to study global problems such as gravitational wave propagation and detection.

Temperature and solute-transport simulation in streamflow using a Lagrangian reference frame

USGS Publications Warehouse

Jobson, Harvey E.

1980-01-01

A computer program for simulating one-dimensional, unsteady temperature and solute transport in a river has been developed and documented for general use. The solution approach to the convective-diffusion equation uses a moving reference frame (Lagrangian) which greatly simplifies the mathematics of the solution procedure and dramatically reduces errors caused by numerical dispersion. The model documentation is presented as a series of four programs of increasing complexity. The conservative transport model can be used to route a single conservative substance. The simplified temperature model is used to predict water temperature in rivers when only temperature and windspeed data are available. The complete temperature model is highly accurate but requires rather complete meteorological data. Finally, the 10-parameter model can be used to route as many as 10 interacting constituents through a river reach. (USGS)

A new solution procedure for a nonlinear infinite beam equation of motion

NASA Astrophysics Data System (ADS)

Jang, T. S.

2016-10-01

Our goal of this paper is of a purely theoretical question, however which would be fundamental in computational partial differential equations: Can a linear solution-structure for the equation of motion for an infinite nonlinear beam be directly manipulated for constructing its nonlinear solution? Here, the equation of motion is modeled as mathematically a fourth-order nonlinear partial differential equation. To answer the question, a pseudo-parameter is firstly introduced to modify the equation of motion. And then, an integral formalism for the modified equation is found here, being taken as a linear solution-structure. It enables us to formulate a nonlinear integral equation of second kind, equivalent to the original equation of motion. The fixed point approach, applied to the integral equation, results in proposing a new iterative solution procedure for constructing the nonlinear solution of the original beam equation of motion, which consists luckily of just the simple regular numerical integration for its iterative process; i.e., it appears to be fairly simple as well as straightforward to apply. A mathematical analysis is carried out on both natures of convergence and uniqueness of the iterative procedure by proving a contractive character of a nonlinear operator. It follows conclusively,therefore, that it would be one of the useful nonlinear strategies for integrating the equation of motion for a nonlinear infinite beam, whereby the preceding question may be answered. In addition, it may be worth noticing that the pseudo-parameter introduced here has double roles; firstly, it connects the original beam equation of motion with the integral equation, second, it is related with the convergence of the iterative method proposed here.

A singularity free analytical solution of artificial satellite motion with drag

NASA Technical Reports Server (NTRS)

Scheifele, G.; Mueller, A. C.; Starke, S. E.

1977-01-01

The connection between the existing Delaunay-Similar and Poincare-Similar satellite theories in the true anomaly version is outlined for the J(2) perturbation and the new drag approach. An overall description of the concept of the approach is given while the necessary expansions and the procedure to arrive at the computer program for the canonical forces is delineated. The procedure for the analytical integration of these developed equations is described. In addition, some numerical results are given. The computer program for the algebraic multiplication of the Fourier series which creates the FORTRAN coding in an automatic manner is described and documented.

Gaussian basis functions for highly oscillatory scattering wavefunctions

NASA Astrophysics Data System (ADS)

Mant, B. P.; Law, M. M.

2018-04-01

We have applied a basis set of distributed Gaussian functions within the S-matrix version of the Kohn variational method to scattering problems involving deep potential energy wells. The Gaussian positions and widths are tailored to the potential using the procedure of Bačić and Light (1986 J. Chem. Phys. 85 4594) which has previously been applied to bound-state problems. The placement procedure is shown to be very efficient and gives scattering wavefunctions and observables in agreement with direct numerical solutions. We demonstrate the basis function placement method with applications to hydrogen atom–hydrogen atom scattering and antihydrogen atom–hydrogen atom scattering.

A numerical performance assessment of a commercial cardiopulmonary by-pass blood heat exchanger.

PubMed

Consolo, Filippo; Fiore, Gianfranco B; Pelosi, Alessandra; Reggiani, Stefano; Redaelli, Alberto

2015-06-01

We developed a numerical model, based on multi-physics computational fluid dynamics (CFD) simulations, to assist the design process of a plastic hollow-fiber bundle blood heat exchanger (BHE) integrated within the INSPIRE(TM), a blood oxygenator (OXY) for cardiopulmonary by-pass procedures, recently released by Sorin Group Italia. In a comparative study, we analyzed five different geometrical design solutions of the BHE module. Quantitative geometrical-dependent parameters providing a comprehensive evaluation of both the hemo- and thermo-dynamics performance of the device were extracted to identify the best-performing prototypical solution. A convenient design configuration was identified, characterized by (i) a uniform blood flow pattern within the fiber bundle, preventing blood flow shunting and the onset of stagnation/recirculation areas and/or high velocity pathways, (ii) an enhanced blood heating efficiency, and (iii) a reduced blood pressure drop. The selected design configuration was then prototyped and tested to experimentally characterize the device performance. Experimental results confirmed numerical predictions, proving the effectiveness of CFD modeling as a reliable tool for in silico identification of suitable working conditions of blood handling medical devices. Notably, the numerical approach limited the need for extensive prototyping, thus reducing the corresponding machinery costs and time-to-market. Copyright © 2015 IPEM. Published by Elsevier Ltd. All rights reserved.

Self-adaptive difference method for the effective solution of computationally complex problems of boundary layer theory

NASA Technical Reports Server (NTRS)

Schoenauer, W.; Daeubler, H. G.; Glotz, G.; Gruening, J.

1986-01-01

An implicit difference procedure for the solution of equations for a chemically reacting hypersonic boundary layer is described. Difference forms of arbitrary error order in the x and y coordinate plane were used to derive estimates for discretization error. Computational complexity and time were minimized by the use of this difference method and the iteration of the nonlinear boundary layer equations was regulated by discretization error. Velocity and temperature profiles are presented for Mach 20.14 and Mach 18.5; variables are velocity profiles, temperature profiles, mass flow factor, Stanton number, and friction drag coefficient; three figures include numeric data.

Laminar supersonic flow over a backstep - A numerical solution at higher Reynolds numbers

NASA Technical Reports Server (NTRS)

Kronzon, Y.; Rom, J.; Seginer, A.

1976-01-01

The Allen-Cheng solution of the flow over a backward facing step is extended to Reynolds numbers up to 16,000 and to inflow boundary-layer height ratios as low as 0.1 by moving the downstream boundary into the recompression region and by smoothing the resulting errors. The boundary conditions in the supersonic outer flow and the downstream boundary conditions in the wake are determined by an extrapolation procedure. Computational results are compared with relevant experimental data. Fair agreement is found between the calculated base pressures and the experimental values, whereas agreement between heat transfer rates appears to be qualitative only.

The Hartree-Fock calculation of the magnetic properties of molecular solutes

NASA Astrophysics Data System (ADS)

Cammi, R.

1998-08-01

In this paper we set the formal bases for the calculation of the magnetic susceptibility and of the nuclear magnetic shielding tensors for molecular solutes described within the framework of the polarizable continuum model (PCM). The theory has been developed at self-consistent field (SCF) level and adapted to be used within the framework of some of the computational procedures of larger use, i.e., the gauge invariant atomic orbital method (GIAO) and the continuous set gauge transformation method (CSGT). The numerical results relative to the magnetizabilities and chemical shielding of acetonitrile and nitrometane in various solvents computed with the PCM-CSGT method are also presented.

Analytic solution for quasi-Lambertian radiation transfer.

PubMed

Braun, Avi; Gordon, Jeffrey M

2010-02-10

An analytic solution is derived for radiation transfer between flat quasi-Lambertian surfaces of arbitrary orientation, i.e., surfaces that radiate in a Lambertian fashion but within a numerical aperture smaller than unity. These formulas obviate the need for ray trace simulations and provide exact, physically transparent results. Illustrative examples that capture the salient features of the flux maps and the efficiency of flux transfer are presented for a few configurations of practical interest. There is also a fundamental reciprocity relation for quasi-Lambertian exchange, akin to the reciprocity theorem for fully Lambertian surfaces. Applications include optical fiber coupling, fiber-optic biomedical procedures, and solar concentrators.

Revealing Numerical Solutions of a Differential Equation

ERIC Educational Resources Information Center

Glaister, P.

2006-01-01

In this article, the author considers a student exercise that involves determining the exact and numerical solutions of a particular differential equation. He shows how a typical student solution is at variance with a numerical solution, suggesting that the numerical solution is incorrect. However, further investigation shows that this numerical…

Numerical Investigation of Hot Gas Ingestion by STOVL Aircraft

NASA Technical Reports Server (NTRS)

Vanka, S. P.

1998-01-01

This report compiles the various research activities conducted under the auspices of the NASA Grant NAG3-1026, "Numerical Investigation of Hot Gas Ingestion by STOVL Aircraft" during the period of April 1989 to April 1994. The effort involved the development of multigrid based algorithms and computer programs for the calculation of the flow and temperature fields generated by Short Take-off and Vertical Landing (STOVL) aircraft, while hovering in ground proximity. Of particular importance has been the interaction of the exhaust jets with the head wind which gives rise to the hot gas ingestion process. The objective of new STOVL designs to reduce the temperature of the gases ingested into the engine. The present work describes a solution algorithm for the multi-dimensional elliptic partial-differential equations governing fluid flow and heat transfer in general curvilinear coordinates. The solution algorithm is based on the multigrid technique which obtains rapid convergence of the iterative numerical procedure for the discrete equations. Initial efforts were concerned with the solution of the Cartesian form of the equations. This algorithm was applied to a simulated STOVL configuration in rectangular coordinates. In the next phase of the work, a computer code for general curvilinear coordinates was constructed. This was applied to model STOVL geometries on curvilinear grids. The code was also validated in model problems. In all these efforts, the standard k-Epsilon model was used.

BRYNTRN: A baryon transport computer code, computation procedures and data base

NASA Technical Reports Server (NTRS)

Wilson, John W.; Townsend, Lawrence W.; Chun, Sang Y.; Buck, Warren W.; Khan, Ferdous; Cucinotta, Frank

1988-01-01

The development is described of an interaction data base and a numerical solution to the transport of baryons through the arbitrary shield material based on a straight ahead approximation of the Boltzmann equation. The code is most accurate for continuous energy boundary values but gives reasonable results for discrete spectra at the boundary with even a relatively coarse energy grid (30 points) and large spatial increments (1 cm in H2O).

Lattice Boltzmann approach for complex nonequilibrium flows.

PubMed

Montessori, A; Prestininzi, P; La Rocca, M; Succi, S

2015-10-01

We present a lattice Boltzmann realization of Grad's extended hydrodynamic approach to nonequilibrium flows. This is achieved by using higher-order isotropic lattices coupled with a higher-order regularization procedure. The method is assessed for flow across parallel plates and three-dimensional flows in porous media, showing excellent agreement of the mass flow with analytical and numerical solutions of the Boltzmann equation across the full range of Knudsen numbers, from the hydrodynamic regime to ballistic motion.

Development of numerical techniques for simulation of magnetogasdynamics and hypersonic chemistry

NASA Astrophysics Data System (ADS)

Damevin, Henri-Marie

Magnetogasdynamics, the science concerned with the mutual interaction between electromagnetic field and flow of electrically conducting gas, offers promising advances in flow control and propulsion of future hypersonic vehicles. Numerical simulations are essential for understanding phenomena, and for research and development. The current dissertation is devoted to the development and validation of numerical algorithms for the solution of multidimensional magnetogasdynamic equations and the simulation of hypersonic high-temperature effects. Governing equations are derived, based on classical magnetogasdynamic assumptions. Two sets of equations are considered, namely the full equations and equations in the low magnetic Reynolds number approximation. Equations are expressed in a suitable formulation for discretization by finite differences in a computational space. For the full equations, Gauss law for magnetism is enforced using Powell's methodology. The time integration method is a four-stage modified Runge-Kutta scheme, amended with a Total Variation Diminishing model in a postprocessing stage. The eigensystem, required for the Total Variation Diminishing scheme, is derived in generalized three-dimensional coordinate system. For the simulation of hypersonic high-temperature effects, two chemical models are utilized, namely a nonequilibrium model and an equilibrium model. A loosely coupled approach is implemented to communicate between the magnetogasdynamic equations and the chemical models. The nonequilibrium model is a one-temperature, five-species, seventeen-reaction model solved by an implicit flux-vector splitting scheme. The chemical equilibrium model computes thermodynamics properties using curve fit procedures. Selected results are provided, which explore the different features of the numerical algorithms. The shock-capturing properties are validated for shock-tube simulations using numerical solutions reported in the literature. The computations of superfast flows over corners and in convergent channels demonstrate the performances of the algorithm in multiple dimensions. The implementation of diffusion terms is validated by solving the magnetic Rayleigh problem and Hartmann problem, for which analytical solutions are available. Prediction of blunt-body type flow are investigated and compared with numerical solutions reported in the literature. The effectiveness of the chemical models for hypersonic flow over blunt body is examined in various flow conditions. It is shown that the proposed schemes perform well in a variety of test cases, though some limitations have been identified.

Proton pump inhibitor-refractory gastroesophageal reflux disease: challenges and solutions

PubMed Central

Mermelstein, Joseph; Chait Mermelstein, Alanna; Chait, Maxwell M

2018-01-01

A significant percentage of patients with gastroesophageal reflux disease (GERD) will not respond to proton pump inhibitor (PPI) therapy. The causes of PPI-refractory GERD are numerous and diverse, and include adherence, persistent acid, functional disorders, nonacid reflux, and PPI bioavailability. The evaluation should start with a symptom assessment and may progress to imaging, endoscopy, and monitoring of esophageal pH, impedance, and bilirubin. There are a variety of pharmacologic and procedural interventions that should be selected based on the underlying mechanism of PPI failure. Pharmacologic treatments can include antacids, prokinetics, alginates, bile acid binders, reflux inhibitors, and antidepressants. Procedural options include laparoscopic fundoplication and LINX as well as endoscopic procedures, such as transoral incisionless fundoplication and Stretta. Several alternative and complementary treatments of possible benefit also exist. PMID:29606884

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.

Numerical Asymptotic Solutions Of Differential Equations

NASA Technical Reports Server (NTRS)

Thurston, Gaylen A.

1992-01-01

Numerical algorithms derived and compared with classical analytical methods. In method, expansions replaced with integrals evaluated numerically. Resulting numerical solutions retain linear independence, main advantage of asymptotic solutions.

Benchmark Results Of Active Tracer Particles In The Open Souce Code ASPECT For Modelling Convection In The Earth's Mantle

NASA Astrophysics Data System (ADS)

Jiang, J.; Kaloti, A. P.; Levinson, H. R.; Nguyen, N.; Puckett, E. G.; Lokavarapu, H. V.

2016-12-01

We present the results of three standard benchmarks for the new active tracer particle algorithm in ASPECT. The three benchmarks are SolKz, SolCx, and SolVI (also known as the 'inclusion benchmark') first proposed by Duretz, May, Gerya, and Tackley (G Cubed, 2011) and in subsequent work by Theilman, May, and Kaus (Pure and Applied Geophysics, 2014). Each of the three benchmarks compares the accuracy of the numerical solution to a steady (time-independent) solution of the incompressible Stokes equations with a known exact solution. These benchmarks are specifically designed to test the accuracy and effectiveness of the numerical method when the viscosity varies up to six orders of magnitude. ASPECT has been shown to converge to the exact solution of each of these benchmarks at the correct design rate when all of the flow variables, including the density and viscosity, are discretized on the underlying finite element grid (Krobichler, Heister, and Bangerth, GJI, 2012). In our work we discretize the density and viscosity by initially placing the true values of the density and viscosity at the intial particle positions. At each time step, including the initialization step, the density and viscosity are interpolated from the particles onto the finite element grid. The resulting Stokes system is solved for the velocity and pressure, and the particle positions are advanced in time according to this new, numerical, velocity field. Note that this procedure effectively changes a steady solution of the Stokes equaton (i.e., one that is independent of time) to a solution of the Stokes equations that is time dependent. Furthermore, the accuracy of the active tracer particle algorithm now also depends on the accuracy of the interpolation algorithm and of the numerical method one uses to advance the particle positions in time. Finally, we will present new interpolation algorithms designed to increase the overall accuracy of the active tracer algorithms in ASPECT and interpolation algotithms designed to conserve properties, such as mass density, that are being carried by the particles.

Compliance matrices for cracked bodies

NASA Technical Reports Server (NTRS)

Ballarini, R.

1986-01-01

An algorithm is developed to construct the compliance matrix for a cracked solid in the integral-equation formulation of two-dimensional linear-elastic fracture mechanics. The integral equation is reduced to a system of algebraic equations for unknown values of the dislocation-density function at discrete points on the interval from -1 to 1, using the numerical procedure described by Gerasoulis (1982). Sample numerical results are presented, and it is suggested that the algorithm is especially useful in cases where iterative solutions are required; e.g., models of fiber-reinforced concrete, rocks, or ceramics where microcracking, fiber bridging, and other nonlinear effects are treated as nonlinear springs along the crack surfaces (Ballarini et al., 1984).

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.

Task 7: ADPAC User's Manual

NASA Technical Reports Server (NTRS)

Hall, E. J.; Topp, D. A.; Delaney, R. A.

1996-01-01

The overall objective of this study was to develop a 3-D numerical analysis for compressor casing treatment flowfields. The current version of the computer code resulting from this study is referred to as ADPAC (Advanced Ducted Propfan Analysis Codes-Version 7). This report is intended to serve as a computer program user's manual for the ADPAC code developed under Tasks 6 and 7 of the NASA Contract. The ADPAC program is based on a flexible multiple- block grid discretization scheme permitting coupled 2-D/3-D mesh block solutions with application to a wide variety of geometries. Aerodynamic calculations are based on a four-stage Runge-Kutta time-marching finite volume solution technique with added numerical dissipation. Steady flow predictions are accelerated by a multigrid procedure. An iterative implicit algorithm is available for rapid time-dependent flow calculations, and an advanced two equation turbulence model is incorporated to predict complex turbulent flows. The consolidated code generated during this study is capable of executing in either a serial or parallel computing mode from a single source code. Numerous examples are given in the form of test cases to demonstrate the utility of this approach for predicting the aerodynamics of modem turbomachinery configurations.

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.

Solution of 3-dimensional time-dependent viscous flows. Part 3: Application to turbulent and unsteady flows

NASA Technical Reports Server (NTRS)

Weinberg, B. C.; Mcdonald, H.

1982-01-01

A numerical scheme is developed for solving the time dependent, three dimensional compressible viscous flow equations to be used as an aid in the design of helicopter rotors. In order to further investigate the numerical procedure, the computer code developed to solve an approximate form of the three dimensional unsteady Navier-Stokes equations employing a linearized block implicit technique in conjunction with a QR operator scheme is tested. Results of calculations are presented for several two dimensional boundary layer flows including steady turbulent and unsteady laminar cases. A comparison of fourth order and second order solutions indicate that increased accuracy can be obtained without any significant increases in cost (run time). The results of the computations also indicate that the computer code can be applied to more complex flows such as those encountered on rotating airfoils. The geometry of a symmetric NACA four digit airfoil is considered and the appropriate geometrical properties are computed.

A low diffusive Lagrange-remap scheme for the simulation of violent air-water free-surface flows

NASA Astrophysics Data System (ADS)

Bernard-Champmartin, Aude; De Vuyst, Florian

2014-10-01

In 2002, Després and Lagoutière [17] proposed a low-diffusive advection scheme for pure transport equation problems, which is particularly accurate for step-shaped solutions, and thus suited for interface tracking procedure by a color function. This has been extended by Kokh and Lagoutière [28] in the context of compressible multifluid flows using a five-equation model. In this paper, we explore a simplified variant approach for gas-liquid three-equation models. The Eulerian numerical scheme has two ingredients: a robust remapped Lagrange solver for the solution of the volume-averaged equations, and a low diffusive compressive scheme for the advection of the gas mass fraction. Numerical experiments show the performance of the computational approach on various flow reference problems: dam break, sloshing of a tank filled with water, water-water impact and finally a case of Rayleigh-Taylor instability. One of the advantages of the present interface capturing solver is its natural implementation on parallel processors or computers.

Robust numerical solution of the reservoir routing equation

NASA Astrophysics Data System (ADS)

Fiorentini, Marcello; Orlandini, Stefano

2013-09-01

The robustness of numerical methods for the solution of the reservoir routing equation is evaluated. The methods considered in this study are: (1) the Laurenson-Pilgrim method, (2) the fourth-order Runge-Kutta method, and (3) the fixed order Cash-Karp method. Method (1) is unable to handle nonmonotonic outflow rating curves. Method (2) is found to fail under critical conditions occurring, especially at the end of inflow recession limbs, when large time steps (greater than 12 min in this application) are used. Method (3) is computationally intensive and it does not solve the limitations of method (2). The limitations of method (2) can be efficiently overcome by reducing the time step in the critical phases of the simulation so as to ensure that water level remains inside the domains of the storage function and the outflow rating curve. The incorporation of a simple backstepping procedure implementing this control into the method (2) yields a robust and accurate reservoir routing method that can be safely used in distributed time-continuous catchment models.

Computational attributes of the integral form of the equation of transfer

NASA Technical Reports Server (NTRS)

Frankel, J. I.

1991-01-01

Difficulties can arise in radiative and neutron transport calculations when a highly anisotropic scattering phase function is present. In the presence of anisotropy, currently used numerical solutions are based on the integro-differential form of the linearized Boltzmann transport equation. This paper, departs from classical thought and presents an alternative numerical approach based on application of the integral form of the transport equation. Use of the integral formalism facilitates the following steps: a reduction in dimensionality of the system prior to discretization, the use of symbolic manipulation to augment the computational procedure, and the direct determination of key physical quantities which are derivable through the various Legendre moments of the intensity. The approach is developed in the context of radiative heat transfer in a plane-parallel geometry, and results are presented and compared with existing benchmark solutions. Encouraging results are presented to illustrate the potential of the integral formalism for computation. The integral formalism appears to possess several computational attributes which are well-suited to radiative and neutron transport calculations.

Applications of computer algebra to distributed parameter systems

NASA Technical Reports Server (NTRS)

Storch, Joel A.

1993-01-01

In the analysis of vibrations of continuous elastic systems, one often encounters complicated transcendental equations with roots directly related to the system's natural frequencies. Typically, these equations contain system parameters whose values must be specified before a numerical solution can be obtained. The present paper presents a method whereby the fundamental frequency can be obtained in analytical form to any desired degree of accuracy. The method is based upon truncation of rapidly converging series involving inverse powers of the system natural frequencies. A straightforward method to developing these series and summing them in closed form is presented. It is demonstrated how Computer Algebra can be exploited to perform the intricate analytical procedures which otherwise would render the technique difficult to apply in practice. We illustrate the method by developing two analytical approximations to the fundamental frequency of a vibrating cantilever carrying a rigid tip body. The results are compared to the numerical solution of the exact (transcendental) frequency equation over a range of system parameters.

A numerical solution method for acoustic radiation from axisymmetric bodies

NASA Technical Reports Server (NTRS)

Caruthers, John E.; Raviprakash, G. K.

1995-01-01

A new and very efficient numerical method for solving equations of the Helmholtz type is specialized for problems having axisymmetric geometry. It is then demonstrated by application to the classical problem of acoustic radiation from a vibrating piston set in a stationary infinite plane. The method utilizes 'Green's Function Discretization', to obtain an accurate resolution of the waves using only 2-3 points per wave. Locally valid free space Green's functions, used in the discretization step, are obtained by quadrature. Results are computed for a range of grid spacing/piston radius ratios at a frequency parameter, omega R/c(sub 0), of 2 pi. In this case, the minimum required grid resolution appears to be fixed by the need to resolve a step boundary condition at the piston edge rather than by the length scale imposed by the wave length of the acoustic radiation. It is also demonstrated that a local near-field radiation boundary procedure allows the domain to be truncated very near the radiating source with little effect on the solution.

Closed-form solution of decomposable stochastic models

NASA Technical Reports Server (NTRS)

Sjogren, Jon A.

1990-01-01

Markov and semi-Markov processes are increasingly being used in the modeling of complex reconfigurable systems (fault tolerant computers). The estimation of the reliability (or some measure of performance) of the system reduces to solving the process for its state probabilities. Such a model may exhibit numerous states and complicated transition distributions, contributing to an expensive and numerically delicate solution procedure. Thus, when a system exhibits a decomposition property, either structurally (autonomous subsystems), or behaviorally (component failure versus reconfiguration), it is desirable to exploit this decomposition in the reliability calculation. In interesting cases there can be failure states which arise from non-failure states of the subsystems. Equations are presented which allow the computation of failure probabilities of the total (combined) model without requiring a complete solution of the combined model. This material is presented within the context of closed-form functional representation of probabilities as utilized in the Symbolic Hierarchical Automated Reliability and Performance Evaluator (SHARPE) tool. The techniques adopted enable one to compute such probability functions for a much wider class of systems at a reduced computational cost. Several examples show how the method is used, especially in enhancing the versatility of the SHARPE tool.

Variational data assimilation for limited-area models: solution of the open boundary control problem and its application for the Gulf of Finland

NASA Astrophysics Data System (ADS)

Sheloput, Tatiana; Agoshkov, Valery

2017-04-01

The problem of modeling water areas with `liquid' (open) lateral boundaries is discussed. There are different known methods dealing with open boundaries in limited-area models, and one of the most efficient is data assimilation. Although this method is popular, there are not so many articles concerning its implementation for recovering boundary functions. However, the problem of specifying boundary conditions at the open boundary of a limited area is still actual and important. The mathematical model of the Baltic Sea circulation, developed in INM RAS, is considered. It is based on the system of thermo-hydrodynamic equations in the Boussinesq and hydrostatic approximations. The splitting method that is used for time approximation in the model allows to consider the data assimilation problem as a sequence of linear problems. One of such `simple' temperature (salinity) assimilation problem is investigated in the study. Using well known techniques of study and solution of inverse problems and optimal control problems [1], we propose an iterative solution algorithm and we obtain conditions for existence of the solution, for unique and dense solvability of the problem and for convergence of the iterative algorithm. The investigation shows that if observations satisfy certain conditions, the proposed algorithm converges to the solution of the boundary control problem. Particularly, it converges when observational data are given on the `liquid' boundary [2]. Theoretical results are confirmed by the results of numerical experiments. The numerical algorithm was implemented to water area of the Baltic Sea. Two numerical experiments were carried out in the Gulf of Finland: one with the application of the assimilation procedure and the other without. The analyses have shown that the surface temperature field in the first experiment is close to the observed one, while the result of the second experiment misfits. Number of iterations depends on the regularisation parameter, but generally the algorithm converges after 10 iterations. The results of the numerical experiments show that the usage of the proposed method makes sense. The work was supported by the Russian Science Foundation (project 14-11-00609, the formulation of the iterative process and numerical experiments) and by the Russian Foundation for Basic Research (project 16-01-00548, the formulation of the problem and its study). [1] Agoshkov V. I. Methods of Optimal Control and Adjoint Equations in Problems of Mathematical Physics. INM RAS, Moscow, 2003 (in Russian). [2] Agoshkov V.I., Sheloput T.O. The study and numerical solution of the problem of heat and salinity transfer assuming 'liquid' boundaries // Russ. J. Numer. Anal. Math. Modelling. 2016. Vol. 31, No. 2. P. 71-80.

Theoretical face pressure and drag characteristics of forward-facing steps in supersonic turbulent boundary layers

NASA Technical Reports Server (NTRS)

Patel, D. K.; Czarnecki, K. R.

1975-01-01

A theoretical investigation of the pressure distributions and drag characteristics was made for forward facing steps in turbulent flow at supersonic speeds. An approximate solution technique proposed by Uebelhack has been modified and extended to obtain a more consistent numerical procedure. A comparison of theoretical calculations with experimental data generally indicated good agreement over the experimentally available range of ratios of step height to boundary layer thickness from 7 to 0.05.

Progress on a generalized coordinates tensor product finite element 3DPNS algorithm for subsonic

NASA Technical Reports Server (NTRS)

Baker, A. J.; Orzechowski, J. A.

1983-01-01

A generalized coordinates form of the penalty finite element algorithm for the 3-dimensional parabolic Navier-Stokes equations for turbulent subsonic flows was derived. This algorithm formulation requires only three distinct hypermatrices and is applicable using any boundary fitted coordinate transformation procedure. The tensor matrix product approximation to the Jacobian of the Newton linear algebra matrix statement was also derived. Tne Newton algorithm was restructured to replace large sparse matrix solution procedures with grid sweeping using alpha-block tridiagonal matrices, where alpha equals the number of dependent variables. Numerical experiments were conducted and the resultant data gives guidance on potentially preferred tensor product constructions for the penalty finite element 3DPNS algorithm.

The effect of the London-van der Waals dispersion force on interline heat transfer

NASA Technical Reports Server (NTRS)

Wayner, P. C., Jr.

1978-01-01

A theoretical procedure to determine the heat transfer characteristics of the interline region (junction of liquid-solid-vapor) from the macroscopic optical and thermophysical properties of the system is outlined. The analysis is based on the premise that the interline transport processes are controlled by the London-van der Waals dispersion force between condensed phases (solid and liquid). Numerical values of the dispersion constant are presented. The procedure is used to compare the relative size of the interline heat sink of various systems using a constant heat flux mode. This solution demonstrates the importance of the interline heat flow number, which is evaluated for various systems.

Application of an enhanced discrete element method to oil and gas drilling processes

NASA Astrophysics Data System (ADS)

Ubach, Pere Andreu; Arrufat, Ferran; Ring, Lev; Gandikota, Raju; Zárate, Francisco; Oñate, Eugenio

2016-03-01

The authors present results on the use of the discrete element method (DEM) for the simulation of drilling processes typical in the oil and gas exploration industry. The numerical method uses advanced DEM techniques using a local definition of the DEM parameters and combined FEM-DEM procedures. This paper presents a step-by-step procedure to build a DEM model for analysis of the soil region coupled to a FEM model for discretizing the drilling tool that reproduces the drilling mechanics of a particular drill bit. A parametric study has been performed to determine the model parameters in order to maintain accurate solutions with reduced computational cost.

Classical Control System Design: A non-Graphical Method for Finding the Exact System Parameters

NASA Astrophysics Data System (ADS)

Hussein, Mohammed Tawfik

2008-06-01

The Root Locus method of control system design was developed in the 1940's. It is a set of rules that helps in sketching the path traced by the roots of the closed loop characteristic equation of the system, as a parameter such as a controller gain, k, is varied. The procedure provides approximate sketching guidelines. Designs on control systems using the method are therefore not exact. This paper aims at a non-graphical method for finding the exact system parameters to place a pair of complex conjugate poles on a specified damping ratio line. The overall procedure is based on the exact solution of complex equations on the PC using numerical methods.

Existence and instability of steady states for a triangular cross-diffusion system: A computer-assisted proof

NASA Astrophysics Data System (ADS)

Breden, Maxime; Castelli, Roberto

2018-05-01

In this paper, we present and apply a computer-assisted method to study steady states of a triangular cross-diffusion system. Our approach consist in an a posteriori validation procedure, that is based on using a fixed point argument around a numerically computed solution, in the spirit of the Newton-Kantorovich theorem. It allows to prove the existence of various non homogeneous steady states for different parameter values. In some situations, we obtain as many as 13 coexisting steady states. We also apply the a posteriori validation procedure to study the linear stability of the obtained steady states, proving that many of them are in fact unstable.

A user's guide for V174, a program using a finite difference method to analyze transonic flow over oscillating wings

NASA Technical Reports Server (NTRS)

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

1977-01-01

The design and usage of a pilot program using a finite difference method for calculating the pressure distributions over harmonically oscillating wings in transonic flow are discussed. The procedure used is based on separating the velocity potential into steady and unsteady parts and linearizing the resulting unsteady differential equation for small disturbances. The steady velocity potential which must be obtained from some other program, is required for input. The unsteady differential equation is linear, complex in form with spatially varying coefficients. Because sinusoidal motion is assumed, time is not a variable. The numerical solution is obtained through a finite difference formulation and a line relaxation solution method.

A multi-layer discrete-ordinate method for vector radiative transfer in a vertically-inhomogeneous, emitting and scattering atmosphere. I - Theory. II - Application

NASA Technical Reports Server (NTRS)

Weng, Fuzhong

1992-01-01

A theory is developed for discretizing the vector integro-differential radiative transfer equation including both solar and thermal radiation. A complete solution and boundary equations are obtained using the discrete-ordinate method. An efficient numerical procedure is presented for calculating the phase matrix and achieving computational stability. With natural light used as a beam source, the Stokes parameters from the model proposed here are compared with the analytical solutions of Chandrasekhar (1960) for a Rayleigh scattering atmosphere. The model is then applied to microwave frequencies with a thermal source, and the brightness temperatures are compared with those from Stamnes'(1988) radiative transfer model.

Numerical solutions of acoustic wave propagation problems using Euler computations

NASA Technical Reports Server (NTRS)

Hariharan, S. I.

1984-01-01

This paper reports solution procedures for problems arising from the study of engine inlet wave propagation. The first problem is the study of sound waves radiated from cylindrical inlets. The second one is a quasi-one-dimensional problem to study the effect of nonlinearities and the third one is the study of nonlinearities in two dimensions. In all three problems Euler computations are done with a fourth-order explicit scheme. For the first problem results are shown in agreement with experimental data and for the second problem comparisons are made with an existing asymptotic theory. The third problem is part of an ongoing work and preliminary results are presented for this case.

A users guide for A344: A program using a finite difference method to analyze transonic flow over oscillating airfoils

NASA Technical Reports Server (NTRS)

Weatherill, W. H.; Ehlers, F. E.

1979-01-01

The design and usage of a pilot program for calculating the pressure distributions over harmonically oscillating airfoils in transonic flow are described. The procedure used is based on separating the velocity potential into steady and unsteady parts and linearizing the resulting unsteady differential equations for small disturbances. The steady velocity potential which must be obtained from some other program, was required for input. The unsteady equation, as solved, is linear with spatially varying coefficients. Since sinusoidal motion was assumed, time was not a variable. The numerical solution was obtained through a finite difference formulation and either a line relaxation or an out of core direct solution method.

Convective and morphological instabilities during crystal growth: Effect of gravity modulation

NASA Technical Reports Server (NTRS)

Coreill, S. R.; Murray, B. T.; Mcfadden, G. B.; Wheeler, A. A.; Saunders, B. V.

1992-01-01

During directional solidification of a binary alloy at constant velocity in the vertical direction, morphological and convective instabilities may occur due to the temperature and solute gradients associated with the solidification process. The effect of time-periodic modulation (vibration) is studied by considering a vertical gravitational acceleration which is sinusoidal in time. The conditions for the onset of solutal convection are calculated numerically, employing two distinct computational procedures based on Floquet theory. In general, a stable state can be destabilized by modulation and an unstable state can be stabilized. In the limit of high frequency modulation, the method of averaging and multiple-scale asymptotic analysis can be used to simplify the calculations.

An economic production model for deteriorating items and time dependent demand with rework and multiple production setups

NASA Astrophysics Data System (ADS)

Uthayakumar, R.; Tharani, S.

2017-12-01

Recently, much emphasis has given to study the control and maintenance of production inventories of the deteriorating items. Rework is one of the main issues in reverse logistic and green supply chain, since it can reduce production cost and the environmental problem. Many researchers have focused on developing rework model, but few of them have developed model for deteriorating items. Due to this fact, we take up productivity and rework with deterioration as the major concern in this paper. In this paper, a production-inventory model with deteriorative items in which one cycle has n production setups and one rework setup (n, 1) policy is considered for deteriorating items with stock-dependent demand in case 1 and exponential demand in case 2. An effective iterative solution procedure is developed to achieve optimal time, so that the total cost of the system is minimized. Numerical and sensitivity analyses are discussed to examine the outcome of the proposed solution procedure presented in this research.

Computational physical oceanography -- A comprehensive approach based on generalized CFD/grid techniques for planetary scale simulations of oceanic flows. Final report, September 1, 1995--August 31, 1996

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

Beddhu, M.; Jiang, M.Y.; Whitfield, D.L.

The original intention for this work was to impart the technology that was developed in the field of computational aeronautics to the field of computational physical oceanography. This technology transfer involved grid generation techniques and solution procedures to solve the governing equations over the grids thus generated. Specifically, boundary fitting non-orthogonal grids would be generated over a sphere taking into account the topography of the ocean floor and the topography of the continents. The solution methodology to be employed involved the application of an upwind, finite volume discretization procedure that uses higher order numerical fluxes at the cell faces tomore » discretize the governing equations and an implicit Newton relaxation technique to solve the discretized equations. This report summarizes the efforts put forth during the past three years to achieve these goals and indicates the future direction of this work as it is still an ongoing effort.« less

A numerical procedure for transient free surface seepage through fracture networks

NASA Astrophysics Data System (ADS)

Jiang, Qinghui; Ye, Zuyang; Zhou, Chuangbing

2014-11-01

A parabolic variational inequality (PVI) formulation is presented for the transient free surface seepage problem defined for a whole fracture network. Because the seepage faces are specified as Signorini-type conditions, the PVI formulation can effectively eliminate the singularity of spillpoints that evolve with time. By introducing a continuous penalty function to replace the original Heaviside function, a finite element procedure based on the PVI formulation is developed to predict the transient free surface response in the fracture network. The effects of the penalty parameter on the solution precision are analyzed. A relative error formula for evaluating the flow losses at steady state caused by the penalty parameter is obtained. To validate the proposed method, three typical examples are solved. The solutions for the first example are compared with the experimental results. The results from the last two examples further demonstrate that the orientation, extent and density of fractures significantly affect the free surface seepage behavior in the fracture network.

A low cost solution for post-biopsy complications using available RFA generator and coaxial core biopsy needle.

PubMed

Azlan, C A; Mohd Nasir, N F; Saifizul, A A; Faizul, M S; Ng, K H; Abdullah, B J J

2007-12-01

Percutaneous image-guided needle biopsy is typically performed in highly vascular organs or in tumours with rich macroscopic and microscopic blood supply. The main risks related to this procedure are haemorrhage and implantation of tumour cells in the needle tract after the biopsy needle is withdrawn. From numerous conducted studies, it was found that heating the needle tract using alternating current in radiofrequency (RF) range has a potential to minimize these effects. However, this solution requires the use of specially designed needles, which would make the procedure relatively expensive and complicated. Thus, we propose a simple solution by using readily available coaxial core biopsy needles connected to a radiofrequency ablation (RFA) generator. In order to do so, we have designed and developed an adapter to interface between these two devices. For evaluation purpose, we used a bovine liver as a sample tissue. The experimental procedure was done to study the effect of different parameter settings on the size of coagulation necrosis caused by the RF current heating on the subject. The delivery of the RF energy was varied by changing the values for delivered power, power delivery duration, and insertion depth. The results showed that the size of the coagulation necrosis is affected by all of the parameters tested. In general, the size of the region is enlarged with higher delivery of RF power, longer duration of power delivery, and shallower needle insertion and become relatively constant after a certain value. We also found that the solution proposed provides a low cost and practical way to minimizes unwanted post-biopsy effects.

Application of multi-grid method on the simulation of incremental forging processes

NASA Astrophysics Data System (ADS)

Ramadan, Mohamad; Khaled, Mahmoud; Fourment, Lionel

2016-10-01

Numerical simulation becomes essential in manufacturing large part by incremental forging processes. It is a splendid tool allowing to show physical phenomena however behind the scenes, an expensive bill should be paid, that is the computational time. That is why many techniques are developed to decrease the computational time of numerical simulation. Multi-Grid method is a numerical procedure that permits to reduce computational time of numerical calculation by performing the resolution of the system of equations on several mesh of decreasing size which allows to smooth faster the low frequency of the solution as well as its high frequency. In this paper a Multi-Grid method is applied to cogging process in the software Forge 3. The study is carried out using increasing number of degrees of freedom. The results shows that calculation time is divide by two for a mesh of 39,000 nodes. The method is promising especially if coupled with Multi-Mesh method.

Acoustic modeling and eigenanalysis of coupled rooms with a transparent coupling aperture of variable size

NASA Astrophysics Data System (ADS)

Shi, Shuangxia; Jin, Guoyong; Xiao, Bin; Liu, Zhigang

2018-04-01

This paper is concerned with the modeling and acoustic eigenanalysis of coupled spaces with a coupling aperture of variable size. A modeling method for this problem is developed based on the energy principle in combination with a 3D modified Fourier cosine series approach. Under this theoretical framework, the energy exchange property and acoustically transparent characteristics of the opening are taken into account via the inflow and outflow sound powers through the opening without any assumptions. The sound pressure in the subrooms is constructed in the form of the three-dimensional modified Fourier series with several auxiliary functions introduced to ensure the uniform convergence of the solution over the entire solution domain. The accuracy of the natural frequencies and mode shapes of three exemplary coupled rooms systems is verified against numerical data obtained by finite element method, with good agreement achieved. The present method offers a unified procedure for a variety of cases because the modification of any parameter from one case to another, such as the size and location of the coupling aperture, is as simple as modifying the material properties, requiring no changes to the solution procedures.

A methodology for the rigorous verification of plasma simulation codes

NASA Astrophysics Data System (ADS)

Riva, Fabio

2016-10-01

The methodology used to assess the reliability of numerical simulation codes constitutes the Verification and Validation (V&V) procedure. V&V is composed by two separate tasks: the verification, which is a mathematical issue targeted to assess that the physical model is correctly solved, and the validation, which determines the consistency of the code results, and therefore of the physical model, with experimental data. In the present talk we focus our attention on the verification, which in turn is composed by the code verification, targeted to assess that a physical model is correctly implemented in a simulation code, and the solution verification, that quantifies the numerical error affecting a simulation. Bridging the gap between plasma physics and other scientific domains, we introduced for the first time in our domain a rigorous methodology for the code verification, based on the method of manufactured solutions, as well as a solution verification based on the Richardson extrapolation. This methodology was applied to GBS, a three-dimensional fluid code based on a finite difference scheme, used to investigate the plasma turbulence in basic plasma physics experiments and in the tokamak scrape-off layer. Overcoming the difficulty of dealing with a numerical method intrinsically affected by statistical noise, we have now generalized the rigorous verification methodology to simulation codes based on the particle-in-cell algorithm, which are employed to solve Vlasov equation in the investigation of a number of plasma physics phenomena.

Importance of inlet boundary conditions for numerical simulation of combustor flows

NASA Technical Reports Server (NTRS)

Sturgess, G. J.; Syed, S. A.; Mcmanus, K. R.

1983-01-01

Fluid dynamic computer codes for the mathematical simulation of problems in gas turbine engine combustion systems are required as design and diagnostic tools. To eventually achieve a performance standard with these codes of more than qualitative accuracy it is desirable to use benchmark experiments for validation studies. Typical of the fluid dynamic computer codes being developed for combustor simulations is the TEACH (Teaching Elliptic Axisymmetric Characteristics Heuristically) solution procedure. It is difficult to find suitable experiments which satisfy the present definition of benchmark quality. For the majority of the available experiments there is a lack of information concerning the boundary conditions. A standard TEACH-type numerical technique is applied to a number of test-case experiments. It is found that numerical simulations of gas turbine combustor-relevant flows can be sensitive to the plane at which the calculations start and the spatial distributions of inlet quantities for swirling flows.

The terminal area simulation system. Volume 1: Theoretical formulation

NASA Technical Reports Server (NTRS)

Proctor, F. H.

1987-01-01

A three-dimensional numerical cloud model was developed for the general purpose of studying convective phenomena. The model utilizes a time splitting integration procedure in the numerical solution of the compressible nonhydrostatic primitive equations. Turbulence closure is achieved by a conventional first-order diagnostic approximation. Open lateral boundaries are incorporated which minimize wave reflection and which do not induce domain-wide mass trends. Microphysical processes are governed by prognostic equations for potential temperature water vapor, cloud droplets, ice crystals, rain, snow, and hail. Microphysical interactions are computed by numerous Orville-type parameterizations. A diagnostic surface boundary layer is parameterized assuming Monin-Obukhov similarity theory. The governing equation set is approximated on a staggered three-dimensional grid with quadratic-conservative central space differencing. Time differencing is approximated by the second-order Adams-Bashforth method. The vertical grid spacing may be either linear or stretched. The model domain may translate along with a convective cell, even at variable speeds.

Residual Distribution Schemes for Conservation Laws Via Adaptive Quadrature

NASA Technical Reports Server (NTRS)

Barth, Timothy; Abgrall, Remi; Biegel, Bryan (Technical Monitor)

2000-01-01

This paper considers a family of nonconservative numerical discretizations for conservation laws which retains the correct weak solution behavior in the limit of mesh refinement whenever sufficient order numerical quadrature is used. Our analysis of 2-D discretizations in nonconservative form follows the 1-D analysis of Hou and Le Floch. For a specific family of nonconservative discretizations, it is shown under mild assumptions that the error arising from non-conservation is strictly smaller than the discretization error in the scheme. In the limit of mesh refinement under the same assumptions, solutions are shown to satisfy an entropy inequality. Using results from this analysis, a variant of the "N" (Narrow) residual distribution scheme of van der Weide and Deconinck is developed for first-order systems of conservation laws. The modified form of the N-scheme supplants the usual exact single-state mean-value linearization of flux divergence, typically used for the Euler equations of gasdynamics, by an equivalent integral form on simplex interiors. This integral form is then numerically approximated using an adaptive quadrature procedure. This renders the scheme nonconservative in the sense described earlier so that correct weak solutions are still obtained in the limit of mesh refinement. Consequently, we then show that the modified form of the N-scheme can be easily applied to general (non-simplicial) element shapes and general systems of first-order conservation laws equipped with an entropy inequality where exact mean-value linearization of the flux divergence is not readily obtained, e.g. magnetohydrodynamics, the Euler equations with certain forms of chemistry, etc. Numerical examples of subsonic, transonic and supersonic flows containing discontinuities together with multi-level mesh refinement are provided to verify the analysis.

A time-efficient implementation of Extended Kalman Filter for sequential orbit determination and a case study for onboard application

NASA Astrophysics Data System (ADS)

Tang, Jingshi; Wang, Haihong; Chen, Qiuli; Chen, Zhonggui; Zheng, Jinjun; Cheng, Haowen; Liu, Lin

2018-07-01

Onboard orbit determination (OD) is often used in space missions, with which mission support can be partially accomplished autonomously, with less dependency on ground stations. In major Global Navigation Satellite Systems (GNSS), inter-satellite link is also an essential upgrade in the future generations. To serve for autonomous operation, sequential OD method is crucial to provide real-time or near real-time solutions. The Extended Kalman Filter (EKF) is an effective and convenient sequential estimator that is widely used in onboard application. The filter requires the solutions of state transition matrix (STM) and the process noise transition matrix, which are always obtained by numerical integration. However, numerically integrating the differential equations is a CPU intensive process and consumes a large portion of the time in EKF procedures. In this paper, we present an implementation that uses the analytical solutions of these transition matrices to replace the numerical calculations. This analytical implementation is demonstrated and verified using a fictitious constellation based on selected medium Earth orbit (MEO) and inclined Geosynchronous orbit (IGSO) satellites. We show that this implementation performs effectively and converges quickly, steadily and accurately in the presence of considerable errors in the initial values, measurements and force models. The filter is able to converge within 2-4 h of flight time in our simulation. The observation residual is consistent with simulated measurement error, which is about a few centimeters in our scenarios. Compared to results implemented with numerically integrated STM, the analytical implementation shows results with consistent accuracy, while it takes only about half the CPU time to filter a 10-day measurement series. The future possible extensions are also discussed to fit in various missions.

A Spectral Algorithm for Solving the Relativistic Vlasov-Maxwell Equations

NASA Technical Reports Server (NTRS)

Shebalin, John V.

2001-01-01

A spectral method algorithm is developed for the numerical solution of the full six-dimensional Vlasov-Maxwell system of equations. Here, the focus is on the electron distribution function, with positive ions providing a constant background. The algorithm consists of a Jacobi polynomial-spherical harmonic formulation in velocity space and a trigonometric formulation in position space. A transform procedure is used to evaluate nonlinear terms. The algorithm is suitable for performing moderate resolution simulations on currently available supercomputers for both scientific and engineering applications.

On the delay analysis of a TDMA channel with finite buffer capacity

NASA Technical Reports Server (NTRS)

Yan, T.-Y.

1982-01-01

The throughput performance of a TDMA channel with finite buffer capacity for transmitting data messages is considered. Each station has limited message buffer capacity and has Poisson message arrivals. Message arrivals will be blocked if the buffers are congested. Using the embedded Markov chain model, the solution procedure for the limiting system-size probabilities is presented in a recursive fashion. Numerical examples are given to demonstrate the tradeoffs between the blocking probabilities and the buffer sizing strategy.

Nonparallel stability of three-dimensional compressible boundary layers. Part 1: Stability analysis

NASA Technical Reports Server (NTRS)

El-Hady, N. M.

1980-01-01

A compressible linear stability theory is presented for nonparallel three-dimensional boundary-layer flows, taking into account the normal velocity component as well as the streamwise and spanwise variations of the basic flow. The method of multiple scales is used to account for the nonparallelism of the basic flow, and equations are derived for the spatial evolution of the disturbance amplitude and wavenumber. The numerical procedure for obtaining the solution of the nonparallel problem is outlined.

Numerical simulation of supersonic inlets using a three-dimensional viscous flow analysis

NASA Technical Reports Server (NTRS)

Anderson, B. H.; Towne, C. E.

1980-01-01

A three dimensional fully viscous computer analysis was evaluated to determine its usefulness in the design of supersonic inlets. This procedure takes advantage of physical approximations to limit the high computer time and storage associated with complete Navier-Stokes solutions. Computed results are presented for a Mach 3.0 supersonic inlet with bleed and a Mach 7.4 hypersonic inlet. Good agreement was obtained between theory and data for both inlets. Results of a mesh sensitivity study are also shown.

Blast Mitigation by Water Mist, (3) Mitigation of Confined and Unconfined Blasts

DTIC Science & Technology

2006-07-14

2 (vv)I1 1 j7(T - TJ) (18) In addition to drag, heat transfer, and vaporization, droplet breakup must also be accounted for when large droplets...Mitigation of Confined and Unconfined Blasts Table of Contents 1 . Introduction 2 . Numerical Model and Solution Procedure 2.1 Gas-phase Model 2.2...enclosure at 1 , 2 , 5, and 15 ms after detonation of a 2.12 kg explosive without water mist present. Temperature contour range is from 300 to 2500 K

Pumping tests in non-uniform aquifers - the linear strip case

USGS Publications Warehouse

Butler, J.J.; Liu, W.Z.

1991-01-01

Many pumping tests are performed in geologic settings that can be conceptualized as a linear infinite strip of one material embedded in a matrix of differing flow properties. A semi-analytical solution is presented to aid the analysis of drawdown data obtained from pumping tests performed in settings that can be represented by such a conceptual model. Integral transform techniques are employed to obtain a solution in transform space that can be numerically inverted to real space. Examination of the numerically transformed solution reveals several interesting features of flow in this configuration. If the transmissivity of the strip is much higher than that of the matrix, linear and bilinear flow are the primary flow regimes during a pumping test. If the contrast between matrix and strip properties is not as extreme, then radial flow should be the primary flow mechanism. Sensitivity analysis is employed to develop insight into the controls on drawdown in this conceptual model and to demonstrate the importance of temporal and spatial placement of observations. Changes in drawdown are sensitive to the transmissivity of the strip for a limited time duration. After that time, only the total drawdown remains a function of strip transmissivity. In the case of storativity, both the total drawdown and changes in drawdown are sensitive to the storativity of the strip for a time of quite limited duration. After that time, essentially no information can be gained about the storage properties of the strip from drawdown data. An example analysis is performed using data previously presented in the literature to demonstrate the viability of the semi-analytical solution and to illustrate a general procedure for analysis of drawdown data in complex geologic settings. This example reinforces the importance of observation well placement and the time of data collection in constraining parameter correlation, a major source of the uncertainty that arises in the parameter estimation procedure. ?? 1991.

Flowing partially penetrating well: solution to a mixed-type boundary value problem

NASA Astrophysics Data System (ADS)

Cassiani, G.; Kabala, Z. J.; Medina, M. A.

A new semi-analytic solution to the mixed-type boundary value problem for a flowing partially penetrating well with infinitesimal skin situated in an anisotropic aquifer is developed. The solution is suited to aquifers having a semi-infinite vertical extent or to packer tests with aquifer horizontal boundaries far enough from the tested area. The problem reduces to a system of dual integral equations (DE) and further to a deconvolution problem. Unlike the analogous Dagan's steady-state solution [Water Resour. Res. 1978; 14:929-34], our DE solution does not suffer from numerical oscillations. The new solution is validated by matching the corresponding finite-difference solution and is computationally much more efficient. An automated (Newton-Raphson) parameter identification algorithm is proposed for field test inversion, utilizing the DE solution for the forward model. The procedure is computationally efficient and converges to correct parameter values. A solution for the partially penetrating flowing well with no skin and a drawdown-drawdown discontinuous boundary condition, analogous to that by Novakowski [Can. Geotech. J. 1993; 30:600-6], is compared to the DE solution. The D-D solution leads to physically inconsistent infinite total flow rate to the well, when no skin effect is considered. The DE solution, on the other hand, produces accurate results.

The method of complex characteristics for design of transonic blade sections

NASA Technical Reports Server (NTRS)

Bledsoe, M. R.

1986-01-01

A variety of computational methods were developed to obtain shockless or near shockless flow past two-dimensional airfoils. The approach used was the method of complex characteristics, which determines smooth solutions to the transonic flow equations based on an input speed distribution. General results from fluid mechanics are presented. An account of the method of complex characteristics is given including a description of the particular spaces and coordinates, conformal transformations, and numerical procedures that are used. The operation of the computer program COMPRES is presented along with examples of blade sections designed with the code. A user manual is included with a glossary to provide additional information which may be helpful. The computer program in Fortran, including numerous comment cards is listed.

A Taylor weak-statement algorithm for hyperbolic conservation laws

NASA Technical Reports Server (NTRS)

Baker, A. J.; Kim, J. W.

1987-01-01

Finite element analysis, applied to computational fluid dynamics (CFD) problem classes, presents a formal procedure for establishing the ingredients of a discrete approximation numerical solution algorithm. A classical Galerkin weak-statement formulation, formed on a Taylor series extension of the conservation law system, is developed herein that embeds a set of parameters eligible for constraint according to specification of suitable norms. The derived family of Taylor weak statements is shown to contain, as special cases, over one dozen independently derived CFD algorithms published over the past several decades for the high speed flow problem class. A theoretical analysis is completed that facilitates direct qualitative comparisons. Numerical results for definitive linear and nonlinear test problems permit direct quantitative performance comparisons.

On approximation of non-Newtonian fluid flow by the finite element method

NASA Astrophysics Data System (ADS)

Svácek, Petr

2008-08-01

In this paper the problem of numerical approximation of non-Newtonian fluid flow with free surface is considered. Namely, the flow of fresh concrete is addressed. Industrial mixtures often behaves like non-Newtonian fluids exhibiting a yield stress that needs to be overcome for the flow to take place, cf. [R.B. Bird, R.C. Armstrong, O. Hassager, Dynamics of Polymeric Liquids, vol. 1, Fluid Mechanics, Wiley, New York, 1987; R.P. Chhabra, J.F. Richardson, Non-Newtonian Flow in the Process Industries, Butterworth-Heinemann, London, 1999]. The main interest is paid to the mathematical formulation of the problem and to discretization with the aid of finite element method. The described numerical procedure is applied onto the solution of several problems.

Analysis of free turbulent shear flows by numerical methods

NASA Technical Reports Server (NTRS)

Korst, H. H.; Chow, W. L.; Hurt, R. F.; White, R. A.; Addy, A. L.

1973-01-01

Studies are described in which the effort was essentially directed to classes of problems where the phenomenologically interpreted effective transport coefficients could be absorbed by, and subsequently extracted from (by comparison with experimental data), appropriate coordinate transformations. The transformed system of differential equations could then be solved without further specifications or assumptions by numerical integration procedures. An attempt was made to delineate different regimes for which specific eddy viscosity models could be formulated. In particular, this would account for the carryover of turbulence from attached boundary layers, the transitory adjustment, and the asymptotic behavior of initially disturbed mixing regions. Such models were subsequently used in seeking solutions for the prescribed two-dimensional test cases, yielding a better insight into overall aspects of the exchange mechanisms.

Modeling of atomization and distribution of drop-liquid fuel in unsteady swirling flows in a combustion chamber and free space

NASA Astrophysics Data System (ADS)

Sviridenkov, A. A.; Toktaliev, P. D.; Tretyakov, V. V.

2018-03-01

Numerical and experimental research of atomization and propagation of drop-liquid phase in swirling flow behind the frontal device of combustion chamber was performed. Numerical procedure was based on steady and unsteady Reynolds equations solution. It's shown that better agreement with experimental data could be obtained with unsteady approach. Fractional time step method was implemented to solve Reynolds equations. Models of primary and secondary breakup of liquid fuel jet in swirling flows are formulated and tested. Typical mean sizes of fuel droplets for base operational regime of swirling device and combustion chamber were calculated. Comparison of main features of internal swirling flow in combustion chamber with unbounded swirling flow was made.

Numerical Simulation of Delamination Growth in Composite Materials

NASA Technical Reports Server (NTRS)

Camanho, P. P.; Davila, C. G.; Ambur, D. R.

2001-01-01

The use of decohesion elements for the simulation of delamination in composite materials is reviewed. The test methods available to measure the interfacial fracture toughness used in the formulation of decohesion elements are described initially. After a brief presentation of the virtual crack closure technique, the technique most widely used to simulate delamination growth, the formulation of interfacial decohesion elements is described. Problems related with decohesion element constitutive equations, mixed-mode crack growth, element numerical integration and solution procedures are discussed. Based on these investigations, it is concluded that the use of interfacial decohesion elements is a promising technique that avoids the need for a pre-existing crack and pre-defined crack paths, and that these elements can be used to simulate both delamination onset and growth.

Extension of transonic flow computational concepts in the analysis of cavitated bearings

NASA Technical Reports Server (NTRS)

Vijayaraghavan, D.; Keith, T. G., Jr.; Brewe, D. E.

1990-01-01

An analogy between the mathematical modeling of transonic potential flow and the flow in a cavitating bearing is described. Based on the similarities, characteristics of the cavitated region and jump conditions across the film reformation and rupture fronts are developed using the method of weak solutions. The mathematical analogy is extended by utilizing a few computational concepts of transonic flow to numerically model the cavitating bearing. Methods of shock fitting and shock capturing are discussed. Various procedures used in transonic flow computations are adapted to bearing cavitation applications, for example, type differencing, grid transformation, an approximate factorization technique, and Newton's iteration method. These concepts have proved to be successful and have vastly improved the efficiency of numerical modeling of cavitated bearings.

Auxiliary variables for numerically solving nonlinear equations with softly broken symmetries.

PubMed

Olum, Ken D; Masoumi, Ali

2017-06-01

General methods for solving simultaneous nonlinear equations work by generating a sequence of approximate solutions that successively improve a measure of the total error. However, if the total error function has a narrow curved valley, the available techniques tend to find the solution after a very large number of steps, if ever. The solver first converges rapidly to the valley, but once there it converges extremely slowly to the solution. In this paper we show that in the specific physically important case where these valleys are the result of a softly broken symmetry, the solution can often be found much more quickly by adding the generators of the softly broken symmetry as auxiliary variables. This makes the number of variables more than the equations and hence there will be a family of solutions, any one of which would be acceptable. We present a procedure for finding solutions in this case and apply it to several simple examples and an important problem in the physics of false vacuum decay. We also provide a Mathematica package that implements Powell's hybrid method with the generalization to allow more variables than equations.

SoftWAXS: a computational tool for modeling wide-angle X-ray solution scattering from biomolecules.

PubMed

Bardhan, Jaydeep; Park, Sanghyun; Makowski, Lee

2009-10-01

This paper describes a computational approach to estimating wide-angle X-ray solution scattering (WAXS) from proteins, which has been implemented in a computer program called SoftWAXS. The accuracy and efficiency of SoftWAXS are analyzed for analytically solvable model problems as well as for proteins. Key features of the approach include a numerical procedure for performing the required spherical averaging and explicit representation of the solute-solvent boundary and the surface of the hydration layer. These features allow the Fourier transform of the excluded volume and hydration layer to be computed directly and with high accuracy. This approach will allow future investigation of different treatments of the electron density in the hydration shell. Numerical results illustrate the differences between this approach to modeling the excluded volume and a widely used model that treats the excluded-volume function as a sum of Gaussians representing the individual atomic excluded volumes. Comparison of the results obtained here with those from explicit-solvent molecular dynamics clarifies shortcomings inherent to the representation of solvent as a time-averaged electron-density profile. In addition, an assessment is made of how the calculated scattering patterns depend on input parameters such as the solute-atom radii, the width of the hydration shell and the hydration-layer contrast. These results suggest that obtaining predictive calculations of high-resolution WAXS patterns may require sophisticated treatments of solvent.

Numerical solution of the stochastic parabolic equation with the dependent operator coefficient

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

Ashyralyev, Allaberen; Department of Mathematics, ITTU, Ashgabat; Okur, Ulker

2015-09-18

In the present paper, a single step implicit difference scheme for the numerical solution of the stochastic parabolic equation with the dependent operator coefficient is presented. Theorem on convergence estimates for the solution of this difference scheme is established. In applications, this abstract result permits us to obtain the convergence estimates for the solution of difference schemes for the numerical solution of initial boundary value problems for parabolic equations. The theoretical statements for the solution of this difference scheme are supported by the results of numerical experiments.

Sedimentary Geothermal Feasibility Study: October 2016

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

Augustine, Chad; Zerpa, Luis

The objective of this project is to analyze the feasibility of commercial geothermal projects using numerical reservoir simulation, considering a sedimentary reservoir with low permeability that requires productivity enhancement. A commercial thermal reservoir simulator (STARS, from Computer Modeling Group, CMG) is used in this work for numerical modeling. In the first stage of this project (FY14), a hypothetical numerical reservoir model was developed, and validated against an analytical solution. The following model parameters were considered to obtain an acceptable match between the numerical and analytical solutions: grid block size, time step and reservoir areal dimensions; the latter related to boundarymore » effects on the numerical solution. Systematic model runs showed that insufficient grid sizing generates numerical dispersion that causes the numerical model to underestimate the thermal breakthrough time compared to the analytic model. As grid sizing is decreased, the model results converge on a solution. Likewise, insufficient reservoir model area introduces boundary effects in the numerical solution that cause the model results to differ from the analytical solution.« less

Simulation of a class of hazardous situations in the ICS «INM RAS - Baltic Sea»

NASA Astrophysics Data System (ADS)

Zakharova, Natalia; Agoshkov, Valery; Aseev, Nikita; Parmuzin, Eugene; Sheloput, Tateana; Shutyaev, Victor

2017-04-01

Development of Informational Computational Systems (ICS) for data assimilation procedures is one of multidisciplinary problems. To study and solve these problems one needs to apply modern results from different disciplines and recent developments in mathematical modeling, theory of adjoint equations and optimal control, inverse problems, numerical methods theory, numerical algebra, scientific computing and processing of satellite data. In this work the results on the ICS development for PC-ICS "INM RAS - Baltic Sea" are presented. We discuss practical problems studied by ICS. The System includes numerical model of the Baltic Sea thermodynamics, the new oil spill model describing the propagation of a slick at the Sea surface (Agoshkov, Aseev et al., 2014) and the optimal ship route calculating block (Agoshkov, Zayachkovsky et al., 2014). The ICS is based on the INMOM numerical model of the Baltic Sea thermodynamics (Zalesny et al., 2013). It is possible to calculate main hydrodynamic parameters (temperature, salinity, velocities, sea level) using user-friendly interface of the ICS. The System includes data assimilation procedures (Agoshkov, 2003, Parmuzin, Agoshkov, 2012) and one can use the block of variational assimilation of the sea surface temperature in order to obtain main hydrodynamic parameters. Main possibilities of the ICS and several numerical experiments are presented in the work. By the problem of risk control is meant a problem of determination of optimal resources quantity which are necessary for decreasing the risk to some acceptable value. Mass of oil slick is chosen as a function of control. For the realization of the random variable the quadratic "functional of cost" is introduced. It comprises cleaning costs and deviation of damage of oil pollution from its acceptable value. The problem of minimization of this functional is solved based on the methods of optimal control and the theory of adjoint equations. The solution of this problem is explicitly found. The study was supported by the Russian Foundation for Basic Research (project 16-31-00510) and by the Russian Science Foundation (project №14-11-00609). V. I. Agoshkov, Methods of Optimal Control and Adjoint Equations in Problems of Mathematical Physics. INM RAS, Moscow, 2003 (in Russian). V. B. Zalesny, A. V. Gusev, V. O. Ivchenko, R. Tamsalu, and R. Aps, Numerical model of the Baltic Sea circulation. Russ. J. Numer. Anal. Math. Modelling 28 (2013), No. 1, 85-100. V.I. Agoshkov, A.O. Zayachkovskiy, R. Aps, P. Kujala, and J. Rytkönen. Risk theory based solution to the problem of optimal vessel route // Russian Journal of Numerical Analysis and Mathematical Modelling. 2014. Volume 29, Issue 2, Pages 69-78. Agoshkov, V., Aseev, N., Aps, R., Kujala, P., Rytkönen, J., Zalesny, V. The problem of control of oil pollution risk in the Baltic Sea // Russian Journal of Numerical Analysis and Mathematical Modelling. 2014. Volume 29, Issue 2, Pages 93-105. E. I. Parmuzin and V. I. Agoshkov, Numerical solution of the variational assimilation problem for sea surface temperature in the model of the Black Sea dynamics. Russ. J. Numer. Anal. Math. Modelling 27 (2012), No. 1, 69-94. Olof Liungman and Johan Mattsson. Scientic Documentation of Seatrack Web; physical processes, algorithms and references, 2011.

Numerical integration of asymptotic solutions of ordinary differential equations

NASA Technical Reports Server (NTRS)

Thurston, Gaylen A.

1989-01-01

Classical asymptotic analysis of ordinary differential equations derives approximate solutions that are numerically stable. However, the analysis also leads to tedious expansions in powers of the relevant parameter for a particular problem. The expansions are replaced with integrals that can be evaluated by numerical integration. The resulting numerical solutions retain the linear independence that is the main advantage of asymptotic solutions. Examples, including the Falkner-Skan equation from laminar boundary layer theory, illustrate the method of asymptotic analysis with numerical integration.

Kidney damage in extracorporeal shock wave lithotripsy: a numerical approach for different shock profiles.

PubMed

Weinberg, Kerstin; Ortiz, Michael

2009-08-01

In shock-wave lithotripsy--a medical procedure to fragment kidney stones--the patient is subjected to hypersonic waves focused at the kidney stone. Although this procedure is widely applied, the physics behind this medical treatment, in particular the question of how the injuries to the surrounding kidney tissue arise, is still under investigation. To contribute to the solution of this problem, two- and three-dimensional numerical simulations of a human kidney under shock-wave loading are presented. For this purpose a constitutive model of the bio-mechanical system kidney is introduced, which is able to map large visco-elastic deformations and, in particular, material damage. The specific phenomena of cavitation induced oscillating bubbles is modeled here as an evolution of spherical pores within the soft kidney tissue. By means of large scale finite element simulations, we study the shock-wave propagation into the kidney tissue, adapt unknown material parameters and analyze the resulting stress states. The simulations predict localized damage in the human kidney in the same regions as observed in animal experiments. Furthermore, the numerical results suggest that in first instance the pressure amplitude of the shock wave impulse (and not so much its exact time-pressure profile) is responsible for damaging the kidney tissue.

Computational benefits using artificial intelligent methodologies for the solution of an environmental design problem: saltwater intrusion.

PubMed

Papadopoulou, Maria P; Nikolos, Ioannis K; Karatzas, George P

2010-01-01

Artificial Neural Networks (ANNs) comprise a powerful tool to approximate the complicated behavior and response of physical systems allowing considerable reduction in computation time during time-consuming optimization runs. In this work, a Radial Basis Function Artificial Neural Network (RBFN) is combined with a Differential Evolution (DE) algorithm to solve a water resources management problem, using an optimization procedure. The objective of the optimization scheme is to cover the daily water demand on the coastal aquifer east of the city of Heraklion, Crete, without reducing the subsurface water quality due to seawater intrusion. The RBFN is utilized as an on-line surrogate model to approximate the behavior of the aquifer and to replace some of the costly evaluations of an accurate numerical simulation model which solves the subsurface water flow differential equations. The RBFN is used as a local approximation model in such a way as to maintain the robustness of the DE algorithm. The results of this procedure are compared to the corresponding results obtained by using the Simplex method and by using the DE procedure without the surrogate model. As it is demonstrated, the use of the surrogate model accelerates the convergence of the DE optimization procedure and additionally provides a better solution at the same number of exact evaluations, compared to the original DE algorithm.

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.

A multiplicative regularization for force reconstruction

NASA Astrophysics Data System (ADS)

Aucejo, M.; De Smet, O.

2017-02-01

Additive regularizations, such as Tikhonov-like approaches, are certainly the most popular methods for reconstructing forces acting on a structure. These approaches require, however, the knowledge of a regularization parameter, that can be numerically computed using specific procedures. Unfortunately, these procedures are generally computationally intensive. For this particular reason, it could be of primary interest to propose a method able to proceed without defining any regularization parameter beforehand. In this paper, a multiplicative regularization is introduced for this purpose. By construction, the regularized solution has to be calculated in an iterative manner. In doing so, the amount of regularization is automatically adjusted throughout the resolution process. Validations using synthetic and experimental data highlight the ability of the proposed approach in providing consistent reconstructions.

The effect of the liquid-solid system properties on the interline heat transfer coefficient

NASA Technical Reports Server (NTRS)

Wayner, P. C., Jr.

1977-01-01

A theoretical procedure to determine the heat transfer characteristics of the interline region of an evaporating meniscus using the macroscopic optical and thermophysical properties of the system is outlined. The analysis is based on the premise that the interline transport processes are controlled by the London-van der Waals forces between condensed phases (solid and liquid). The procedure is used to compare the relative size of the interline heat sink of various systems using a constant heat flux model. This solution demonstrates the importance of the interline heat flow number which is evaluated for various systems. The heat transfer characteristics of the decane-steel system are numerically compared with those of the carbon tetrachloride-quartz system.

An efficient and accurate solution methodology for bilevel multi-objective programming problems using a hybrid evolutionary-local-search algorithm.

PubMed

Deb, Kalyanmoy; Sinha, Ankur

2010-01-01

Bilevel optimization problems involve two optimization tasks (upper and lower level), in which every feasible upper level solution must correspond to an optimal solution to a lower level optimization problem. These problems commonly appear in many practical problem solving tasks including optimal control, process optimization, game-playing strategy developments, transportation problems, and others. However, they are commonly converted into a single level optimization problem by using an approximate solution procedure to replace the lower level optimization task. Although there exist a number of theoretical, numerical, and evolutionary optimization studies involving single-objective bilevel programming problems, not many studies look at the context of multiple conflicting objectives in each level of a bilevel programming problem. In this paper, we address certain intricate issues related to solving multi-objective bilevel programming problems, present challenging test problems, and propose a viable and hybrid evolutionary-cum-local-search based algorithm as a solution methodology. The hybrid approach performs better than a number of existing methodologies and scales well up to 40-variable difficult test problems used in this study. The population sizing and termination criteria are made self-adaptive, so that no additional parameters need to be supplied by the user. The study indicates a clear niche of evolutionary algorithms in solving such difficult problems of practical importance compared to their usual solution by a computationally expensive nested procedure. The study opens up many issues related to multi-objective bilevel programming and hopefully this study will motivate EMO and other researchers to pay more attention to this important and difficult problem solving activity.

The wide-angle equation and its solution through the short-time iterative Lanczos method.

PubMed

Campos-Martínez, José; Coalson, Rob D

2003-03-20

Properties of the wide-angle equation (WAEQ), a nonparaxial scalar wave equation used to propagate light through media characterized by inhomogeneous refractive-index profiles, are studied. In particular, it is shown that the WAEQ is not equivalent to the more complicated but more fundamental Helmholtz equation (HEQ) when the index of refraction profile depends on the position along the propagation axis. This includes all nonstraight waveguides. To study the quality of the WAEQ approximation, we present a novel method for computing solutions to the WAEQ. This method, based on a short-time iterative Lanczos (SIL) algorithm, can be applied directly to the full three-dimensional case, i.e., systems consisting of the propagation axis coordinate and two transverse coordinates. Furthermore, the SIL method avoids series-expansion procedures (e.g., Padé approximants) and thus convergence problems associated with such procedures. Detailed comparisons of solutions to the HEQ, WAEQ, and the paraxial equation (PEQ) are presented for two cases in which numerically exact solutions to the HEQ can be obtained by independent analysis, namely, (i) propagation in a uniform dielectric medium and (ii) propagation along a straight waveguide that has been tilted at an angle to the propagation axis. The quality of WAEQ and PEQ, compared with exact HEQ results, is investigated. Cases are found for which the WAEQ actually performs worse than the PEQ.

Two-photon double ionization of helium in the region of photon energies 42-50eV

NASA Astrophysics Data System (ADS)

Ivanov, I. A.; Kheifets, A. S.

2007-03-01

We report the total integrated cross section (TICS) of two-photon double ionization of helium in the photon energy range from 42to50eV . Our computational procedure relies on a numerical solution of the time-dependent Schrödinger equation on a square-integrable basis and subsequent projection of this solution on a set of final field-free states describing correlation in the two-electron continuum. Our results suggest that the TICS grows monotonically as a function of photon energy in the region of 42-50eV , possibly reaching a maximum in the vicinity of 50eV . We also present fully resolved triple-differential cross sections for selected photon energies.

Adaptive Grid Generation for Numerical Solution of Partial Differential Equations.

DTIC Science & Technology

1983-12-01

numerical solution of fluid dynamics problems is presented. However, the method is applicable to the numer- ical evaluation of any partial differential...emphasis is being placed on numerical solution of the governing differential equations by finite difference methods . In the past two decades, considerable...original equations presented in that paper. The solution of the second problem is more difficult. 2 The method of Thompson et al. provides control for

Segmented Domain Decomposition Multigrid For 3-D Turbomachinery Flows

NASA Technical Reports Server (NTRS)

Celestina, M. L.; Adamczyk, J. J.; Rubin, S. G.

2001-01-01

A Segmented Domain Decomposition Multigrid (SDDMG) procedure was developed for three-dimensional viscous flow problems as they apply to turbomachinery flows. The procedure divides the computational domain into a coarse mesh comprised of uniformly spaced cells. To resolve smaller length scales such as the viscous layer near a surface, segments of the coarse mesh are subdivided into a finer mesh. This is repeated until adequate resolution of the smallest relevant length scale is obtained. Multigrid is used to communicate information between the different grid levels. To test the procedure, simulation results will be presented for a compressor and turbine cascade. These simulations are intended to show the ability of the present method to generate grid independent solutions. Comparisons with data will also be presented. These comparisons will further demonstrate the usefulness of the present work for they allow an estimate of the accuracy of the flow modeling equations independent of error attributed to numerical discretization.

Alternative formulations of the Laplace transform boundary element (LTBE) numerical method for the solution of diffusion-type equations

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

Moridis, G.

1992-03-01

The Laplace Transform Boundary Element (LTBE) method is a recently introduced numerical method, and has been used for the solution of diffusion-type PDEs. It completely eliminates the time dependency of the problem and the need for time discretization, yielding solutions numerical in space and semi-analytical in time. In LTBE solutions are obtained in the Laplace spare, and are then inverted numerically to yield the solution in time. The Stehfest and the DeHoog formulations of LTBE, based on two different inversion algorithms, are investigated. Both formulations produce comparable, extremely accurate solutions.

An Investigation of Two Finite Element Modeling Solutions for Biomechanical Simulation Using a Case Study of a Mandibular Bone.

PubMed

Liu, Yun-Feng; Fan, Ying-Ying; Dong, Hui-Yue; Zhang, Jian-Xing

2017-12-01

The method used in biomechanical modeling for finite element method (FEM) analysis needs to deliver accurate results. There are currently two solutions used in FEM modeling for biomedical model of human bone from computerized tomography (CT) images: one is based on a triangular mesh and the other is based on the parametric surface model and is more popular in practice. The outline and modeling procedures for the two solutions are compared and analyzed. Using a mandibular bone as an example, several key modeling steps are then discussed in detail, and the FEM calculation was conducted. Numerical calculation results based on the models derived from the two methods, including stress, strain, and displacement, are compared and evaluated in relation to accuracy and validity. Moreover, a comprehensive comparison of the two solutions is listed. The parametric surface based method is more helpful when using powerful design tools in computer-aided design (CAD) software, but the triangular mesh based method is more robust and efficient.

Langevin approach to a chemical wave front: Selection of the propagation velocity in the presence of internal noise

NASA Astrophysics Data System (ADS)

Lemarchand, A.; Lesne, A.; Mareschal, M.

1995-05-01

The reaction-diffusion equation associated with the Fisher chemical model A+B-->2A admits wave-front solutions by replacing an unstable stationary state with a stable one. The deterministic analysis concludes that their propagation velocity is not prescribed by the dynamics. For a large class of initial conditions the velocity which is spontaneously selected is equal to the minimum allowed velocity vmin, as predicted by the marginal stability criterion. In order to test the relevance of this deterministic description we investigate the macroscopic consequences, on the velocity and the width of the front, of the intrinsic stochasticity due to the underlying microscopic dynamics. We solve numerically the Langevin equations, deduced analytically from the master equation within a system size expansion procedure. We show that the mean profile associated with the stochastic solution propagates faster than the deterministic solution at a velocity up to 25% greater than vmin.

Filtering of non-linear instabilities. [from finite difference solution of fluid dynamics equations

NASA Technical Reports Server (NTRS)

Khosla, P. K.; Rubin, S. G.

1979-01-01

For Courant numbers larger than one and cell Reynolds numbers larger than two, oscillations and in some cases instabilities are typically found with implicit numerical solutions of the fluid dynamics equations. This behavior has sometimes been associated with the loss of diagonal dominance of the coefficient matrix. It is shown here that these problems can in fact be related to the choice of the spatial differences, with the resulting instability related to aliasing or nonlinear interaction. Appropriate 'filtering' can reduce the intensity of these oscillations and in some cases possibly eliminate the instability. These filtering procedures are equivalent to a weighted average of conservation and non-conservation differencing. The entire spectrum of filtered equations retains a three-point character as well as second-order spatial accuracy. Burgers equation has been considered as a model. Several filters are examined in detail, and smooth solutions have been obtained for extremely large cell Reynolds numbers.

Mixed-mode fracture mechanics parameters of elliptical interface cracks in anisotropic bimaterials

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

Xue, Y.; Qu, J.

1999-07-01

Two-dimensional interface cracks in anisotropic bimaterials have been studied extensively in the literature. However, solutions to three-dimensional interface cracks in anisotropic bimaterials are not available, except for circular (penny-shaped) cracks. In this paper, an elliptical crack on the interface between two anisotropic elastic half-spaces is considered. A formal solution is obtained by using the Stroh method in two dimensional elasticity in conjunction with the Fourier transform method. To illustrate the solution procedure, an elliptical delamination in a cross-ply composite is solved. Numerical results of the stress intensity factors and energy release rate along the crack front are obtained terms ofmore » the interfacial matrix M. It is found that the fields near the crack front are often in mixed mode, due to material anisotropy and the three dimensional nature of the crack front.« less

A new multi-step technique with differential transform method for analytical solution of some nonlinear variable delay differential equations.

PubMed

Benhammouda, Brahim; Vazquez-Leal, Hector

2016-01-01

This work presents an analytical solution of some nonlinear delay differential equations (DDEs) with variable delays. Such DDEs are difficult to treat numerically and cannot be solved by existing general purpose codes. A new method of steps combined with the differential transform method (DTM) is proposed as a powerful tool to solve these DDEs. This method reduces the DDEs to ordinary differential equations that are then solved by the DTM. Furthermore, we show that the solutions can be improved by Laplace-Padé resummation method. Two examples are presented to show the efficiency of the proposed technique. The main advantage of this technique is that it possesses a simple procedure based on a few straight forward steps and can be combined with any analytical method, other than the DTM, like the homotopy perturbation method.

Marching iterative methods for the parabolized and thin layer Navier-Stokes equations

NASA Technical Reports Server (NTRS)

Israeli, M.

1985-01-01

Downstream marching iterative schemes for the solution of the Parabolized or Thin Layer (PNS or TL) Navier-Stokes equations are described. Modifications of the primitive equation global relaxation sweep procedure result in efficient second-order marching schemes. These schemes take full account of the reduced order of the approximate equations as they behave like the SLOR for a single elliptic equation. The improved smoothing properties permit the introduction of Multi-Grid acceleration. The proposed algorithm is essentially Reynolds number independent and therefore can be applied to the solution of the subsonic Euler equations. The convergence rates are similar to those obtained by the Multi-Grid solution of a single elliptic equation; the storage is also comparable as only the pressure has to be stored on all levels. Extensions to three-dimensional and compressible subsonic flows are discussed. Numerical results are presented.

Statistical mechanics of an ideal active fluid confined in a channel

NASA Astrophysics Data System (ADS)

Wagner, Caleb; Baskaran, Aparna; Hagan, Michael

The statistical mechanics of ideal active Brownian particles (ABPs) confined in a channel is studied by obtaining the exact solution of the steady-state Smoluchowski equation for the 1-particle distribution function. The solution is derived using results from the theory of two-way diffusion equations, combined with an iterative procedure that is justified by numerical results. Using this solution, we quantify the effects of confinement on the spatial and orientational order of the ensemble. Moreover, we rigorously show that both the bulk density and the fraction of particles on the channel walls obey simple scaling relations as a function of channel width. By considering a constant-flux steady state, an effective diffusivity for ABPs is derived which shows signatures of the persistent motion that characterizes ABP trajectories. Finally, we discuss how our techniques generalize to other active models, including systems whose activity is modeled in terms of an Ornstein-Uhlenbeck process.

Radiative interactions in laminar duct flows

NASA Technical Reports Server (NTRS)

Trivedi, P. A.; Tiwari, S. N.

1990-01-01

Analyses and numerical procedures are presented for infrared radiative energy transfer in gases when other modes of energy transfer occur simultaneously. Two types of geometries are considered, a parallel plate duct and a circular duct. Fully developed laminar incompressible flows of absorbing-emitting species in black surfaced ducts are considered under the conditions of uniform wall heat flux. The participating species considered are OH, CO, CO2, and H2O. Nongray as well as gray formulations are developed for both geometries. Appropriate limiting solutions of the governing equations are obtained and conduction-radiation interaction parameters are evaluated. Tien and Lowder's wide band model correlation was used in nongray formulation. Numerical procedures are presented to solve the integro-differential equations for both geometries. The range of physical variables considered are 300 to 2000 K for temperature, 0.1 to 100.0 atm for pressure, and 0.1 to 100 cm spacings between plates/radius of the tube. An extensive parametric study based on nongray formulation is presented. Results obtained for different flow conditions indicate that the radiative interactions can be quite significant in fully developed incompressible flows.

A spectral-finite difference solution of the Navier-Stokes equations in three dimensions

NASA Astrophysics Data System (ADS)

Alfonsi, Giancarlo; Passoni, Giuseppe; Pancaldo, Lea; Zampaglione, Domenico

1998-07-01

A new computational code for the numerical integration of the three-dimensional Navier-Stokes equations in their non-dimensional velocity-pressure formulation is presented. The system of non-linear partial differential equations governing the time-dependent flow of a viscous incompressible fluid in a channel is managed by means of a mixed spectral-finite difference method, in which different numerical techniques are applied: Fourier decomposition is used along the homogeneous directions, second-order Crank-Nicolson algorithms are employed for the spatial derivatives in the direction orthogonal to the solid walls and a fourth-order Runge-Kutta procedure is implemented for both the calculation of the convective term and the time advancement. The pressure problem, cast in the Helmholtz form, is solved with the use of a cyclic reduction procedure. No-slip boundary conditions are used at the walls of the channel and cyclic conditions are imposed at the other boundaries of the computing domain.Results are provided for different values of the Reynolds number at several time steps of integration and are compared with results obtained by other authors.

Acoustic scattering of a cylindrical quasi-Gaussian beam with arbitrary incidence focused on a rigid elliptical cylinder

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

Mitri, F. G., E-mail: F.G.Mitri@ieee.org

2015-11-14

Using the partial-wave series expansion method in cylindrical coordinates, a formal analytical solution for the acoustical scattering of a 2D cylindrical quasi-Gaussian beam with an arbitrary angle of incidence θ{sub i}, focused on a rigid elliptical cylinder in a non-viscous fluid, is developed. The cylindrical focused beam expression is an exact solution of the Helmholtz equation. The scattering coefficients for the elliptical cylinder are determined by forcing the expression of the total (incident + scattered) field to satisfy the Neumann boundary condition for a rigid immovable surface, and performing the product of matrices involving an inversion procedure. Computations for the matrices elementsmore » require a single numerical integration procedure for each partial-wave mode. Numerical results are performed with particular emphasis on the focusing properties of the incident beam and its angle of incidence with respect to the major axis a of the ellipse as well as the aspect ratio a/b where b is the minor axis (assuming a > b). The method is validated and verified against previous results obtained via the T-matrix for plane waves. The present analysis is the first to consider an acoustical beam on an elliptic cylinder of variable cross-section as opposed to plane waves of infinite extent. Other 2D non-spherical and Chebyshev surfaces are mentioned that may be examined throughout this analytical formalism assuming a small deformation parameter ε.« less

Modelling CO2 flow in naturally fractured geological media using MINC and multiple subregion upscaling procedure

NASA Astrophysics Data System (ADS)

Tatomir, Alexandru Bogdan A. C.; Flemisch, Bernd; Class, Holger; Helmig, Rainer; Sauter, Martin

2017-04-01

Geological storage of CO2 represents one viable solution to reduce greenhouse gas emission in the atmosphere. Potential leakage of CO2 storage can occur through networks of interconnected fractures. The geometrical complexity of these networks is often very high involving fractures occurring at various scales and having hierarchical structures. Such multiphase flow systems are usually hard to solve with a discrete fracture modelling (DFM) approach. Therefore, continuum fracture models assuming average properties are usually preferred. The multiple interacting continua (MINC) model is an extension of the classic double porosity model (Warren and Root, 1963) which accounts for the non-linear behaviour of the matrix-fracture interactions. For CO2 storage applications the transient representation of the inter-porosity two phase flow plays an important role. This study tests the accuracy and computational efficiency of the MINC method complemented with the multiple sub-region (MSR) upscaling procedure versus the DFM. The two phase flow MINC simulator is implemented in the free-open source numerical toolbox DuMux (www.dumux.org). The MSR (Gong et al., 2009) determines the inter-porosity terms by solving simplified local single-phase flow problems. The DFM is considered as the reference solution. The numerical examples consider a quasi-1D reservoir with a quadratic fracture system , a five-spot radial symmetric reservoir, and a completely random generated fracture system. Keywords: MINC, upscaling, two-phase flow, fractured porous media, discrete fracture model, continuum fracture model

Application of advanced grid generation techniques for flow field computations about complex configurations

NASA Technical Reports Server (NTRS)

Kathong, Monchai; Tiwari, Surendra N.

1988-01-01

In the computation of flowfields about complex configurations, it is very difficult to construct a boundary-fitted coordinate system. An alternative approach is to use several grids at once, each of which is generated independently. This procedure is called the multiple grids or zonal grids approach; its applications are investigated. The method conservative providing conservation of fluxes at grid interfaces. The Euler equations are solved numerically on such grids for various configurations. The numerical scheme used is the finite-volume technique with a three-stage Runge-Kutta time integration. The code is vectorized and programmed to run on the CDC VPS-32 computer. Steady state solutions of the Euler equations are presented and discussed. The solutions include: low speed flow over a sphere, high speed flow over a slender body, supersonic flow through a duct, and supersonic internal/external flow interaction for an aircraft configuration at various angles of attack. The results demonstrate that the multiple grids approach along with the conservative interfacing is capable of computing the flows about the complex configurations where the use of a single grid system is not possible.

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

Jo, J.C.; Shin, W.K.; Choi, C.Y.

Transient heat transfer problems with phase changes (Stefan problems) occur in many engineering situations, including potential core melting and solidification during pressurized-water-reactor severe accidents, ablation of thermal shields, melting and solidification of alloys, and many others. This article addresses the numerical analysis of nonlinear transient heat transfer with melting or solidification. An effective and simple procedure is presented for the simulation of the motion of the boundary and the transient temperature field during the phase change process. To accomplish this purpose, an iterative implicit solution algorithm has been developed by employing the dual-reciprocity boundary-element method. The dual-reciprocity boundary-element approach providedmore » in this article is much simpler than the usual boundary-element method in applying a reciprocity principle and an available technique for dealing with the domain integral of the boundary element formulation simultaneously. In this article, attention is focused on two-dimensional melting (ablation)/solidification problems for simplicity. The accuracy and effectiveness of the present analysis method have been illustrated through comparisons of the calculation results of some examples of one-phase ablation/solidification problems with their known semianalytical or numerical solutions where available.« less

Two-relaxation-time lattice Boltzmann method for the anisotropic dispersive Henry problem

NASA Astrophysics Data System (ADS)

Servan-Camas, Borja; Tsai, Frank T.-C.

2010-02-01

This study develops a lattice Boltzmann method (LBM) with a two-relaxation-time collision operator (TRT) to cope with anisotropic heterogeneous hydraulic conductivity and anisotropic velocity-dependent hydrodynamic dispersion in the saltwater intrusion problem. The directional-speed-of-sound technique is further developed to address anisotropic hydraulic conductivity and dispersion tensors. Forcing terms are introduced in the LBM to correct numerical errors that arise during the recovery procedure and to describe the sink/source terms in the flow and transport equations. In order to facilitate the LBM implementation, the forcing terms are combined with the equilibrium distribution functions (EDFs) to create pseudo-EDFs. This study performs linear stability analysis and derives LBM stability domains to solve the anisotropic advection-dispersion equation. The stability domains are used to select the time step at which the lattice Boltzmann method provides stable solutions to the numerical examples. The LBM was implemented for the anisotropic dispersive Henry problem with high ratios of longitudinal to transverse dispersivities, and the results compared well to the solutions in the work of Abarca et al. (2007).

Numerical aspects and implementation of a two-layer zonal wall model for LES of compressible turbulent flows on unstructured meshes

NASA Astrophysics Data System (ADS)

Park, George Ilhwan; Moin, Parviz

2016-01-01

This paper focuses on numerical and practical aspects associated with a parallel implementation of a two-layer zonal wall model for large-eddy simulation (LES) of compressible wall-bounded turbulent flows on unstructured meshes. A zonal wall model based on the solution of unsteady three-dimensional Reynolds-averaged Navier-Stokes (RANS) equations on a separate near-wall grid is implemented in an unstructured, cell-centered finite-volume LES solver. The main challenge in its implementation is to couple two parallel, unstructured flow solvers for efficient boundary data communication and simultaneous time integrations. A coupling strategy with good load balancing and low processors underutilization is identified. Face mapping and interpolation procedures at the coupling interface are explained in detail. The method of manufactured solution is used for verifying the correct implementation of solver coupling, and parallel performance of the combined wall-modeled LES (WMLES) solver is investigated. The method has successfully been applied to several attached and separated flows, including a transitional flow over a flat plate and a separated flow over an airfoil at an angle of attack.

Estimation of Sonic Fatigue by Reduced-Order Finite Element Based Analyses

NASA Technical Reports Server (NTRS)

Rizzi, Stephen A.; Przekop, Adam

2006-01-01

A computationally efficient, reduced-order method is presented for prediction of sonic fatigue of structures exhibiting geometrically nonlinear response. A procedure to determine the nonlinear modal stiffness using commercial finite element codes allows the coupled nonlinear equations of motion in physical degrees of freedom to be transformed to a smaller coupled system of equations in modal coordinates. The nonlinear modal system is first solved using a computationally light equivalent linearization solution to determine if the structure responds to the applied loading in a nonlinear fashion. If so, a higher fidelity numerical simulation in modal coordinates is undertaken to more accurately determine the nonlinear response. Comparisons of displacement and stress response obtained from the reduced-order analyses are made with results obtained from numerical simulation in physical degrees-of-freedom. Fatigue life predictions from nonlinear modal and physical simulations are made using the rainflow cycle counting method in a linear cumulative damage analysis. Results computed for a simple beam structure under a random acoustic loading demonstrate the effectiveness of the approach and compare favorably with results obtained from the solution in physical degrees-of-freedom.

Numerical Studies of Boundary-Layer Receptivity

NASA Technical Reports Server (NTRS)

Reed, Helen L.

1995-01-01

Direct numerical simulations (DNS) of the acoustic receptivity process on a semi-infinite flat plate with a modified-super-elliptic (MSE) leading edge are performed. The incompressible Navier-Stokes equations are solved in stream-function/vorticity form in a general curvilinear coordinate system. The steady basic-state solution is found by solving the governing equations using an alternating direction implicit (ADI) procedure which takes advantage of the parallelism present in line-splitting techniques. Time-harmonic oscillations of the farfield velocity are applied as unsteady boundary conditions to the unsteady disturbance equations. An efficient time-harmonic scheme is used to produce the disturbance solutions. Buffer-zone techniques have been applied to eliminate wave reflection from the outflow boundary. The spatial evolution of Tollmien-Schlichting (T-S) waves is analyzed and compared with experiment and theory. The effects of nose-radius, frequency, Reynolds number, angle of attack, and amplitude of the acoustic wave are investigated. This work is being performed in conjunction with the experiments at the Arizona State University Unsteady Wind Tunnel under the direction of Professor William Saric. The simulations are of the same configuration and parameters used in the wind-tunnel experiments.

Efficient solution of 3D electromagnetic eddy-current problems within the finite volume framework of OpenFOAM

NASA Astrophysics Data System (ADS)

Beckstein, Pascal; Galindo, Vladimir; Vukčević, Vuko

2017-09-01

Eddy-current problems occur in a wide range of industrial and metallurgical applications where conducting material is processed inductively. Motivated by realising coupled multi-physics simulations, we present a new method for the solution of such problems in the finite volume framework of foam-extend, an extended version of the very popular OpenFOAM software. The numerical procedure involves a semi-coupled multi-mesh approach to solve Maxwell's equations for non-magnetic materials by means of the Coulomb gauged magnetic vector potential A and the electric scalar potential ϕ. The concept is further extended on the basis of the impressed and reduced magnetic vector potential and its usage in accordance with Biot-Savart's law to achieve a very efficient overall modelling even for complex three-dimensional geometries. Moreover, we present a special discretisation scheme to account for possible discontinuities in the electrical conductivity. To complement our numerical method, an extensive validation is completing the paper, which provides insight into the behaviour and the potential of our approach.

Buckling delamination of the circular sandwich plate with piezoelectric face and elastic core layers under rotationally symmetric external pressure

NASA Astrophysics Data System (ADS)

Akbarov, Surkay D.; Cafarova, Fazile I.; Yahnioglu, Nazmiye

2017-02-01

The axisymmetric buckling delamination of the piezoelectric circular sandwich plate with piezoelectric face and elastic (metal) core layers around the interface penny-shaped cracks is investigated. The case is considered where short-circuit conditions with respect to the electrical potential on the upper and lower and also lateral surfaces of face layers are satisfied. It is assumed that the edge surfaces of the cracks have an infinitesimal rotationally symmetric initial imperfection and the development of this imperfection with rotationally symmetric compressive forces acting on the lateral surface of the plate is studied by employing the exact geometrically non-linear field equations and relations of electro-elasticity for piezoelectric materials. Solution to the considered nonlinear problem is reduced to solution of the series boundary value problems derived by applying the linearization procedure with respect to small imperfection of the sought values. Numerical results reveal the effect of piezoelectricity as well as geometrical and material parameters on the critical values are determined numerically by employing finite element method (FEM).

Spurious Numerical Solutions Of Differential Equations

NASA Technical Reports Server (NTRS)

Lafon, A.; Yee, H. C.

1995-01-01

Paper presents detailed study of spurious steady-state numerical solutions of differential equations that contain nonlinear source terms. Main objectives of this study are (1) to investigate how well numerical steady-state solutions of model nonlinear reaction/convection boundary-value problem mimic true steady-state solutions and (2) to relate findings of this investigation to implications for interpretation of numerical results from computational-fluid-dynamics algorithms and computer codes used to simulate reacting flows.

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.

Application of numerical grid generation for improved CFD analysis of multiphase screw machines

NASA Astrophysics Data System (ADS)

Rane, S.; Kovačević, A.

2017-08-01

Algebraic grid generation is widely used for discretization of the working domain of twin screw machines. Algebraic grid generation is fast and has good control over the placement of grid nodes. However, the desired qualities of grid which should be able to handle multiphase flows such as oil injection, may be difficult to achieve at times. In order to obtain fast solution of multiphase screw machines, it is important to further improve the quality and robustness of the computational grid. In this paper, a deforming grid of a twin screw machine is generated using algebraic transfinite interpolation to produce initial mesh upon which an elliptic partial differential equations (PDE) of the Poisson’s form is solved numerically to produce smooth final computational mesh. The quality of numerical cells and their distribution obtained by the differential method is greatly improved. In addition, a similar procedure was introduced to fully smoothen the transition of the partitioning rack curve between the rotors thus improving continuous movement of grid nodes and in turn improve robustness and speed of the Computational Fluid Dynamic (CFD) solver. Analysis of an oil injected twin screw compressor is presented to compare the improvements in grid quality factors in the regions of importance such as interlobe space, radial tip and the core of the rotor. The proposed method that combines algebraic and differential grid generation offer significant improvement in grid quality and robustness of numerical solution.

A globally well-posed finite element algorithm for aerodynamics applications

NASA Technical Reports Server (NTRS)

Iannelli, G. S.; Baker, A. J.

1991-01-01

A finite element CFD algorithm is developed for Euler and Navier-Stokes aerodynamic applications. For the linear basis, the resultant approximation is at least second-order-accurate in time and space for synergistic use of three procedures: (1) a Taylor weak statement, which provides for derivation of companion conservation law systems with embedded dispersion-error control mechanisms; (2) a stiffly stable second-order-accurate implicit Rosenbrock-Runge-Kutta temporal algorithm; and (3) a matrix tensor product factorization that permits efficient numerical linear algebra handling of the terminal large-matrix statement. Thorough analyses are presented regarding well-posed boundary conditions for inviscid and viscous flow specifications. Numerical solutions are generated and compared for critical evaluation of quasi-one- and two-dimensional Euler and Navier-Stokes benchmark test problems.

Singular perturbation techniques for real time aircraft trajectory optimization and control

NASA Technical Reports Server (NTRS)

Calise, A. J.; Moerder, D. D.

1982-01-01

The usefulness of singular perturbation methods for developing real time computer algorithms to control and optimize aircraft flight trajectories is examined. A minimum time intercept problem using F-8 aerodynamic and propulsion data is used as a baseline. This provides a framework within which issues relating to problem formulation, solution methodology and real time implementation are examined. Theoretical questions relating to separability of dynamics are addressed. With respect to implementation, situations leading to numerical singularities are identified, and procedures for dealing with them are outlined. Also, particular attention is given to identifying quantities that can be precomputed and stored, thus greatly reducing the on-board computational load. Numerical results are given to illustrate the minimum time algorithm, and the resulting flight paths. An estimate is given for execution time and storage requirements.

Computational strategies for tire monitoring and analysis

NASA Technical Reports Server (NTRS)

Danielson, Kent T.; Noor, Ahmed K.; Green, James S.

1995-01-01

Computational strategies are presented for the modeling and analysis of tires in contact with pavement. A procedure is introduced for simple and accurate determination of tire cross-sectional geometric characteristics from a digitally scanned image. Three new strategies for reducing the computational effort in the finite element solution of tire-pavement contact are also presented. These strategies take advantage of the observation that footprint loads do not usually stimulate a significant tire response away from the pavement contact region. The finite element strategies differ in their level of approximation and required amount of computer resources. The effectiveness of the strategies is demonstrated by numerical examples of frictionless and frictional contact of the space shuttle Orbiter nose-gear tire. Both an in-house research code and a commercial finite element code are used in the numerical studies.

Exploring a multi-scale method for molecular simulation in continuum solvent model: Explicit simulation of continuum solvent as an incompressible fluid.

PubMed

Xiao, Li; Luo, Ray

2017-12-07

We explored a multi-scale algorithm for the Poisson-Boltzmann continuum solvent model for more robust simulations of biomolecules. In this method, the continuum solvent/solute interface is explicitly simulated with a numerical fluid dynamics procedure, which is tightly coupled to the solute molecular dynamics simulation. There are multiple benefits to adopt such a strategy as presented below. At this stage of the development, only nonelectrostatic interactions, i.e., van der Waals and hydrophobic interactions, are included in the algorithm to assess the quality of the solvent-solute interface generated by the new method. Nevertheless, numerical challenges exist in accurately interpolating the highly nonlinear van der Waals term when solving the finite-difference fluid dynamics equations. We were able to bypass the challenge rigorously by merging the van der Waals potential and pressure together when solving the fluid dynamics equations and by considering its contribution in the free-boundary condition analytically. The multi-scale simulation method was first validated by reproducing the solute-solvent interface of a single atom with analytical solution. Next, we performed the relaxation simulation of a restrained symmetrical monomer and observed a symmetrical solvent interface at equilibrium with detailed surface features resembling those found on the solvent excluded surface. Four typical small molecular complexes were then tested, both volume and force balancing analyses showing that these simple complexes can reach equilibrium within the simulation time window. Finally, we studied the quality of the multi-scale solute-solvent interfaces for the four tested dimer complexes and found that they agree well with the boundaries as sampled in the explicit water simulations.

The method of lines in analyzing solids containing cracks

NASA Technical Reports Server (NTRS)

Gyekenyesi, John P.

1990-01-01

A semi-numerical method is reviewed for solving a set of coupled partial differential equations subject to mixed and possibly coupled boundary conditions. The line method of analysis is applied to the Navier-Cauchy equations of elastic and elastoplastic equilibrium to calculate the displacement distributions in various, simple geometry bodies containing cracks. The application of this method to the appropriate field equations leads to coupled sets of simultaneous ordinary differential equations whose solutions are obtained along sets of lines in a discretized region. When decoupling of the equations and their boundary conditions is not possible, the use of a successive approximation procedure permits the analytical solution of the resulting ordinary differential equations. The use of this method is illustrated by reviewing and presenting selected solutions of mixed boundary value problems in three dimensional fracture mechanics. These solutions are of great importance in fracture toughness testing, where accurate stress and displacement distributions are required for the calculation of certain fracture parameters. Computations obtained for typical flawed specimens include that for elastic as well as elastoplastic response. Problems in both Cartesian and cylindrical coordinate systems are included. Results are summarized for a finite geometry rectangular bar with a central through-the-thickness or rectangular surface crack under remote uniaxial tension. In addition, stress and displacement distributions are reviewed for finite circular bars with embedded penny-shaped cracks, and rods with external annular or ring cracks under opening mode tension. The results obtained show that the method of lines presents a systematic approach to the solution of some three-dimensional mechanics problems with arbitrary boundary conditions. The advantage of this method over other numerical solutions is that good results are obtained even from the use of a relatively coarse grid.

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.

A numerical study of confined turbulent jets

NASA Technical Reports Server (NTRS)

Zhu, J.; Shih, T.-H.

1993-01-01

A numerical investigation is reported of turbulent incompressible jets confined in two ducts, one cylindrical and the other conical with a 5 degree divergence. In each case, three Craya-Curtet numbers are considered which correspond, respectively, to flow situations with no moderate and strong recirculation. Turbulence closure is achieved by using the k-epsilon model and a recently proposed realizable Reynolds stress algebraic equation model that relates the Reynolds stresses explicitly to the quadratic terms of the mean velocity gradients and ensures the positiveness of each component of the turbulent kinetic energy. Calculations are carried out with a finite-volume procedure using boundary-fitted curvilinear coordinates. A second-order accurate, bounded convection scheme and sufficiently fine grids are used to prevent the solutions from being contaminated by numerical diffusion. The calculated results are compared extensively with the available experimental data. It is shown that the numerical methods presented are capable of capturing the essential flow features observed in the experiments and that the realizable Reynolds stress algebraic equation model performs much better than the k-epsilon model for this class of flows of great practical importance.

Curvilinear immersed-boundary method for simulating unsteady flows in shallow natural streams with arbitrarily complex obstacles

NASA Astrophysics Data System (ADS)

Kang, Seokkoo; Borazjani, Iman; Sotiropoulos, Fotis

2008-11-01

Unsteady 3D simulations of flows in natural streams is a challenging task due to the complexity of the bathymetry, the shallowness of the flow, and the presence of multiple nature- and man-made obstacles. This work is motivated by the need to develop a powerful numerical method for simulating such flows using coherent-structure-resolving turbulence models. We employ the curvilinear immersed boundary method of Ge and Sotiropoulos (Journal of Computational Physics, 2007) and address the critical issue of numerical efficiency in large aspect ratio computational domains and grids such as those encountered in long and shallow open channels. We show that the matrix-free Newton-Krylov method for solving the momentum equations coupled with an algebraic multigrid method with incomplete LU preconditioner for solving the Poisson equation yield a robust and efficient procedure for obtaining time-accurate solutions in such problems. We demonstrate the potential of the numerical approach by carrying out a direct numerical simulation of flow in a long and shallow meandering stream with multiple hydraulic structures.

A numerical study of the 3-periodic wave solutions to KdV-type equations

NASA Astrophysics Data System (ADS)

Zhang, Yingnan; Hu, Xingbiao; Sun, Jianqing

2018-02-01

In this paper, by using the direct method of calculating periodic wave solutions proposed by Akira Nakamura, we present a numerical process to calculate the 3-periodic wave solutions to several KdV-type equations: the Korteweg-de Vries equation, the Sawada-Koterra equation, the Boussinesq equation, the Ito equation, the Hietarinta equation and the (2 + 1)-dimensional Kadomtsev-Petviashvili equation. Some detailed numerical examples are given to show the existence of the three-periodic wave solutions numerically.

Numerical Algorithm for Delta of Asian Option

PubMed Central

Zhang, Boxiang; Yu, Yang; Wang, Weiguo

2015-01-01

We study the numerical solution of the Greeks of Asian options. In particular, we derive a close form solution of Δ of Asian geometric option and use this analytical form as a control to numerically calculate Δ of Asian arithmetic option, which is known to have no explicit close form solution. We implement our proposed numerical method and compare the standard error with other classical variance reduction methods. Our method provides an efficient solution to the hedging strategy with Asian options. PMID:26266271

NASA automatic system for computer program documentation, volume 2

NASA Technical Reports Server (NTRS)

Simmons, D. B.

1972-01-01

The DYNASOR 2 program is used for the dynamic nonlinear analysis of shells of revolution. The equations of motion of the shell are solved using Houbolt's numerical procedure. The displacements and stress resultants are determined for both symmetrical and asymmetrical loading conditions. Asymmetrical dynamic buckling can be investigated. Solutions can be obtained for highly nonlinear problems utilizing as many as five of the harmonics generated by SAMMSOR program. A restart capability allows the user to restart the program at a specified time. For Vol. 1, see N73-22129.

An analysis method for two-dimensional transonic viscous flow

NASA Technical Reports Server (NTRS)

Bavitz, P. C.

1975-01-01

A method for the approximate calculation of transonic flow over airfoils, including shock waves and viscous effects, is described. Numerical solutions are obtained by use of a computer program which is discussed in the appendix. The importance of including the boundary layer in the analysis is clearly demonstrated, as well as the need to improve on existing procedures near the trailing edge. Comparisons between calculations and experimental data are presented for both conventional and supercritical airfoils, emphasis being on the surface pressure distribution, and good agreement is indicated.

The analysis of delays in simulator digital computing systems. Volume 1: Formulation of an analysis approach using a central example simulator model

NASA Technical Reports Server (NTRS)

Heffley, R. K.; Jewell, W. F.; Whitbeck, R. F.; Schulman, T. M.

1980-01-01

The effects of spurious delays in real time digital computing systems are examined. Various sources of spurious delays are defined and analyzed using an extant simulator system as an example. A specific analysis procedure is set forth and four cases are viewed in terms of their time and frequency domain characteristics. Numerical solutions are obtained for three single rate one- and two-computer examples, and the analysis problem is formulated for a two-rate, two-computer example.

Ocean tides from Seasat-A

NASA Technical Reports Server (NTRS)

Hendershott, M. C.; Munk, W. H.; Zetler, B. D.

1974-01-01

Two procedures for the evaluation of global tides from SEASAT-A altimetry data are elaborated: an empirical method leading to the response functions for a grid of about 500 points from which the tide can be predicted for any point in the oceans, and a dynamic method which consists of iteratively modifying the parameters in a numerical solution to Laplace tide equations. It is assumed that the shape of the received altimeter signal can be interpreted for sea state and that orbit calculations are available so that absolute sea levels can be obtained.

Accurate Monotonicity - Preserving Schemes With Runge-Kutta Time Stepping

NASA Technical Reports Server (NTRS)

Suresh, A.; Huynh, H. T.

1997-01-01

A new class of high-order monotonicity-preserving schemes for the numerical solution of conservation laws is presented. The interface value in these schemes is obtained by limiting a higher-order polynominal reconstruction. The limiting is designed to preserve accuracy near extrema and to work well with Runge-Kutta time stepping. Computational efficiency is enhanced by a simple test that determines whether the limiting procedure is needed. For linear advection in one dimension, these schemes are shown as well as the Euler equations also confirm their high accuracy, good shock resolution, and computational efficiency.

General Analytical Procedure for Determination of Acidity Parameters of Weak Acids and Bases

PubMed Central

Pilarski, Bogusław; Kaliszan, Roman; Wyrzykowski, Dariusz; Młodzianowski, Janusz; Balińska, Agata

2015-01-01

The paper presents a new convenient, inexpensive, and reagent-saving general methodology for the determination of pK a values for components of the mixture of diverse chemical classes weak organic acids and bases in water solution, without the need to separate individual analytes. The data obtained from simple pH-metric microtitrations are numerically processed into reliable pK a values for each component of the mixture. Excellent agreement has been obtained between the determined pK a values and the reference literature data for compounds studied. PMID:25692072

General analytical procedure for determination of acidity parameters of weak acids and bases.

PubMed

Pilarski, Bogusław; Kaliszan, Roman; Wyrzykowski, Dariusz; Młodzianowski, Janusz; Balińska, Agata

2015-01-01

The paper presents a new convenient, inexpensive, and reagent-saving general methodology for the determination of pK a values for components of the mixture of diverse chemical classes weak organic acids and bases in water solution, without the need to separate individual analytes. The data obtained from simple pH-metric microtitrations are numerically processed into reliable pK a values for each component of the mixture. Excellent agreement has been obtained between the determined pK a values and the reference literature data for compounds studied.

A three-dimensional finite-volume Eulerian-Lagrangian Localized Adjoint Method (ELLAM) for solute-transport modeling

USGS Publications Warehouse

Heberton, C.I.; Russell, T.F.; Konikow, Leonard F.; Hornberger, G.Z.

2000-01-01

This report documents the U.S. Geological Survey Eulerian-Lagrangian Localized Adjoint Method (ELLAM) algorithm that solves an integral form of the solute-transport equation, incorporating an implicit-in-time difference approximation for the dispersive and sink terms. Like the algorithm in the original version of the U.S. Geological Survey MOC3D transport model, ELLAM uses a method of characteristics approach to solve the transport equation on the basis of the velocity field. The ELLAM algorithm, however, is based on an integral formulation of conservation of mass and uses appropriate numerical techniques to obtain global conservation of mass. The implicit procedure eliminates several stability criteria required for an explicit formulation. Consequently, ELLAM allows large transport time increments to be used. ELLAM can produce qualitatively good results using a small number of transport time steps. A description of the ELLAM numerical method, the data-input requirements and output options, and the results of simulator testing and evaluation are presented. The ELLAM algorithm was evaluated for the same set of problems used to test and evaluate Version 1 and Version 2 of MOC3D. These test results indicate that ELLAM offers a viable alternative to the explicit and implicit solvers in MOC3D. Its use is desirable when mass balance is imperative or a fast, qualitative model result is needed. Although accurate solutions can be generated using ELLAM, its efficiency relative to the two previously documented solution algorithms is problem dependent.

A compositional multiphase model for groundwater contamination by petroleum products: 2. Numerical solution

USGS Publications Warehouse

Baehr, Arthur L.; Corapcioglu, M. Yavuz

1987-01-01

In this paper we develop a numerical solution to equations developed in part 1 (M. Y. Corapcioglu and A. L. Baehr, this issue) to predict the fate of an immiscible organic contaminant such as gasoline in the unsaturated zone subsequent to plume establishment. This solution, obtained by using a finite difference scheme and a method of forward projection to evaluate nonlinear coefficients, provides estimates of the flux of solubilized hydrocarbon constituents to groundwater from the portion of a spill which remains trapped in a soil after routine remedial efforts to recover the product have ceased. The procedure was used to solve the one-dimensional (vertical) form of the system of nonlinear partial differential equations defining the transport for each constituent of the product. Additionally, a homogeneous, isothermal soil with constant water content was assumed. An equilibrium assumption partitions the constituents between air, water, adsorbed, and immiscible phases. Free oxygen transport in the soil was also simulated to provide an upper bound estimate of aerobic biodgradation rates. Results are presented for a hypothetical gasoline consisting of eight groups of hydrocarbon constituents. Rates at which hydrocarbon mass is removed from the soil, entering either the atmosphere or groundwater, or is biodegraded are presented. A significant sensitivity to model parameters, particularly the parameters characterizing diffusive vapor transport, was discovered. We conclude that hydrocarbon solute composition in groundwater beneath a gasoline contaminated soil would be heavily weighted toward aromatic constituents like benzene, toluene, and xylene.

Numerical simulation of KdV equation by finite difference method

NASA Astrophysics Data System (ADS)

Yokus, A.; Bulut, H.

2018-05-01

In this study, the numerical solutions to the KdV equation with dual power nonlinearity by using the finite difference method are obtained. Discretize equation is presented in the form of finite difference operators. The numerical solutions are secured via the analytical solution to the KdV equation with dual power nonlinearity which is present in the literature. Through the Fourier-Von Neumann technique and linear stable, we have seen that the FDM is stable. Accuracy of the method is analyzed via the L2 and L_{∞} norm errors. The numerical, exact approximations and absolute error are presented in tables. We compare the numerical solutions with the exact solutions and this comparison is supported with the graphic plots. Under the choice of suitable values of parameters, the 2D and 3D surfaces for the used analytical solution are plotted.

Finite-analytic numerical solution of heat transfer in two-dimensional cavity flow

NASA Technical Reports Server (NTRS)

Chen, C.-J.; Naseri-Neshat, H.; Ho, K.-S.

1981-01-01

Heat transfer in cavity flow is numerically analyzed by a new numerical method called the finite-analytic method. The basic idea of the finite-analytic method is the incorporation of local analytic solutions in the numerical solutions of linear or nonlinear partial differential equations. In the present investigation, the local analytic solutions for temperature, stream function, and vorticity distributions are derived. When the local analytic solution is evaluated at a given nodal point, it gives an algebraic relationship between a nodal value in a subregion and its neighboring nodal points. A system of algebraic equations is solved to provide the numerical solution of the problem. The finite-analytic method is used to solve heat transfer in the cavity flow at high Reynolds number (1000) for Prandtl numbers of 0.1, 1, and 10.

A stability analysis on forced convection boundary layer stagnation-point slip flow in Darcy-Forchheimer porous medium towards a shrinking sheet

NASA Astrophysics Data System (ADS)

Bakar, Shahirah Abu; Arifin, Norihan Md; Ali, Fadzilah Md; Bachok, Norfifah; Nazar, Roslinda

2017-08-01

The stagnation-point flow over a shrinking sheet in Darcy-Forchheimer porous medium is numerically studied. The governing partial differential equations are transformed into ordinary differential equations using a similarity transformation, and then solved numerically by using shooting technique method with Maple implementation. Dual solutions are observed in a certain range of the shrinking parameter. Regarding on numerical solutions, we prepared stability analysis to identify which solution is stable between non-unique solutions by bvp4c solver in Matlab. Further we obtain numerical results or each solution, which enable us to discuss the features of the respective solutions.

A numerical solution for two-dimensional Fredholm integral equations of the second kind with kernels of the logarithmic potential form

NASA Technical Reports Server (NTRS)

Gabrielsen, R. E.; Uenal, A.

1981-01-01

Two dimensional Fredholm integral equations with logarithmic potential kernels are numerically solved. The explicit consequence of these solutions to their true solutions is demonstrated. The results are based on a previous work in which numerical solutions were obtained for Fredholm integral equations of the second kind with continuous kernels.

Rapid method to extract DNA from Cryptococcus neoformans.

PubMed Central

Varma, A; Kwon-Chung, K J

1991-01-01

A rapid and easy method for the extraction of total cellular DNA from Cryptococcus neoformans is described. This procedure modifies and considerably simplifies previously reported methods. Numerous steps were either eliminated or replaced, including preincubations with cell wall permeability agents such as beta-mercaptoethanol and dithiothreitol. The commercially available enzyme preparation Novozyme 234 was found to contain a potent concentration of DNases which actively degrade DNA. Degradation and loss of DNA was prevented by maintaining a high concentration of EDTA in the lysing solution. This procedure resulted in high yields (150 to 200 micrograms of DNA from 100 ml of culture) of good-quality (undegraded), high-molecular-weight DNA which was readily digested by restriction endonucleases, making it suitable for use in various molecular applications. Images PMID:1909713

Small Modifications of Curvilinear Coordinates and Successive Approximations Applied in Geopotential Determination

NASA Astrophysics Data System (ADS)

Holota, P.; Nesvadba, O.

2016-12-01

The mathematical apparatus currently applied for geopotential determination is undoubtedly quite developed. This concerns numerical methods as well as methods based on classical analysis, equally as classical and weak solution concepts. Nevertheless, the nature of the real surface of the Earth has its specific features and is still rather complex. The aim of this paper is to consider these limits and to seek a balance between the performance of an apparatus developed for the surface of the Earth smoothed (or simplified) up to a certain degree and an iteration procedure used to bridge the difference between the real and smoothed topography. The approach is applied for the solution of the linear gravimetric boundary value problem in geopotential determination. Similarly as in other branches of engineering and mathematical physics a transformation of coordinates is used that offers a possibility to solve an alternative between the boundary complexity and the complexity of the coefficients of the partial differential equation governing the solution. As examples the use of modified spherical and also modified ellipsoidal coordinates for the transformation of the solution domain is discussed. However, the complexity of the boundary is then reflected in the structure of Laplace's operator. This effect is taken into account by means of successive approximations. The structure of the respective iteration steps is derived and analyzed. On the level of individual iteration steps the attention is paid to the representation of the solution in terms of function bases or in terms of Green's functions. The convergence of the procedure and the efficiency of its use for geopotential determination is discussed.

A heuristic approach to worst-case carrier-to-interference ratio maximization in satellite system synthesis

NASA Technical Reports Server (NTRS)

Reilly, Charles H.; Walton, Eric K.; Mata, Fernando; Mount-Campbell, Clark A.; Olen, Carl A.

1990-01-01

Consideration is given to the problem of allotting GEO locations to communication satellites so as to maximize the smallest aggregate carrier-to-interference (C/I) ratio calculated at any test point (assumed earth station). The location allotted to each satellite must be within the satellite's service arc, and angular separation constraints are enforced for each pair of satellites to control single-entry EMI. Solutions to this satellite system synthesis problem (SSSP) are found by embedding two heuristic procedures for the satellite location problem (SLP), in a binary search routine to find an estimate of the largest increment to the angular separation values that permits a feasible solution to SLP and SSSP. Numerical results for a 183-satellite, 208-beam example problem are presented.

The Proteus Navier-Stokes code

NASA Technical Reports Server (NTRS)

Towne, Charles E.; Bui, Trong T.; Cavicchi, Richard H.; Conley, Julianne M.; Molls, Frank B.; Schwab, John R.

1992-01-01

An effort is currently underway at NASA Lewis to develop two- and three-dimensional Navier-Stokes codes, called Proteus, for aerospace propulsion applications. The emphasis in the development of Proteus is not algorithm development or research on numerical methods, but rather the development of the code itself. The objective is to develop codes that are user-oriented, easily-modified, and well-documented. Well-proven, state-of-the-art solution algorithms are being used. Code readability, documentation (both internal and external), and validation are being emphasized. This paper is a status report on the Proteus development effort. The analysis and solution procedure are described briefly, and the various features in the code are summarized. The results from some of the validation cases that have been run are presented for both the two- and three-dimensional codes.

Analysis of the interaction of a weak normal shock wave with a turbulent boundary layer

NASA Technical Reports Server (NTRS)

Melnik, R. E.; Grossman, B.

1974-01-01

The method of matched asymptotic expansions is used to analyze the interaction of a normal shock wave with an unseparated turbulent boundary layer on a flat surface at transonic speeds. The theory leads to a three-layer description of the interaction in the double limit of Reynolds number approaching infinity and Mach number approaching unity. The interaction involves an outer, inviscid rotational layer, a constant shear-stress wall layer, and a blending region between them. The pressure distribution is obtained from a numerical solution of the outer-layer equations by a mixed-flow relaxation procedure. An analytic solution for the skin friction is determined from the inner-layer equations. The significance of the mathematical model is discussed with reference to existing experimental data.

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

Santhanagopalan, Shriram; White, Ralph E.

Rotating ring disc electrode (RRDE) experiments are a classic tool for investigating kinetics of electrochemical reactions. Several standardized methods exist for extracting transport parameters and reaction rate constants using RRDE measurements. Here in this work, we compare some approximate solutions to the convective diffusion used popularly in the literature to a rigorous numerical solution of the Nernst-Planck equations coupled to the three dimensional flow problem. In light of these computational advancements, we explore design aspects of the RRDE that will help improve sensitivity of our parameter estimation procedure to experimental data. We use the oxygen reduction in acidic media involvingmore » three charge transfer reactions and a chemical reaction as an example, and identify ways to isolate reaction currents for the individual processes in order to accurately estimate the exchange current densities.« less

Genetic algorithms for the vehicle routing problem

NASA Astrophysics Data System (ADS)

Volna, Eva

2016-06-01

The Vehicle Routing Problem (VRP) is one of the most challenging combinatorial optimization tasks. This problem consists in designing the optimal set of routes for fleet of vehicles in order to serve a given set of customers. Evolutionary algorithms are general iterative algorithms for combinatorial optimization. These algorithms have been found to be very effective and robust in solving numerous problems from a wide range of application domains. This problem is known to be NP-hard; hence many heuristic procedures for its solution have been suggested. For such problems it is often desirable to obtain approximate solutions, so they can be found fast enough and are sufficiently accurate for the purpose. In this paper we have performed an experimental study that indicates the suitable use of genetic algorithms for the vehicle routing problem.

Three-Dimensional Incompressible Navier-Stokes Flow Computations about Complete Configurations Using a Multiblock Unstructured Grid Approach

NASA Technical Reports Server (NTRS)

Sheng, Chunhua; Hyams, Daniel G.; Sreenivas, Kidambi; Gaither, J. Adam; Marcum, David L.; Whitfield, David L.

2000-01-01

A multiblock unstructured grid approach is presented for solving three-dimensional incompressible inviscid and viscous turbulent flows about complete configurations. The artificial compressibility form of the governing equations is solved by a node-based, finite volume implicit scheme which uses a backward Euler time discretization. Point Gauss-Seidel relaxations are used to solve the linear system of equations at each time step. This work employs a multiblock strategy to the solution procedure, which greatly improves the efficiency of the algorithm by significantly reducing the memory requirements by a factor of 5 over the single-grid algorithm while maintaining a similar convergence behavior. The numerical accuracy of solutions is assessed by comparing with the experimental data for a submarine with stem appendages and a high-lift configuration.

Numerical Determination of Critical Conditions for Thermal Ignition

NASA Technical Reports Server (NTRS)

Luo, W.; Wake, G. C.; Hawk, C. W.; Litchford, R. J.

2008-01-01

The determination of ignition or thermal explosion in an oxidizing porous body of material, as described by a dimensionless reaction-diffusion equation of the form .tu = .2u + .e-1/u over the bounded region O, is critically reexamined from a modern perspective using numerical methodologies. First, the classic stationary model is revisited to establish the proper reference frame for the steady-state solution space, and it is demonstrated how the resulting nonlinear two-point boundary value problem can be reexpressed as an initial value problem for a system of first-order differential equations, which may be readily solved using standard algorithms. Then, the numerical procedure is implemented and thoroughly validated against previous computational results based on sophisticated path-following techniques. Next, the transient nonstationary model is attacked, and the full nonlinear form of the reaction-diffusion equation, including a generalized convective boundary condition, is discretized and expressed as a system of linear algebraic equations. The numerical methodology is implemented as a computer algorithm, and validation computations are carried out as a prelude to a broad-ranging evaluation of the assembly problem and identification of the watershed critical initial temperature conditions for thermal ignition. This numerical methodology is then used as the basis for studying the relationship between the shape of the critical initial temperature distribution and the corresponding spatial moments of its energy content integral and an attempt to forge a fundamental conjecture governing this relation. Finally, the effects of dynamic boundary conditions on the classic storage problem are investigated and the groundwork is laid for the development of an approximate solution methodology based on adaptation of the standard stationary model.

Improved diffusion Monte Carlo propagators for bosonic systems using Itô calculus

NASA Astrophysics Data System (ADS)

Hâkansson, P.; Mella, M.; Bressanini, Dario; Morosi, Gabriele; Patrone, Marta

2006-11-01

The construction of importance sampled diffusion Monte Carlo (DMC) schemes accurate to second order in the time step is discussed. A central aspect in obtaining efficient second order schemes is the numerical solution of the stochastic differential equation (SDE) associated with the Fokker-Plank equation responsible for the importance sampling procedure. In this work, stochastic predictor-corrector schemes solving the SDE and consistent with Itô calculus are used in DMC simulations of helium clusters. These schemes are numerically compared with alternative algorithms obtained by splitting the Fokker-Plank operator, an approach that we analyze using the analytical tools provided by Itô calculus. The numerical results show that predictor-corrector methods are indeed accurate to second order in the time step and that they present a smaller time step bias and a better efficiency than second order split-operator derived schemes when computing ensemble averages for bosonic systems. The possible extension of the predictor-corrector methods to higher orders is also discussed.

Numerical analysis of transient fields near thin-wire antennas and scatterers

NASA Astrophysics Data System (ADS)

Landt, J. A.

1981-11-01

Under the premise that `accelerated charge radiates,' one would expect radiation on wire structures to occur from driving points, ends of wires, bends in wires, or locations of lumped loading. Here, this premise is investigated in a series of numerical experiments. The numerical procedure is based on a moment-method solution of a thin-wire time-domain electric-field integral equation. The fields in the vicinity of wire structures are calculated for short impulsive-type excitations, and are viewed in a series of time sequences or snapshots. For these excitations, the fields are spatially limited in the radial dimension, and expand in spheres centered about points of radiation. These centers of radiation coincide with the above list of possible source regions. Time retardation permits these observations to be made clearly in the time domain, similar to time-range gating. In addition to providing insight into transient radiation processes, these studies show that the direction of energy flow is not always defined by Poynting's vector near wire structures.

Numerical pricing of options using high-order compact finite difference schemes

NASA Astrophysics Data System (ADS)

Tangman, D. Y.; Gopaul, A.; Bhuruth, M.

2008-09-01

We consider high-order compact (HOC) schemes for quasilinear parabolic partial differential equations to discretise the Black-Scholes PDE for the numerical pricing of European and American options. We show that for the heat equation with smooth initial conditions, the HOC schemes attain clear fourth-order convergence but fail if non-smooth payoff conditions are used. To restore the fourth-order convergence, we use a grid stretching that concentrates grid nodes at the strike price for European options. For an American option, an efficient procedure is also described to compute the option price, Greeks and the optimal exercise curve. Comparisons with a fourth-order non-compact scheme are also done. However, fourth-order convergence is not experienced with this strategy. To improve the convergence rate for American options, we discuss the use of a front-fixing transformation with the HOC scheme. We also show that the HOC scheme with grid stretching along the asset price dimension gives accurate numerical solutions for European options under stochastic volatility.

Coupled Neutron Transport for HZETRN

NASA Technical Reports Server (NTRS)

Slaba, Tony C.; Blattnig, Steve R.

2009-01-01

Exposure estimates inside space vehicles, surface habitats, and high altitude aircrafts exposed to space radiation are highly influenced by secondary neutron production. The deterministic transport code HZETRN has been identified as a reliable and efficient tool for such studies, but improvements to the underlying transport models and numerical methods are still necessary. In this paper, the forward-backward (FB) and directionally coupled forward-backward (DC) neutron transport models are derived, numerical methods for the FB model are reviewed, and a computationally efficient numerical solution is presented for the DC model. Both models are compared to the Monte Carlo codes HETC-HEDS, FLUKA, and MCNPX, and the DC model is shown to agree closely with the Monte Carlo results. Finally, it is found in the development of either model that the decoupling of low energy neutrons from the light particle transport procedure adversely affects low energy light ion fluence spectra and exposure quantities. A first order correction is presented to resolve the problem, and it is shown to be both accurate and efficient.

Numerical solutions of ideal quantum gas dynamical flows governed by semiclassical ellipsoidal-statistical distribution.

PubMed

Yang, Jaw-Yen; Yan, Chih-Yuan; Diaz, Manuel; Huang, Juan-Chen; Li, Zhihui; Zhang, Hanxin

2014-01-08

The ideal quantum gas dynamics as manifested by the semiclassical ellipsoidal-statistical (ES) equilibrium distribution derived in Wu et al. (Wu et al . 2012 Proc. R. Soc. A 468 , 1799-1823 (doi:10.1098/rspa.2011.0673)) is numerically studied for particles of three statistics. This anisotropic ES equilibrium distribution was derived using the maximum entropy principle and conserves the mass, momentum and energy, but differs from the standard Fermi-Dirac or Bose-Einstein distribution. The present numerical method combines the discrete velocity (or momentum) ordinate method in momentum space and the high-resolution shock-capturing method in physical space. A decoding procedure to obtain the necessary parameters for determining the ES distribution is also devised. Computations of two-dimensional Riemann problems are presented, and various contours of the quantities unique to this ES model are illustrated. The main flow features, such as shock waves, expansion waves and slip lines and their complex nonlinear interactions, are depicted and found to be consistent with existing calculations for a classical gas.

Numerical analysis of the asymptotic two-point boundary value solution for N-body trajectories.

NASA Technical Reports Server (NTRS)

Lancaster, J. E.; Allemann, R. A.

1972-01-01

Previously published asymptotic solutions for lunar and interplanetary trajectories have been modified and combined to formulate a general analytical boundary value solution applicable to a broad class of trajectory problems. In addition, the earlier first-order solutions have been extended to second-order to determine if improved accuracy is possible. Comparisons between the asymptotic solution and numerical integration for several lunar and interplanetary trajectories show that the asymptotic solution is generally quite accurate. Also, since no iterations are required, a solution to the boundary value problem is obtained in a fraction of the time required for numerically integrated solutions.

A coupled chemo-thermo-hygro-mechanical model of concrete at high temperature and failure analysis

NASA Astrophysics Data System (ADS)

Li, Xikui; Li, Rongtao; Schrefler, B. A.

2006-06-01

A hierarchical mathematical model for analyses of coupled chemo-thermo-hygro-mechanical behaviour in concretes at high temperature is presented. The concretes are modelled as unsaturated deforming reactive porous media filled with two immiscible pore fluids, i.e. the gas mixture and the liquid mixture, in immiscible-miscible levels. The thermo-induced desalination process is particularly integrated into the model. The chemical effects of both the desalination and the dehydration processes on the material damage and the degradation of the material strength are taken into account. The mathematical model consists of a set of coupled, partial differential equations governing the mass balance of the dry air, the mass balance of the water species, the mass balance of the matrix components dissolved in the liquid phases, the enthalpy (energy) balance and momentum balance of the whole medium mixture. The governing equations, the state equations for the model and the constitutive laws used in the model are given. A mixed weak form for the finite element solution procedure is formulated for the numerical simulation of chemo-thermo-hygro-mechanical behaviours. Special considerations are given to spatial discretization of hyperbolic equation with non-self-adjoint operator nature. Numerical results demonstrate the performance and the effectiveness of the proposed model and its numerical procedure in reproducing coupled chemo-thermo-hygro-mechanical behaviour in concretes subjected to fire and thermal radiation.

A numerical method for solving systems of linear ordinary differential equations with rapidly oscillating solutions

NASA Technical Reports Server (NTRS)

Bernstein, Ira B.; Brookshaw, Leigh; Fox, Peter A.

1992-01-01

The present numerical method for accurate and efficient solution of systems of linear equations proceeds by numerically developing a set of basis solutions characterized by slowly varying dependent variables. The solutions thus obtained are shown to have a computational overhead largely independent of the small size of the scale length which characterizes the solutions; in many cases, the technique obviates series solutions near singular points, and its known sources of error can be easily controlled without a substantial increase in computational time.

A new method for constructing analytic elements for groundwater flow.

NASA Astrophysics Data System (ADS)

Strack, O. D.

2007-12-01

The analytic element method is based upon the superposition of analytic functions that are defined throughout the infinite domain, and can be used to meet a variety of boundary conditions. Analytic elements have been use successfully for a number of problems, mainly dealing with the Poisson equation (see, e.g., Theory and Applications of the Analytic Element Method, Reviews of Geophysics, 41,2/1005 2003 by O.D.L. Strack). The majority of these analytic elements consists of functions that exhibit jumps along lines or curves. Such linear analytic elements have been developed also for other partial differential equations, e.g., the modified Helmholz equation and the heat equation, and were constructed by integrating elementary solutions, the point sink and the point doublet, along a line. This approach is limiting for two reasons. First, the existence is required of the elementary solutions, and, second, the integration tends to limit the range of solutions that can be obtained. We present a procedure for generating analytic elements that requires merely the existence of a harmonic function with the desired properties; such functions exist in abundance. The procedure to be presented is used to generalize this harmonic function in such a way that the resulting expression satisfies the applicable differential equation. The approach will be applied, along with numerical examples, for the modified Helmholz equation and for the heat equation, while it is noted that the method is in no way restricted to these equations. The procedure is carried out entirely in terms of complex variables, using Wirtinger calculus.

Improve Problem Solving Skills through Adapting Programming Tools

NASA Technical Reports Server (NTRS)

Shaykhian, Linda H.; Shaykhian, Gholam Ali

2007-01-01

There are numerous ways for engineers and students to become better problem-solvers. The use of command line and visual programming tools can help to model a problem and formulate a solution through visualization. The analysis of problem attributes and constraints provide insight into the scope and complexity of the problem. The visualization aspect of the problem-solving approach tends to make students and engineers more systematic in their thought process and help them catch errors before proceeding too far in the wrong direction. The problem-solver identifies and defines important terms, variables, rules, and procedures required for solving a problem. Every step required to construct the problem solution can be defined in program commands that produce intermediate output. This paper advocates improved problem solving skills through using a programming tool. MatLab created by MathWorks, is an interactive numerical computing environment and programming language. It is a matrix-based system that easily lends itself to matrix manipulation, and plotting of functions and data. MatLab can be used as an interactive command line or a sequence of commands that can be saved in a file as a script or named functions. Prior programming experience is not required to use MatLab commands. The GNU Octave, part of the GNU project, a free computer program for performing numerical computations, is comparable to MatLab. MatLab visual and command programming are presented here.

Special data base of Informational - Computational System 'INM RAS - Black Sea' for solving inverse and data assimilation problems

NASA Astrophysics Data System (ADS)

Zakharova, Natalia; Piskovatsky, Nicolay; Gusev, Anatoly

2014-05-01

Development of Informational-Computational Systems (ICS) for data assimilation procedures is one of multidisciplinary problems. To study and solve these problems one needs to apply modern results from different disciplines and recent developments in: mathematical modeling; theory of adjoint equations and optimal control; inverse problems; numerical methods theory; numerical algebra and scientific computing. The above problems are studied in the Institute of Numerical Mathematics of the Russian Academy of Science (INM RAS) in ICS for personal computers. In this work the results on the Special data base development for ICS "INM RAS - Black Sea" are presented. In the presentation the input information for ICS is discussed, some special data processing procedures are described. In this work the results of forecast using ICS "INM RAS - Black Sea" with operational observation data assimilation are presented. This study was supported by the Russian Foundation for Basic Research (project No 13-01-00753) and by Presidium Program of Russian Academy of Sciences (project P-23 "Black sea as an imitational ocean model"). References 1. V.I. Agoshkov, M.V. Assovskii, S.A. Lebedev, Numerical simulation of Black Sea hydrothermodynamics taking into account tide-forming forces. Russ. J. Numer. Anal. Math. Modelling (2012) 27, No.1, pp. 5-31. 2. E.I. Parmuzin, V.I. Agoshkov, Numerical solution of the variational assimilation problem for sea surface temperature in the model of the Black Sea dynamics. Russ. J. Numer. Anal. Math. Modelling (2012) 27, No.1, pp. 69-94. 3. V.B. Zalesny, N.A. Diansky, V.V. Fomin, S.N. Moshonkin, S.G. Demyshev, Numerical model of the circulation of Black Sea and Sea of Azov. Russ. J. Numer. Anal. Math. Modelling (2012) 27, No.1, pp. 95-111. 4. Agoshkov V.I.,Assovsky M.B., Giniatulin S. V., Zakharova N.B., Kuimov G.V., Parmuzin E.I., Fomin V.V. Informational Computational system of variational assimilation of observation data "INM RAS - Black sea"// Ecological safety of coastal and shelf zones and complex use of shelf resources: Collection of scientific works. Issue 26, Volume 2. - National Academy of Sciences of Ukraine, Marine Hydrophysical Institute, Sebastopol, 2012. Pages 352-360. (In russian)

Space-time adaptive ADER-DG schemes for dissipative flows: Compressible Navier-Stokes and resistive MHD equations

NASA Astrophysics Data System (ADS)

Fambri, Francesco; Dumbser, Michael; Zanotti, Olindo

2017-11-01

This paper presents an arbitrary high-order accurate ADER Discontinuous Galerkin (DG) method on space-time adaptive meshes (AMR) for the solution of two important families of non-linear time dependent partial differential equations for compressible dissipative flows : the compressible Navier-Stokes equations and the equations of viscous and resistive magnetohydrodynamics in two and three space-dimensions. The work continues a recent series of papers concerning the development and application of a proper a posteriori subcell finite volume limiting procedure suitable for discontinuous Galerkin methods (Dumbser et al., 2014, Zanotti et al., 2015 [40,41]). It is a well known fact that a major weakness of high order DG methods lies in the difficulty of limiting discontinuous solutions, which generate spurious oscillations, namely the so-called 'Gibbs phenomenon'. In the present work, a nonlinear stabilization of the scheme is sequentially and locally introduced only for troubled cells on the basis of a novel a posteriori detection criterion, i.e. the MOOD approach. The main benefits of the MOOD paradigm, i.e. the computational robustness even in the presence of strong shocks, are preserved and the numerical diffusion is considerably reduced also for the limited cells by resorting to a proper sub-grid. In practice the method first produces a so-called candidate solution by using a high order accurate unlimited DG scheme. Then, a set of numerical and physical detection criteria is applied to the candidate solution, namely: positivity of pressure and density, absence of floating point errors and satisfaction of a discrete maximum principle in the sense of polynomials. Furthermore, in those cells where at least one of these criteria is violated the computed candidate solution is detected as troubled and is locally rejected. Subsequently, a more reliable numerical solution is recomputed a posteriori by employing a more robust but still very accurate ADER-WENO finite volume scheme on the subgrid averages within that troubled cell. Finally, a high order DG polynomial is reconstructed back from the evolved subcell averages. We apply the whole approach for the first time to the equations of compressible gas dynamics and magnetohydrodynamics in the presence of viscosity, thermal conductivity and magnetic resistivity, therefore extending our family of adaptive ADER-DG schemes to cases for which the numerical fluxes also depend on the gradient of the state vector. The distinguished high-resolution properties of the presented numerical scheme standout against a wide number of non-trivial test cases both for the compressible Navier-Stokes and the viscous and resistive magnetohydrodynamics equations. The present results show clearly that the shock-capturing capability of the news schemes is significantly enhanced within a cell-by-cell Adaptive Mesh Refinement (AMR) implementation together with time accurate local time stepping (LTS).

Numerical simulations to the nonlinear model of interpersonal relationships with time fractional derivative

NASA Astrophysics Data System (ADS)

Gencoglu, Muharrem Tuncay; Baskonus, Haci Mehmet; Bulut, Hasan

2017-01-01

The main aim of this manuscript is to obtain numerical solutions for the nonlinear model of interpersonal relationships with time fractional derivative. The variational iteration method is theoretically implemented and numerically conducted only to yield the desired solutions. Numerical simulations of desired solutions are plotted by using Wolfram Mathematica 9. The authors would like to thank the reviewers for their comments that help improve the manuscript.

A robust interpolation procedure for producing tidal current ellipse inputs for regional and coastal ocean numerical models

NASA Astrophysics Data System (ADS)

Byun, Do-Seong; Hart, Deirdre E.

2017-04-01

Regional and/or coastal ocean models can use tidal current harmonic forcing, together with tidal harmonic forcing along open boundaries in order to successfully simulate tides and tidal currents. These inputs can be freely generated using online open-access data, but the data produced are not always at the resolution required for regional or coastal models. Subsequent interpolation procedures can produce tidal current forcing data errors for parts of the world's coastal ocean where tidal ellipse inclinations and phases move across the invisible mathematical "boundaries" between 359° and 0° degrees (or 179° and 0°). In nature, such "boundaries" are in fact smooth transitions, but if these mathematical "boundaries" are not treated correctly during interpolation, they can produce inaccurate input data and hamper the accurate simulation of tidal currents in regional and coastal ocean models. These avoidable errors arise due to procedural shortcomings involving vector embodiment problems (i.e., how a vector is represented mathematically, for example as velocities or as coordinates). Automated solutions for producing correct tidal ellipse parameter input data are possible if a series of steps are followed correctly, including the use of Cartesian coordinates during interpolation. This note comprises the first published description of scenarios where tidal ellipse parameter interpolation errors can arise, and of a procedure to successfully avoid these errors when generating tidal inputs for regional and/or coastal ocean numerical models. We explain how a straightforward sequence of data production, format conversion, interpolation, and format reconversion steps may be used to check for the potential occurrence and avoidance of tidal ellipse interpolation and phase errors. This sequence is demonstrated via a case study of the M2 tidal constituent in the seas around Korea but is designed to be universally applicable. We also recommend employing tidal ellipse parameter calculation methods that avoid the use of Foreman's (1978) "northern semi-major axis convention" since, as revealed in our analysis, this commonly used conversion can result in inclination interpolation errors even when Cartesian coordinate-based "vector embodiment" solutions are employed.

Direct Solution of the Chemical Master Equation Using Quantized Tensor Trains

PubMed Central

Kazeev, Vladimir; Khammash, Mustafa; Nip, Michael; Schwab, Christoph

2014-01-01

The Chemical Master Equation (CME) is a cornerstone of stochastic analysis and simulation of models of biochemical reaction networks. Yet direct solutions of the CME have remained elusive. Although several approaches overcome the infinite dimensional nature of the CME through projections or other means, a common feature of proposed approaches is their susceptibility to the curse of dimensionality, i.e. the exponential growth in memory and computational requirements in the number of problem dimensions. We present a novel approach that has the potential to “lift” this curse of dimensionality. The approach is based on the use of the recently proposed Quantized Tensor Train (QTT) formatted numerical linear algebra for the low parametric, numerical representation of tensors. The QTT decomposition admits both, algorithms for basic tensor arithmetics with complexity scaling linearly in the dimension (number of species) and sub-linearly in the mode size (maximum copy number), and a numerical tensor rounding procedure which is stable and quasi-optimal. We show how the CME can be represented in QTT format, then use the exponentially-converging -discontinuous Galerkin discretization in time to reduce the CME evolution problem to a set of QTT-structured linear equations to be solved at each time step using an algorithm based on Density Matrix Renormalization Group (DMRG) methods from quantum chemistry. Our method automatically adapts the “basis” of the solution at every time step guaranteeing that it is large enough to capture the dynamics of interest but no larger than necessary, as this would increase the computational complexity. Our approach is demonstrated by applying it to three different examples from systems biology: independent birth-death process, an example of enzymatic futile cycle, and a stochastic switch model. The numerical results on these examples demonstrate that the proposed QTT method achieves dramatic speedups and several orders of magnitude storage savings over direct approaches. PMID:24626049

Elastic interactions of a fatigue crack with a micro-defect by the mixed boundary integral equation method

NASA Technical Reports Server (NTRS)

Lua, Yuan J.; Liu, Wing K.; Belytschko, Ted

1993-01-01

In this paper, the mixed boundary integral equation method is developed to study the elastic interactions of a fatigue crack and a micro-defect such as a void, a rigid inclusion or a transformation inclusion. The method of pseudo-tractions is employed to study the effect of a transformation inclusion. An enriched element which incorporates the mixed-mode stress intensity factors is applied to characterize the singularity at a moving crack tip. In order to evaluate the accuracy of the numerical procedure, the analysis of a crack emanating from a circular hole in a finite plate is performed and the results are compared with the available numerical solution. The effects of various micro-defects on the crack path and fatigue life are investigated. The results agree with the experimental observations.

Numeric calculation of unsteady forces over thin pointed wings in sonic flow

NASA Technical Reports Server (NTRS)

Kimble, K. R.; Wu, J. M.

1975-01-01

A fast and reasonably accurate numerical procedure is proposed for the solution of a simplified unsteady transonic equation. The approach described takes into account many of the effects of the steady flow field. The resulting accuracy is within a few per cent and can be carried out on a computer in less than one minute per case (one frequency and one mode of oscillation). The problem concerns a rigid pointed wing which performs harmonic pitching oscillations of small amplitude in a steady uniform transonic flow. Wake influence is ignored and shocks must be weak. It is shown that the method is more flexible than the transonic box method proposed by Rodemich and Andrew (1965) in that it can easily account for variable local Mach number and rather arbitrary planform so long as the basic assumptions are fulfilled.

The numerical solution of ordinary differential equations by the Taylor series method

NASA Technical Reports Server (NTRS)

Silver, A. H.; Sullivan, E.

1973-01-01

A programming implementation of the Taylor series method is presented for solving ordinary differential equations. The compiler is written in PL/1, and the target language is FORTRAN IV. The reduction of a differential system to rational form is described along with the procedures required for automatic numerical integration. The Taylor method is compared with two other methods for a number of differential equations. Algorithms using the Taylor method to find the zeroes of a given differential equation and to evaluate partial derivatives are presented. An annotated listing of the PL/1 program which performs the reduction and code generation is given. Listings of the FORTRAN routines used by the Taylor series method are included along with a compilation of all the recurrence formulas used to generate the Taylor coefficients for non-rational functions.

An Adaptively-Refined, Cartesian, Cell-Based Scheme for the Euler and Navier-Stokes Equations. Ph.D. Thesis - Michigan Univ.

NASA Technical Reports Server (NTRS)

Coirier, William John

1994-01-01

A Cartesian, cell-based scheme for solving the Euler and Navier-Stokes equations in two dimensions is developed and tested. Grids about geometrically complicated bodies are generated automatically, by recursive subdivision of a single Cartesian cell encompassing the entire flow domain. Where the resulting cells intersect bodies, polygonal 'cut' cells are created. The geometry of the cut cells is computed using polygon-clipping algorithms. The grid is stored in a binary-tree data structure which provides a natural means of obtaining cell-to-cell connectivity and of carrying out solution-adaptive refinement. The Euler and Navier-Stokes equations are solved on the resulting grids using a finite-volume formulation. The convective terms are upwinded, with a limited linear reconstruction of the primitive variables used to provide input states to an approximate Riemann solver for computing the fluxes between neighboring cells. A multi-stage time-stepping scheme is used to reach a steady-state solution. Validation of the Euler solver with benchmark numerical and exact solutions is presented. An assessment of the accuracy of the approach is made by uniform and adaptive grid refinements for a steady, transonic, exact solution to the Euler equations. The error of the approach is directly compared to a structured solver formulation. A non smooth flow is also assessed for grid convergence, comparing uniform and adaptively refined results. Several formulations of the viscous terms are assessed analytically, both for accuracy and positivity. The two best formulations are used to compute adaptively refined solutions of the Navier-Stokes equations. These solutions are compared to each other, to experimental results and/or theory for a series of low and moderate Reynolds numbers flow fields. The most suitable viscous discretization is demonstrated for geometrically-complicated internal flows. For flows at high Reynolds numbers, both an altered grid-generation procedure and a different formulation of the viscous terms are shown to be necessary. A hybrid Cartesian/body-fitted grid generation approach is demonstrated. In addition, a grid-generation procedure based on body-aligned cell cutting coupled with a viscous stensil-construction procedure based on quadratic programming is presented.

Theory of precipitation effects on dead cylindrical fuels

Treesearch

Michael A. Fosberg

1972-01-01

Numerical and analytical solutions of the Fickian diffusion equation were used to determine the effects of precipitation on dead cylindrical forest fuels. The analytical solution provided a physical framework. The numerical solutions were then used to refine the analytical solution through a similarity argument. The theoretical solutions predicted realistic rates of...

Microwave Heating of a Liquid Stably Flowing in a Circular Channel Under the Conditions of Nonstationary Radiative-Convective Heat Transfer

NASA Astrophysics Data System (ADS)

Salomatov, V. V.; Puzyrev, E. M.; Salomatov, A. V.

2018-05-01

A class of nonlinear problems of nonstationary radiative-convective heat transfer under the microwave action with a small penetration depth is considered in a stabilized coolant flow in a circular channel. The solutions to these problems are obtained, using asymptotic procedures at the stages of nonstationary and stationary convective heat transfer on the heat-radiating channel surface. The nonstationary and stationary stages of the solution are matched, using the "longitudinal coordinate-time" characteristic. The approximate solutions constructed on such principles correlate reliably with the exact ones at the limiting values of the operation parameters, as well as with numerical and experimental data of other researchers. An important advantage of these solutions is that they allow the determination of the main regularities of the microwave and thermal radiation influence on convective heat transfer in a channel even before performing cumbersome calculations. It is shown that, irrespective of the heat exchange regime (nonstationary or stationary), the Nusselt number decreases and the rate of the surface temperature change increases with increase in the intensity of thermal action.

Resolution of an uncertain closed-loop logistics model: an application to fuzzy linear programs with risk analysis.

PubMed

Wang, Hsiao-Fan; Hsu, Hsin-Wei

2010-11-01

With the urgency of global warming, green supply chain management, logistics in particular, has drawn the attention of researchers. Although there are closed-loop green logistics models in the literature, most of them do not consider the uncertain environment in general terms. In this study, a generalized model is proposed where the uncertainty is expressed by fuzzy numbers. An interval programming model is proposed by the defined means and mean square imprecision index obtained from the integrated information of all the level cuts of fuzzy numbers. The resolution for interval programming is based on the decision maker (DM)'s preference. The resulting solution provides useful information on the expected solutions under a confidence level containing a degree of risk. The results suggest that the more optimistic the DM is, the better is the resulting solution. However, a higher risk of violation of the resource constraints is also present. By defining this probable risk, a solution procedure was developed with numerical illustrations. This provides a DM trade-off mechanism between logistic cost and the risk. Copyright 2010 Elsevier Ltd. All rights reserved.

Analysis of periodically excited non-linear systems by a parametric continuation technique

NASA Astrophysics Data System (ADS)

Padmanabhan, C.; Singh, R.

1995-07-01

The dynamic behavior and frequency response of harmonically excited piecewise linear and/or non-linear systems has been the subject of several recent investigations. Most of the prior studies employed harmonic balance or Galerkin schemes, piecewise linear techniques, analog simulation and/or direct numerical integration (digital simulation). Such techniques are somewhat limited in their ability to predict all of the dynamic characteristics, including bifurcations leading to the occurrence of unstable, subharmonic, quasi-periodic and/or chaotic solutions. To overcome this problem, a parametric continuation scheme, based on the shooting method, is applied specifically to a periodically excited piecewise linear/non-linear system, in order to improve understanding as well as to obtain the complete dynamic response. Parameter regions exhibiting bifurcations to harmonic, subharmonic or quasi-periodic solutions are obtained quite efficiently and systematically. Unlike other techniques, the proposed scheme can follow period-doubling bifurcations, and with some modifications obtain stable quasi-periodic solutions and their bifurcations. This knowledge is essential in establishing conditions for the occurrence of chaotic oscillations in any non-linear system. The method is first validated through the Duffing oscillator example, the solutions to which are also obtained by conventional one-term harmonic balance and perturbation methods. The second example deals with a clearance non-linearity problem for both harmonic and periodic excitations. Predictions from the proposed scheme match well with available analog simulation data as well as with multi-term harmonic balance results. Potential savings in computational time over direct numerical integration is demonstrated for some of the example cases. Also, this work has filled in some of the solution regimes for an impact pair, which were missed previously in the literature. Finally, one main limitation associated with the proposed procedure is discussed.

MIB Galerkin method for elliptic interface problems.

PubMed

Xia, Kelin; Zhan, Meng; Wei, Guo-Wei

2014-12-15

Material interfaces are omnipresent in the real-world structures and devices. Mathematical modeling of material interfaces often leads to elliptic partial differential equations (PDEs) with discontinuous coefficients and singular sources, which are commonly called elliptic interface problems. The development of high-order numerical schemes for elliptic interface problems has become a well defined field in applied and computational mathematics and attracted much attention in the past decades. Despite of significant advances, challenges remain in the construction of high-order schemes for nonsmooth interfaces, i.e., interfaces with geometric singularities, such as tips, cusps and sharp edges. The challenge of geometric singularities is amplified when they are associated with low solution regularities, e.g., tip-geometry effects in many fields. The present work introduces a matched interface and boundary (MIB) Galerkin method for solving two-dimensional (2D) elliptic PDEs with complex interfaces, geometric singularities and low solution regularities. The Cartesian grid based triangular elements are employed to avoid the time consuming mesh generation procedure. Consequently, the interface cuts through elements. To ensure the continuity of classic basis functions across the interface, two sets of overlapping elements, called MIB elements, are defined near the interface. As a result, differentiation can be computed near the interface as if there is no interface. Interpolation functions are constructed on MIB element spaces to smoothly extend function values across the interface. A set of lowest order interface jump conditions is enforced on the interface, which in turn, determines the interpolation functions. The performance of the proposed MIB Galerkin finite element method is validated by numerical experiments with a wide range of interface geometries, geometric singularities, low regularity solutions and grid resolutions. Extensive numerical studies confirm the designed second order convergence of the MIB Galerkin method in the L ∞ and L 2 errors. Some of the best results are obtained in the present work when the interface is C 1 or Lipschitz continuous and the solution is C 2 continuous.

Graph Theory-Based Technique for Isolating Corrupted Boundary Conditions in Continental-Scale River Network Hydrodynamic Simulation

NASA Astrophysics Data System (ADS)

Yu, C. W.; Hodges, B. R.; Liu, F.

2017-12-01

Development of continental-scale river network models creates challenges where the massive amount of boundary condition data encounters the sensitivity of a dynamic nu- merical model. The topographic data sets used to define the river channel characteristics may include either corrupt data or complex configurations that cause instabilities in a numerical solution of the Saint-Venant equations. For local-scale river models (e.g. HEC- RAS), modelers typically rely on past experience to make ad hoc boundary condition adjustments that ensure a stable solution - the proof of the adjustment is merely the sta- bility of the solution. To date, there do not exist any formal methodologies or automated procedures for a priori detecting/fixing boundary conditions that cause instabilities in a dynamic model. Formal methodologies for data screening and adjustment are a critical need for simulations with a large number of river reaches that draw their boundary con- dition data from a wide variety of sources. At the continental scale, we simply cannot assume that we will have access to river-channel cross-section data that has been ade- quately analyzed and processed. Herein, we argue that problematic boundary condition data for unsteady dynamic modeling can be identified through numerical modeling with the steady-state Saint-Venant equations. The fragility of numerical stability increases with the complexity of branching in river network system and instabilities (even in an unsteady solution) are typically triggered by the nonlinear advection term in Saint-Venant equations. It follows that the behavior of the simpler steady-state equations (which retain the nonlin- ear term) can be used to screen the boundary condition data for problematic regions. In this research, we propose a graph-theory based method to isolate the location of corrupted boundary condition data in a continental-scale river network and demonstrate its utility with a network of O(10^4) elements. Acknowledgement: This research is supported by the National Science Foundation un- der grant number CCF-1331610.

Determination of the Fracture Parameters in a Stiffened Composite Panel

NASA Technical Reports Server (NTRS)

Lin, Chung-Yi

2000-01-01

A modified J-integral, namely the equivalent domain integral, is derived for a three-dimensional anisotropic cracked solid to evaluate the stress intensity factor along the crack front using the finite element method. Based on the equivalent domain integral method with auxiliary fields, an interaction integral is also derived to extract the second fracture parameter, the T-stress, from the finite element results. The auxiliary fields are the two-dimensional plane strain solutions of monoclinic materials with the plane of symmetry at x(sub 3) = 0 under point loads applied at the crack tip. These solutions are expressed in a compact form based on the Stroh formalism. Both integrals can be implemented into a single numerical procedure to determine the distributions of stress intensity factor and T-stress components, T11, T13, and thus T33, along a three-dimensional crack front. The effects of plate thickness and crack length on the variation of the stress intensity factor and T-stresses through the thickness are investigated in detail for through-thickness center-cracked plates (isotropic and orthotropic) and orthotropic stiffened panels under pure mode-I loading conditions. For all the cases studied, T11 remains negative. For plates with the same dimensions, a larger size of crack yields larger magnitude of the normalized stress intensity factor and normalized T-stresses. The results in orthotropic stiffened panels exhibit an opposite trend in general. As expected, for the thicker panels, the fracture parameters evaluated through the thickness, except the region near the free surfaces, approach two-dimensional plane strain solutions. In summary, the numerical methods presented in this research demonstrate their high computational effectiveness and good numerical accuracy in extracting these fracture parameters from the finite element results in three-dimensional cracked solids.

The CE/SE Method: a CFD Framework for the Challenges of the New Millennium

NASA Technical Reports Server (NTRS)

Chang, Sin-Chung; Yu, Sheng-Tao

2001-01-01

The space-time conservation element and solution element (CE/SE) method, which was originated and is continuously being developed at NASA Glenn Research Center, is a high-resolution, genuinely multidimensional and unstructured-mesh compatible numerical method for solving conservation laws. Since its inception in 1991, the CE/SE method has been used to obtain highly accurate numerical solutions for 1D, 2D and 3D flow problems involving shocks, contact discontinuities, acoustic waves, vortices, shock/acoustic waves/vortices interactions, shock/boundary layers interactions and chemical reactions. Without the aid of preconditioning or other special techniques, it has been applied to both steady and unsteady flows with speeds ranging from Mach number = 0.00288 to 10. In addition, the method has unique features that allow for (i) the use of very simple non-reflecting boundary conditions, and (ii) a unified wall boundary treatment for viscous and inviscid flows. The CE/SE method was developed with the conviction that, with a solid foundation in physics, a robust, coherent and accurate numerical framework can be built without involving overly complex mathematics. As a result, the method was constructed using a set of design principles that facilitate simplicity, robustness and accuracy. The most important among them are: (i) enforcing both local and global flux conservation in space and time, with flux evaluation at an interface being an integral part of the solution procedure and requiring no interpolation or extrapolation; (ii) unifying space and time and treating them as a single entity; and (iii) requiring that a numerical scheme be built from a nondissipative core scheme such that the numerical dissipation can be effectively controlled and, as a result, will not overwhelm the physical dissipation. Part I of the workshop will be devoted to a discussion of these principles along with a description of how the ID, 2D and 3D CE/SE schemes are constructed. In Part II, various applications of the CE/SE method, particularly those involving chemical reactions and acoustics, will be presented. The workshop will be concluded with a sketch of the future research directions.

Crank-Nicholson difference scheme for a stochastic parabolic equation with a dependent operator coefficient

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

Ashyralyev, Allaberen; Okur, Ulker

In the present paper, the Crank-Nicolson difference scheme for the numerical solution of the stochastic parabolic equation with the dependent operator coefficient is considered. Theorem on convergence estimates for the solution of this difference scheme is established. In applications, convergence estimates for the solution of difference schemes for the numerical solution of three mixed problems for parabolic equations are obtained. The numerical results are given.

Automatic yield-line analysis of slabs using discontinuity layout optimization

PubMed Central

Gilbert, Matthew; He, Linwei; Smith, Colin C.; Le, Canh V.

2014-01-01

The yield-line method of analysis is a long established and extremely effective means of estimating the maximum load sustainable by a slab or plate. However, although numerous attempts to automate the process of directly identifying the critical pattern of yield-lines have been made over the past few decades, to date none has proved capable of reliably analysing slabs of arbitrary geometry. Here, it is demonstrated that the discontinuity layout optimization (DLO) procedure can successfully be applied to such problems. The procedure involves discretization of the problem using nodes inter-connected by potential yield-line discontinuities, with the critical layout of these then identified using linear programming. The procedure is applied to various benchmark problems, demonstrating that highly accurate solutions can be obtained, and showing that DLO provides a truly systematic means of directly and reliably automatically identifying yield-line patterns. Finally, since the critical yield-line patterns for many problems are found to be quite complex in form, a means of automatically simplifying these is presented. PMID:25104905

Standards and Guidelines for Numerical Models for Tsunami Hazard Mitigation

NASA Astrophysics Data System (ADS)

Titov, V.; Gonzalez, F.; Kanoglu, U.; Yalciner, A.; Synolakis, C. E.

2006-12-01

An increased number of nations around the workd need to develop tsunami mitigation plans which invariably involve inundation maps for warning guidance and evacuation planning. There is the risk that inundation maps may be produced with older or untested methodology, as there are currently no standards for modeling tools. In the aftermath of the 2004 megatsunami, some models were used to model inundation for Cascadia events with results much larger than sediment records and existing state-of-the-art studies suggest leading to confusion among emergency management. Incorrectly assessing tsunami impact is hazardous, as recent events in 2006 in Tonga, Kythira, Greece and Central Java have suggested (Synolakis and Bernard, 2006). To calculate tsunami currents, forces and runup on coastal structures, and inundation of coastlines one must calculate the evolution of the tsunami wave from the deep ocean to its target site, numerically. No matter what the numerical model, validation (the process of ensuring that the model solves the parent equations of motion accurately) and verification (the process of ensuring that the model used represents geophysical reality appropriately) both are an essential. Validation ensures that the model performs well in a wide range of circumstances and is accomplished through comparison with analytical solutions. Verification ensures that the computational code performs well over a range of geophysical problems. A few analytic solutions have been validated themselves with laboratory data. Even fewer existing numerical models have been both validated with the analytical solutions and verified with both laboratory measurements and field measurements, thus establishing a gold standard for numerical codes for inundation mapping. While there is in principle no absolute certainty that a numerical code that has performed well in all the benchmark tests will also produce correct inundation predictions with any given source motions, validated codes reduce the level of uncertainty in their results to the uncertainty in the geophysical initial conditions. Further, when coupled with real--time free--field tsunami measurements from tsunameters, validated codes are the only choice for realistic forecasting of inundation; the consequences of failure are too ghastly to take chances with numerical procedures that have not been validated. We discuss a ten step process of benchmark tests for models used for inundation mapping. The associated methodology and algorithmes have to first be validated with analytical solutions, then verified with laboratory measurements and field data. The models need to be published in the scientific literature in peer-review journals indexed by ISI. While this process may appear onerous, it reflects our state of knowledge, and is the only defensible methodology when human lives are at stake. Synolakis, C.E., and Bernard, E.N, Tsunami science before and beyond Boxing Day 2004, Phil. Trans. R. Soc. A 364 1845, 2231--2263, 2005.

A numerical study of transient heat and mass transfer in crystal growth

NASA Technical Reports Server (NTRS)

Han, Samuel Bang-Moo

1987-01-01

A numerical analysis of transient heat and solute transport across a rectangular cavity is performed. Five nonlinear partial differential equations which govern the conservation of mass, momentum, energy and solute concentration related to crystal growth in solution, are simultaneously integrated by a numerical method based on the SIMPLE algorithm. Numerical results showed that the flow, temperature and solute fields are dependent on thermal and solutal Grashoff number, Prandtl number, Schmidt number and aspect ratio. The average Nusselt and Sherwood numbers evaluated at the center of the cavity decrease markedly when the solutal buoyancy force acts in the opposite direction to the thermal buoyancy force. When the solutal and thermal buoyancy forces act in the same direction, however, Sherwood number increases significantly and yet Nusselt number decreases. Overall effects of convection on the crystal growth are seen to be an enhancement of growth rate as expected but with highly nonuniform spatial growth variations.

A systematic linear space approach to solving partially described inverse eigenvalue problems

NASA Astrophysics Data System (ADS)

Hu, Sau-Lon James; Li, Haujun

2008-06-01

Most applications of the inverse eigenvalue problem (IEP), which concerns the reconstruction of a matrix from prescribed spectral data, are associated with special classes of structured matrices. Solving the IEP requires one to satisfy both the spectral constraint and the structural constraint. If the spectral constraint consists of only one or few prescribed eigenpairs, this kind of inverse problem has been referred to as the partially described inverse eigenvalue problem (PDIEP). This paper develops an efficient, general and systematic approach to solve the PDIEP. Basically, the approach, applicable to various structured matrices, converts the PDIEP into an ordinary inverse problem that is formulated as a set of simultaneous linear equations. While solving simultaneous linear equations for model parameters, the singular value decomposition method is applied. Because of the conversion to an ordinary inverse problem, other constraints associated with the model parameters can be easily incorporated into the solution procedure. The detailed derivation and numerical examples to implement the newly developed approach to symmetric Toeplitz and quadratic pencil (including mass, damping and stiffness matrices of a linear dynamic system) PDIEPs are presented. Excellent numerical results for both kinds of problem are achieved under the situations that have either unique or infinitely many solutions.

ADPAC v1.0: User's Manual

NASA Technical Reports Server (NTRS)

Hall, Edward J.; Heidegger, Nathan J.; Delaney, Robert A.

1999-01-01

The overall objective of this study was to evaluate the effects of turbulence models in a 3-D numerical analysis on the wake prediction capability. The current version of the computer code resulting from this study is referred to as ADPAC v7 (Advanced Ducted Propfan Analysis Codes -Version 7). This report is intended to serve as a computer program user's manual for the ADPAC code used and modified under Task 15 of NASA Contract NAS3-27394. The ADPAC program is based on a flexible multiple-block and discretization scheme permitting coupled 2-D/3-D mesh block solutions with application to a wide variety of geometries. Aerodynamic calculations are based on a four-stage Runge-Kutta time-marching finite volume solution technique with added numerical dissipation. Steady flow predictions are accelerated by a multigrid procedure. Turbulence models now available in the ADPAC code are: a simple mixing-length model, the algebraic Baldwin-Lomax model with user defined coefficients, the one-equation Spalart-Allmaras model, and a two-equation k-R model. The consolidated ADPAC code is capable of executing in either a serial or parallel computing mode from a single source code.

Non-linear eigensolver-based alternative to traditional SCF methods

NASA Astrophysics Data System (ADS)

Gavin, Brendan; Polizzi, Eric

2013-03-01

The self-consistent iterative procedure in Density Functional Theory calculations is revisited using a new, highly efficient and robust algorithm for solving the non-linear eigenvector problem (i.e. H(X)X = EX;) of the Kohn-Sham equations. This new scheme is derived from a generalization of the FEAST eigenvalue algorithm, and provides a fundamental and practical numerical solution for addressing the non-linearity of the Hamiltonian with the occupied eigenvectors. In contrast to SCF techniques, the traditional outer iterations are replaced by subspace iterations that are intrinsic to the FEAST algorithm, while the non-linearity is handled at the level of a projected reduced system which is orders of magnitude smaller than the original one. Using a series of numerical examples, it will be shown that our approach can outperform the traditional SCF mixing techniques such as Pulay-DIIS by providing a high converge rate and by converging to the correct solution regardless of the choice of the initial guess. We also discuss a practical implementation of the technique that can be achieved effectively using the FEAST solver package. This research is supported by NSF under Grant #ECCS-0846457 and Intel Corporation.

Numerical Evaluation of Lateral Diffusion Inside Diffusive Gradients in Thin Films Samplers

PubMed Central

2015-01-01

Using numerical simulation of diffusion inside diffusive gradients in thin films (DGT) samplers, we show that the effect of lateral diffusion inside the sampler on the solute flux into the sampler is a nonlinear function of the diffusion layer thickness and the physical sampling window size. In contrast, earlier work concluded that this effect was constant irrespective of parameters of the sampler geometry. The flux increase caused by lateral diffusion inside the sampler was determined to be ∼8.8% for standard samplers, which is considerably lower than the previous estimate of ∼20%. Lateral diffusion is also propagated to the diffusive boundary layer (DBL), where it leads to a slightly stronger decrease in the mass uptake than suggested by the common 1D diffusion model that is applied for evaluating DGT results. We introduce a simple correction procedure for lateral diffusion and demonstrate how the effect of lateral diffusion on diffusion in the DBL can be accounted for. These corrections often result in better estimates of the DBL thickness (δ) and the DGT-measured concentration than earlier approaches and will contribute to more accurate concentration measurements in solute monitoring in waters. PMID:25877251

An accurate and efficient acoustic eigensolver based on a fast multipole BEM and a contour integral method

NASA Astrophysics Data System (ADS)

Zheng, Chang-Jun; Gao, Hai-Feng; Du, Lei; Chen, Hai-Bo; Zhang, Chuanzeng

2016-01-01

An accurate numerical solver is developed in this paper for eigenproblems governed by the Helmholtz equation and formulated through the boundary element method. A contour integral method is used to convert the nonlinear eigenproblem into an ordinary eigenproblem, so that eigenvalues can be extracted accurately by solving a set of standard boundary element systems of equations. In order to accelerate the solution procedure, the parameters affecting the accuracy and efficiency of the method are studied and two contour paths are compared. Moreover, a wideband fast multipole method is implemented with a block IDR (s) solver to reduce the overall solution cost of the boundary element systems of equations with multiple right-hand sides. The Burton-Miller formulation is employed to identify the fictitious eigenfrequencies of the interior acoustic problems with multiply connected domains. The actual effect of the Burton-Miller formulation on tackling the fictitious eigenfrequency problem is investigated and the optimal choice of the coupling parameter as α = i / k is confirmed through exterior sphere examples. Furthermore, the numerical eigenvalues obtained by the developed method are compared with the results obtained by the finite element method to show the accuracy and efficiency of the developed method.

Numerical Simulation of Flow Through an Artificial Heart

NASA Technical Reports Server (NTRS)

Rogers, Stuart E.; Kutler, Paul; Kwak, Dochan; Kiris, Cetin

1989-01-01

A solution procedure was developed that solves the unsteady, incompressible Navier-Stokes equations, and was used to numerically simulate viscous incompressible flow through a model of the Pennsylvania State artificial heart. The solution algorithm is based on the artificial compressibility method, and uses flux-difference splitting to upwind the convective terms; a line-relaxation scheme is used to solve the equations. The time-accuracy of the method is obtained by iteratively solving the equations at each physical time step. The artificial heart geometry involves a piston-type action with a moving solid wall. A single H-grid is fit inside the heart chamber. The grid is continuously compressed and expanded with a constant number of grid points to accommodate the moving piston. The computational domain ends at the valve openings where nonreflective boundary conditions based on the method of characteristics are applied. Although a number of simplifing assumptions were made regarding the geometry, the computational results agreed reasonably well with an experimental picture. The computer time requirements for this flow simulation, however, are quite extensive. Computational study of this type of geometry would benefit greatly from improvements in computer hardware speed and algorithm efficiency enhancements.

Simulation of 2-dimensional viscous flow through cascades using a semi-elliptic analysis and hybrid C-H grids

NASA Technical Reports Server (NTRS)

Ramamurti, R.; Ghia, U.; Ghia, K. N.

1988-01-01

A semi-elliptic formulation, termed the interacting parabolized Navier-Stokes (IPNS) formulation, is developed for the analysis of a class of subsonic viscous flows for which streamwise diffusion is neglible but which are significantly influenced by upstream interactions. The IPNS equations are obtained from the Navier-Stokes equations by dropping the streamwise viscous-diffusion terms but retaining upstream influence via the streamwise pressure-gradient. A two-step alternating-direction-explicit numerical scheme is developed to solve these equations. The quasi-linearization and discretization of the equations are carefully examined so that no artificial viscosity is added externally to the scheme. Also, solutions to compressible as well as nearly compressible flows are obtained without any modification either in the analysis or in the solution process. The procedure is applied to constricted channels and cascade passages formed by airfoils of various shapes. These geometries are represented using numerically generated curilinear boundary-oriented coordinates forming an H-grid. A hybrid C-H grid, more appropriate for cascade of airfoils with rounded leading edges, was also developed. Satisfactory results are obtained for flows through cascades of Joukowski airfoils.

Modal element method for potential flow in non-uniform ducts: Combining closed form analysis with CFD

NASA Technical Reports Server (NTRS)

Baumeister, Kenneth J.; Baumeister, Joseph F.

1994-01-01

An analytical procedure is presented, called the modal element method, that combines numerical grid based algorithms with eigenfunction expansions developed by separation of variables. A modal element method is presented for solving potential flow in a channel with two-dimensional cylindrical like obstacles. The infinite computational region is divided into three subdomains; the bounded finite element domain, which is characterized by the cylindrical obstacle and the surrounding unbounded uniform channel entrance and exit domains. The velocity potential is represented approximately in the grid based domain by a finite element solution and is represented analytically by an eigenfunction expansion in the uniform semi-infinite entrance and exit domains. The calculated flow fields are in excellent agreement with exact analytical solutions. By eliminating the grid surrounding the obstacle, the modal element method reduces the numerical grid size, employs a more precise far field boundary condition, as well as giving theoretical insight to the interaction of the obstacle with the mean flow. Although the analysis focuses on a specific geometry, the formulation is general and can be applied to a variety of problems as seen by a comparison to companion theories in aeroacoustics and electromagnetics.

Evaluation of transverse dispersion effects in tank experiments by numerical modeling: parameter estimation, sensitivity analysis and revision of experimental design.

PubMed

Ballarini, E; Bauer, S; Eberhardt, C; Beyer, C

2012-06-01

Transverse dispersion represents an important mixing process for transport of contaminants in groundwater and constitutes an essential prerequisite for geochemical and biodegradation reactions. Within this context, this work describes the detailed numerical simulation of highly controlled laboratory experiments using uranine, bromide and oxygen depleted water as conservative tracers for the quantification of transverse mixing in porous media. Synthetic numerical experiments reproducing an existing laboratory experimental set-up of quasi two-dimensional flow through tank were performed to assess the applicability of an analytical solution of the 2D advection-dispersion equation for the estimation of transverse dispersivity as fitting parameter. The fitted dispersivities were compared to the "true" values introduced in the numerical simulations and the associated error could be precisely estimated. A sensitivity analysis was performed on the experimental set-up in order to evaluate the sensitivities of the measurements taken at the tank experiment on the individual hydraulic and transport parameters. From the results, an improved experimental set-up as well as a numerical evaluation procedure could be developed, which allow for a precise and reliable determination of dispersivities. The improved tank set-up was used for new laboratory experiments, performed at advective velocities of 4.9 m d(-1) and 10.5 m d(-1). Numerical evaluation of these experiments yielded a unique and reliable parameter set, which closely fits the measured tracer concentration data. For the porous medium with a grain size of 0.25-0.30 mm, the fitted longitudinal and transverse dispersivities were 3.49×10(-4) m and 1.48×10(-5) m, respectively. The procedures developed in this paper for the synthetic and rigorous design and evaluation of the experiments can be generalized and transferred to comparable applications. Copyright © 2012 Elsevier B.V. All rights reserved.

Integrated Targeting and Guidance for Powered Planetary Descent

NASA Astrophysics Data System (ADS)

Azimov, Dilmurat M.; Bishop, Robert H.

2018-02-01

This paper presents an on-board guidance and targeting design that enables explicit state and thrust vector control and on-board targeting for planetary descent and landing. These capabilities are developed utilizing a new closed-form solution for the constant thrust arc of the braking phase of the powered descent trajectory. The key elements of proven targeting and guidance architectures, including braking and approach phase quartics, are employed. It is demonstrated that implementation of the proposed solution avoids numerical simulation iterations, thereby facilitating on-board execution of targeting procedures during the descent. It is shown that the shape of the braking phase constant thrust arc is highly dependent on initial mass and propulsion system parameters. The analytic solution process is explicit in terms of targeting and guidance parameters, while remaining generic with respect to planetary body and descent trajectory design. These features increase the feasibility of extending the proposed integrated targeting and guidance design to future cargo and robotic landing missions.

The MHOST finite element program: 3-D inelastic analysis methods for hot section components. Volume 1: Theoretical manual

NASA Technical Reports Server (NTRS)

Nakazawa, Shohei

1991-01-01

Formulations and algorithms implemented in the MHOST finite element program are discussed. The code uses a novel concept of the mixed iterative solution technique for the efficient 3-D computations of turbine engine hot section components. The general framework of variational formulation and solution algorithms are discussed which were derived from the mixed three field Hu-Washizu principle. This formulation enables the use of nodal interpolation for coordinates, displacements, strains, and stresses. Algorithmic description of the mixed iterative method includes variations for the quasi static, transient dynamic and buckling analyses. The global-local analysis procedure referred to as the subelement refinement is developed in the framework of the mixed iterative solution, of which the detail is presented. The numerically integrated isoparametric elements implemented in the framework is discussed. Methods to filter certain parts of strain and project the element discontinuous quantities to the nodes are developed for a family of linear elements. Integration algorithms are described for linear and nonlinear equations included in MHOST program.

VS2DI: Model use, calibration, and validation

USGS Publications Warehouse

Healy, Richard W.; Essaid, Hedeff I.

2012-01-01

VS2DI is a software package for simulating water, solute, and heat transport through soils or other porous media under conditions of variable saturation. The package contains a graphical preprocessor for constructing simulations, a postprocessor for displaying simulation results, and numerical models that solve for flow and solute transport (VS2DT) and flow and heat transport (VS2DH). Flow is described by the Richards equation, and solute and heat transport are described by advection-dispersion equations; the finite-difference method is used to solve these equations. Problems can be simulated in one, two, or three (assuming radial symmetry) dimensions. This article provides an overview of calibration techniques that have been used with VS2DI; included is a detailed description of calibration procedures used in simulating the interaction between groundwater and a stream fed by drainage from agricultural fields in central Indiana. Brief descriptions of VS2DI and the various types of problems that have been addressed with the software package are also presented.

Integrated Targeting and Guidance for Powered Planetary Descent

NASA Astrophysics Data System (ADS)

Azimov, Dilmurat M.; Bishop, Robert H.

2018-06-01

This paper presents an on-board guidance and targeting design that enables explicit state and thrust vector control and on-board targeting for planetary descent and landing. These capabilities are developed utilizing a new closed-form solution for the constant thrust arc of the braking phase of the powered descent trajectory. The key elements of proven targeting and guidance architectures, including braking and approach phase quartics, are employed. It is demonstrated that implementation of the proposed solution avoids numerical simulation iterations, thereby facilitating on-board execution of targeting procedures during the descent. It is shown that the shape of the braking phase constant thrust arc is highly dependent on initial mass and propulsion system parameters. The analytic solution process is explicit in terms of targeting and guidance parameters, while remaining generic with respect to planetary body and descent trajectory design. These features increase the feasibility of extending the proposed integrated targeting and guidance design to future cargo and robotic landing missions.

An iterative method for tri-level quadratic fractional programming problems using fuzzy goal programming approach

NASA Astrophysics Data System (ADS)

Kassa, Semu Mitiku; Tsegay, Teklay Hailay

2017-08-01

Tri-level optimization problems are optimization problems with three nested hierarchical structures, where in most cases conflicting objectives are set at each level of hierarchy. Such problems are common in management, engineering designs and in decision making situations in general, and are known to be strongly NP-hard. Existing solution methods lack universality in solving these types of problems. In this paper, we investigate a tri-level programming problem with quadratic fractional objective functions at each of the three levels. A solution algorithm has been proposed by applying fuzzy goal programming approach and by reformulating the fractional constraints to equivalent but non-fractional non-linear constraints. Based on the transformed formulation, an iterative procedure is developed that can yield a satisfactory solution to the tri-level problem. The numerical results on various illustrative examples demonstrated that the proposed algorithm is very much promising and it can also be used to solve larger-sized as well as n-level problems of similar structure.

Progress in incompressible Navier-Stokes computations for propulsion flows and its dual-use applications

NASA Technical Reports Server (NTRS)

Kiris, Cetin

1995-01-01

Development of an incompressible Navier-Stokes solution procedure was performed for the analysis of a liquid rocket engine pump components and for the mechanical heart assist devices. The solution procedure for the propulsion systems is applicable to incompressible Navier-Stokes flows in a steadily rotating frame of reference for any general complex configurations. The computer codes were tested on different complex configurations such as liquid rocket engine inducer and impellers. As a spin-off technology from the turbopump component simulations, the flow analysis for an axial heart pump was conducted. The baseline Left Ventricular Assist Device (LVAD) design was improved by adding an inducer geometry by adapting from the liquid rocket engine pump. The time-accurate mode of the incompressible Navier-Stokes code was validated with flapping foil experiment by using different domain decomposition methods. In the flapping foil experiment, two upstream NACA 0025 foils perform high-frequency synchronized motion and generate unsteady flow conditions for a downstream larger stationary foil. Fairly good agreement was obtained between unsteady experimental data and numerical results from two different moving boundary procedures. Incompressible Navier-Stokes code (INS3D) has been extended for heat transfer applications. The temperature equation was written for both forced and natural convection phenomena. Flow in a square duct case was used for the validation of the code in both natural and forced convection.

Comparing the development of the multiplication of fractions in Turkish and American textbooks

NASA Astrophysics Data System (ADS)

Kar, Tuğrul; Güler, Gürsel; Şen, Ceylan; Özdemir, Ercan

2018-02-01

This study analyzed the methods used to teach the multiplication of fractions in Turkish and American textbooks. Two Turkish textbooks and two American textbooks, Everyday Mathematics (EM) and Connected Mathematics 3 (CM), were analyzed. The analyses focused on the content and the nature of the mathematical problems presented in the textbooks. The findings of the study showed that the American textbooks aimed at developing conceptual understanding first and then procedural fluency, whereas the Turkish textbooks aimed at developing both concurrently. The American textbooks provided more opportunities for different computational strategies. The solutions to most problems in all textbooks required a single computational step, a numerical answer, and procedural knowledge. Furthermore, compared with the Turkish textbooks, the American textbooks contained a greater number of problems that required high-level cognitive skills such as mathematical reasoning.

Active magnetic bearing control loop modeling for a finite element rotordynamics code

NASA Technical Reports Server (NTRS)

Genta, Giancarlo; Delprete, Cristiana; Carabelli, Stefano

1994-01-01

A mathematical model of an active electromagnetic bearing which includes the actuator, the sensor and the control system is developed and implemented in a specialized finite element code for rotordynamic analysis. The element formulation and its incorporation in the model of the machine are described in detail. A solution procedure, based on a modal approach in which the number of retained modes is controlled by the user, is then shown together with other procedures for computing the steady-state response to both static and unbalance forces. An example of application shows the numerical results obtained on a model of an electric motor suspended on a five active-axis magnetic suspension. The comparison of some of these results with the experimental characteristics of the actual system shows the ability of the present model to predict its performance.

Advances in contact algorithms and their application to tires

NASA Technical Reports Server (NTRS)

Noor, Ahmed K.; Tanner, John A.

1988-01-01

Currently used techniques for tire contact analysis are reviewed. Discussion focuses on the different techniques used in modeling frictional forces and the treatment of contact conditions. A status report is presented on a new computational strategy for the modeling and analysis of tires, including the solution of the contact problem. The key elements of the proposed strategy are: (1) use of semianalytic mixed finite elements in which the shell variables are represented by Fourier series in the circumferential direction and piecewise polynomials in the meridional direction; (2) use of perturbed Lagrangian formulation for the determination of the contact area and pressure; and (3) application of multilevel iterative procedures and reduction techniques to generate the response of the tire. Numerical results are presented to demonstrate the effectiveness of a proposed procedure for generating the tire response associated with different Fourier harmonics.

Computational study of generic hypersonic vehicle flow fields

NASA Technical Reports Server (NTRS)

Narayan, Johnny R.

1994-01-01

The geometric data of the generic hypersonic vehicle configuration included body definitions and preliminary grids for the forebody (nose cone excluded), midsection (propulsion system excluded), and afterbody sections. This data was to be augmented by the nose section geometry (blunt conical section mated with the noncircular cross section of the forebody initial plane) along with a grid and a detailed supersonic combustion ramjet (scramjet) geometry (inlet and combustor) which should be merged with the nozzle portion of the afterbody geometry. The solutions were to be obtained by using a Navier-Stokes (NS) code such as TUFF for the nose portion, a parabolized Navier-Stokes (PNS) solver such as the UPS and STUFF codes for the forebody, a NS solver with finite rate hydrogen-air chemistry capability such as TUFF and SPARK for the scramjet and a suitable solver (NS or PNS) for the afterbody and external nozzle flows. The numerical simulation of the hypersonic propulsion system for the generic hypersonic vehicle is the major focus of this entire work. Supersonic combustion ramjet is such a propulsion system, hence the main thrust of the present task has been to establish a solution procedure for the scramjet flow. The scramjet flow is compressible, turbulent, and reacting. The fuel used is hydrogen and the combustion process proceeds at a finite rate. As a result, the solution procedure must be capable of addressing such flows.

Structural equation modeling for observational studies

USGS Publications Warehouse

Grace, J.B.

2008-01-01

Structural equation modeling (SEM) represents a framework for developing and evaluating complex hypotheses about systems. This method of data analysis differs from conventional univariate and multivariate approaches familiar to most biologists in several ways. First, SEMs are multiequational and capable of representing a wide array of complex hypotheses about how system components interrelate. Second, models are typically developed based on theoretical knowledge and designed to represent competing hypotheses about the processes responsible for data structure. Third, SEM is conceptually based on the analysis of covariance relations. Most commonly, solutions are obtained using maximum-likelihood solution procedures, although a variety of solution procedures are used, including Bayesian estimation. Numerous extensions give SEM a very high degree of flexibility in dealing with nonnormal data, categorical responses, latent variables, hierarchical structure, multigroup comparisons, nonlinearities, and other complicating factors. Structural equation modeling allows researchers to address a variety of questions about systems, such as how different processes work in concert, how the influences of perturbations cascade through systems, and about the relative importance of different influences. I present 2 example applications of SEM, one involving interactions among lynx (Lynx pardinus), mongooses (Herpestes ichneumon), and rabbits (Oryctolagus cuniculus), and the second involving anuran species richness. Many wildlife ecologists may find SEM useful for understanding how populations function within their environments. Along with the capability of the methodology comes a need for care in the proper application of SEM.

Analytical and Numerical solutions of a nonlinear alcoholism model via variable-order fractional differential equations

NASA Astrophysics Data System (ADS)

Gómez-Aguilar, J. F.

2018-03-01

In this paper, we analyze an alcoholism model which involves the impact of Twitter via Liouville-Caputo and Atangana-Baleanu-Caputo fractional derivatives with constant- and variable-order. Two fractional mathematical models are considered, with and without delay. Special solutions using an iterative scheme via Laplace and Sumudu transform were obtained. We studied the uniqueness and existence of the solutions employing the fixed point postulate. The generalized model with variable-order was solved numerically via the Adams method and the Adams-Bashforth-Moulton scheme. Stability and convergence of the numerical solutions were presented in details. Numerical examples of the approximate solutions are provided to show that the numerical methods are computationally efficient. Therefore, by including both the fractional derivatives and finite time delays in the alcoholism model studied, we believe that we have established a more complete and more realistic indicator of alcoholism model and affect the spread of the drinking.

Long-time asymptotic solution structure of Camassa-Holm equation subject to an initial condition with non-zero reflection coefficient of the scattering data

NASA Astrophysics Data System (ADS)

Chang, Chueh-Hsin; Yu, Ching-Hao; Sheu, Tony Wen-Hann

2016-10-01

In this article, we numerically revisit the long-time solution behavior of the Camassa-Holm equation ut - uxxt + 2ux + 3uux = 2uxuxx + uuxxx. The finite difference solution of this integrable equation is sought subject to the newly derived initial condition with Delta-function potential. Our underlying strategy of deriving a numerical phase accurate finite difference scheme in time domain is to reduce the numerical dispersion error through minimization of the derived discrepancy between the numerical and exact modified wavenumbers. Additionally, to achieve the goal of conserving Hamiltonians in the completely integrable equation of current interest, a symplecticity-preserving time-stepping scheme is developed. Based on the solutions computed from the temporally symplecticity-preserving and the spatially wavenumber-preserving schemes, the long-time asymptotic CH solution characters can be accurately depicted in distinct regions of the space-time domain featuring with their own quantitatively very different solution behaviors. We also aim to numerically confirm that in the two transition zones their long-time asymptotics can indeed be described in terms of the theoretically derived Painlevé transcendents. Another attempt of this study is to numerically exhibit a close connection between the presently predicted finite-difference solution and the solution of the Painlevé ordinary differential equation of type II in two different transition zones.

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.

HYDRA-II: A hydrothermal analysis computer code: Volume 2, User's manual

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

McCann, R.A.; Lowery, P.S.; Lessor, D.L.

1987-09-01

HYDRA-II is a hydrothermal computer code capable of three-dimensional analysis of coupled conduction, convection, and thermal radiation problems. This code is especially appropriate for simulating the steady-state performance of spent fuel storage systems. The code has been evaluated for this application for the US Department of Energy's Commercial Spent Fuel Management Program. HYDRA-II provides a finite-difference solution in cartesian coordinates to the equations governing the conservation of mass, momentum, and energy. A cylindrical coordinate system may also be used to enclose the cartesian coordinate system. This exterior coordinate system is useful for modeling cylindrical cask bodies. The difference equations formore » conservation of momentum incorporate directional porosities and permeabilities that are available to model solid structures whose dimensions may be smaller than the computational mesh. The equation for conservation of energy permits modeling of orthotropic physical properties and film resistances. Several automated methods are available to model radiation transfer within enclosures and from fuel rod to fuel rod. The documentation of HYDRA-II is presented in three separate volumes. Volume 1 - Equations and Numerics describes the basic differential equations, illustrates how the difference equations are formulated, and gives the solution procedures employed. This volume, Volume 2 - User's Manual, contains code flow charts, discusses the code structure, provides detailed instructions for preparing an input file, and illustrates the operation of the code by means of a sample problem. The final volume, Volume 3 - Verification/Validation Assessments, provides a comparison between the analytical solution and the numerical simulation for problems with a known solution. 6 refs.« less

Design of transonic airfoil sections using a similarity theory

NASA Technical Reports Server (NTRS)

Nixon, D.

1978-01-01

A study of the available methods for transonic airfoil and wing design indicates that the most powerful technique is the numerical optimization procedure. However, the computer time for this method is relatively large because of the amount of computation required in the searches during optimization. The optimization method requires that base and calibration solutions be computed to determine a minimum drag direction. The design space is then computationally searched in this direction; it is these searches that dominate the computation time. A recent similarity theory allows certain transonic flows to be calculated rapidly from the base and calibration solutions. In this paper the application of the similarity theory to design problems is examined with the object of at least partially eliminating the costly searches of the design optimization method. An example of an airfoil design is presented.

Estimating parameters from rotating ring disc electrode measurements

DOE PAGES

Santhanagopalan, Shriram; White, Ralph E.

2017-10-21

Rotating ring disc electrode (RRDE) experiments are a classic tool for investigating kinetics of electrochemical reactions. Several standardized methods exist for extracting transport parameters and reaction rate constants using RRDE measurements. Here in this work, we compare some approximate solutions to the convective diffusion used popularly in the literature to a rigorous numerical solution of the Nernst-Planck equations coupled to the three dimensional flow problem. In light of these computational advancements, we explore design aspects of the RRDE that will help improve sensitivity of our parameter estimation procedure to experimental data. We use the oxygen reduction in acidic media involvingmore » three charge transfer reactions and a chemical reaction as an example, and identify ways to isolate reaction currents for the individual processes in order to accurately estimate the exchange current densities.« less

Numerical simulation of transverse fuel injection

NASA Technical Reports Server (NTRS)

Mao, Marlon; Riggins, David W.; Mcclinton, Charles R.

1991-01-01

A review of recent work at NASA Langley Research Center to compare the predictions of transverse fuel injector flow fields and mixing performance with experimental results is presented. Various cold (non-reactive) mixing studies were selected for code calibration which include the effects of boundary layer thickness and injection angle for sonic hydrogen injection into supersonic air. Angled injection of helium is also included. This study was performed using both the three-dimensional elliptic and the parabolized Navier-Stokes (PNS) versions of SPARK. Axial solution planes were passed from PNS to elliptic and elliptic to PNS in order to efficiently generate solutions. The PNS version is used both upstream and far downstream of the injector where the flow can be considered parabolic in nature. The comparisons are used to identify experimental deficiencies and computational procedures to improve agreement.

Transport coefficients in ultrarelativistic kinetic theory

NASA Astrophysics Data System (ADS)

Ambruş, Victor E.

2018-02-01

A spatially periodic longitudinal wave is considered in relativistic dissipative hydrodynamics. At sufficiently small wave amplitudes, an analytic solution is obtained in the linearized limit of the macroscopic conservation equations within the first- and second-order relativistic hydrodynamics formulations. A kinetic solver is used to obtain the numerical solution of the relativistic Boltzmann equation for massless particles in the Anderson-Witting approximation for the collision term. It is found that, at small values of the Anderson-Witting relaxation time τ , the transport coefficients emerging from the relativistic Boltzmann equation agree with those predicted through the Chapman-Enskog procedure, while the relaxation times of the heat flux and shear pressure are equal to τ . These claims are further strengthened by considering a moment-type approximation based on orthogonal polynomials under which the Chapman-Enskog results for the transport coefficients are exactly recovered.

Investigation of radiative interaction in laminar flows using Monte Carlo simulation

NASA Technical Reports Server (NTRS)

Liu, Jiwen; Tiwari, S. N.

1993-01-01

The Monte Carlo method (MCM) is employed to study the radiative interactions in fully developed laminar flow between two parallel plates. Taking advantage of the characteristics of easy mathematical treatment of the MCM, a general numerical procedure is developed for nongray radiative interaction. The nongray model is based on the statistical narrow band model with an exponential-tailed inverse intensity distribution. To validate the Monte Carlo simulation for nongray radiation problems, the results of radiative dissipation from the MCM are compared with two available solutions for a given temperature profile between two plates. After this validation, the MCM is employed to solve the present physical problem and results for the bulk temperature are compared with available solutions. In general, good agreement is noted and reasons for some discrepancies in certain ranges of parameters are explained.

Generic Procedure for Coupling the PHREEQC Geochemical Modeling Framework with Flow and Solute Transport Simulators

NASA Astrophysics Data System (ADS)

Wissmeier, L. C.; Barry, D. A.

2009-12-01

Computer simulations of water availability and quality play an important role in state-of-the-art water resources management. However, many of the most utilized software programs focus either on physical flow and transport phenomena (e.g., MODFLOW, MT3DMS, FEFLOW, HYDRUS) or on geochemical reactions (e.g., MINTEQ, PHREEQC, CHESS, ORCHESTRA). In recent years, several couplings between both genres of programs evolved in order to consider interactions between flow and biogeochemical reactivity (e.g., HP1, PHWAT). Software coupling procedures can be categorized as ‘close couplings’, where programs pass information via the memory stack at runtime, and ‘remote couplings’, where the information is exchanged at each time step via input/output files. The former generally involves modifications of software codes and therefore expert programming skills are required. We present a generic recipe for remotely coupling the PHREEQC geochemical modeling framework and flow and solute transport (FST) simulators. The iterative scheme relies on operator splitting with continuous re-initialization of PHREEQC and the FST of choice at each time step. Since PHREEQC calculates the geochemistry of aqueous solutions in contact with soil minerals, the procedure is primarily designed for couplings to FST’s for liquid phase flow in natural environments. It requires the accessibility of initial conditions and numerical parameters such as time and space discretization in the input text file for the FST and control of the FST via commands to the operating system (batch on Windows; bash/shell on Unix/Linux). The coupling procedure is based on PHREEQC’s capability to save the state of a simulation with all solid, liquid and gaseous species as a PHREEQC input file by making use of the dump file option in the TRANSPORT keyword. The output from one reaction calculation step is therefore reused as input for the following reaction step where changes in element amounts due to advection/dispersion are introduced as irreversible reactions. An example for the coupling of PHREEQC and MATLAB for the solution of unsaturated flow and transport is provided.

Kinetic model of turbulence in an incompressible fluid

NASA Technical Reports Server (NTRS)

Tchen, C. M.

1978-01-01

A statistical description of turbulence in an incompressible fluid obeying the Navier-Stokes equations is proposed, where pressure is regarded as a potential for the interaction between fluid elements. A scaling procedure divides a fluctuation into three ranks representing the three transport processes of macroscopic evolution, transport property, and relaxation. Closure is obtained by relaxation, and a kinetic equation is obtained for the fluctuation of the macroscopic rank of the distribution function. The solution gives the transfer function and eddy viscosity. When applied to the inertia subrange of the energy spectrum the analysis recovers the Kolmogorov law and its numerical coefficient.

On analytic modeling of lunar perturbations of artificial satellites of the earth

NASA Astrophysics Data System (ADS)

Lane, M. T.

1989-06-01

Two different procedures for analytically modeling the effects of the moon's direct gravitational force on artificial earth satellites are discussed from theoretical and numerical viewpoints. One is developed using classical series expansions of inclination and eccentricity for both the satellite and the moon, and the other employs the method of averaging. Both solutions are seen to have advantages, but it is shown that while the former is more accurate in special situations, the latter is quicker and more practical for the general orbit determination problem where observed data are used to correct the orbit in near real time.

Design and Analysis of Enhanced Modulation Response in Integrated Coupled Cavities DBR Lasers Using Photon-Photon Resonance

DOE PAGES

Bardella, Paolo; Chow, Weng; Montrosset, Ivo

2016-01-08

In the last decades, various solutions have been proposed to increase the modulation bandwidth and consequently the transmission bit rate of integrated semiconductor lasers. In this manuscript we discuss a design procedure for a recently proposed laser structure realized with the integration of two DBR lasers. Design guidelines will be proposed and dynamic small and large signal simulations, calculated using a Finite Difference Traveling Wave numerical simulator, will be performed to confirm the design results and the effectiveness of the analyzed integrated configuration to achieve a direct modulation bandwidth up to 80 GHz

Evaluation of a research circulation control airfoil using Navier-Stokes methods

NASA Technical Reports Server (NTRS)

Shrewsbury, George D.

1987-01-01

The compressible Reynolds time averaged Navier-Stokes equations were used to obtain solutions for flows about a two dimensional circulation control airfoil. The governing equations were written in conservation form for a body-fitted coordinate system and solved using an Alternating Direction Implicit (ADI) procedure. A modified algebraic eddy viscosity model was used to define the turbulent characteristics of the flow, including the wall jet flow over the Coanda surface at the trailing edge. Numerical results are compared to experimental data obtained for a research circulation control airfoil geometry. Excellent agreement with the experimental results was obtained.

Bistatic passive radar simulator with spatial filtering subsystem

NASA Astrophysics Data System (ADS)

Hossa, Robert; Szlachetko, Boguslaw; Lewandowski, Andrzej; Górski, Maksymilian

2009-06-01

The purpose of this paper is to briefly introduce the structure and features of the developed virtual passive FM radar implemented in Matlab system of numerical computations and to present many alternative ways of its performance. An idea of the proposed solution is based on analytic representation of transmitted direct signals and reflected echo signals. As a spatial filtering subsystem a beamforming network of ULA and UCA dipole configuration dedicated to bistatic radar concept is considered and computationally efficient procedures are presented in details. Finally, exemplary results of the computer simulations of the elaborated virtual simulator are provided and discussed.

On the use of attachment modes in substructure coupling for dynamic analysis

NASA Technical Reports Server (NTRS)

Craig, R. R., Jr.; Chang, C.-J.

1977-01-01

Substructure coupling or component-mode synthesis may be employed in the solution of dynamics problems for complex structures. Although numerous substructure-coupling methods have been devised, little attention has been devoted to methods employing attachment modes. In the present paper the various mode sets (normal modes, constraint modes, attachment modes) are defined. A generalized substructure-coupling procedure is described. Those substructure-coupling methods which employ attachment modes are described in detail. One of these methods is shown to lead to results (e.g., system natural frequencies) comparable to or better than those obtained by the Hurty (1965) method.

On hairpin vortices as model of wall turbulence structure

NASA Technical Reports Server (NTRS)

Liu, N.-S.; Shamroth, S. J.; Mcdonald, H.

1985-01-01

A model of the hairpin vortex has been constructed and used in two distinct but related approaches. The first approach is kinematic in nature in which a synthesis procedure using hairpin vortices to provide a quantitative link between mean flow quantities and the statistical quantities of near wall turbulence has become developed. The second approach is dynamic in nature, and the evolution of an incipient 'representative' hairpin vortex as well as the distortion of a background laminar boundary layer flow, in which the hairpin vortex is immersed, has been simulated by numerical solution of the unsteady, three-dimensional Navier-Stokes equations.

European option pricing under the Student's t noise with jumps

NASA Astrophysics Data System (ADS)

Wang, Xiao-Tian; Li, Zhe; Zhuang, Le

2017-03-01

In this paper we present a new approach to price European options under the Student's t noise with jumps. Through the conditional delta hedging strategy and the minimal mean-square-error hedging, a closed-form solution of the European option value is obtained under the incomplete information case. In particular, we propose a Value-at-Risk-type procedure to estimate the volatility parameter σ such that the pricing error is in accord with the risk preferences of investors. In addition, the numerical results of us show that options are not priced in some cases in an incomplete information market.

Time-dependent grid adaptation for meshes of triangles and tetrahedra

NASA Technical Reports Server (NTRS)

Rausch, Russ D.

1993-01-01

This paper presents in viewgraph form a method of optimizing grid generation for unsteady CFD flow calculations that distributes the numerical error evenly throughout the mesh. Adaptive meshing is used to locally enrich in regions of relatively large errors and to locally coarsen in regions of relatively small errors. The enrichment/coarsening procedures are robust for isotropic cells; however, enrichment of high aspect ratio cells may fail near boundary surfaces with relatively large curvature. The enrichment indicator worked well for the cases shown, but in general requires user supervision for a more efficient solution.

Adaptive implicit-explicit and parallel element-by-element iteration schemes

NASA Technical Reports Server (NTRS)

Tezduyar, T. E.; Liou, J.; Nguyen, T.; Poole, S.

1989-01-01

Adaptive implicit-explicit (AIE) and grouped element-by-element (GEBE) iteration schemes are presented for the finite element solution of large-scale problems in computational mechanics and physics. The AIE approach is based on the dynamic arrangement of the elements into differently treated groups. The GEBE procedure, which is a way of rewriting the EBE formulation to make its parallel processing potential and implementation more clear, is based on the static arrangement of the elements into groups with no inter-element coupling within each group. Various numerical tests performed demonstrate the savings in the CPU time and memory.

Analysis of swimming motions.

NASA Technical Reports Server (NTRS)

Gallenstein, J.; Huston, R. L.

1973-01-01

This paper presents an analysis of swimming motion with specific attention given to the flutter kick, the breast-stroke kick, and the breast stroke. The analysis is completely theoretical. It employs a mathematical model of the human body consisting of frustrums of elliptical cones. Dynamical equations are written for this model including both viscous and inertia forces. These equations are then applied with approximated swimming strokes and solved numerically using a digital computer. The procedure is to specify the input of the swimming motion. The computer solution then provides the output displacement, velocity, and rotation or body roll of the swimmer.

Accurate expansion of cylindrical paraxial waves for its straightforward implementation in electromagnetic scattering

NASA Astrophysics Data System (ADS)

Naserpour, Mahin; Zapata-Rodríguez, Carlos J.

2018-01-01

The evaluation of vector wave fields can be accurately performed by means of diffraction integrals, differential equations and also series expansions. In this paper, a Bessel series expansion which basis relies on the exact solution of the Helmholtz equation in cylindrical coordinates is theoretically developed for the straightforward yet accurate description of low-numerical-aperture focal waves. The validity of this approach is confirmed by explicit application to Gaussian beams and apertured focused fields in the paraxial regime. Finally we discuss how our procedure can be favorably implemented in scattering problems.

Non-linear analysis of stick/slip motion

NASA Astrophysics Data System (ADS)

Pratt, T. K.; Williams, R.

1981-02-01

The steady state relative motion of two masses with dry (Coulomb) friction contact is investigated. The bodies are assumed to have the same mass and stiffness and are subjected to harmonic excitation. By means of a combined analytical—numerical procedure, results are obtained for arbitrary values of Coulomb friction, excitation frequency, and natural frequencies of the bodies. For certain values of these parameters, multiple lockups per cycle are possible. In this respect, the problem investigated here is a natural extension of the one considered by Den Hartog, who in obtaining his closed form solution assumed a maximum of two lockups per cycle.

Energy: Economic activity and energy demand; link to energy flow. Example: France

NASA Astrophysics Data System (ADS)

1980-10-01

The data derived from the EXPLOR and EPOM, Energy Flow Optimization Model are described. The core of the EXPLOR model is a circular system of relations involving consumer's demand, producer's outputs, and market prices. The solution of this system of relations is obtained by successive iterations; the final output is a coherent system of economic accounts. The computer program for this transition is described. The work conducted by comparing different energy demand models is summarized. The procedure is illustrated by a numerical projection to 1980 and 1985 using the existing version of the EXPLOR France model.

A meshless method using radial basis functions for numerical solution of the two-dimensional KdV-Burgers equation

NASA Astrophysics Data System (ADS)

Zabihi, F.; Saffarian, M.

2016-07-01

The aim of this article is to obtain the numerical solution of the two-dimensional KdV-Burgers equation. We construct the solution by using a different approach, that is based on using collocation points. The solution is based on using the thin plate splines radial basis function, which builds an approximated solution with discretizing the time and the space to small steps. We use a predictor-corrector scheme to avoid solving the nonlinear system. The results of numerical experiments are compared with analytical solutions to confirm the accuracy and efficiency of the presented scheme.

Characterization of bonded stationary phase performance as a function of qualitative and quantitative chromatographic factors in chaotropic chromatography with risperidone and its impurities as model substances.

PubMed

Čolović, Jelena; Rmandić, Milena; Malenović, Anđelija

2018-05-17

Numerous stationary phases have been developed with the aim to provide desired performances during chromatographic analysis of the basic solutes in their protonated form. In this work, the procedure for the characterization of bonded stationary phase performance, when both qualitative and quantitative chromatographic factors were varied in chaotropic chromatography, was proposed. Risperidone and its three impurities were selected as model substances, while acetonitrile content in the mobile phase (20-30%), the pH of the aqueous phase (3.00-5.00), the content of chaotropic agents in the aqueous phase (10-100 mM), type of chaotropic agent (NaClO 4 , CF 3 COONa), and stationary phase type (Zorbax Eclipse XDB, Zorbax Extend) were studied as chromatographic factors. The proposed procedure implies the combination of D-optimal experimental design, indirect modeling, and polynomial-modified Gaussian model, while grid point search method was selected for the final choice of the experimental conditions which lead to the best possible stationary phase performance for basic solutes. Good agreement between experimentally obtained chromatogram and simulated chromatogram for chosen experimental conditions (25% acetonitrile, 75 mM of NaClO 4 , pH 4.00 on Zorbax Eclipse XDB column) confirmed the applicability of the proposed procedure. The additional point was selected for the verification of proposed procedure ability to distinguish changes in solutes' elution order. Simulated chromatogram for 21.5% acetonitrile, 85 mM of NaClO 4 , pH 5.00 on Zorbax Eclipse XDB column was in line with experimental data. Furthermore, the values of left and right peak half-widths obtained from indirect modeling were used in order to evaluate performances of differently modified stationary phases applying a half-width plots approach. The results from half-width plot approach as well as from the proposed procedure indicate higher efficiency and better separation performance of the stationary phase extra densely bonded and double end-capped with trimethylsilyl group than the stationary phase with the combination of end-capping and bidentate silane bonding for chromatographic analysis of basic solutes in RP-HPLC systems with chaotropic agents. Graphical abstract ᅟ.

Modeling flow and solute transport in irrigation furrows

USDA-ARS?s Scientific Manuscript database

This paper presents an internally coupled flow and solute transport model for free-draining irrigation furrows. Furrow hydraulics is simulated with a numerical zero-inertia model and solute transport is computed with a model based on a numerical solution of the cross-section averaged advection-dispe...

Numerical experiments with a symmetric high-resolution shock-capturing scheme

NASA Technical Reports Server (NTRS)

Yee, H. C.

1986-01-01

Characteristic-based explicit and implicit total variation diminishing (TVD) schemes for the two-dimensional compressible Euler equations have recently been developed. This is a generalization of recent work of Roe and Davis to a wider class of symmetric (non-upwind) TVD schemes other than Lax-Wendroff. The Roe and Davis schemes can be viewed as a subset of the class of explicit methods. The main properties of the present class of schemes are that they can be implicit, and, when steady-state calculations are sought, the numerical solution is independent of the time step. In a recent paper, a comparison of a linearized form of the present implicit symmetric TVD scheme with an implicit upwind TVD scheme originally developed by Harten and modified by Yee was given. Results favored the symmetric method. It was found that the latter is just as accurate as the upwind method while requiring less computational effort. Currently, more numerical experiments are being conducted on time-accurate calculations and on the effect of grid topology, numerical boundary condition procedures, and different flow conditions on the behavior of the method for steady-state applications. The purpose here is to report experiences with this type of scheme and give guidelines for its use.

A systematic approach to numerical dispersion in Maxwell solvers

NASA Astrophysics Data System (ADS)

Blinne, Alexander; Schinkel, David; Kuschel, Stephan; Elkina, Nina; Rykovanov, Sergey G.; Zepf, Matt

2018-03-01

The finite-difference time-domain (FDTD) method is a well established method for solving the time evolution of Maxwell's equations. Unfortunately the scheme introduces numerical dispersion and therefore phase and group velocities which deviate from the correct values. The solution to Maxwell's equations in more than one dimension results in non-physical predictions such as numerical dispersion or numerical Cherenkov radiation emitted by a relativistic electron beam propagating in vacuum. Improved solvers, which keep the staggered Yee-type grid for electric and magnetic fields, generally modify the spatial derivative operator in the Maxwell-Faraday equation by increasing the computational stencil. These modified solvers can be characterized by different sets of coefficients, leading to different dispersion properties. In this work we introduce a norm function to rewrite the choice of coefficients into a minimization problem. We solve this problem numerically and show that the minimization procedure leads to phase and group velocities that are considerably closer to c as compared to schemes with manually set coefficients available in the literature. Depending on a specific problem at hand (e.g. electron beam propagation in plasma, high-order harmonic generation from plasma surfaces, etc.), the norm function can be chosen accordingly, for example, to minimize the numerical dispersion in a certain given propagation direction. Particle-in-cell simulations of an electron beam propagating in vacuum using our solver are provided.

A numerical procedure for failure mode detection of masonry arches reinforced with fiber reinforced polymeric materials

NASA Astrophysics Data System (ADS)

Galassi, S.

2018-05-01

In this paper a mechanical model of masonry arches strengthened with fibre-reinforced composite materials and the relevant numerical procedure for the analysis are proposed. The arch is modelled by using an assemblage of rigid blocks that are connected together and, also to the supporting structures, by mortar joints. The presence of the reinforcement, usually a sheet placed at the intrados or the extrados, prevents the occurrence of cracks that could activate possible collapse mechanisms, due to tensile failure of the mortar joints. Therefore, in a reinforced arch failure generally occurs in a different way from the URM arch. The numerical procedure proposed checks, as a function of an external incremental load, the inner stress state in the arch, in the reinforcement and in the adhesive layer. In so doing, it then provides a prediction of failure modes. Results obtained from experimental tests, carried out on four in-scale models performed in a laboratory, have been compared with those provided by the numerical procedure, implemented in ArchiVAULT, a software developed by the author. In this regard, the numerical procedure is an extension of previous works. Although additional experimental investigations are necessary, these former results confirm that the proposed numerical procedure is promising.

Flexible Automatic Discretization for Finite Differences: Eliminating the Human Factor

NASA Astrophysics Data System (ADS)

Pranger, Casper

2017-04-01

In the geophysical numerical modelling community, finite differences are (in part due to their small footprint) a popular spatial discretization method for PDEs in the regular-shaped continuum that is the earth. However, they rapidly become prone to programming mistakes when physics increase in complexity. To eliminate opportunities for human error, we have designed an automatic discretization algorithm using Wolfram Mathematica, in which the user supplies symbolic PDEs, the number of spatial dimensions, and a choice of symbolic boundary conditions, and the script transforms this information into matrix- and right-hand-side rules ready for use in a C++ code that will accept them. The symbolic PDEs are further used to automatically develop and perform manufactured solution benchmarks, ensuring at all stages physical fidelity while providing pragmatic targets for numerical accuracy. We find that this procedure greatly accelerates code development and provides a great deal of flexibility in ones choice of physics.

Development of a computational testbed for numerical simulation of combustion instability

NASA Technical Reports Server (NTRS)

Grenda, Jeffrey; Venkateswaran, Sankaran; Merkle, Charles L.

1993-01-01

A synergistic hierarchy of analytical and computational fluid dynamic techniques is used to analyze three-dimensional combustion instabilities in liquid rocket engines. A mixed finite difference/spectral procedure is employed to study the effects of a distributed vaporization zone on standing and spinning instability modes within the chamber. Droplet atomization and vaporization are treated by a variety of classical models found in the literature. A multi-zone, linearized analytical solution is used to validate the accuracy of the numerical simulations at small amplitudes for a distributed vaporization region. This comparison indicates excellent amplitude and phase agreement under both stable and unstable operating conditions when amplitudes are small and proper grid resolution is used. As amplitudes get larger, expected nonlinearities are observed. The effect of liquid droplet temperature fluctuations was found to be of critical importance in driving the instabilities of the combustion chamber.

The numerical design of a spherical baroclinic experiment for Spacelab flights

NASA Technical Reports Server (NTRS)

Fowlis, W. W.; Roberts, G. O.

1982-01-01

The near-zero G environment of Spacelab is the basis of a true spherical experimental model of synoptic scale baroclinic atmospheric processes, using a radial dielectric body force analogous to gravity over a volume of liquid within two concentric spheres. The baroclinic motions are generated by corotating the spheres and imposing thermal boundary conditions, such that the liquid is subjected to a stable radial gradient and a latitudinal gradient. Owing to mathematical difficulties associated with the spherical geometry, quantitative design criteria can be acquired only by means of numerical models. The procedure adopted required the development of two computer codes based on the Navier-Stokes equations. The codes, of which the first calculates axisymmetric steady flow solutions and the second determines the growth or decay rates of linear wave perturbations with different wave numbers, are combined to generate marginal stability curves.

Numerical simulation of interaction between chemically active exhaust and a jet blast deflector

NASA Astrophysics Data System (ADS)

Korotaeva, T. A.; Turchinovich, A. O.

2017-10-01

The interaction of chemically active exhausts of aircraft engines with jet blast deflector (JBD) of various configurations has been considered at the stage of ground run procedure. The problem is modeled in the 3-D approximation in the framework of the numerical solution of the Navier-Stokes equations taking into account the kinetic model of the interaction of between the components of engine exhaust and air. A complex field of gasdynamic flow that is realized when jets emerge from nozzles and interact with each other, with air, with a gas deflector has been studied. The main purpose of the study is to prove the concept that it is possible to generate a vortex flow that can not only change the direction of the jets, but also contribute to the lifting of the mass of pollutants and their dispersion in the atmosphere using a gas deflector shape.

Efficient Trajectory Propagation for Orbit Determination Problems

NASA Technical Reports Server (NTRS)

Roa, Javier; Pelaez, Jesus

2015-01-01

Regularized formulations of orbital motion apply a series of techniques to improve the numerical integration of the orbit. Despite their advantages and potential applications little attention has been paid to the propagation of the partial derivatives of the corresponding set of elements or coordinates, required in many orbit-determination scenarios and optimization problems. This paper fills this gap by presenting the general procedure for integrating the state-transition matrix of the system together with the nominal trajectory using regularized formulations and different sets of elements. The main difficulty comes from introducing an independent variable different from time, because the solution needs to be synchronized. The correction of the time delay is treated from a generic perspective not focused on any particular formulation. The synchronization using time-elements is also discussed. Numerical examples include strongly-perturbed orbits in the Pluto system, motivated by the recent flyby of the New Horizons spacecraft, together with a geocentric flyby of the NEAR spacecraft.

A numerical formulation and algorithm for limit and shakedown analysis of large-scale elastoplastic structures

NASA Astrophysics Data System (ADS)

Peng, Heng; Liu, Yinghua; Chen, Haofeng

2018-05-01

In this paper, a novel direct method called the stress compensation method (SCM) is proposed for limit and shakedown analysis of large-scale elastoplastic structures. Without needing to solve the specific mathematical programming problem, the SCM is a two-level iterative procedure based on a sequence of linear elastic finite element solutions where the global stiffness matrix is decomposed only once. In the inner loop, the static admissible residual stress field for shakedown analysis is constructed. In the outer loop, a series of decreasing load multipliers are updated to approach to the shakedown limit multiplier by using an efficient and robust iteration control technique, where the static shakedown theorem is adopted. Three numerical examples up to about 140,000 finite element nodes confirm the applicability and efficiency of this method for two-dimensional and three-dimensional elastoplastic structures, with detailed discussions on the convergence and the accuracy of the proposed algorithm.

Optimization of block-floating-point realizations for digital controllers with finite-word-length considerations.

PubMed

Wu, Jun; Hu, Xie-he; Chen, Sheng; Chu, Jian

2003-01-01

The closed-loop stability issue of finite-precision realizations was investigated for digital controllers implemented in block-floating-point format. The controller coefficient perturbation was analyzed resulting from using finite word length (FWL) block-floating-point representation scheme. A block-floating-point FWL closed-loop stability measure was derived which considers both the dynamic range and precision. To facilitate the design of optimal finite-precision controller realizations, a computationally tractable block-floating-point FWL closed-loop stability measure was then introduced and the method of computing the value of this measure for a given controller realization was developed. The optimal controller realization is defined as the solution that maximizes the corresponding measure, and a numerical optimization approach was adopted to solve the resulting optimal realization problem. A numerical example was used to illustrate the design procedure and to compare the optimal controller realization with the initial realization.

SDF technology in location and navigation procedures: a survey of applications

NASA Astrophysics Data System (ADS)

Kelner, Jan M.; Ziółkowski, Cezary

2017-04-01

The basis for development the Doppler location method, also called the signal Doppler frequency (SDF) method or technology is the analytical solution of the wave equation for a mobile source. This paper presents an overview of the simulations, numerical analysis and empirical studies of the possibilities and the range of SDF method applications. In the paper, the various applications from numerous publications are collected and described. They mainly focus on the use of SDF method in: emitter positioning, electronic warfare, crisis management, search and rescue, navigation. The developed method is characterized by an innovative, unique property among other location methods, because it allows the simultaneous location of the many radio emitters. Moreover, this is the first method based on the Doppler effect, which allows positioning of transmitters, using a single mobile platform. In the paper, the results of the using SDF method by the other teams are also presented.

Evolution of hairpin vortices in a shear flow

NASA Technical Reports Server (NTRS)

Hon, T.-L.; Walker, J. D. A.

1988-01-01

Recent experimental studies suggest that the hairpin vortex plays an important (and perhaps dominant) role in the dynamics of turbulent flows near walls. In this study a numerical procedure is developed to allow the accurate computation of the trajectory of a 3-D vortex having a small core radius. For hairpin vortices which are convected in a shear flow above a wall, the calculated results show that a 2-D vortex containing a small 3-D disturbance distorts into a complex shape with subsidiary hairpin vortices forming outboard of the original hairpin vortex. As the vortex moves above the wall, it induces unsteady motion in the viscous flow near the wall: numerical solutions suggest that the boundary-layer flow near the wall will ultimately erupt in response to the motion of the hairpin vortex and in the process a secondary hairpin vortex will be created. The computer results agree with recent experimental investigations.

An improvement of convergence of a dispersion-relation preserving method for the classical Boussinesq equation

NASA Astrophysics Data System (ADS)

Jang, T. S.

2018-03-01

A dispersion-relation preserving (DRP) method, as a semi-analytic iterative procedure, has been proposed by Jang (2017) for integrating the classical Boussinesq equation. It has been shown to be a powerful numerical procedure for simulating a nonlinear dispersive wave system because it preserves the dispersion-relation, however, there still exists a potential flaw, e.g., a restriction on nonlinear wave amplitude and a small region of convergence (ROC) and so on. To remedy the flaw, a new DRP method is proposed in this paper, aimed at improving convergence performance. The improved method is proved to have convergence properties and dispersion-relation preserving nature for small waves; of course, unique existence of the solutions is also proved. In addition, by a numerical experiment, the method is confirmed to be good at observing nonlinear wave phenomena such as moving solitary waves and their binary collision with different wave amplitudes. Especially, it presents a ROC (much) wider than that of the previous method by Jang (2017). Moreover, it gives the numerical simulation of a high (or large-amplitude) nonlinear dispersive wave. In fact, it is demonstrated to simulate a large-amplitude solitary wave and the collision of two solitary waves with large-amplitudes that we have failed to simulate with the previous method. Conclusively, it is worth noting that better convergence results are achieved compared to Jang (2017); i.e., they represent a major improvement in practice over the previous method.

Spectral methods in general relativity and large Randall-Sundrum II black holes

NASA Astrophysics Data System (ADS)

Abdolrahimi, Shohreh; Cattoën, Céline; Page, Don N.; \\\\; Yaghoobpour-Tari, Shima

2013-06-01

Using a novel numerical spectral method, we have found solutions for large static Randall-Sundrum II (RSII) black holes by perturbing a numerical AdS5-CFT4 solution to the Einstein equation with a negative cosmological constant Λ that is asymptotically conformal to the Schwarzschild metric. We used a numerical spectral method independent of the Ricci-DeTurck-flow method used by Figueras, Lucietti, and Wiseman for a similar numerical solution. We have compared our black-hole solution to the one Figueras and Wiseman have derived by perturbing their numerical AdS5-CFT4 solution, showing that our solution agrees closely with theirs. We have obtained a closed-form approximation to the metric of the black hole on the brane. We have also deduced the new results that to first order in 1/(-ΛM2), the Hawking temperature and entropy of an RSII static black hole have the same values as the Schwarzschild metric with the same mass, but the horizon area is increased by about 4.7/(-Λ).

Theoretical models of the electrical discharge machining process. III. The variable mass, cylindrical plasma model

NASA Astrophysics Data System (ADS)

Eubank, Philip T.; Patel, Mukund R.; Barrufet, Maria A.; Bozkurt, Bedri

1993-06-01

A variable mass, cylindrical plasma model (VMCPM) is developed for sparks created by electrical discharge in a liquid media. The model consist of three differential equations—one each from fluid dynamics, an energy balance, and the radiation equation—combined with a plasma equation of state. A thermophysical property subroutine allows realistic estimation of plasma enthalpy, mass density, and particle fractions by inclusion of the heats of dissociation and ionization for a plasma created from deionized water. Problems with the zero-time boundary conditions are overcome by an electron balance procedure. Numerical solution of the model provides plasma radius, temperature, pressure, and mass as a function of pulse time for fixed current, electrode gap, and power fraction remaining in the plasma. Moderately high temperatures (≳5000 K) and pressures (≳4 bar) persist in the sparks even after long pulse times (to ˜500 μs). Quantitative proof that superheating is the dominant mechanism for electrical discharge machining (EDM) erosion is thus provided for the first time. Some quantitative inconsistencies developed between our (1) cathode, (2) anode, and (3) plasma models (this series) are discussed with indication as to how they will be rectified in a fourth article to follow shortly in this journal. While containing oversimplifications, these three models are believed to contain the respective dominant physics of the EDM process but need be brought into numerical consistency for each time increment of the numerical solution.

Fluid-solid coupled simulation of the ignition transient of solid rocket motor

NASA Astrophysics Data System (ADS)

Li, Qiang; Liu, Peijin; He, Guoqiang

2015-05-01

The first period of the solid rocket motor operation is the ignition transient, which involves complex processes and, according to chronological sequence, can be divided into several stages, namely, igniter jet injection, propellant heating and ignition, flame spreading, chamber pressurization and solid propellant deformation. The ignition transient should be comprehensively analyzed because it significantly influences the overall performance of the solid rocket motor. A numerical approach is presented in this paper for simulating the fluid-solid interaction problems in the ignition transient of the solid rocket motor. In the proposed procedure, the time-dependent numerical solutions of the governing equations of internal compressible fluid flow are loosely coupled with those of the geometrical nonlinearity problems to determine the propellant mechanical response and deformation. The well-known Zeldovich-Novozhilov model was employed to model propellant ignition and combustion. The fluid-solid coupling interface data interpolation scheme and coupling instance for different computational agents were also reported. Finally, numerical validation was performed, and the proposed approach was applied to the ignition transient of one laboratory-scale solid rocket motor. For the application, the internal ballistics were obtained from the ground hot firing test, and comparisons were made. Results show that the integrated framework allows us to perform coupled simulations of the propellant ignition, strong unsteady internal fluid flow, and propellant mechanical response in SRMs with satisfactory stability and efficiency and presents a reliable and accurate solution to complex multi-physics problems.

Hybrid Upwind Splitting (HUS) by a Field-by-Field Decomposition

NASA Technical Reports Server (NTRS)

Coquel, Frederic; Liou, Meng-Sing

1995-01-01

We introduce and develop a new approach for upwind biasing: the hybrid upwind splitting (HUS) method. This original procedure is based on a suitable hybridization of current prominent flux vector splitting (FVS) and flux difference splitting (FDS) methods. The HUS method is designed to naturally combine the respective strengths of the above methods while excluding their main deficiencies. Specifically, the HUS strategy yields a family of upwind methods that exhibit the robustness of FVS schemes in the capture of nonlinear waves and the accuracy of some FDS schemes in the resolution of linear waves. We give a detailed construction of the HUS methods following a general and systematic procedure directly performed at the basic level of the field by field (i.e. waves) decomposition involved in FDS methods. For such a given decomposition, each field is endowed either with FVS or FDS numerical fluxes, depending on the nonlinear nature of the field under consideration. Such a design principle is made possible thanks to the introduction of a convenient formalism that provides us with a unified framework for upwind methods. The HUS methods we propose bring significant improvements over current methods in terms of accuracy and robustness. They yield entropy-satisfying approximate solutions as they are strongly supported in numerical experiments. Field by field hybrid numerical fluxes also achieve fairly simple and explicit expressions and hence require a computational effort between that of the FVS and FDS. Several numerical experiments ranging from stiff 1D shock-tube to high speed viscous flows problems are displayed, intending to illustrate the benefits of the present approach. We assess in particular the relevance of our HUS schemes to viscous flow calculations.

Multiresolution representation and numerical algorithms: A brief review

NASA Technical Reports Server (NTRS)

Harten, Amiram

1994-01-01

In this paper we review recent developments in techniques to represent data in terms of its local scale components. These techniques enable us to obtain data compression by eliminating scale-coefficients which are sufficiently small. This capability for data compression can be used to reduce the cost of many numerical solution algorithms by either applying it to the numerical solution operator in order to get an approximate sparse representation, or by applying it to the numerical solution itself in order to reduce the number of quantities that need to be computed.

Comparitive Study of High-Order Positivity-Preserving WENO Schemes

NASA Technical Reports Server (NTRS)

Kotov, D. V.; Yee, H. C.; Sjogreen, B.

2014-01-01

In gas dynamics and magnetohydrodynamics flows, physically, the density ? and the pressure p should both be positive. In a standard conservative numerical scheme, however, the computed internal energy is The ideas of Zhang & Shu (2012) and Hu et al. (2012) precisely address the aforementioned issue. Zhang & Shu constructed a new conservative positivity-preserving procedure to preserve positive density and pressure for high-order Weighted Essentially Non-Oscillatory (WENO) schemes by the Lax-Friedrichs flux (WENO/LLF). In general, WENO/LLF is obtained by subtracting the kinetic energy from the total energy, resulting in a computed p that may be negative. Examples are problems in which the dominant energy is kinetic. Negative ? may often emerge in computing blast waves. In such situations the computed eigenvalues of the Jacobian will become imaginary. Consequently, the initial value problem for the linearized system will be ill posed. This explains why failure of preserving positivity of density or pressure may cause blow-ups of the numerical algorithm. The adhoc methods in numerical strategy which modify the computed negative density and/or the computed negative pressure to be positive are neither a conservative cure nor a stable solution. Conservative positivity-preserving schemes are more appropriate for such flow problems. too dissipative for flows such as turbulence with strong shocks computed in direct numerical simulations (DNS) and large eddy simulations (LES). The new conservative positivity-preserving procedure proposed in Hu et al. (2012) can be used with any high-order shock-capturing scheme, including high-order WENO schemes using the Roe's flux (WENO/Roe). The goal of this study is to compare the results obtained by non-positivity-preserving methods with the recently developed positivity-preserving schemes for representative test cases. In particular the more di cult 3D Noh and Sedov problems are considered. These test cases are chosen because of the negative pressure/density most often exhibited by standard high-order shock-capturing schemes. The simulation of a hypersonic nonequilibrium viscous shock tube that is related to the NASA Electric Arc Shock Tube (EAST) is also included. EAST is a high-temperature and high Mach number viscous nonequilibrium ow consisting of 13 species. In addition, as most common shock-capturing schemes have been developed for problems without source terms, when applied to problems with nonlinear and/or sti source terms these methods can result in spurious solutions, even when solving a conservative system of equations with a conservative scheme. This kind of behavior can be observed even for a scalar case as well as for the case consisting of two species and one reaction.. This EAST example indicated that standard high-order shock-capturing methods exhibit instability of density/pressure in addition to grid-dependent discontinuity locations with insufficient grid points. The evaluation of these test cases is based on the stability of the numerical schemes together with the accuracy of the obtained solutions.

Constructing exact symmetric informationally complete measurements from numerical solutions

NASA Astrophysics Data System (ADS)

Appleby, Marcus; Chien, Tuan-Yow; Flammia, Steven; Waldron, Shayne

2018-04-01

Recently, several intriguing conjectures have been proposed connecting symmetric informationally complete quantum measurements (SIC POVMs, or SICs) and algebraic number theory. These conjectures relate the SICs to their minimal defining algebraic number field. Testing or sharpening these conjectures requires that the SICs are expressed exactly, rather than as numerical approximations. While many exact solutions of SICs have been constructed previously using Gröbner bases, this method has probably been taken as far as is possible with current computer technology (except in special cases where there are additional symmetries). Here, we describe a method for converting high-precision numerical solutions into exact ones using an integer relation algorithm in conjunction with the Galois symmetries of an SIC. Using this method, we have calculated 69 new exact solutions, including nine new dimensions, where previously only numerical solutions were known—which more than triples the number of known exact solutions. In some cases, the solutions require number fields with degrees as high as 12 288. We use these solutions to confirm that they obey the number-theoretic conjectures, and address two questions suggested by the previous work.

Analytical and numerical solution for wave reflection from a porous wave absorber

NASA Astrophysics Data System (ADS)

Magdalena, Ikha; Roque, Marian P.

2018-03-01

In this paper, wave reflection from a porous wave absorber is investigated theoretically and numerically. The equations that we used are based on shallow water type model. Modification of motion inside the absorber is by including linearized friction term in momentum equation and introducing a filtered velocity. Here, an analytical solution for wave reflection coefficient from a porous wave absorber over a flat bottom is derived. Numerically, we solve the equations using the finite volume method on a staggered grid. To validate our numerical model, comparison of the numerical reflection coefficient is made against the analytical solution. Further, we implement our numerical scheme to study the evolution of surface waves pass through a porous absorber over varied bottom topography.

Quasi-2D Unsteady Flow Solver Module for Rocket Engine and Propulsion System Simulations

DTIC Science & Technology

2006-06-14

Conference, Sacramento, CA, 9-12 July 2006. 14. ABSTRACT A new quasi-two-dimensional procedure is presented for the transient solution of real-fluid flows...solution procedures is being developed in parallel to provide verification test cases. The solution procedure for both codes is coupled with a state-of...Davis, Davis, CA, 95616 A new quasi-two-dimensional procedure is presented for the transient solution of real- fluid flows in lines and volumes

Neutron Transport Models and Methods for HZETRN and Coupling to Low Energy Light Ion Transport

NASA Technical Reports Server (NTRS)

Blattnig, S.R.; Slaba, T.C.; Heinbockel, J.H.

2008-01-01

Exposure estimates inside space vehicles, surface habitats, and high altitude aircraft exposed to space radiation are highly influenced by secondary neutron production. The deterministic transport code HZETRN has been identified as a reliable and efficient tool for such studies, but improvements to the underlying transport models and numerical methods are still necessary. In this paper, the forward-backward (FB) and directionally coupled forward-backward (DC) neutron transport models are derived, numerical methods for the FB model are reviewed, and a computationally efficient numerical solution is presented for the DC model. Both models are compared to the Monte Carlo codes HETCHEDS and FLUKA, and the DC model is shown to agree closely with the Monte Carlo results. Finally, it is found in the development of either model that the decoupling of low energy neutrons from the light ion (A<4) transport procedure adversely affects low energy light ion fluence spectra and exposure quantities. A first order correction is presented to resolve the problem, and it is shown to be both accurate and efficient.

Numerical Analysis of an H 1-Galerkin Mixed Finite Element Method for Time Fractional Telegraph Equation

PubMed Central

Wang, Jinfeng; Zhao, Meng; Zhang, Min; Liu, Yang; Li, Hong

2014-01-01

We discuss and analyze an H 1-Galerkin mixed finite element (H 1-GMFE) method to look for the numerical solution of time fractional telegraph equation. We introduce an auxiliary variable to reduce the original equation into lower-order coupled equations and then formulate an H 1-GMFE scheme with two important variables. We discretize the Caputo time fractional derivatives using the finite difference methods and approximate the spatial direction by applying the H 1-GMFE method. Based on the discussion on the theoretical error analysis in L 2-norm for the scalar unknown and its gradient in one dimensional case, we obtain the optimal order of convergence in space-time direction. Further, we also derive the optimal error results for the scalar unknown in H 1-norm. Moreover, we derive and analyze the stability of H 1-GMFE scheme and give the results of a priori error estimates in two- or three-dimensional cases. In order to verify our theoretical analysis, we give some results of numerical calculation by using the Matlab procedure. PMID:25184148

Counterflow diffusion flames: effects of thermal expansion and non-unity Lewis numbers

NASA Astrophysics Data System (ADS)

Koundinyan, Sushilkumar P.; Matalon, Moshe; Stewart, D. Scott

2018-05-01

In this work we re-examine the counterflow diffusion flame problem focusing in particular on the flame-flow interactions due to thermal expansion and its influence on various flame properties such as flame location, flame temperature, reactant leakage and extinction conditions. The analysis follows two different procedures: an asymptotic approximation for large activation energy chemical reactions, and a direct numerical approach. The asymptotic treatment follows the general theory of Cheatham and Matalon, which consists of a free-boundary problem with jump conditions across the surface representing the reaction sheet, and is well suited for variable-density flows and for mixtures with non-unity and distinct Lewis numbers for the fuel and oxidiser. Due to density variations, the species and energy transport equations are coupled to the Navier-Stokes equations and the problem does not possess an analytical solution. We thus propose and implement a methodology for solving the free-boundary problem numerically. Results based on the asymptotic approximation are then verified against those obtained from the 'exact' numerical integration of the governing equations, comparing predictions of the various flame properties.

Numerical solutions of ideal quantum gas dynamical flows governed by semiclassical ellipsoidal-statistical distribution

PubMed Central

Yang, Jaw-Yen; Yan, Chih-Yuan; Diaz, Manuel; Huang, Juan-Chen; Li, Zhihui; Zhang, Hanxin

2014-01-01

The ideal quantum gas dynamics as manifested by the semiclassical ellipsoidal-statistical (ES) equilibrium distribution derived in Wu et al. (Wu et al. 2012 Proc. R. Soc. A 468, 1799–1823 (doi:10.1098/rspa.2011.0673)) is numerically studied for particles of three statistics. This anisotropic ES equilibrium distribution was derived using the maximum entropy principle and conserves the mass, momentum and energy, but differs from the standard Fermi–Dirac or Bose–Einstein distribution. The present numerical method combines the discrete velocity (or momentum) ordinate method in momentum space and the high-resolution shock-capturing method in physical space. A decoding procedure to obtain the necessary parameters for determining the ES distribution is also devised. Computations of two-dimensional Riemann problems are presented, and various contours of the quantities unique to this ES model are illustrated. The main flow features, such as shock waves, expansion waves and slip lines and their complex nonlinear interactions, are depicted and found to be consistent with existing calculations for a classical gas. PMID:24399919

Aragonite coating solutions (ACS) based on artificial seawater

NASA Astrophysics Data System (ADS)

Tas, A. Cuneyt

2015-03-01

Aragonite (CaCO3, calcium carbonate) is an abundant biomaterial of marine life. It is the dominant inorganic phase of coral reefs, mollusc bivalve shells and the stalactites or stalagmites of geological sediments. Inorganic and initially precipitate-free aragonite coating solutions (ACS) of pH 7.4 were developed in this study to deposit monolayers of aragonite spherules or ooids on biomaterial (e.g., UHMWPE, ultrahigh molecular weight polyethylene) surfaces soaked in ACS at 30 °C. The ACS solutions of this study have been developed for the surface engineering of synthetic biomaterials. The abiotic ACS solutions, enriched with calcium and bicarbonate ions at different concentrations, essentially mimicked the artificial seawater composition and started to deposit aragonite after a long (4 h) incubation period at the tropical sea surface temperature of 30 °C. While numerous techniques for the solution deposition of calcium hydroxyapatite (Ca10(PO4)6(OH)2), of low thermodynamic solubility, on synthetic biomaterials have been demonstrated, procedures related to the solution-based surface deposition of high solubility aragonite remained uncommon. Monolayers of aragonite ooids deposited at 30 °C on UHMWPE substrates soaked in organic-free ACS solutions were found to possess nano-structures similar to the mortar-and-brick-type botryoids observed in biogenic marine shells. Samples were characterized using SEM, XRD, FTIR, ICP-AES and contact angle goniometry.

A test of a vortex method for the computation of flap side edge noise

NASA Technical Reports Server (NTRS)

Martin, James E.

1995-01-01

Upon approach to landing, a major source location of airframe noise occurs at the side edges of the part span, trailing edge flaps. In the vicinity of these flaps, a complex arrangement of spanwise flow with primary and secondary tip vortices may form. Each of these vortices is observed to become fully three-dimensional. In the present study, a numerical model is developed to investigate the noise radiated from the side edge of a flap. The inherent three-dimensionality of this flow forces us to carefully consider a numerical scheme which will be both accurate in its prediction of the flow acoustics and also computationally efficient. Vortex methods have offered a fast and efficient means of simulating many two and three-dimensional, vortex dominated flows. In vortex methods, the time development of the flow is tracked by following exclusively the vorticity containing regions. Through the Biot-Savart law, knowledge of the vorticity field enables one to obtain flow quantities at any desired location during the flow evolution. In the present study, a numerical procedure has been developed which incorporates the Lagrangian approach of vortex methods into a calculation for the noise radiated by a flow-surface interaction. In particular, the noise generated by a vortex in the presence of a flat half plane is considered. This problem serves as a basic model of flap edge flow. It also permits the direct comparison between our computed results and previous acoustic analyses performed for this problem. In our numerical simulations, the mean flow is represented by the complex potential W(z) = Aiz(exp l/2), which is obtained through conformal mapping techniques. The magnitude of the mean flow is controlled by the parameter A. This mean flow has been used in the acoustic analysis by Hardin and is considered a reasonable model of the flow field in the vicinity of the edge and away from the leading and trailing edges of the flap. To represent the primary vortex which occurs near the flap, a point vortex is introduced just below the flat half plane. Using a technique from panel methods, boundary conditions on the flap surface are satisfied by the introduction of a row of stationary point vortices along the extent of the flap. At each time step in the calculation, the strength of these vortices is chosen to eliminate the normal velocity at intermediary collocation points. The time development of the overall flow field is then tracked using standard techniques from vortex methods. Vortex trajectories obtained through this computation are in good agreement with those predicted by the analytical solution given by Hardin, thus verifying the viability of this procedure for more complex flow arrangements. For the flow acoustics, the Ffowcs Williams-Hawkings equation is numerically integrated. This equation supplies the far field acoustic pressure based upon pressures occurring along the flap surface. With our vortex method solution, surface pressures may be obtained with exceptional resolution. The Ffowcs Williams-Hawkings equation is integrated using a spatially fourth order accurate Simpson's rule. Rational function interpolation is used to obtain the surface pressures at the appropriate retarded times. Comparisons between our numerical results for the acoustic pressure and those predicted by the Hardin analysis have been made. Preliminary results indicate the need for an improved integration technique. In the future, the numerical procedure developed in this study will be applied to the case of a rectangular flap of finite thickness and ultimately modified for application to the fully three-dimensional problem.

A GENERAL MASS-CONSERVATIVE NUMERICAL SOLUTION FOR THE UNSATURATED FLOW EQUATION

EPA Science Inventory

Numerical approximations based on different forms of the governing partial differential equation can lead to significantly different results for unsaturated flow problems. Numerical solution based on the standard h-based form of Richards equation generally yields poor results, ch...

Flow and Heat Transfer Analysis of an Eyring-Powell Fluid in a Pipe

NASA Astrophysics Data System (ADS)

Ali, N.; Nazeer, F.; Nazeer, Mubbashar

2018-02-01

The steady non-isothermal flow of an Eyring-Powell fluid in a pipe is investigated using both perturbation and numerical methods. The results are presented for two viscosity models, namely the Reynolds model and the Vogel model. The shooting method is employed to compute the numerical solution. Criteria for validity of perturbation solution are developed. When these criteria are met, it is shown that the perturbation solution is in good agreement with the numerical solution. The influence of various emerging parameters on the velocity and temperature field is also shown.

A 1D radiative transfer benchmark with polarization via doubling and adding

NASA Astrophysics Data System (ADS)

Ganapol, B. D.

2017-11-01

Highly precise numerical solutions to the radiative transfer equation with polarization present a special challenge. Here, we establish a precise numerical solution to the radiative transfer equation with combined Rayleigh and isotropic scattering in a 1D-slab medium with simple polarization. The 2-Stokes vector solution for the fully discretized radiative transfer equation in space and direction derives from the method of doubling and adding enhanced through convergence acceleration. Updates to benchmark solutions found in the literature to seven places for reflectance and transmittance as well as for angular flux follow. Finally, we conclude with the numerical solution in a partially randomly absorbing heterogeneous medium.

Existence and numerical simulation of periodic traveling wave solutions to the Casimir equation for the Ito system

NASA Astrophysics Data System (ADS)

Abbasbandy, S.; Van Gorder, R. A.; Hajiketabi, M.; Mesrizadeh, M.

2015-10-01

We consider traveling wave solutions to the Casimir equation for the Ito system (a two-field extension of the KdV equation). These traveling waves are governed by a nonlinear initial value problem with an interesting nonlinearity (which actually amplifies in magnitude as the size of the solution becomes small). The nonlinear problem is parameterized by two initial constant values, and we demonstrate that the existence of solutions is strongly tied to these parameter values. For our interests, we are concerned with positive, bounded, periodic wave solutions. We are able to classify parameter regimes which admit such solutions in full generality, thereby obtaining a nice existence result. Using the existence result, we are then able to numerically simulate the positive, bounded, periodic solutions. We elect to employ a group preserving scheme in order to numerically study these solutions, and an outline of this approach is provided. The numerical simulations serve to illustrate the properties of these solutions predicted analytically through the existence result. Physically, these results demonstrate the existence of a type of space-periodic structure in the Casimir equation for the Ito model, which propagates as a traveling wave.

Toward a CFD nose-to-tail capability - Hypersonic unsteady Navier-Stokes code validation

NASA Technical Reports Server (NTRS)

Edwards, Thomas A.; Flores, Jolen

1989-01-01

Computational fluid dynamics (CFD) research for hypersonic flows presents new problems in code validation because of the added complexity of the physical models. This paper surveys code validation procedures applicable to hypersonic flow models that include real gas effects. The current status of hypersonic CFD flow analysis is assessed with the Compressible Navier-Stokes (CNS) code as a case study. The methods of code validation discussed to beyond comparison with experimental data to include comparisons with other codes and formulations, component analyses, and estimation of numerical errors. Current results indicate that predicting hypersonic flows of perfect gases and equilibrium air are well in hand. Pressure, shock location, and integrated quantities are relatively easy to predict accurately, while surface quantities such as heat transfer are more sensitive to the solution procedure. Modeling transition to turbulence needs refinement, though preliminary results are promising.

Variational data assimilation system "INM RAS - Black Sea"

NASA Astrophysics Data System (ADS)

Parmuzin, Eugene; Agoshkov, Valery; Assovskiy, Maksim; Giniatulin, Sergey; Zakharova, Natalia; Kuimov, Grigory; Fomin, Vladimir

2013-04-01

Development of Informational-Computational Systems (ICS) for Data Assimilation Procedures is one of multidisciplinary problems. To study and solve these problems one needs to apply modern results from different disciplines and recent developments in: mathematical modeling; theory of adjoint equations and optimal control; inverse problems; numerical methods theory; numerical algebra and scientific computing. The problems discussed above are studied in the Institute of Numerical Mathematics of the Russian Academy of Science (INM RAS) in ICS for Personal Computers (PC). Special problems and questions arise while effective ICS versions for PC are being developed. These problems and questions can be solved with applying modern methods of numerical mathematics and by solving "parallelism problem" using OpenMP technology and special linear algebra packages. In this work the results on the ICS development for PC-ICS "INM RAS - Black Sea" are presented. In the work the following problems and questions are discussed: practical problems that can be studied by ICS; parallelism problems and their solutions with applying of OpenMP technology and the linear algebra packages used in ICS "INM - Black Sea"; Interface of ICS. The results of ICS "INM RAS - Black Sea" testing are presented. Efficiency of technologies and methods applied are discussed. The work was supported by RFBR, grants No. 13-01-00753, 13-05-00715 and by The Ministry of education and science of Russian Federation, project 8291, project 11.519.11.1005 References: [1] V.I. Agoshkov, M.V. Assovskii, S.A. Lebedev, Numerical simulation of Black Sea hydrothermodynamics taking into account tide-forming forces. Russ. J. Numer. Anal. Math. Modelling (2012) 27, No.1, 5-31 [2] E.I. Parmuzin, V.I. Agoshkov, Numerical solution of the variational assimilation problem for sea surface temperature in the model of the Black Sea dynamics. Russ. J. Numer. Anal. Math. Modelling (2012) 27, No.1, 69-94 [3] V.B. Zalesny, N.A. Diansky, V.V. Fomin, S.N. Moshonkin, S.G. Demyshev, Numerical model of the circulation of Black Sea and Sea of Azov. Russ. J. Numer. Anal. Math. Modelling (2012) 27, No.1, 95-111 [4] V.I. Agoshkov, S.V. Giniatulin, G.V. Kuimov. OpenMP technology and linear algebra packages in the variation data assimilation systems. - Abstracts of the 1-st China-Russia Conference on Numerical Algebra with Applications in Radiactive Hydrodynamics, Beijing, China, October 16-18, 2012. [5] Zakharova N.B., Agoshkov V.I., Parmuzin E.I., The new method of ARGO buoys system observation data interpolation. Russian Journal of Numerical Analysis and Mathematical Modelling. Vol. 28, Issue 1, 2013.

How Near is a Near-Optimal Solution: Confidence Limits for the Global Optimum.

DTIC Science & Technology

1980-05-01

or near-optimal solutions are the only practical solutions available. This paper identifies and compares some procedures which use independent near...approximate or near-optimal solutions are the only practical solutions available. This paper identifies and compares some procedures which use inde- pendent...The objective of this paper is to indicate some relatively new statistical procedures for obtaining an upper confidence limit on G Each of these

Users manual for Streamtube Curvature Analysis: Analytical method for predicting the pressure distribution about a nacelle at transonic speeds, volume 1

NASA Technical Reports Server (NTRS)

Keith, J. S.; Ferguson, D. R.; Heck, P. H.

1972-01-01

The computer program, Streamtube Curvature Analysis, is described for the engineering user and for the programmer. The user oriented documentation includes a description of the mathematical governing equations, their use in the solution, and the method of solution. The general logical flow of the program is outlined and detailed instructions for program usage and operation are explained. General procedures for program use and the program capabilities and limitations are described. From the standpoint of the grammar, the overlay structure of the program is described. The various storage tables are defined and their uses explained. The input and output are discussed in detail. The program listing includes numerous comments so that the logical flow within the program is easily followed. A test case showing input data and output format is included as well as an error printout description.