Technical Feasibility of Centrifugal Techniques for Evaluating Hazardous Waste Migration

DTIC Science & Technology

1987-12-01

direct evaluation of the -influence of acceleration on soil moisture movement. A fully implicit finite difference solution scheme was used. The...using the finite difference scheme mentioned earlier. 2. The soil test apparatus for the centrifuge tests was designed and constructed. 110 3...npcr3 f~nJPX 115 S.. 0i U 4 I3 u cc/ U) C~j tC LL~~*- Lý u ’ uiu ’ 4-’ Uju x~j~r3np~~r~tj~jpU W3= 116 Finite Difference Model The finite difference

Boundary conditions for the solution of compressible Navier-Stokes equations by an implicit factored method

NASA Technical Reports Server (NTRS)

Shih, T. I.-P.; Smith, G. E.; Springer, G. S.; Rimon, Y.

1983-01-01

A method is presented for formulating the boundary conditions in implicit finite-difference form needed for obtaining solutions to the compressible Navier-Stokes equations by the Beam and Warming implicit factored method. The usefulness of the method was demonstrated (a) by establishing the boundary conditions applicable to the analysis of the flow inside an axisymmetric piston-cylinder configuration and (b) by calculating velocities and mass fractions inside the cylinder for different geometries and different operating conditions. Stability, selection of time step and grid sizes, and computer time requirements are discussed in reference to the piston-cylinder problem analyzed.

Parallel Implementation of a High Order Implicit Collocation Method for the Heat Equation

NASA Technical Reports Server (NTRS)

Kouatchou, Jules; Halem, Milton (Technical Monitor)

2000-01-01

We combine a high order compact finite difference approximation and collocation techniques to numerically solve the two dimensional heat equation. The resulting method is implicit arid can be parallelized with a strategy that allows parallelization across both time and space. We compare the parallel implementation of the new method with a classical implicit method, namely the Crank-Nicolson method, where the parallelization is done across space only. Numerical experiments are carried out on the SGI Origin 2000.

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

NASA Technical Reports Server (NTRS)

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

1987-01-01

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

Parallelized implicit propagators for the finite-difference Schrödinger equation

NASA Astrophysics Data System (ADS)

Parker, Jonathan; Taylor, K. T.

1995-08-01

We describe the application of block Gauss-Seidel and block Jacobi iterative methods to the design of implicit propagators for finite-difference models of the time-dependent Schrödinger equation. The block-wise iterative methods discussed here are mixed direct-iterative methods for solving simultaneous equations, in the sense that direct methods (e.g. LU decomposition) are used to invert certain block sub-matrices, and iterative methods are used to complete the solution. We describe parallel variants of the basic algorithm that are well suited to the medium- to coarse-grained parallelism of work-station clusters, and MIMD supercomputers, and we show that under a wide range of conditions, fine-grained parallelism of the computation can be achieved. Numerical tests are conducted on a typical one-electron atom Hamiltonian. The methods converge robustly to machine precision (15 significant figures), in some cases in as few as 6 or 7 iterations. The rate of convergence is nearly independent of the finite-difference grid-point separations.

The assessment of nanofluid in a Von Karman flow with temperature relied viscosity

NASA Astrophysics Data System (ADS)

Tanveer, Anum; Salahuddin, T.; Khan, Mumtaz; Alshomrani, Ali Saleh; Malik, M. Y.

2018-06-01

This work endeavor to study the heat and mass transfer viscous nanofluid features in a Von Karman flow invoking the variable viscosity mechanism. Moreover, we have extended our study in view of heat generation and uniform suction effects. The flow triggering non-linear partial differential equations are inscribed in the non-dimensional form by manipulating suitable transformations. The resulting non-linear ordinary differential equations are solved numerically via implicit finite difference scheme in conjecture with the Newton's linearization scheme afterwards. The sought solutions are plotted graphically to present comparison between MATLAB routine bvp4c and implicit finite difference schemes. Impact of different parameters on the concentration/temperature/velocity profiles are highlighted. Further Nusselt number, skin friction and Sherwood number characteristics are discussed for better exposition.

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

NASA Technical Reports Server (NTRS)

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

1978-01-01

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

Development Of A Navier-Stokes Computer Code

NASA Technical Reports Server (NTRS)

Yoon, Seokkwan; Kwak, Dochan

1993-01-01

Report discusses aspects of development of CENS3D computer code, solving three-dimensional Navier-Stokes equations of compressible, viscous, unsteady flow. Implements implicit finite-difference or finite-volume numerical-integration scheme, called "lower-upper symmetric-Gauss-Seidel" (LU-SGS), offering potential for very low computer time per iteration and for fast convergence.

Numerical Simulation of the Interaction of a Vortex with Stationary Airfoil in Transonic Flow,

DTIC Science & Technology

1984-01-12

Goorjian, P. M., "Implicit Vortex Wakes ," AIAA Journal, Vol. 15, No. 4, April Finite- Difference Computations of Unsteady Transonic 1977, pp. 581-590... Difference Simulations of Three- tion of Wing- Vortex Interaction in Transonic Flow Dimensional Flow," AIAA Journal, Vol. 18, No. 2, Using Implicit...assumptions are made in p = density modeling the nonlinear vortex wake structure. Numerical algorithms based on the Euler equations p_ = free stream density

On the use of finite difference matrix-vector products in Newton-Krylov solvers for implicit climate dynamics with spectral elements

DOE PAGES

Woodward, Carol S.; Gardner, David J.; Evans, Katherine J.

2015-01-01

Efficient solutions of global climate models require effectively handling disparate length and time scales. Implicit solution approaches allow time integration of the physical system with a step size governed by accuracy of the processes of interest rather than by stability of the fastest time scales present. Implicit approaches, however, require the solution of nonlinear systems within each time step. Usually, a Newton's method is applied to solve these systems. Each iteration of the Newton's method, in turn, requires the solution of a linear model of the nonlinear system. This model employs the Jacobian of the problem-defining nonlinear residual, but thismore » Jacobian can be costly to form. If a Krylov linear solver is used for the solution of the linear system, the action of the Jacobian matrix on a given vector is required. In the case of spectral element methods, the Jacobian is not calculated but only implemented through matrix-vector products. The matrix-vector multiply can also be approximated by a finite difference approximation which may introduce inaccuracy in the overall nonlinear solver. In this paper, we review the advantages and disadvantages of finite difference approximations of these matrix-vector products for climate dynamics within the spectral element shallow water dynamical core of the Community Atmosphere Model.« less

Fokker-Planck Equations of Stochastic Acceleration: A Study of Numerical Methods

NASA Astrophysics Data System (ADS)

Park, Brian T.; Petrosian, Vahe

1996-03-01

Stochastic wave-particle acceleration may be responsible for producing suprathermal particles in many astrophysical situations. The process can be described as a diffusion process through the Fokker-Planck equation. If the acceleration region is homogeneous and the scattering mean free path is much smaller than both the energy change mean free path and the size of the acceleration region, then the Fokker-Planck equation reduces to a simple form involving only the time and energy variables. in an earlier paper (Park & Petrosian 1995, hereafter Paper 1), we studied the analytic properties of the Fokker-Planck equation and found analytic solutions for some simple cases. In this paper, we study the numerical methods which must be used to solve more general forms of the equation. Two classes of numerical methods are finite difference methods and Monte Carlo simulations. We examine six finite difference methods, three fully implicit and three semi-implicit, and a stochastic simulation method which uses the exact correspondence between the Fokker-Planck equation and the it5 stochastic differential equation. As discussed in Paper I, Fokker-Planck equations derived under the above approximations are singular, causing problems with boundary conditions and numerical overflow and underflow. We evaluate each method using three sample equations to test its stability, accuracy, efficiency, and robustness for both time-dependent and steady state solutions. We conclude that the most robust finite difference method is the fully implicit Chang-Cooper method, with minor extensions to account for the escape and injection terms. Other methods suffer from stability and accuracy problems when dealing with some Fokker-Planck equations. The stochastic simulation method, although simple to implement, is susceptible to Poisson noise when insufficient test particles are used and is computationally very expensive compared to the finite difference method.

Fourth order Douglas implicit scheme for solving three dimension reaction diffusion equation with non-linear source term

NASA Astrophysics Data System (ADS)

Hasnain, Shahid; Saqib, Muhammad; Mashat, Daoud Suleiman

2017-07-01

This research paper represents a numerical approximation to non-linear three dimension reaction diffusion equation with non-linear source term from population genetics. Since various initial and boundary value problems exist in three dimension reaction diffusion phenomena, which are studied numerically by different numerical methods, here we use finite difference schemes (Alternating Direction Implicit and Fourth Order Douglas Implicit) to approximate the solution. Accuracy is studied in term of L2, L∞ and relative error norms by random selected grids along time levels for comparison with analytical results. The test example demonstrates the accuracy, efficiency and versatility of the proposed schemes. Numerical results showed that Fourth Order Douglas Implicit scheme is very efficient and reliable for solving 3-D non-linear reaction diffusion equation.

On a fourth order accurate implicit finite difference scheme for hyperbolic conservation laws. I - Nonstiff strongly dynamic problems

NASA Technical Reports Server (NTRS)

Harten, A.; Tal-Ezer, H.

1981-01-01

An implicit finite difference method of fourth order accuracy in space and time is introduced for the numerical solution of one-dimensional systems of hyperbolic conservation laws. The basic form of the method is a two-level scheme which is unconditionally stable and nondissipative. The scheme uses only three mesh points at level t and three mesh points at level t + delta t. The dissipative version of the basic method given is conditionally stable under the CFL (Courant-Friedrichs-Lewy) condition. This version is particularly useful for the numerical solution of problems with strong but nonstiff dynamic features, where the CFL restriction is reasonable on accuracy grounds. Numerical results are provided to illustrate properties of the proposed method.

Stability analysis of Eulerian-Lagrangian methods for the one-dimensional shallow-water equations

USGS Publications Warehouse

Casulli, V.; Cheng, R.T.

1990-01-01

In this paper stability and error analyses are discussed for some finite difference methods when applied to the one-dimensional shallow-water equations. Two finite difference formulations, which are based on a combined Eulerian-Lagrangian approach, are discussed. In the first part of this paper the results of numerical analyses for an explicit Eulerian-Lagrangian method (ELM) have shown that the method is unconditionally stable. This method, which is a generalized fixed grid method of characteristics, covers the Courant-Isaacson-Rees method as a special case. Some artificial viscosity is introduced by this scheme. However, because the method is unconditionally stable, the artificial viscosity can be brought under control either by reducing the spatial increment or by increasing the size of time step. The second part of the paper discusses a class of semi-implicit finite difference methods for the one-dimensional shallow-water equations. This method, when the Eulerian-Lagrangian approach is used for the convective terms, is also unconditionally stable and highly accurate for small space increments or large time steps. The semi-implicit methods seem to be more computationally efficient than the explicit ELM; at each time step a single tridiagonal system of linear equations is solved. The combined explicit and implicit ELM is best used in formulating a solution strategy for solving a network of interconnected channels. The explicit ELM is used at channel junctions for each time step. The semi-implicit method is then applied to the interior points in each channel segment. Following this solution strategy, the channel network problem can be reduced to a set of independent one-dimensional open-channel flow problems. Numerical results support properties given by the stability and error analyses. ?? 1990.

An implicit finite-difference solution to the viscous shock layer, including the effects of radiation and strong blowing

NASA Technical Reports Server (NTRS)

Garrett, L. B.; Smith, G. L.; Perkins, J. N.

1972-01-01

An implicit finite-difference scheme is developed for the fully coupled solution of the viscous, radiating stagnation-streamline equations, including strong blowing. Solutions are presented for both air injection and injection of carbon-phenolic ablation products into air at conditions near the peak radiative heating point in an earth entry trajectory from interplanetary return missions. A detailed radiative-transport code that accounts for the important radiative exchange processes for gaseous mixtures in local thermodynamic and chemical equilibrium is utilized in the study. With minimum number of assumptions for the initially unknown parameters and profile distributions, convergent solutions to the full stagnation-line equations are rapidly obtained by a method of successive approximations. Damping of selected profiles is required to aid convergence of the solutions for massive blowing. It is shown that certain finite-difference approximations to the governing differential equations stabilize and improve the solutions. Detailed comparisons are made with the numerical results of previous investigations. Results of the present study indicate lower radiative heat fluxes at the wall for carbonphenolic ablation than previously predicted.

Semi-implicit finite difference methods for three-dimensional shallow water flow

USGS Publications Warehouse

Casulli, Vincenzo; Cheng, Ralph T.

1992-01-01

A semi-implicit finite difference method for the numerical solution of three-dimensional shallow water flows is presented and discussed. The governing equations are the primitive three-dimensional turbulent mean flow equations where the pressure distribution in the vertical has been assumed to be hydrostatic. In the method of solution a minimal degree of implicitness has been adopted in such a fashion that the resulting algorithm is stable and gives a maximal computational efficiency at a minimal computational cost. At each time step the numerical method requires the solution of one large linear system which can be formally decomposed into a set of small three-diagonal systems coupled with one five-diagonal system. All these linear systems are symmetric and positive definite. Thus the existence and uniquencess of the numerical solution are assured. When only one vertical layer is specified, this method reduces as a special case to a semi-implicit scheme for solving the corresponding two-dimensional shallow water equations. The resulting two- and three-dimensional algorithm has been shown to be fast, accurate and mass-conservative and can also be applied to simulate flooding and drying of tidal mud-flats in conjunction with three-dimensional flows. Furthermore, the resulting algorithm is fully vectorizable for an efficient implementation on modern vector computers.

Modeling highly transient flow, mass, and heat transport in the Chattahoochee River near Atlanta, Georgia

USGS Publications Warehouse

Jobson, Harvey E.; Keefer, Thomas N.

1979-01-01

A coupled flow-temperature model has been developed and verified for a 27.9-km reach of the Chattahoochee River between Buford Dam and Norcross, Ga. Flow in this reach of the Chattahoochee is continuous but highly regulated by Buford Dam, a flood-control and hydroelectric facility located near Buford, Ga. Calibration and verification utilized two sets of data collected under highly unsteady discharge conditions. Existing solution techniques, with certain minor improvements, were applied to verify the existing technology of flow and transport modeling. A linear, implicit finite-difference flow model was coupled with implicit, finite-difference transport and temperature models. Both the conservative and nonconservative forms of the transport equation were solved, and the difference in the predicted concentrations of dye were found to be insignificant. The temperature model, therefore, was based on the simpler nonconservative form of the transport equation. (Woodard-USGS)

Comprehensive Numerical Analysis of Finite Difference Time Domain Methods for Improving Optical Waveguide Sensor Accuracy

PubMed Central

Samak, M. Mosleh E. Abu; Bakar, A. Ashrif A.; Kashif, Muhammad; Zan, Mohd Saiful Dzulkifly

2016-01-01

This paper discusses numerical analysis methods for different geometrical features that have limited interval values for typically used sensor wavelengths. Compared with existing Finite Difference Time Domain (FDTD) methods, the alternating direction implicit (ADI)-FDTD method reduces the number of sub-steps by a factor of two to three, which represents a 33% time savings in each single run. The local one-dimensional (LOD)-FDTD method has similar numerical equation properties, which should be calculated as in the previous method. Generally, a small number of arithmetic processes, which result in a shorter simulation time, are desired. The alternating direction implicit technique can be considered a significant step forward for improving the efficiency of unconditionally stable FDTD schemes. This comparative study shows that the local one-dimensional method had minimum relative error ranges of less than 40% for analytical frequencies above 42.85 GHz, and the same accuracy was generated by both methods.

A review of hybrid implicit explicit finite difference time domain method

NASA Astrophysics Data System (ADS)

Chen, Juan

2018-06-01

The finite-difference time-domain (FDTD) method has been extensively used to simulate varieties of electromagnetic interaction problems. However, because of its Courant-Friedrich-Levy (CFL) condition, the maximum time step size of this method is limited by the minimum size of cell used in the computational domain. So the FDTD method is inefficient to simulate the electromagnetic problems which have very fine structures. To deal with this problem, the Hybrid Implicit Explicit (HIE)-FDTD method is developed. The HIE-FDTD method uses the hybrid implicit explicit difference in the direction with fine structures to avoid the confinement of the fine spatial mesh on the time step size. So this method has much higher computational efficiency than the FDTD method, and is extremely useful for the problems which have fine structures in one direction. In this paper, the basic formulations, time stability condition and dispersion error of the HIE-FDTD method are presented. The implementations of several boundary conditions, including the connect boundary, absorbing boundary and periodic boundary are described, then some applications and important developments of this method are provided. The goal of this paper is to provide an historical overview and future prospects of the HIE-FDTD method.

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.

TRIM—3D: a three-dimensional model for accurate simulation of shallow water flow

USGS Publications Warehouse

Casulli, Vincenzo; Bertolazzi, Enrico; Cheng, Ralph T.

1993-01-01

A semi-implicit finite difference formulation for the numerical solution of three-dimensional tidal circulation is discussed. The governing equations are the three-dimensional Reynolds equations in which the pressure is assumed to be hydrostatic. A minimal degree of implicitness has been introduced in the finite difference formula so that the resulting algorithm permits the use of large time steps at a minimal computational cost. This formulation includes the simulation of flooding and drying of tidal flats, and is fully vectorizable for an efficient implementation on modern vector computers. The high computational efficiency of this method has made it possible to provide the fine details of circulation structure in complex regions that previous studies were unable to obtain. For proper interpretation of the model results suitable interactive graphics is also an essential tool.

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.

Formulation of the relativistic moment implicit particle-in-cell method

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

Noguchi, Koichi; Tronci, Cesare; Zuccaro, Gianluca

2007-04-15

A new formulation is presented for the implicit moment method applied to the time-dependent relativistic Vlasov-Maxwell system. The new approach is based on a specific formulation of the implicit moment method that allows us to retain the same formalism that is valid in the classical case despite the formidable complication introduced by the nonlinear nature of the relativistic equations of motion. To demonstrate the validity of the new formulation, an implicit finite difference algorithm is developed to solve the Maxwell's equations and equations of motion. A number of benchmark problems are run: two stream instability, ion acoustic wave damping, Weibelmore » instability, and Poynting flux acceleration. The numerical results are all in agreement with analytical solutions.« less

Ablative Thermal Response Analysis Using the Finite Element Method

NASA Technical Reports Server (NTRS)

Dec John A.; Braun, Robert D.

2009-01-01

A review of the classic techniques used to solve ablative thermal response problems is presented. The advantages and disadvantages of both the finite element and finite difference methods are described. As a first step in developing a three dimensional finite element based ablative thermal response capability, a one dimensional computer tool has been developed. The finite element method is used to discretize the governing differential equations and Galerkin's method of weighted residuals is used to derive the element equations. A code to code comparison between the current 1-D tool and the 1-D Fully Implicit Ablation and Thermal Response Program (FIAT) has been performed.

Calculation of three-dimensional compressible laminar and turbulent boundary layers. An implicit finite-difference procedure for solving the three-dimensional compressible laminar, transitional, and turbulent boundary-layer equations

NASA Technical Reports Server (NTRS)

Harris, J. E.

1975-01-01

An implicit finite-difference procedure is presented for solving the compressible three-dimensional boundary-layer equations. The method is second-order accurate, unconditionally stable (conditional stability for reverse cross flow), and efficient from the viewpoint of computer storage and processing time. The Reynolds stress terms are modeled by (1) a single-layer mixing length model and (2) a two-layer eddy viscosity model. These models, although simple in concept, accurately predicted the equilibrium turbulent flow for the conditions considered. Numerical results are compared with experimental wall and profile data for a cone at an angle of attack larger than the cone semiapex angle. These comparisons clearly indicate that the numerical procedure and turbulence models accurately predict the experimental data with as few as 21 nodal points in the plane normal to the wall boundary.

Pentadiagonal alternating-direction-implicit finite-difference time-domain method for two-dimensional Schrödinger equation

NASA Astrophysics Data System (ADS)

Tay, Wei Choon; Tan, Eng Leong

2014-07-01

In this paper, we have proposed a pentadiagonal alternating-direction-implicit (Penta-ADI) finite-difference time-domain (FDTD) method for the two-dimensional Schrödinger equation. Through the separation of complex wave function into real and imaginary parts, a pentadiagonal system of equations for the ADI method is obtained, which results in our Penta-ADI method. The Penta-ADI method is further simplified into pentadiagonal fundamental ADI (Penta-FADI) method, which has matrix-operator-free right-hand-sides (RHS), leading to the simplest and most concise update equations. As the Penta-FADI method involves five stencils in the left-hand-sides (LHS) of the pentadiagonal update equations, special treatments that are required for the implementation of the Dirichlet's boundary conditions will be discussed. Using the Penta-FADI method, a significantly higher efficiency gain can be achieved over the conventional Tri-ADI method, which involves a tridiagonal system of equations.

Computational Fluid Dynamics: Algorithms and Supercomputers

DTIC Science & Technology

1988-03-01

1985. 1.2. Pulliam, T., and Steger, J. , Implicit Finite Difference Simulations of Three Dimensional Compressible Flow, AIAA Journal , Vol. 18, No. 2...approaches infinity, assuming N is bounded. The question as to actual performance when M is finite and N varies, is a different matter. (Note: the CYBER...PARTICLE-IN-CELL 9i% 3.b7 j.48 WEATHER FORECAST 98% 3.77 3.55 SEISMIC MIGRATION 98% 3.85 3.45 MONTE CARLO 99% 3.85 3.75 LATTICE GAUGE 100% 4.00 3.77

An Implicit Characteristic Based Method for Electromagnetics

NASA Technical Reports Server (NTRS)

Beggs, John H.; Briley, W. Roger

2001-01-01

An implicit characteristic-based approach for numerical solution of Maxwell's time-dependent curl equations in flux conservative form is introduced. This method combines a characteristic based finite difference spatial approximation with an implicit lower-upper approximate factorization (LU/AF) time integration scheme. This approach is advantageous for three-dimensional applications because the characteristic differencing enables a two-factor approximate factorization that retains its unconditional stability in three space dimensions, and it does not require solution of tridiagonal systems. Results are given both for a Fourier analysis of stability, damping and dispersion properties, and for one-dimensional model problems involving propagation and scattering for free space and dielectric materials using both uniform and nonuniform grids. The explicit Finite Difference Time Domain Method (FDTD) algorithm is used as a convenient reference algorithm for comparison. The one-dimensional results indicate that for low frequency problems on a highly resolved uniform or nonuniform grid, this LU/AF algorithm can produce accurate solutions at Courant numbers significantly greater than one, with a corresponding improvement in efficiency for simulating a given period of time. This approach appears promising for development of dispersion optimized LU/AF schemes for three dimensional applications.

A comparison of two central difference schemes for solving the Navier-Stokes equations

NASA Technical Reports Server (NTRS)

Maksymiuk, C. M.; Swanson, R. C.; Pulliam, T. H.

1990-01-01

Five viscous transonic airfoil cases were computed by two significantly different computational fluid dynamics codes: An explicit finite-volume algorithm with multigrid, and an implicit finite-difference approximate-factorization method with Eigenvector diagonalization. Both methods are described in detail, and their performance on the test cases is compared. The codes utilized the same grids, turbulence model, and computer to provide the truest test of the algorithms. The two approaches produce very similar results, which, for attached flows, also agree well with experimental results; however, the explicit code is considerably faster.

Scalable Implementation of Finite Elements by NASA _ Implicit (ScIFEi)

NASA Technical Reports Server (NTRS)

Warner, James E.; Bomarito, Geoffrey F.; Heber, Gerd; Hochhalter, Jacob D.

2016-01-01

Scalable Implementation of Finite Elements by NASA (ScIFEN) is a parallel finite element analysis code written in C++. ScIFEN is designed to provide scalable solutions to computational mechanics problems. It supports a variety of finite element types, nonlinear material models, and boundary conditions. This report provides an overview of ScIFEi (\\Sci-Fi"), the implicit solid mechanics driver within ScIFEN. A description of ScIFEi's capabilities is provided, including an overview of the tools and features that accompany the software as well as a description of the input and output le formats. Results from several problems are included, demonstrating the efficiency and scalability of ScIFEi by comparing to finite element analysis using a commercial code.

A simple level set method for solving Stefan problems

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

Chen, S.; Merriman, B.; Osher, S.

1997-07-15

Discussed in this paper is an implicit finite difference scheme for solving a heat equation and a simple level set method for capturing the interface between solid and liquid phases which are used to solve Stefan problems.

Implementation of Implicit Adaptive Mesh Refinement in an Unstructured Finite-Volume Flow Solver

NASA Technical Reports Server (NTRS)

Schwing, Alan M.; Nompelis, Ioannis; Candler, Graham V.

2013-01-01

This paper explores the implementation of adaptive mesh refinement in an unstructured, finite-volume solver. Unsteady and steady problems are considered. The effect on the recovery of high-order numerics is explored and the results are favorable. Important to this work is the ability to provide a path for efficient, implicit time advancement. A method using a simple refinement sensor based on undivided differences is discussed and applied to a practical problem: a shock-shock interaction on a hypersonic, inviscid double-wedge. Cases are compared to uniform grids without the use of adapted meshes in order to assess error and computational expense. Discussion of difficulties, advances, and future work prepare this method for additional research. The potential for this method in more complicated flows is described.

Effect of analysis parameters on non-linear implicit finite element analysis of marine corroded steel plate

NASA Astrophysics Data System (ADS)

Islam, Muhammad Rabiul; Sakib-Ul-Alam, Md.; Nazat, Kazi Kaarima; Hassan, M. Munir

2017-12-01

FEA results greatly depend on analysis parameters. MSC NASTRAN nonlinear implicit analysis code has been used in large deformation finite element analysis of pitted marine SM490A steel rectangular plate. The effect of two types actual pit shape on parameters of integrity of structure has been analyzed. For 3-D modeling, a proposed method for simulation of pitted surface by probabilistic corrosion model has been used. The result has been verified with the empirical formula proposed by finite element analysis of steel surface generated with different pitted data where analyses have been carried out by the code of LS-DYNA 971. In the both solver, an elasto-plastic material has been used where an arbitrary stress versus strain curve can be defined. In the later one, the material model is based on the J2 flow theory with isotropic hardening where a radial return algorithm is used. The comparison shows good agreement between the two results which ensures successful simulation with comparatively less energy and time.

Nonlinear truncation error analysis of finite difference schemes for the Euler equations

NASA Technical Reports Server (NTRS)

Klopfer, G. H.; Mcrae, D. S.

1983-01-01

It is pointed out that, in general, dissipative finite difference integration schemes have been found to be quite robust when applied to the Euler equations of gas dynamics. The present investigation considers a modified equation analysis of both implicit and explicit finite difference techniques as applied to the Euler equations. The analysis is used to identify those error terms which contribute most to the observed solution errors. A technique for analytically removing the dominant error terms is demonstrated, resulting in a greatly improved solution for the explicit Lax-Wendroff schemes. It is shown that the nonlinear truncation errors are quite large and distributed quite differently for each of the three conservation equations as applied to a one-dimensional shock tube problem.

Radiation Diffusion:. AN Overview of Physical and Numerical Concepts

NASA Astrophysics Data System (ADS)

Graziani, Frank

2005-12-01

An overview of the physical and mathematical foundations of radiation transport is given. Emphasis is placed on how the diffusion approximation and its transport corrections arise. An overview of the numerical handling of radiation diffusion coupled to matter is also given. Discussions center on partial temperature and grey methods with comments concerning fully implicit methods. In addition finite difference, finite element and Pert representations of the div-grad operator is also discussed

An implict LU scheme for the Euler equations applied to arbitrary cascades. [new method of factoring

NASA Technical Reports Server (NTRS)

Buratynski, E. K.; Caughey, D. A.

1984-01-01

An implicit scheme for solving the Euler equations is derived and demonstrated. The alternating-direction implicit (ADI) technique is modified, using two implicit-operator factors corresponding to lower-block-diagonal (L) or upper-block-diagonal (U) algebraic systems which can be easily inverted. The resulting LU scheme is implemented in finite-volume mode and applied to 2D subsonic and transonic cascade flows with differing degrees of geometric complexity. The results are presented graphically and found to be in good agreement with those of other numerical and analytical approaches. The LU method is also 2.0-3.4 times faster than ADI, suggesting its value in calculating 3D problems.

On the performance of explicit and implicit algorithms for transient thermal analysis

NASA Astrophysics Data System (ADS)

Adelman, H. M.; Haftka, R. T.

1980-09-01

The status of an effort to increase the efficiency of calculating transient temperature fields in complex aerospace vehicle structures is described. The advantages and disadvantages of explicit and implicit algorithms are discussed. A promising set of implicit algorithms, known as the GEAR package is described. Four test problems, used for evaluating and comparing various algorithms, have been selected and finite element models of the configurations are discribed. These problems include a space shuttle frame component, an insulated cylinder, a metallic panel for a thermal protection system and a model of the space shuttle orbiter wing. Calculations were carried out using the SPAR finite element program, the MITAS lumped parameter program and a special purpose finite element program incorporating the GEAR algorithms. Results generally indicate a preference for implicit over explicit algorithms for solution of transient structural heat transfer problems when the governing equations are stiff. Careful attention to modeling detail such as avoiding thin or short high-conducting elements can sometimes reduce the stiffness to the extent that explicit methods become advantageous.

Flowfield-Dependent Mixed Explicit-Implicit (FDMEL) Algorithm for Computational Fluid Dynamics

NASA Technical Reports Server (NTRS)

Garcia, S. M.; Chung, T. J.

1997-01-01

Despite significant achievements in computational fluid dynamics, there still remain many fluid flow phenomena not well understood. For example, the prediction of temperature distributions is inaccurate when temperature gradients are high, particularly in shock wave turbulent boundary layer interactions close to the wall. Complexities of fluid flow phenomena include transition to turbulence, relaminarization separated flows, transition between viscous and inviscid incompressible and compressible flows, among others, in all speed regimes. The purpose of this paper is to introduce a new approach, called the Flowfield-Dependent Mixed Explicit-Implicit (FDMEI) method, in an attempt to resolve these difficult issues in Computational Fluid Dynamics (CFD). In this process, a total of six implicitness parameters characteristic of the current flowfield are introduced. They are calculated from the current flowfield or changes of Mach numbers, Reynolds numbers, Peclet numbers, and Damkoehler numbers (if reacting) at each nodal point and time step. This implies that every nodal point or element is provided with different or unique numerical scheme according to their current flowfield situations, whether compressible, incompressible, viscous, inviscid, laminar, turbulent, reacting, or nonreacting. In this procedure, discontinuities or fluctuations of an variables between adjacent nodal points are determined accurately. If these implicitness parameters are fixed to certain numbers instead of being calculated from the flowfield information, then practically all currently available schemes of finite differences or finite elements arise as special cases. Some benchmark problems to be presented in this paper will show the validity, accuracy, and efficiency of the proposed methodology.

Practical aspects of prestack depth migration with finite differences

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

Ober, C.C.; Oldfield, R.A.; Womble, D.E.

1997-07-01

Finite-difference, prestack, depth migrations offers significant improvements over Kirchhoff methods in imaging near or under salt structures. The authors have implemented a finite-difference prestack depth migration algorithm for use on massively parallel computers which is discussed. The image quality of the finite-difference scheme has been investigated and suggested improvements are discussed. In this presentation, the authors discuss an implicit finite difference migration code, called Salvo, that has been developed through an ACTI (Advanced Computational Technology Initiative) joint project. This code is designed to be efficient on a variety of massively parallel computers. It takes advantage of both frequency and spatialmore » parallelism as well as the use of nodes dedicated to data input/output (I/O). Besides giving an overview of the finite-difference algorithm and some of the parallelism techniques used, migration results using both Kirchhoff and finite-difference migration will be presented and compared. The authors start out with a very simple Cartoon model where one can intuitively see the multiple travel paths and some of the potential problems that will be encountered with Kirchhoff migration. More complex synthetic models as well as results from actual seismic data from the Gulf of Mexico will be shown.« less

Development of Implicit Methods in CFD NASA Ames Research Center 1970's - 1980's

NASA Technical Reports Server (NTRS)

Pulliam, Thomas H.

2010-01-01

The focus here is on the early development (mid 1970's-1980's) at NASA Ames Research Center of implicit methods in Computational Fluid Dynamics (CFD). A class of implicit finite difference schemes of the Beam and Warming approximate factorization type will be addressed. The emphasis will be on the Euler equations. A review of material pertinent to the solution of the Euler equations within the framework of implicit methods will be presented. The eigensystem of the equations will be used extensively in developing a framework for various methods applied to the Euler equations. The development and analysis of various aspects of this class of schemes will be given along with the motivations behind many of the choices. Various acceleration and efficiency modifications such as matrix reduction, diagonalization and flux split schemes will be presented.

On a fourth order accurate implicit finite difference scheme for hyperbolic conservation laws. II - Five-point schemes

NASA Technical Reports Server (NTRS)

Harten, A.; Tal-Ezer, H.

1981-01-01

This paper presents a family of two-level five-point implicit schemes for the solution of one-dimensional systems of hyperbolic conservation laws, which generalized the Crank-Nicholson scheme to fourth order accuracy (4-4) in both time and space. These 4-4 schemes are nondissipative and unconditionally stable. Special attention is given to the system of linear equations associated with these 4-4 implicit schemes. The regularity of this system is analyzed and efficiency of solution-algorithms is examined. A two-datum representation of these 4-4 implicit schemes brings about a compactification of the stencil to three mesh points at each time-level. This compact two-datum representation is particularly useful in deriving boundary treatments. Numerical results are presented to illustrate some properties of the proposed scheme.

Implicit method for the computation of unsteady flows on unstructured grids

NASA Technical Reports Server (NTRS)

Venkatakrishnan, V.; Mavriplis, D. J.

1995-01-01

An implicit method for the computation of unsteady flows on unstructured grids is presented. Following a finite difference approximation for the time derivative, the resulting nonlinear system of equations is solved at each time step by using an agglomeration multigrid procedure. The method allows for arbitrarily large time steps and is efficient in terms of computational effort and storage. Inviscid and viscous unsteady flows are computed to validate the procedure. The issue of the mass matrix which arises with vertex-centered finite volume schemes is addressed. The present formulation allows the mass matrix to be inverted indirectly. A mesh point movement and reconnection procedure is described that allows the grids to evolve with the motion of bodies. As an example of flow over bodies in relative motion, flow over a multi-element airfoil system undergoing deployment is computed.

Numerical study of supersonic combustion using a finite rate chemistry model

NASA Technical Reports Server (NTRS)

Chitsomboon, T.; Tiwari, S. N.; Kumar, A.; Drummond, J. P.

1986-01-01

The governing equations of two-dimensional chemically reacting flows are presented together with a global two-step chemistry model for H2-air combustion. The explicit unsplit MacCormack finite difference algorithm is used to advance the discrete system of the governing equations in time until convergence is attained. The source terms in the species equations are evaluated implicitly to alleviate stiffness associated with fast reactions. With implicit source terms, the species equations give rise to a block-diagonal system which can be solved very efficiently on vector-processing computers. A supersonic reacting flow in an inlet-combustor configuration is calculated for the case where H2 is injected into the flow from the side walls and the strut. Results of the calculation are compared against the results obtained by using a complete reaction model.

An unconditionally stable staggered algorithm for transient finite element analysis of coupled thermoelastic problems

NASA Technical Reports Server (NTRS)

Farhat, C.; Park, K. C.; Dubois-Pelerin, Y.

1991-01-01

An unconditionally stable second order accurate implicit-implicit staggered procedure for the finite element solution of fully coupled thermoelasticity transient problems is proposed. The procedure is stabilized with a semi-algebraic augmentation technique. A comparative cost analysis reveals the superiority of the proposed computational strategy to other conventional staggered procedures. Numerical examples of one and two-dimensional thermomechanical coupled problems demonstrate the accuracy of the proposed numerical solution algorithm.

Second order accurate finite difference approximations for the transonic small disturbance equation and the full potential equation

NASA Technical Reports Server (NTRS)

Mostrel, M. M.

1988-01-01

New shock-capturing finite difference approximations for solving two scalar conservation law nonlinear partial differential equations describing inviscid, isentropic, compressible flows of aerodynamics at transonic speeds are presented. A global linear stability theorem is applied to these schemes in order to derive a necessary and sufficient condition for the finite element method. A technique is proposed to render the described approximations total variation-stable by applying the flux limiters to the nonlinear terms of the difference equation dimension by dimension. An entropy theorem applying to the approximations is proved, and an implicit, forward Euler-type time discretization of the approximation is presented. Results of some numerical experiments using the approximations are reported.

Finite element dynamic analysis on CDC STAR-100 computer

NASA Technical Reports Server (NTRS)

Noor, A. K.; Lambiotte, J. J., Jr.

1978-01-01

Computational algorithms are presented for the finite element dynamic analysis of structures on the CDC STAR-100 computer. The spatial behavior is described using higher-order finite elements. The temporal behavior is approximated by using either the central difference explicit scheme or Newmark's implicit scheme. In each case the analysis is broken up into a number of basic macro-operations. Discussion is focused on the organization of the computation and the mode of storage of different arrays to take advantage of the STAR pipeline capability. The potential of the proposed algorithms is discussed and CPU times are given for performing the different macro-operations for a shell modeled by higher order composite shallow shell elements having 80 degrees of freedom.

An implicit-iterative solution of the heat conduction equation with a radiation boundary condition

NASA Technical Reports Server (NTRS)

Williams, S. D.; Curry, D. M.

1977-01-01

For the problem of predicting one-dimensional heat transfer between conducting and radiating mediums by an implicit finite difference method, four different formulations were used to approximate the surface radiation boundary condition while retaining an implicit formulation for the interior temperature nodes. These formulations are an explicit boundary condition, a linearized boundary condition, an iterative boundary condition, and a semi-iterative boundary method. The results of these methods in predicting surface temperature on the space shuttle orbiter thermal protection system model under a variety of heating rates were compared. The iterative technique caused the surface temperature to be bounded at each step. While the linearized and explicit methods were generally more efficient, the iterative and semi-iterative techniques provided a realistic surface temperature response without requiring step size control techniques.

Numerical aerodynamic simulation facility. [for flows about three-dimensional configurations

NASA Technical Reports Server (NTRS)

Bailey, F. R.; Hathaway, A. W.

1978-01-01

Critical to the advancement of computational aerodynamics capability is the ability to simulate flows about three-dimensional configurations that contain both compressible and viscous effects, including turbulence and flow separation at high Reynolds numbers. Analyses were conducted of two solution techniques for solving the Reynolds averaged Navier-Stokes equations describing the mean motion of a turbulent flow with certain terms involving the transport of turbulent momentum and energy modeled by auxiliary equations. The first solution technique is an implicit approximate factorization finite-difference scheme applied to three-dimensional flows that avoids the restrictive stability conditions when small grid spacing is used. The approximate factorization reduces the solution process to a sequence of three one-dimensional problems with easily inverted matrices. The second technique is a hybrid explicit/implicit finite-difference scheme which is also factored and applied to three-dimensional flows. Both methods are applicable to problems with highly distorted grids and a variety of boundary conditions and turbulence models.

An implicit flux-split algorithm to calculate hypersonic flowfields in chemical equilibrium

NASA Technical Reports Server (NTRS)

Palmer, Grant

1987-01-01

An implicit, finite-difference, shock-capturing algorithm that calculates inviscid, hypersonic flows in chemical equilibrium is presented. The flux vectors and flux Jacobians are differenced using a first-order, flux-split technique. The equilibrium composition of the gas is determined by minimizing the Gibbs free energy at every node point. The code is validated by comparing results over an axisymmetric hemisphere against previously published results. The algorithm is also applied to more practical configurations. The accuracy, stability, and versatility of the algorithm have been promising.

Numerical solution of the Saint-Venant equations by an efficient hybrid finite-volume/finite-difference method

NASA Astrophysics Data System (ADS)

Lai, Wencong; Khan, Abdul A.

2018-04-01

A computationally efficient hybrid finite-volume/finite-difference method is proposed for the numerical solution of Saint-Venant equations in one-dimensional open channel flows. The method adopts a mass-conservative finite volume discretization for the continuity equation and a semi-implicit finite difference discretization for the dynamic-wave momentum equation. The spatial discretization of the convective flux term in the momentum equation employs an upwind scheme and the water-surface gradient term is discretized using three different schemes. The performance of the numerical method is investigated in terms of efficiency and accuracy using various examples, including steady flow over a bump, dam-break flow over wet and dry downstream channels, wetting and drying in a parabolic bowl, and dam-break floods in laboratory physical models. Numerical solutions from the hybrid method are compared with solutions from a finite volume method along with analytic solutions or experimental measurements. Comparisons demonstrates that the hybrid method is efficient, accurate, and robust in modeling various flow scenarios, including subcritical, supercritical, and transcritical flows. In this method, the QUICK scheme for the surface slope discretization is more accurate and less diffusive than the center difference and the weighted average schemes.

An in-depth stability analysis of nonuniform FDTD combined with novel local implicitization techniques

NASA Astrophysics Data System (ADS)

Van Londersele, Arne; De Zutter, Daniël; Vande Ginste, Dries

2017-08-01

This work focuses on efficient full-wave solutions of multiscale electromagnetic problems in the time domain. Three local implicitization techniques are proposed and carefully analyzed in order to relax the traditional time step limit of the Finite-Difference Time-Domain (FDTD) method on a nonuniform, staggered, tensor product grid: Newmark, Crank-Nicolson (CN) and Alternating-Direction-Implicit (ADI) implicitization. All of them are applied in preferable directions, alike Hybrid Implicit-Explicit (HIE) methods, as to limit the rank of the sparse linear systems. Both exponential and linear stability are rigorously investigated for arbitrary grid spacings and arbitrary inhomogeneous, possibly lossy, isotropic media. Numerical examples confirm the conservation of energy inside a cavity for a million iterations if the time step is chosen below the proposed, relaxed limit. Apart from the theoretical contributions, new accomplishments such as the development of the leapfrog Alternating-Direction-Hybrid-Implicit-Explicit (ADHIE) FDTD method and a less stringent Courant-like time step limit for the conventional, fully explicit FDTD method on a nonuniform grid, have immediate practical applications.

An implicit fast Fourier transform method for integration of the time dependent Schrodinger equation

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

Riley, M.E.; Ritchie, A.B.

1997-12-31

One finds that the conventional exponentiated split operator procedure is subject to difficulties when solving the time-dependent Schrodinger equation for Coulombic systems. By rearranging the kinetic and potential energy terms in the temporal propagator of the finite difference equations, one can find a propagation algorithm for three dimensions that looks much like the Crank-Nicholson and alternating direction implicit methods for one- and two-space-dimensional partial differential equations. The authors report investigations of this novel implicit split operator procedure. The results look promising for a purely numerical approach to certain electron quantum mechanical problems. A charge exchange calculation is presented as anmore » example of the power of the method.« less

A multi-dimensional nonlinearly implicit, electromagnetic Vlasov-Darwin particle-in-cell (PIC) algorithm

NASA Astrophysics Data System (ADS)

Chen, Guangye; Chacón, Luis; CoCoMans Team

2014-10-01

For decades, the Vlasov-Darwin model has been recognized to be attractive for PIC simulations (to avoid radiative noise issues) in non-radiative electromagnetic regimes. However, the Darwin model results in elliptic field equations that renders explicit time integration unconditionally unstable. Improving on linearly implicit schemes, fully implicit PIC algorithms for both electrostatic and electromagnetic regimes, with exact discrete energy and charge conservation properties, have been recently developed in 1D. This study builds on these recent algorithms to develop an implicit, orbit-averaged, time-space-centered finite difference scheme for the particle-field equations in multiple dimensions. The algorithm conserves energy, charge, and canonical-momentum exactly, even with grid packing. A simple fluid preconditioner allows efficient use of large timesteps, O (√{mi/me}c/veT) larger than the explicit CFL. We demonstrate the accuracy and efficiency properties of the of the algorithm with various numerical experiments in 2D3V.

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.

Tidal, Residual, Intertidal Mudflat (TRIM) Model and its Applications to San Francisco Bay, California

USGS Publications Warehouse

Cheng, R.T.; Casulli, V.; Gartner, J.W.

1993-01-01

A numerical model using a semi-implicit finite-difference method for solving the two-dimensional shallow-water equations is presented. The gradient of the water surface elevation in the momentum equations and the velocity divergence in the continuity equation are finite-differenced implicitly, the remaining terms are finite-differenced explicitly. The convective terms are treated using an Eulerian-Lagrangian method. The combination of the semi-implicit finite-difference solution for the gravity wave propagation, and the Eulerian-Lagrangian treatment of the convective terms renders the numerical model unconditionally stable. When the baroclinic forcing is included, a salt transport equation is coupled to the momentum equations, and the numerical method is subject to a weak stability condition. The method of solution and the properties of the numerical model are given. This numerical model is particularly suitable for applications to coastal plain estuaries and tidal embayments in which tidal currents are dominant, and tidally generated residual currents are important. The model is applied to San Francisco Bay, California where extensive historical tides and current-meter data are available. The model calibration is considered by comparing time-series of the field data and of the model results. Alternatively, and perhaps more meaningfully, the model is calibrated by comparing the harmonic constants of tides and tidal currents derived from field data with those derived from the model. The model is further verified by comparing the model results with an independent data set representing the wet season. The strengths and the weaknesses of the model are assessed based on the results of model calibration and verification. Using the model results, the properties of tides and tidal currents in San Francisco Bay are characterized and discussed. Furthermore, using the numerical model, estimates of San Francisco Bay's volume, surface area, mean water depth, tidal prisms, and tidal excursions at spring and neap tides are computed. Additional applications of the model reveal, qualitatively the spatial distribution of residual variables. ?? 1993 Academic Press. All rights reserved.

Flux vector splitting of the inviscid equations with application to finite difference methods

NASA Technical Reports Server (NTRS)

Steger, J. L.; Warming, R. F.

1979-01-01

The conservation-law form of the inviscid gasdynamic equations has the remarkable property that the nonlinear flux vectors are homogeneous functions of degree one. This property readily permits the splitting of flux vectors into subvectors by similarity transformations so that each subvector has associated with it a specified eigenvalue spectrum. As a consequence of flux vector splitting, new explicit and implicit dissipative finite-difference schemes are developed for first-order hyperbolic systems of equations. Appropriate one-sided spatial differences for each split flux vector are used throughout the computational field even if the flow is locally subsonic. The results of some preliminary numerical computations are included.

Numerical study of hydrogen-air supersonic combustion by using elliptic and parabolized equations

NASA Technical Reports Server (NTRS)

Chitsomboon, T.; Tiwari, S. N.

1986-01-01

The two-dimensional Navier-Stokes and species continuity equations are used to investigate supersonic chemically reacting flow problems which are related to scramjet-engine configurations. A global two-step finite-rate chemistry model is employed to represent the hydrogen-air combustion in the flow. An algebraic turbulent model is adopted for turbulent flow calculations. The explicit unsplit MacCormack finite-difference algorithm is used to develop a computer program suitable for a vector processing computer. The computer program developed is then used to integrate the system of the governing equations in time until convergence is attained. The chemistry source terms in the species continuity equations are evaluated implicitly to alleviate stiffness associated with fast chemical reactions. The problems solved by the elliptic code are re-investigated by using a set of two-dimensional parabolized Navier-Stokes and species equations. A linearized fully-coupled fully-implicit finite difference algorithm is used to develop a second computer code which solves the governing equations by marching in spce rather than time, resulting in a considerable saving in computer resources. Results obtained by using the parabolized formulation are compared with the results obtained by using the fully-elliptic equations. The comparisons indicate fairly good agreement of the results of the two formulations.

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.

Algorithm For Hypersonic Flow In Chemical Equilibrium

NASA Technical Reports Server (NTRS)

Palmer, Grant

1989-01-01

Implicit, finite-difference, shock-capturing algorithm calculates inviscid, hypersonic flows in chemical equilibrium. Implicit formulation chosen because overcomes limitation on mathematical stability encountered in explicit formulations. For dynamical portion of problem, Euler equations written in conservation-law form in Cartesian coordinate system for two-dimensional or axisymmetric flow. For chemical portion of problem, equilibrium state of gas at each point in computational grid determined by minimizing local Gibbs free energy, subject to local conservation of molecules, atoms, ions, and total enthalpy. Major advantage: resulting algorithm naturally stable and captures strong shocks without help of artificial-dissipation terms to damp out spurious numerical oscillations.

A Modular Three-Dimensional Finite-Difference Ground-Water Flow Model

USGS Publications Warehouse

McDonald, Michael G.; Harbaugh, Arlen W.; Guo, Weixing; Lu, Guoping

1988-01-01

This report presents a finite-difference model and its associated modular computer program. The model simulates flow in three dimensions. The report includes detailed explanations of physical and mathematical concepts on which the model is based and an explanation of how those concepts are incorporated in the modular structure of the computer program. The modular structure consists of a Main Program and a series of highly independent subroutines called 'modules.' The modules are grouped into 'packages.' Each package deals with a specific feature of the hydrologic system which is to be simulated, such as flow from rivers or flow into drains, or with a specific method of solving linear equations which describe the flow system, such as the Strongly Implicit Procedure or Slice-Successive Overrelaxation. The division of the program into modules permits the user to examine specific hydrologic features of the model independently. This also facilita development of additional capabilities because new packages can be added to the program without modifying the existing packages. The input and output systems of the computer program are also designed to permit maximum flexibility. Ground-water flow within the aquifer is simulated using a block-centered finite-difference approach. Layers can be simulated as confined, unconfined, or a combination of confined and unconfined. Flow associated with external stresses, such as wells, areal recharge, evapotranspiration, drains, and streams, can also be simulated. The finite-difference equations can be solved using either the Strongly Implicit Procedure or Slice-Successive Overrelaxation. The program is written in FORTRAN 77 and will run without modification on most computers that have a FORTRAN 77 compiler. For each program ,module, this report includes a narrative description, a flow chart, a list of variables, and a module listing.

An implicit dispersive transport algorithm for the US Geological Survey MOC3D solute-transport model

USGS Publications Warehouse

Kipp, K.L.; Konikow, Leonard F.; Hornberger, G.Z.

1998-01-01

This report documents an extension to the U.S. Geological Survey MOC3D transport model that incorporates an implicit-in-time difference approximation for the dispersive transport equation, including source/sink terms. The original MOC3D transport model (Version 1) uses the method of characteristics to solve the transport equation on the basis of the velocity field. The original MOC3D solution algorithm incorporates particle tracking to represent advective processes and an explicit finite-difference formulation to calculate dispersive fluxes. The new implicit procedure eliminates several stability criteria required for the previous explicit formulation. This allows much larger transport time increments to be used in dispersion-dominated problems. The decoupling of advective and dispersive transport in MOC3D, however, is unchanged. With the implicit extension, the MOC3D model is upgraded to Version 2. A description of the numerical method of the implicit dispersion calculation, the data-input requirements and output options, and the results of simulator testing and evaluation are presented. Version 2 of MOC3D was evaluated for the same set of problems used for verification of Version 1. These test results indicate that the implicit calculation of Version 2 matches the accuracy of Version 1, yet is more efficient than the explicit calculation for transport problems that are characterized by a grid Peclet number less than about 1.0.

An efficient nonlinear finite-difference approach in the computational modeling of the dynamics of a nonlinear diffusion-reaction equation in microbial ecology.

PubMed

Macías-Díaz, J E; Macías, Siegfried; Medina-Ramírez, I E

2013-12-01

In this manuscript, we present a computational model to approximate the solutions of a partial differential equation which describes the growth dynamics of microbial films. The numerical technique reported in this work is an explicit, nonlinear finite-difference methodology which is computationally implemented using Newton's method. Our scheme is compared numerically against an implicit, linear finite-difference discretization of the same partial differential equation, whose computer coding requires an implementation of the stabilized bi-conjugate gradient method. Our numerical results evince that the nonlinear approach results in a more efficient approximation to the solutions of the biofilm model considered, and demands less computer memory. Moreover, the positivity of initial profiles is preserved in the practice by the nonlinear scheme proposed. Copyright © 2013 Elsevier Ltd. All rights reserved.

An implicit numerical model for multicomponent compressible two-phase flow in porous media

NASA Astrophysics Data System (ADS)

Zidane, Ali; Firoozabadi, Abbas

2015-11-01

We introduce a new implicit approach to model multicomponent compressible two-phase flow in porous media with species transfer between the phases. In the implicit discretization of the species transport equation in our formulation we calculate for the first time the derivative of the molar concentration of component i in phase α (cα, i) with respect to the total molar concentration (ci) under the conditions of a constant volume V and temperature T. The species transport equation is discretized by the finite volume (FV) method. The fluxes are calculated based on powerful features of the mixed finite element (MFE) method which provides the pressure at grid-cell interfaces in addition to the pressure at the grid-cell center. The efficiency of the proposed model is demonstrated by comparing our results with three existing implicit compositional models. Our algorithm has low numerical dispersion despite the fact it is based on first-order space discretization. The proposed algorithm is very robust.

Analysis of composite ablators using massively parallel computation

NASA Technical Reports Server (NTRS)

Shia, David

1995-01-01

In this work, the feasibility of using massively parallel computation to study the response of ablative materials is investigated. Explicit and implicit finite difference methods are used on a massively parallel computer, the Thinking Machines CM-5. The governing equations are a set of nonlinear partial differential equations. The governing equations are developed for three sample problems: (1) transpiration cooling, (2) ablative composite plate, and (3) restrained thermal growth testing. The transpiration cooling problem is solved using a solution scheme based solely on the explicit finite difference method. The results are compared with available analytical steady-state through-thickness temperature and pressure distributions and good agreement between the numerical and analytical solutions is found. It is also found that a solution scheme based on the explicit finite difference method has the following advantages: incorporates complex physics easily, results in a simple algorithm, and is easily parallelizable. However, a solution scheme of this kind needs very small time steps to maintain stability. A solution scheme based on the implicit finite difference method has the advantage that it does not require very small times steps to maintain stability. However, this kind of solution scheme has the disadvantages that complex physics cannot be easily incorporated into the algorithm and that the solution scheme is difficult to parallelize. A hybrid solution scheme is then developed to combine the strengths of the explicit and implicit finite difference methods and minimize their weaknesses. This is achieved by identifying the critical time scale associated with the governing equations and applying the appropriate finite difference method according to this critical time scale. The hybrid solution scheme is then applied to the ablative composite plate and restrained thermal growth problems. The gas storage term is included in the explicit pressure calculation of both problems. Results from ablative composite plate problems are compared with previous numerical results which did not include the gas storage term. It is found that the through-thickness temperature distribution is not affected much by the gas storage term. However, the through-thickness pressure and stress distributions, and the extent of chemical reactions are different from the previous numerical results. Two types of chemical reaction models are used in the restrained thermal growth testing problem: (1) pressure-independent Arrhenius type rate equations and (2) pressure-dependent Arrhenius type rate equations. The numerical results are compared to experimental results and the pressure-dependent model is able to capture the trend better than the pressure-independent one. Finally, a performance study is done on the hybrid algorithm using the ablative composite plate problem. It is found that there is a good speedup of performance on the CM-5. For 32 CPU's, the speedup of performance is 20. The efficiency of the algorithm is found to be a function of the size and execution time of a given problem and the effective parallelization of the algorithm. It also seems that there is an optimum number of CPU's to use for a given problem.

A conservative finite difference algorithm for the unsteady transonic potential equation in generalized coordinates

NASA Technical Reports Server (NTRS)

Bridgeman, J. O.; Steger, J. L.; Caradonna, F. X.

1982-01-01

An implicit, approximate-factorization, finite-difference algorithm has been developed for the computation of unsteady, inviscid transonic flows in two and three dimensions. The computer program solves the full-potential equation in generalized coordinates in conservation-law form in order to properly capture shock-wave position and speed. A body-fitted coordinate system is employed for the simple and accurate treatment of boundary conditions on the body surface. The time-accurate algorithm is modified to a conventional ADI relaxation scheme for steady-state computations. Results from two- and three-dimensional steady and two-dimensional unsteady calculations are compared with existing methods.

Implicit schemes and parallel computing in unstructured grid CFD

NASA Technical Reports Server (NTRS)

Venkatakrishnam, V.

1995-01-01

The development of implicit schemes for obtaining steady state solutions to the Euler and Navier-Stokes equations on unstructured grids is outlined. Applications are presented that compare the convergence characteristics of various implicit methods. Next, the development of explicit and implicit schemes to compute unsteady flows on unstructured grids is discussed. Next, the issues involved in parallelizing finite volume schemes on unstructured meshes in an MIMD (multiple instruction/multiple data stream) fashion are outlined. Techniques for partitioning unstructured grids among processors and for extracting parallelism in explicit and implicit solvers are discussed. Finally, some dynamic load balancing ideas, which are useful in adaptive transient computations, are presented.

A new finite element and finite difference hybrid method for computing electrostatics of ionic solvated biomolecule

NASA Astrophysics Data System (ADS)

Ying, Jinyong; Xie, Dexuan

2015-10-01

The Poisson-Boltzmann equation (PBE) is one widely-used implicit solvent continuum model for calculating electrostatics of ionic solvated biomolecule. In this paper, a new finite element and finite difference hybrid method is presented to solve PBE efficiently based on a special seven-overlapped box partition with one central box containing the solute region and surrounded by six neighboring boxes. In particular, an efficient finite element solver is applied to the central box while a fast preconditioned conjugate gradient method using a multigrid V-cycle preconditioning is constructed for solving a system of finite difference equations defined on a uniform mesh of each neighboring box. Moreover, the PBE domain, the box partition, and an interface fitted tetrahedral mesh of the central box can be generated adaptively for a given PQR file of a biomolecule. This new hybrid PBE solver is programmed in C, Fortran, and Python as a software tool for predicting electrostatics of a biomolecule in a symmetric 1:1 ionic solvent. Numerical results on two test models with analytical solutions and 12 proteins validate this new software tool, and demonstrate its high performance in terms of CPU time and memory usage.

Application of fast Fourier transforms to the direct solution of a class of two-dimensional separable elliptic equations on the sphere

NASA Technical Reports Server (NTRS)

Moorthi, Shrinivas; Higgins, R. W.

1993-01-01

An efficient, direct, second-order solver for the discrete solution of a class of two-dimensional separable elliptic equations on the sphere (which generally arise in implicit and semi-implicit atmospheric models) is presented. The method involves a Fourier transformation in longitude and a direct solution of the resulting coupled second-order finite-difference equations in latitude. The solver is made efficient by vectorizing over longitudinal wave-number and by using a vectorized fast Fourier transform routine. It is evaluated using a prescribed solution method and compared with a multigrid solver and the standard direct solver from FISHPAK.

Development and application of the GIM code for the Cyber 203 computer

NASA Technical Reports Server (NTRS)

Stainaker, J. F.; Robinson, M. A.; Rawlinson, E. G.; Anderson, P. G.; Mayne, A. W.; Spradley, L. W.

1982-01-01

The GIM computer code for fluid dynamics research was developed. Enhancement of the computer code, implicit algorithm development, turbulence model implementation, chemistry model development, interactive input module coding and wing/body flowfield computation are described. The GIM quasi-parabolic code development was completed, and the code used to compute a number of example cases. Turbulence models, algebraic and differential equations, were added to the basic viscous code. An equilibrium reacting chemistry model and implicit finite difference scheme were also added. Development was completed on the interactive module for generating the input data for GIM. Solutions for inviscid hypersonic flow over a wing/body configuration are also presented.

Numerical simulation of one-dimensional heat transfer in composite bodies with phase change. M.S. Thesis, 1980 Final Report; [wing deicing pads

NASA Technical Reports Server (NTRS)

Dewitt, K. J.; Baliga, G.

1982-01-01

A numerical simulation was developed to investigate the one dimensional heat transfer occurring in a system composed of a layered aircraft blade having an ice deposit on its surface. The finite difference representation of the heat conduction equations was done using the Crank-Nicolson implicit finite difference formulation. The simulation considers uniform or time dependent heat sources, from heaters which can be either point sources or of finite thickness. For the ice water phase change, a numerical method which approximates the latent heat effect by a large heat capacity over a small temperature interval was applied. The simulation describes the temperature profiles within the various layers of the de-icer pad, as well as the movement of the ice water interface. The simulation could also be used to predict the one dimensional temperature profiles in any composite slab having different boundary conditions.

A diagonal implicit scheme for computing flows with finite-rate chemistry

NASA Technical Reports Server (NTRS)

Eberhardt, Scott; Imlay, Scott

1990-01-01

A new algorithm for solving steady, finite-rate chemistry, flow problems is presented. The new scheme eliminates the expense of inverting large block matrices that arise when species conservation equations are introduced. The source Jacobian matrix is replaced by a diagonal matrix which is tailored to account for the fastest reactions in the chemical system. A point-implicit procedure is discussed and then the algorithm is included into the LU-SGS scheme. Solutions are presented for hypervelocity reentry and Hydrogen-Oxygen combustion. For the LU-SGS scheme a CFL number in excess of 10,000 has been achieved.

GroPBS: Fast Solver for Implicit Electrostatics of Biomolecules

PubMed Central

Bertelshofer, Franziska; Sun, Liping; Greiner, Günther; Böckmann, Rainer A.

2015-01-01

Knowledge about the electrostatic potential on the surface of biomolecules or biomembranes under physiological conditions is an important step in the attempt to characterize the physico-chemical properties of these molecules and, in particular, also their interactions with each other. Additionally, knowledge about solution electrostatics may also guide the design of molecules with specified properties. However, explicit water models come at a high computational cost, rendering them unsuitable for large design studies or for docking purposes. Implicit models with the water phase treated as a continuum require the numerical solution of the Poisson–Boltzmann equation (PBE). Here, we present a new flexible program for the numerical solution of the PBE, allowing for different geometries, and the explicit and implicit inclusion of membranes. It involves a discretization of space and the computation of the molecular surface. The PBE is solved using finite differences, the resulting set of equations is solved using a Gauss–Seidel method. It is shown for the example of the sucrose transporter ScrY that the implicit inclusion of a surrounding membrane has a strong effect also on the electrostatics within the pore region and, thus, needs to be carefully considered, e.g., in design studies on membrane proteins. PMID:26636074

A time-spectral approach to numerical weather prediction

NASA Astrophysics Data System (ADS)

Scheffel, Jan; Lindvall, Kristoffer; Yik, Hiu Fai

2018-05-01

Finite difference methods are traditionally used for modelling the time domain in numerical weather prediction (NWP). Time-spectral solution is an attractive alternative for reasons of accuracy and efficiency and because time step limitations associated with causal CFL-like criteria, typical for explicit finite difference methods, are avoided. In this work, the Lorenz 1984 chaotic equations are solved using the time-spectral algorithm GWRM (Generalized Weighted Residual Method). Comparisons of accuracy and efficiency are carried out for both explicit and implicit time-stepping algorithms. It is found that the efficiency of the GWRM compares well with these methods, in particular at high accuracy. For perturbative scenarios, the GWRM was found to be as much as four times faster than the finite difference methods. A primary reason is that the GWRM time intervals typically are two orders of magnitude larger than those of the finite difference methods. The GWRM has the additional advantage to produce analytical solutions in the form of Chebyshev series expansions. The results are encouraging for pursuing further studies, including spatial dependence, of the relevance of time-spectral methods for NWP modelling.

Development of an energy storage tank model

NASA Astrophysics Data System (ADS)

Buckley, Robert Christopher

A linearized, one-dimensional finite difference model employing an implicit finite difference method for energy storage tanks is developed, programmed with MATLAB, and demonstrated for different applications. A set of nodal energy equations is developed by considering the energy interactions on a small control volume. The general method of solving these equations is described as are other features of the simulation program. Two modeling applications are presented: the first using a hot water storage tank with a solar collector and an absorption chiller to cool a building in the summer, the second using a molten salt storage system with a solar collector and steam power plant to generate electricity. Recommendations for further study as well as all of the source code generated in the project are also provided.

Explicit and implicit springback simulation in sheet metal forming using fully coupled ductile damage and distortional hardening model

NASA Astrophysics Data System (ADS)

Yetna n'jock, M.; Houssem, B.; Labergere, C.; Saanouni, K.; Zhenming, Y.

2018-05-01

The springback is an important phenomenon which accompanies the forming of metallic sheets especially for high strength materials. A quantitative prediction of springback becomes very important for newly developed material with high mechanical characteristics. In this work, a numerical methodology is developed to quantify this undesirable phenomenon. This methodoly is based on the use of both explicit and implicit finite element solvers of Abaqus®. The most important ingredient of this methodology consists on the use of highly predictive mechanical model. A thermodynamically-consistent, non-associative and fully anisotropic elastoplastic constitutive model strongly coupled with isotropic ductile damage and accounting for distortional hardening is then used. An algorithm for local integration of the complete set of the constitutive equations is developed. This algorithm considers the rotated frame formulation (RFF) to ensure the incremental objectivity of the model in the framework of finite strains. This algorithm is implemented in both explicit (Abaqus/Explicit®) and implicit (Abaqus/Standard®) solvers of Abaqus® through the users routine VUMAT and UMAT respectively. The implicit solver of Abaqus® has been used to study spingback as it is generally a quasi-static unloading. In order to compare the methods `efficiency, the explicit method (Dynamic Relaxation Method) proposed by Rayleigh has been also used for springback prediction. The results obtained within U draw/bending benchmark are studied, discussed and compared with experimental results as reference. Finally, the purpose of this work is to evaluate the reliability of different methods predict efficiently springback in sheet metal forming.

Finite-Difference Solution for Laminar or Turbulent Boundary Layer Flow over Axisymmetric Bodies with Ideal Gas, CF4, or Equilibrium Air Chemistry

NASA Technical Reports Server (NTRS)

Hamilton, H. Harris, II; Millman, Daniel R.; Greendyke, Robert B.

1992-01-01

A computer code was developed that uses an implicit finite-difference technique to solve nonsimilar, axisymmetric boundary layer equations for both laminar and turbulent flow. The code can treat ideal gases, air in chemical equilibrium, and carbon tetrafluoride (CF4), which is a useful gas for hypersonic blunt-body simulations. This is the only known boundary layer code that can treat CF4. Comparisons with experimental data have demonstrated that accurate solutions are obtained. The method should prove useful as an analysis tool for comparing calculations with wind tunnel experiments and for making calculations about flight vehicles where equilibrium air chemistry assumptions are valid.

Finite-difference solution for laminar or turbulent boundary layer flow over axisymmetric bodies with ideal gas, CF4, or equilibrium air chemistry

NASA Astrophysics Data System (ADS)

Hamilton, H. Harris, II; Millman, Daniel R.; Greendyke, Robert B.

1992-12-01

A computer code was developed that uses an implicit finite-difference technique to solve nonsimilar, axisymmetric boundary layer equations for both laminar and turbulent flow. The code can treat ideal gases, air in chemical equilibrium, and carbon tetrafluoride (CF4), which is a useful gas for hypersonic blunt-body simulations. This is the only known boundary layer code that can treat CF4. Comparisons with experimental data have demonstrated that accurate solutions are obtained. The method should prove useful as an analysis tool for comparing calculations with wind tunnel experiments and for making calculations about flight vehicles where equilibrium air chemistry assumptions are valid.

A gradient enhanced plasticity-damage microplane model for concrete

NASA Astrophysics Data System (ADS)

Zreid, Imadeddin; Kaliske, Michael

2018-03-01

Computational modeling of concrete poses two main types of challenges. The first is the mathematical description of local response for such a heterogeneous material under all stress states, and the second is the stability and efficiency of the numerical implementation in finite element codes. The paper at hand presents a comprehensive approach addressing both issues. Adopting the microplane theory, a combined plasticity-damage model is formulated and regularized by an implicit gradient enhancement. The plasticity part introduces a new microplane smooth 3-surface cap yield function, which provides a stable numerical solution within an implicit finite element algorithm. The damage part utilizes a split, which can describe the transition of loading between tension and compression. Regularization of the model by the implicit gradient approach eliminates the mesh sensitivity and numerical instabilities. Identification methods for model parameters are proposed and several numerical examples of plain and reinforced concrete are carried out for illustration.

Computational plasticity algorithm for particle dynamics simulations

NASA Astrophysics Data System (ADS)

Krabbenhoft, K.; Lyamin, A. V.; Vignes, C.

2018-01-01

The problem of particle dynamics simulation is interpreted in the framework of computational plasticity leading to an algorithm which is mathematically indistinguishable from the common implicit scheme widely used in the finite element analysis of elastoplastic boundary value problems. This algorithm provides somewhat of a unification of two particle methods, the discrete element method and the contact dynamics method, which usually are thought of as being quite disparate. In particular, it is shown that the former appears as the special case where the time stepping is explicit while the use of implicit time stepping leads to the kind of schemes usually labelled contact dynamics methods. The framing of particle dynamics simulation within computational plasticity paves the way for new approaches similar (or identical) to those frequently employed in nonlinear finite element analysis. These include mixed implicit-explicit time stepping, dynamic relaxation and domain decomposition schemes.

A matrix-free implicit unstructured multigrid finite volume method for simulating structural dynamics and fluid structure interaction

NASA Astrophysics Data System (ADS)

Lv, X.; Zhao, Y.; Huang, X. Y.; Xia, G. H.; Su, X. H.

2007-07-01

A new three-dimensional (3D) matrix-free implicit unstructured multigrid finite volume (FV) solver for structural dynamics is presented in this paper. The solver is first validated using classical 2D and 3D cantilever problems. It is shown that very accurate predictions of the fundamental natural frequencies of the problems can be obtained by the solver with fast convergence rates. This method has been integrated into our existing FV compressible solver [X. Lv, Y. Zhao, et al., An efficient parallel/unstructured-multigrid preconditioned implicit method for simulating 3d unsteady compressible flows with moving objects, Journal of Computational Physics 215(2) (2006) 661-690] based on the immersed membrane method (IMM) [X. Lv, Y. Zhao, et al., as mentioned above]. Results for the interaction between the fluid and an immersed fixed-free cantilever are also presented to demonstrate the potential of this integrated fluid-structure interaction approach.

Implicit approximate-factorization schemes for the low-frequency transonic equation

NASA Technical Reports Server (NTRS)

Ballhaus, W. F.; Steger, J. L.

1975-01-01

Two- and three-level implicit finite-difference algorithms for the low-frequency transonic small disturbance-equation are constructed using approximate factorization techniques. The schemes are unconditionally stable for the model linear problem. For nonlinear mixed flows, the schemes maintain stability by the use of conservatively switched difference operators for which stability is maintained only if shock propagation is restricted to be less than one spatial grid point per time step. The shock-capturing properties of the schemes were studied for various shock motions that might be encountered in problems of engineering interest. Computed results for a model airfoil problem that produces a flow field similar to that about a helicopter rotor in forward flight show the development of a shock wave and its subsequent propagation upstream off the front of the airfoil.

Implicit Acquisition of Grammars with Crossed and Nested Non-Adjacent Dependencies: Investigating the Push-Down Stack Model

ERIC Educational Resources Information Center

Udden, Julia; Ingvar, Martin; Hagoort, Peter; Petersson, Karl M.

2012-01-01

A recent hypothesis in empirical brain research on language is that the fundamental difference between animal and human communication systems is captured by the distinction between finite-state and more complex phrase-structure grammars, such as context-free and context-sensitive grammars. However, the relevance of this distinction for the study…

Nonlinear 3D visco-resistive MHD modeling of fusion plasmas: a comparison between numerical codes

NASA Astrophysics Data System (ADS)

Bonfiglio, D.; Chacon, L.; Cappello, S.

2008-11-01

Fluid plasma models (and, in particular, the MHD model) are extensively used in the theoretical description of laboratory and astrophysical plasmas. We present here a successful benchmark between two nonlinear, three-dimensional, compressible visco-resistive MHD codes. One is the fully implicit, finite volume code PIXIE3D [1,2], which is characterized by many attractive features, notably the generalized curvilinear formulation (which makes the code applicable to different geometries) and the possibility to include in the computation the energy transport equation and the extended MHD version of Ohm's law. In addition, the parallel version of the code features excellent scalability properties. Results from this code, obtained in cylindrical geometry, are compared with those produced by the semi-implicit cylindrical code SpeCyl, which uses finite differences radially, and spectral formulation in the other coordinates [3]. Both single and multi-mode simulations are benchmarked, regarding both reversed field pinch (RFP) and ohmic tokamak magnetic configurations. [1] L. Chacon, Computer Physics Communications 163, 143 (2004). [2] L. Chacon, Phys. Plasmas 15, 056103 (2008). [3] S. Cappello, Plasma Phys. Control. Fusion 46, B313 (2004) & references therein.

Development of cost-effective surfactant flooding technology. Final report

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

Pope, G.A.; Sepehrnoori, K.

1996-11-01

Task 1 of this research was the development of a high-resolution, fully implicit, finite-difference, multiphase, multicomponent, compositional simulator for chemical flooding. The major physical phenomena modeled in this simulator are dispersion, heterogeneous permeability and porosity, adsorption, interfacial tension, relative permeability and capillary desaturation, compositional phase viscosity, compositional phase density and gravity effects, capillary pressure, and aqueous-oleic-microemulsion phase behavior. Polymer and its non-Newtonian rheology properties include shear-thinning viscosity, permeability reduction, inaccessible pore volume, and adsorption. Options of constant or variable space grids and time steps, constant-pressure or constant-rate well conditions, horizontal and vertical wells, and multiple slug injections are also availablemore » in the simulator. The solution scheme used in this simulator is fully implicit. The pressure equation and the mass-conservation equations are solved simultaneously for the aqueous-phase pressure and the total concentrations of each component. A third-order-in-space, second-order-in-time finite-difference method and a new total-variation-diminishing (TVD) third-order flux limiter are used that greatly reduce numerical dispersion effects. Task 2 was the optimization of surfactant flooding. The code UTCHEM was used to simulate surfactant polymer flooding.« less

Computational modeling of chemo-electro-mechanical coupling: A novel implicit monolithic finite element approach

PubMed Central

Wong, J.; Göktepe, S.; Kuhl, E.

2014-01-01

Summary Computational modeling of the human heart allows us to predict how chemical, electrical, and mechanical fields interact throughout a cardiac cycle. Pharmacological treatment of cardiac disease has advanced significantly over the past decades, yet it remains unclear how the local biochemistry of an individual heart cell translates into global cardiac function. Here we propose a novel, unified strategy to simulate excitable biological systems across three biological scales. To discretize the governing chemical, electrical, and mechanical equations in space, we propose a monolithic finite element scheme. We apply a highly efficient and inherently modular global-local split, in which the deformation and the transmembrane potential are introduced globally as nodal degrees of freedom, while the chemical state variables are treated locally as internal variables. To ensure unconditional algorithmic stability, we apply an implicit backward Euler finite difference scheme to discretize the resulting system in time. To increase algorithmic robustness and guarantee optimal quadratic convergence, we suggest an incremental iterative Newton-Raphson scheme. The proposed algorithm allows us to simulate the interaction of chemical, electrical, and mechanical fields during a representative cardiac cycle on a patient-specific geometry, robust and stable, with calculation times on the order of four days on a standard desktop computer. PMID:23798328

Explicit and implicit calculations of turbulent cavity flows with and without yaw angle

NASA Astrophysics Data System (ADS)

Yen, Guan-Wei

1989-08-01

Computations were performed to simulate turbulent supersonic flows past three-dimensional deep cavities with and without yaw. Simulation of these self-sustained oscillatory flows were generated through time accurate solutions of the Reynolds averaged complete Navier-Stokes equations using two different schemes: (1) MacCormack, finite-difference; and (2) implicit, upwind, finite-volume schemes. The second scheme, which is approximately 30 percent faster, is found to produce better time accurate results. The Reynolds stresses were modeled, using the Baldwin-Lomax algebraic turbulence model with certain modifications. The computational results include instantaneous and time averaged flow properties everywhere in the computational domain. Time series analyses were performed for the instantaneous pressure values on the cavity floor. The time averaged computational results show good agreement with the experimental data along the cavity floor and walls. When the yaw angle is nonzero, there is no longer a single length scale (length-to-depth ratio) for the flow, as is the case for zero yaw angle flow. The dominant directions and inclinations of the vortices are dramatically different for this nonsymmetric flow. The vortex shedding from the cavity into the mainstream flow is captured computationally. This phenomenon, which is due to the oscillation of the shear layer, is confirmed by the solutions of both schemes.

Explicit and implicit calculations of turbulent cavity flows with and without yaw angle. M.S. Thesis

NASA Technical Reports Server (NTRS)

Yen, Guan-Wei

1989-01-01

Computations were performed to simulate turbulent supersonic flows past three-dimensional deep cavities with and without yaw. Simulation of these self-sustained oscillatory flows were generated through time accurate solutions of the Reynolds averaged complete Navier-Stokes equations using two different schemes: (1) MacCormack, finite-difference; and (2) implicit, upwind, finite-volume schemes. The second scheme, which is approximately 30 percent faster, is found to produce better time accurate results. The Reynolds stresses were modeled, using the Baldwin-Lomax algebraic turbulence model with certain modifications. The computational results include instantaneous and time averaged flow properties everywhere in the computational domain. Time series analyses were performed for the instantaneous pressure values on the cavity floor. The time averaged computational results show good agreement with the experimental data along the cavity floor and walls. When the yaw angle is nonzero, there is no longer a single length scale (length-to-depth ratio) for the flow, as is the case for zero yaw angle flow. The dominant directions and inclinations of the vortices are dramatically different for this nonsymmetric flow. The vortex shedding from the cavity into the mainstream flow is captured computationally. This phenomenon, which is due to the oscillation of the shear layer, is confirmed by the solutions of both schemes.

Memory-optimized shift operator alternating direction implicit finite difference time domain method for plasma

NASA Astrophysics Data System (ADS)

Song, Wanjun; Zhang, Hou

2017-11-01

Through introducing the alternating direction implicit (ADI) technique and the memory-optimized algorithm to the shift operator (SO) finite difference time domain (FDTD) method, the memory-optimized SO-ADI FDTD for nonmagnetized collisional plasma is proposed and the corresponding formulae of the proposed method for programming are deduced. In order to further the computational efficiency, the iteration method rather than Gauss elimination method is employed to solve the equation set in the derivation of the formulae. Complicated transformations and convolutions are avoided in the proposed method compared with the Z transforms (ZT) ADI FDTD method and the piecewise linear JE recursive convolution (PLJERC) ADI FDTD method. The numerical dispersion of the SO-ADI FDTD method with different plasma frequencies and electron collision frequencies is analyzed and the appropriate ratio of grid size to the minimum wavelength is given. The accuracy of the proposed method is validated by the reflection coefficient test on a nonmagnetized collisional plasma sheet. The testing results show that the proposed method is advantageous for improving computational efficiency and saving computer memory. The reflection coefficient of a perfect electric conductor (PEC) sheet covered by multilayer plasma and the RCS of the objects coated by plasma are calculated by the proposed method and the simulation results are analyzed.

Efficiency Study of Implicit and Explicit Time Integration Operators for Finite Element Applications

DTIC Science & Technology

1977-07-01

cffiAciency, wherein Beta =0 provides anl exp~licit algorithm, wvhile Beta &0 provides anl implicit algorithm. Both algorithmns arc used in the same...Hlueneme CA: CO, Code C44A Port j IHuenemne, CA NAVSEC Cod,. 6034 (Library), Washington DC NAVSI*CGRUAC’I’ PWO, ’rorri Sta, OkinawaI NAVSIIIPRBFTAC Library

A comparison of the Method of Lines to finite difference techniques in solving time-dependent partial differential equations. [with applications to Burger equation and stream function-vorticity problem

NASA Technical Reports Server (NTRS)

Kurtz, L. A.; Smith, R. E.; Parks, C. L.; Boney, L. R.

1978-01-01

Steady state solutions to two time dependent partial differential systems have been obtained by the Method of Lines (MOL) and compared to those obtained by efficient standard finite difference methods: (1) Burger's equation over a finite space domain by a forward time central space explicit method, and (2) the stream function - vorticity form of viscous incompressible fluid flow in a square cavity by an alternating direction implicit (ADI) method. The standard techniques were far more computationally efficient when applicable. In the second example, converged solutions at very high Reynolds numbers were obtained by MOL, whereas solution by ADI was either unattainable or impractical. With regard to 'set up' time, solution by MOL is an attractive alternative to techniques with complicated algorithms, as much of the programming difficulty is eliminated.

Semi-implicit integration factor methods on sparse grids for high-dimensional systems

NASA Astrophysics Data System (ADS)

Wang, Dongyong; Chen, Weitao; Nie, Qing

2015-07-01

Numerical methods for partial differential equations in high-dimensional spaces are often limited by the curse of dimensionality. Though the sparse grid technique, based on a one-dimensional hierarchical basis through tensor products, is popular for handling challenges such as those associated with spatial discretization, the stability conditions on time step size due to temporal discretization, such as those associated with high-order derivatives in space and stiff reactions, remain. Here, we incorporate the sparse grids with the implicit integration factor method (IIF) that is advantageous in terms of stability conditions for systems containing stiff reactions and diffusions. We combine IIF, in which the reaction is treated implicitly and the diffusion is treated explicitly and exactly, with various sparse grid techniques based on the finite element and finite difference methods and a multi-level combination approach. The overall method is found to be efficient in terms of both storage and computational time for solving a wide range of PDEs in high dimensions. In particular, the IIF with the sparse grid combination technique is flexible and effective in solving systems that may include cross-derivatives and non-constant diffusion coefficients. Extensive numerical simulations in both linear and nonlinear systems in high dimensions, along with applications of diffusive logistic equations and Fokker-Planck equations, demonstrate the accuracy, efficiency, and robustness of the new methods, indicating potential broad applications of the sparse grid-based integration factor method.

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

NASA Astrophysics Data System (ADS)

Zhan, Lei; Xiong, Juntao; Liu, Feng

2016-05-01

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

Least-squares finite element methods for compressible Euler equations

NASA Technical Reports Server (NTRS)

Jiang, Bo-Nan; Carey, G. F.

1990-01-01

A method based on backward finite differencing in time and a least-squares finite element scheme for first-order systems of partial differential equations in space is applied to the Euler equations for gas dynamics. The scheme minimizes the L-sq-norm of the residual within each time step. The method naturally generates numerical dissipation proportional to the time step size. An implicit method employing linear elements has been implemented and proves robust. For high-order elements, computed solutions based on the L-sq method may have oscillations for calculations at similar time step sizes. To overcome this difficulty, a scheme which minimizes the weighted H1-norm of the residual is proposed and leads to a successful scheme with high-degree elements. Finally, a conservative least-squares finite element method is also developed. Numerical results for two-dimensional problems are given to demonstrate the shock resolution of the methods and compare different approaches.

Numerical Treatment of Degenerate Diffusion Equations via Feller's Boundary Classification, and Applications

NASA Technical Reports Server (NTRS)

Cacio, Emanuela; Cohn, Stephen E.; Spigler, Renato

2011-01-01

A numerical method is devised to solve a class of linear boundary-value problems for one-dimensional parabolic equations degenerate at the boundaries. Feller theory, which classifies the nature of the boundary points, is used to decide whether boundary conditions are needed to ensure uniqueness, and, if so, which ones they are. The algorithm is based on a suitable preconditioned implicit finite-difference scheme, grid, and treatment of the boundary data. Second-order accuracy, unconditional stability, and unconditional convergence of solutions of the finite-difference scheme to a constant as the time-step index tends to infinity are further properties of the method. Several examples, pertaining to financial mathematics, physics, and genetics, are presented for the purpose of illustration.

Integration of the shallow water equations on the sphere using a vector semi-Lagrangian scheme with a multigrid solver

NASA Technical Reports Server (NTRS)

Bates, J. R.; Semazzi, F. H. M.; Higgins, R. W.; Barros, Saulo R. M.

1990-01-01

A vector semi-Lagrangian semi-implicit two-time-level finite-difference integration scheme for the shallow water equations on the sphere is presented. A C-grid is used for the spatial differencing. The trajectory-centered discretization of the momentum equation in vector form eliminates pole problems and, at comparable cost, gives greater accuracy than a previous semi-Lagrangian finite-difference scheme which used a rotated spherical coordinate system. In terms of the insensitivity of the results to increasing timestep, the new scheme is as successful as recent spectral semi-Lagrangian schemes. In addition, the use of a multigrid method for solving the elliptic equation for the geopotential allows efficient integration with an operation count which, at high resolution, is of lower order than in the case of the spectral models. The properties of the new scheme should allow finite-difference models to compete with spectral models more effectively than has previously been possible.

Finite Volume Method for Pricing European Call Option with Regime-switching Volatility

NASA Astrophysics Data System (ADS)

Lista Tauryawati, Mey; Imron, Chairul; Putri, Endah RM

2018-03-01

In this paper, we present a finite volume method for pricing European call option using Black-Scholes equation with regime-switching volatility. In the first step, we formulate the Black-Scholes equations with regime-switching volatility. we use a finite volume method based on fitted finite volume with spatial discretization and an implicit time stepping technique for the case. We show that the regime-switching scheme can revert to the non-switching Black Scholes equation, both in theoretical evidence and numerical simulations.

Noniterative implicit method for tracking particles in mixed Lagrangian-Eulerian formulations

NASA Technical Reports Server (NTRS)

Shih, T. I.-P.; Dasgupta, A.

1993-01-01

The existing implicit methods for the current initial value problems (IVPs) concerning particle-laden flows are complicated and iterative in nature. This paper presents a noniterative implicit method which can be used with pressure-based as well as with density-based algorithms. The method is illustrated by analyzing a dilute dispersion of noninteracting solid particles in an isothermal flow in a passage bounded by one straight wall and one wavy wall, in which all particles are spherical and have a finite velociy relative to the continuum phase at the inflow boundary.

A Solution Adaptive Structured/Unstructured Overset Grid Flow Solver with Applications to Helicopter Rotor Flows

NASA Technical Reports Server (NTRS)

Duque, Earl P. N.; Biswas, Rupak; Strawn, Roger C.

1995-01-01

This paper summarizes a method that solves both the three dimensional thin-layer Navier-Stokes equations and the Euler equations using overset structured and solution adaptive unstructured grids with applications to helicopter rotor flowfields. The overset structured grids use an implicit finite-difference method to solve the thin-layer Navier-Stokes/Euler equations while the unstructured grid uses an explicit finite-volume method to solve the Euler equations. Solutions on a helicopter rotor in hover show the ability to accurately convect the rotor wake. However, isotropic subdivision of the tetrahedral mesh rapidly increases the overall problem size.

Studies of implicit and explicit solution techniques in transient thermal analysis of structures

NASA Technical Reports Server (NTRS)

Adelman, H. M.; Haftka, R. T.; Robinson, J. C.

1982-01-01

Studies aimed at an increase in the efficiency of calculating transient temperature fields in complex aerospace vehicle structures are reported. The advantages and disadvantages of explicit and implicit algorithms are discussed and a promising set of implicit algorithms with variable time steps, known as GEARIB, is described. Test problems, used for evaluating and comparing various algorithms, are discussed and finite element models of the configurations are described. These problems include a coarse model of the Space Shuttle wing, an insulated frame tst article, a metallic panel for a thermal protection system, and detailed models of sections of the Space Shuttle wing. Results generally indicate a preference for implicit over explicit algorithms for transient structural heat transfer problems when the governing equations are stiff (typical of many practical problems such as insulated metal structures). The effects on algorithm performance of different models of an insulated cylinder are demonstrated. The stiffness of the problem is highly sensitive to modeling details and careful modeling can reduce the stiffness of the equations to the extent that explicit methods may become the best choice. Preliminary applications of a mixed implicit-explicit algorithm and operator splitting techniques for speeding up the solution of the algebraic equations are also described.

Multidimensional, fully implicit, exactly conserving electromagnetic particle-in-cell simulations

NASA Astrophysics Data System (ADS)

Chacon, Luis

2015-09-01

We discuss a new, conservative, fully implicit 2D-3V particle-in-cell algorithm for non-radiative, electromagnetic kinetic plasma simulations, based on the Vlasov-Darwin model. Unlike earlier linearly implicit PIC schemes and standard explicit PIC schemes, fully implicit PIC algorithms are unconditionally stable and allow exact discrete energy and charge conservation. This has been demonstrated in 1D electrostatic and electromagnetic contexts. In this study, we build on these recent algorithms to develop an implicit, orbit-averaged, time-space-centered finite difference scheme for the Darwin field and particle orbit equations for multiple species in multiple dimensions. The Vlasov-Darwin model is very attractive for PIC simulations because it avoids radiative noise issues in non-radiative electromagnetic regimes. The algorithm conserves global energy, local charge, and particle canonical-momentum exactly, even with grid packing. The nonlinear iteration is effectively accelerated with a fluid preconditioner, which allows efficient use of large timesteps, O(√{mi/me}c/veT) larger than the explicit CFL. In this presentation, we will introduce the main algorithmic components of the approach, and demonstrate the accuracy and efficiency properties of the algorithm with various numerical experiments in 1D and 2D. Support from the LANL LDRD program and the DOE-SC ASCR office.

Studies of implicit and explicit solution techniques in transient thermal analysis of structures

NASA Astrophysics Data System (ADS)

Adelman, H. M.; Haftka, R. T.; Robinson, J. C.

1982-08-01

Studies aimed at an increase in the efficiency of calculating transient temperature fields in complex aerospace vehicle structures are reported. The advantages and disadvantages of explicit and implicit algorithms are discussed and a promising set of implicit algorithms with variable time steps, known as GEARIB, is described. Test problems, used for evaluating and comparing various algorithms, are discussed and finite element models of the configurations are described. These problems include a coarse model of the Space Shuttle wing, an insulated frame tst article, a metallic panel for a thermal protection system, and detailed models of sections of the Space Shuttle wing. Results generally indicate a preference for implicit over explicit algorithms for transient structural heat transfer problems when the governing equations are stiff (typical of many practical problems such as insulated metal structures). The effects on algorithm performance of different models of an insulated cylinder are demonstrated. The stiffness of the problem is highly sensitive to modeling details and careful modeling can reduce the stiffness of the equations to the extent that explicit methods may become the best choice. Preliminary applications of a mixed implicit-explicit algorithm and operator splitting techniques for speeding up the solution of the algebraic equations are also described.

A cubic spline approximation for problems in fluid mechanics

NASA Technical Reports Server (NTRS)

Rubin, S. G.; Graves, R. A., Jr.

1975-01-01

A cubic spline approximation is presented which is suited for many fluid-mechanics problems. This procedure provides a high degree of accuracy, even with a nonuniform mesh, and leads to an accurate treatment of derivative boundary conditions. The truncation errors and stability limitations of several implicit and explicit integration schemes are presented. For two-dimensional flows, a spline-alternating-direction-implicit method is evaluated. The spline procedure is assessed, and results are presented for the one-dimensional nonlinear Burgers' equation, as well as the two-dimensional diffusion equation and the vorticity-stream function system describing the viscous flow in a driven cavity. Comparisons are made with analytic solutions for the first two problems and with finite-difference calculations for the cavity flow.

Transient modeling/analysis of hyperbolic heat conduction problems employing mixed implicit-explicit alpha method

NASA Technical Reports Server (NTRS)

Tamma, Kumar K.; D'Costa, Joseph F.

1991-01-01

This paper describes the evaluation of mixed implicit-explicit finite element formulations for hyperbolic heat conduction problems involving non-Fourier effects. In particular, mixed implicit-explicit formulations employing the alpha method proposed by Hughes et al. (1987, 1990) are described for the numerical simulation of hyperbolic heat conduction models, which involves time-dependent relaxation effects. Existing analytical approaches for modeling/analysis of such models involve complex mathematical formulations for obtaining closed-form solutions, while in certain numerical formulations the difficulties include severe oscillatory solution behavior (which often disguises the true response) in the vicinity of the thermal disturbances, which propagate with finite velocities. In view of these factors, the alpha method is evaluated to assess the control of the amount of numerical dissipation for predicting the transient propagating thermal disturbances. Numerical test models are presented, and pertinent conclusions are drawn for the mixed-time integration simulation of hyperbolic heat conduction models involving non-Fourier effects.

SUPG Finite Element Simulations of Compressible Flows for Aerothermodynamic Applications

NASA Technical Reports Server (NTRS)

Kirk, Benjamin S.

2007-01-01

This viewgraph presentation reviews the Streamline-Upwind Petrov-Galerkin (SUPG) Finite Element Simulation. It covers the background, governing equations, weak formulation, shock capturing, inviscid flux discretization, time discretization, linearization, and implicit solution strategies. It also reviews some applications such as Type IV Shock Interaction, Forward-Facing Cavity and AEDC Sharp Double Cone.

Automatic partitioning of unstructured meshes for the parallel solution of problems in computational mechanics

NASA Technical Reports Server (NTRS)

Farhat, Charbel; Lesoinne, Michel

1993-01-01

Most of the recently proposed computational methods for solving partial differential equations on multiprocessor architectures stem from the 'divide and conquer' paradigm and involve some form of domain decomposition. For those methods which also require grids of points or patches of elements, it is often necessary to explicitly partition the underlying mesh, especially when working with local memory parallel processors. In this paper, a family of cost-effective algorithms for the automatic partitioning of arbitrary two- and three-dimensional finite element and finite difference meshes is presented and discussed in view of a domain decomposed solution procedure and parallel processing. The influence of the algorithmic aspects of a solution method (implicit/explicit computations), and the architectural specifics of a multiprocessor (SIMD/MIMD, startup/transmission time), on the design of a mesh partitioning algorithm are discussed. The impact of the partitioning strategy on load balancing, operation count, operator conditioning, rate of convergence and processor mapping is also addressed. Finally, the proposed mesh decomposition algorithms are demonstrated with realistic examples of finite element, finite volume, and finite difference meshes associated with the parallel solution of solid and fluid mechanics problems on the iPSC/2 and iPSC/860 multiprocessors.

Computation of Laminar and Turbulent Flow in 90-Degree Square-Duct and Pipe Bends Using the Navier-Stokes Equations

DTIC Science & Technology

1982-04-01

R.M. and Warming, R.F.: An Implicit Finite - Difference Algorithm for Hyperbolic Systems in Conservation Law Form. Journal of Computational Physics...Quincy Street C-40) Arlington, VA 22217 D 82 05-.10 I0, S4CURITY CLASSIFICATION OF THIS ’E(Wha, Doae Entotwed) Slength scale. Six different flow cases...forces upstream have produced a non-zero velocity gradient normal to the plane of curvature. Fluid with above (/below) average nioiiiei.tuili migrates

Numerical approach to optimal portfolio in a power utility regime-switching model

NASA Astrophysics Data System (ADS)

Gyulov, Tihomir B.; Koleva, Miglena N.; Vulkov, Lubin G.

2017-12-01

We consider a system of weakly coupled degenerate semi-linear parabolic equations of optimal portfolio in a regime-switching with power utility function, derived by A.R. Valdez and T. Vargiolu [14]. First, we discuss some basic properties of the solution of this system. Then, we develop and analyze implicit-explicit, flux limited finite difference schemes for the differential problem. Numerical experiments are discussed.

Unsteady streamflow simulation using a linear implicit finite-difference model

USGS Publications Warehouse

Land, Larry F.

1978-01-01

A computer program for simulating one-dimensional subcritical, gradually varied, unsteady flow in a stream has been developed and documented. Given upstream and downstream boundary conditions and channel geometry data, roughness coefficients, stage, and discharge can be calculated anywhere within the reach as a function of time. The program uses a linear implicit finite-difference technique that discritizes the partial differential equations. Then it arranges the coefficients of the continuity and momentum equations into a pentadiagonal matrix for solution. Because it is a reasonable compromise between computational accuracy, speed and ease of use,the technique is one of the most commonly used. The upstream boundary condition is a depth hydrograph. However, options also allow the boundary condition to be discharge or water-surface elevation. The downstream boundary condition is a depth which may be constant, self-setting, or unsteady. The reach may be divided into uneven increments and the cross sections may be nonprismatic and may vary from one to the other. Tributary and lateral inflow may enter the reach. The digital model will simulate such common problems as (1) flood waves, (2) releases from dams, and (3) channels where storage is a consideration. It may also supply the needed flow information for mass-transport simulation. (Woodard-USGS)

A semi-implicit augmented IIM for Navier–Stokes equations with open, traction, or free boundary conditions

PubMed Central

Li, Zhilin; Xiao, Li; Cai, Qin; Zhao, Hongkai; Luo, Ray

2016-01-01

In this paper, a new Navier–Stokes solver based on a finite difference approximation is proposed to solve incompressible flows on irregular domains with open, traction, and free boundary conditions, which can be applied to simulations of fluid structure interaction, implicit solvent model for biomolecular applications and other free boundary or interface problems. For some problems of this type, the projection method and the augmented immersed interface method (IIM) do not work well or does not work at all. The proposed new Navier–Stokes solver is based on the local pressure boundary method, and a semi-implicit augmented IIM. A fast Poisson solver can be used in our algorithm which gives us the potential for developing fast overall solvers in the future. The time discretization is based on a second order multi-step method. Numerical tests with exact solutions are presented to validate the accuracy of the method. Application to fluid structure interaction between an incompressible fluid and a compressible gas bubble is also presented. PMID:27087702

A semi-implicit augmented IIM for Navier-Stokes equations with open, traction, or free boundary conditions.

PubMed

Li, Zhilin; Xiao, Li; Cai, Qin; Zhao, Hongkai; Luo, Ray

2015-08-15

In this paper, a new Navier-Stokes solver based on a finite difference approximation is proposed to solve incompressible flows on irregular domains with open, traction, and free boundary conditions, which can be applied to simulations of fluid structure interaction, implicit solvent model for biomolecular applications and other free boundary or interface problems. For some problems of this type, the projection method and the augmented immersed interface method (IIM) do not work well or does not work at all. The proposed new Navier-Stokes solver is based on the local pressure boundary method, and a semi-implicit augmented IIM. A fast Poisson solver can be used in our algorithm which gives us the potential for developing fast overall solvers in the future. The time discretization is based on a second order multi-step method. Numerical tests with exact solutions are presented to validate the accuracy of the method. Application to fluid structure interaction between an incompressible fluid and a compressible gas bubble is also presented.

User`s guide for UTCHEM implicit (1.0) a three dimensional chemical flood simulator. Final report, September 30, 1992--December 31, 1995

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

NONE

1996-07-01

UTCHEM IMPLICIT is a three-dimensional chemical flooding simulator. The solution scheme is fully implicit. The pressure equation and the mass conservation equations are solved simultaneously for the aqueous phase pressure and the total concentrations of each component. A third-order-in-space, second-order-in-time finite-difference method and a new total-variation-diminishing (TVD) third-order flux limiter are used to reduce numerical dispersion effects. Saturations and phase concentrations are solved in a flash routine. The major physical phenomena modeled in the simulator are: dispersion, adsorption, aqueous-oleic-microemulsion phase behavior, interfacial tension, relative permeability, capillary trapping, compositional phase viscosity, capillary pressure, phase density, polymer properties: shear thinning viscosity, inaccessiblemore » pore volume, permeability reduction, and adsorption. The following options are available in the simulator: constant or variable time-step sizes, uniform or nonuniform grid, pressure or rate constrained wells, horizontal and vertical wells.« less

Element-topology-independent preconditioners for parallel finite element computations

NASA Technical Reports Server (NTRS)

Park, K. C.; Alexander, Scott

1992-01-01

A family of preconditioners for the solution of finite element equations are presented, which are element-topology independent and thus can be applicable to element order-free parallel computations. A key feature of the present preconditioners is the repeated use of element connectivity matrices and their left and right inverses. The properties and performance of the present preconditioners are demonstrated via beam and two-dimensional finite element matrices for implicit time integration computations.

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.

Engine dynamic analysis with general nonlinear finite element codes. Part 2: Bearing element implementation overall numerical characteristics and benchmaking

NASA Technical Reports Server (NTRS)

Padovan, J.; Adams, M.; Fertis, J.; Zeid, I.; Lam, P.

1982-01-01

Finite element codes are used in modelling rotor-bearing-stator structure common to the turbine industry. Engine dynamic simulation is used by developing strategies which enable the use of available finite element codes. benchmarking the elements developed are benchmarked by incorporation into a general purpose code (ADINA); the numerical characteristics of finite element type rotor-bearing-stator simulations are evaluated through the use of various types of explicit/implicit numerical integration operators. Improving the overall numerical efficiency of the procedure is improved.

Finite element simulations of the Portevin Le Chatelier effect in aluminium alloy

NASA Astrophysics Data System (ADS)

Hopperstad, O. S.; Børvik, T.; Berstad, T.; Benallal, A.

2006-08-01

Finite element simulations of the Portevin-Le Chatelier effect in aluminium alloy 5083-H116 are presented and evaluated against existing experimental results. The constitutive model of McCormick (1988) for materials exhibiting negative steady-state strain-rate sensitivity is incorporated into an elastic-viscoplastic model for large plastic deformations and implemented in LS-DYNA for use with the explicit or implicit solver. Axisymmetric tensile specimens loaded at different strain rates are studied numerically, and it is shown that the model predicts the experimental behaviour with reasonable accuracy; including serrated yielding and propagating bands of localized plastic deformation along the gauge length of the specimen at intermediate strain rates.

Exactly energy conserving semi-implicit particle in cell formulation

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

Lapenta, Giovanni, E-mail: giovanni.lapenta@kuleuven.be

We report a new particle in cell (PIC) method based on the semi-implicit approach. The novelty of the new method is that unlike any of its semi-implicit predecessors at the same time it retains the explicit computational cycle and conserves energy exactly. Recent research has presented fully implicit methods where energy conservation is obtained as part of a non-linear iteration procedure. The new method (referred to as Energy Conserving Semi-Implicit Method, ECSIM), instead, does not require any non-linear iteration and its computational cycle is similar to that of explicit PIC. The properties of the new method are: i) it conservesmore » energy exactly to round-off for any time step or grid spacing; ii) it is unconditionally stable in time, freeing the user from the need to resolve the electron plasma frequency and allowing the user to select any desired time step; iii) it eliminates the constraint of the finite grid instability, allowing the user to select any desired resolution without being forced to resolve the Debye length; iv) the particle mover has a computational complexity identical to that of the explicit PIC, only the field solver has an increased computational cost. The new ECSIM is tested in a number of benchmarks where accuracy and computational performance are tested. - Highlights: • We present a new fully energy conserving semi-implicit particle in cell (PIC) method based on the implicit moment method (IMM). The new method is called Energy Conserving Implicit Moment Method (ECIMM). • The novelty of the new method is that unlike any of its predecessors at the same time it retains the explicit computational cycle and conserves energy exactly. • The new method is unconditionally stable in time, freeing the user from the need to resolve the electron plasma frequency. • The new method eliminates the constraint of the finite grid instability, allowing the user to select any desired resolution without being forced to resolve the Debye length. • These features are achieved at a reduced cost compared with either previous IMM or fully implicit implementation of PIC.« less

Penalty methods for the numerical solution of American multi-asset option problems

NASA Astrophysics Data System (ADS)

Nielsen, Bjørn Fredrik; Skavhaug, Ola; Tveito, Aslak

2008-12-01

We derive and analyze a penalty method for solving American multi-asset option problems. A small, non-linear penalty term is added to the Black-Scholes equation. This approach gives a fixed solution domain, removing the free and moving boundary imposed by the early exercise feature of the contract. Explicit, implicit and semi-implicit finite difference schemes are derived, and in the case of independent assets, we prove that the approximate option prices satisfy some basic properties of the American option problem. Several numerical experiments are carried out in order to investigate the performance of the schemes. We give examples indicating that our results are sharp. Finally, the experiments indicate that in the case of correlated underlying assets, the same properties are valid as in the independent case.

A fast efficient implicit scheme for the gasdynamic equations using a matrix reduction technique

NASA Technical Reports Server (NTRS)

Barth, T. J.; Steger, J. L.

1985-01-01

An efficient implicit finite-difference algorithm for the gasdynamic equations utilizing matrix reduction techniques is presented. A significant reduction in arithmetic operations is achieved without loss of the stability characteristics generality found in the Beam and Warming approximate factorization algorithm. Steady-state solutions to the conservative Euler equations in generalized coordinates are obtained for transonic flows and used to show that the method offers computational advantages over the conventional Beam and Warming scheme. Existing Beam and Warming codes can be retrofit with minimal effort. The theoretical extension of the matrix reduction technique to the full Navier-Stokes equations in Cartesian coordinates is presented in detail. Linear stability, using a Fourier stability analysis, is demonstrated and discussed for the one-dimensional Euler equations.

Gradient-Based Aerodynamic Shape Optimization Using ADI Method for Large-Scale Problems

NASA Technical Reports Server (NTRS)

Pandya, Mohagna J.; Baysal, Oktay

1997-01-01

A gradient-based shape optimization methodology, that is intended for practical three-dimensional aerodynamic applications, has been developed. It is based on the quasi-analytical sensitivities. The flow analysis is rendered by a fully implicit, finite volume formulation of the Euler equations.The aerodynamic sensitivity equation is solved using the alternating-direction-implicit (ADI) algorithm for memory efficiency. A flexible wing geometry model, that is based on surface parameterization and platform schedules, is utilized. The present methodology and its components have been tested via several comparisons. Initially, the flow analysis for for a wing is compared with those obtained using an unfactored, preconditioned conjugate gradient approach (PCG), and an extensively validated CFD code. Then, the sensitivities computed with the present method have been compared with those obtained using the finite-difference and the PCG approaches. Effects of grid refinement and convergence tolerance on the analysis and shape optimization have been explored. Finally the new procedure has been demonstrated in the design of a cranked arrow wing at Mach 2.4. Despite the expected increase in the computational time, the results indicate that shape optimization, which require large numbers of grid points can be resolved with a gradient-based approach.

A Review of High-Order and Optimized Finite-Difference Methods for Simulating Linear Wave Phenomena

NASA Technical Reports Server (NTRS)

Zingg, David W.

1996-01-01

This paper presents a review of high-order and optimized finite-difference methods for numerically simulating the propagation and scattering of linear waves, such as electromagnetic, acoustic, or elastic waves. The spatial operators reviewed include compact schemes, non-compact schemes, schemes on staggered grids, and schemes which are optimized to produce specific characteristics. The time-marching methods discussed include Runge-Kutta methods, Adams-Bashforth methods, and the leapfrog method. In addition, the following fourth-order fully-discrete finite-difference methods are considered: a one-step implicit scheme with a three-point spatial stencil, a one-step explicit scheme with a five-point spatial stencil, and a two-step explicit scheme with a five-point spatial stencil. For each method studied, the number of grid points per wavelength required for accurate simulation of wave propagation over large distances is presented. Recommendations are made with respect to the suitability of the methods for specific problems and practical aspects of their use, such as appropriate Courant numbers and grid densities. Avenues for future research are suggested.

Simulating incompressible flow on moving meshfree grids using General Finite Differences (GFD)

NASA Astrophysics Data System (ADS)

Vasyliv, Yaroslav; Alexeev, Alexander

2016-11-01

We simulate incompressible flow around an oscillating cylinder at different Reynolds numbers using General Finite Differences (GFD) on a meshfree grid. We evolve the meshfree grid by treating each grid node as a particle. To compute velocities and accelerations, we consider the particles at a particular instance as Eulerian observation points. The incompressible Navier-Stokes equations are directly discretized using GFD with boundary conditions enforced using a sharp interface treatment. Cloud sizes are set such that the local approximations use only 16 neighbors. To enforce incompressibility, we apply a semi-implicit approximate projection method. To prevent overlapping particles and formation of voids in the grid, we propose a particle regularization scheme based on a local minimization principle. We validate the GFD results for an oscillating cylinder against the lattice Boltzmann method and find good agreement. Financial support provided by National Science Foundation (NSF) Graduate Research Fellowship, Grant No. DGE-1148903.

A finite element solver for 3-D compressible viscous flows

NASA Technical Reports Server (NTRS)

Reddy, K. C.; Reddy, J. N.; Nayani, S.

1990-01-01

Computation of the flow field inside a space shuttle main engine (SSME) requires the application of state of the art computational fluid dynamic (CFD) technology. Several computer codes are under development to solve 3-D flow through the hot gas manifold. Some algorithms were designed to solve the unsteady compressible Navier-Stokes equations, either by implicit or explicit factorization methods, using several hundred or thousands of time steps to reach a steady state solution. A new iterative algorithm is being developed for the solution of the implicit finite element equations without assembling global matrices. It is an efficient iteration scheme based on a modified nonlinear Gauss-Seidel iteration with symmetric sweeps. The algorithm is analyzed for a model equation and is shown to be unconditionally stable. Results from a series of test problems are presented. The finite element code was tested for couette flow, which is flow under a pressure gradient between two parallel plates in relative motion. Another problem that was solved is viscous laminar flow over a flat plate. The general 3-D finite element code was used to compute the flow in an axisymmetric turnaround duct at low Mach numbers.

Development and Verification of the Charring Ablating Thermal Protection Implicit System Solver

NASA Technical Reports Server (NTRS)

Amar, Adam J.; Calvert, Nathan D.; Kirk, Benjamin S.

2010-01-01

The development and verification of the Charring Ablating Thermal Protection Implicit System Solver is presented. This work concentrates on the derivation and verification of the stationary grid terms in the equations that govern three-dimensional heat and mass transfer for charring thermal protection systems including pyrolysis gas flow through the porous char layer. The governing equations are discretized according to the Galerkin finite element method with first and second order implicit time integrators. The governing equations are fully coupled and are solved in parallel via Newton's method, while the fully implicit linear system is solved with the Generalized Minimal Residual method. Verification results from exact solutions and the Method of Manufactured Solutions are presented to show spatial and temporal orders of accuracy as well as nonlinear convergence rates.

Impact of the Parameter Identification of Plastic Potentials on the Finite Element Simulation of Sheet Metal Forming

NASA Astrophysics Data System (ADS)

Rabahallah, M.; Bouvier, S.; Balan, T.; Bacroix, B.; Teodosiu, C.

2007-04-01

In this work, an implicit, backward Euler time integration scheme is developed for an anisotropic, elastic-plastic model based on strain-rate potentials. The constitutive algorithm includes a sub-stepping procedure to deal with the strong nonlinearity of the plastic potentials when applied to FCC materials. The algorithm is implemented in the static implicit version of the Abaqus finite element code. Several recent plastic potentials have been implemented in this framework. The most accurate potentials require the identification of about twenty material parameters. Both mechanical tests and micromechanical simulations have been used for their identification, for a number of BCC and FCC materials. The impact of the identification procedure on the prediction of ears in cup drawing is investigated.

High-order solution methods for grey discrete ordinates thermal radiative transfer

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

Maginot, Peter G., E-mail: maginot1@llnl.gov; Ragusa, Jean C., E-mail: jean.ragusa@tamu.edu; Morel, Jim E., E-mail: morel@tamu.edu

This work presents a solution methodology for solving the grey radiative transfer equations that is both spatially and temporally more accurate than the canonical radiative transfer solution technique of linear discontinuous finite element discretization in space with implicit Euler integration in time. We solve the grey radiative transfer equations by fully converging the nonlinear temperature dependence of the material specific heat, material opacities, and Planck function. The grey radiative transfer equations are discretized in space using arbitrary-order self-lumping discontinuous finite elements and integrated in time with arbitrary-order diagonally implicit Runge–Kutta time integration techniques. Iterative convergence of the radiation equation ismore » accelerated using a modified interior penalty diffusion operator to precondition the full discrete ordinates transport operator.« less

High-order solution methods for grey discrete ordinates thermal radiative transfer

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

Maginot, Peter G.; Ragusa, Jean C.; Morel, Jim E.

This paper presents a solution methodology for solving the grey radiative transfer equations that is both spatially and temporally more accurate than the canonical radiative transfer solution technique of linear discontinuous finite element discretization in space with implicit Euler integration in time. We solve the grey radiative transfer equations by fully converging the nonlinear temperature dependence of the material specific heat, material opacities, and Planck function. The grey radiative transfer equations are discretized in space using arbitrary-order self-lumping discontinuous finite elements and integrated in time with arbitrary-order diagonally implicit Runge–Kutta time integration techniques. Iterative convergence of the radiation equation ismore » accelerated using a modified interior penalty diffusion operator to precondition the full discrete ordinates transport operator.« less

High-order solution methods for grey discrete ordinates thermal radiative transfer

DOE PAGES

Maginot, Peter G.; Ragusa, Jean C.; Morel, Jim E.

2016-09-29

This paper presents a solution methodology for solving the grey radiative transfer equations that is both spatially and temporally more accurate than the canonical radiative transfer solution technique of linear discontinuous finite element discretization in space with implicit Euler integration in time. We solve the grey radiative transfer equations by fully converging the nonlinear temperature dependence of the material specific heat, material opacities, and Planck function. The grey radiative transfer equations are discretized in space using arbitrary-order self-lumping discontinuous finite elements and integrated in time with arbitrary-order diagonally implicit Runge–Kutta time integration techniques. Iterative convergence of the radiation equation ismore » accelerated using a modified interior penalty diffusion operator to precondition the full discrete ordinates transport operator.« less

Implicit filtered P{sub N} for high-energy density thermal radiation transport using discontinuous Galerkin finite elements

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

Laboure, Vincent M., E-mail: vincent.laboure@tamu.edu; McClarren, Ryan G., E-mail: rgm@tamu.edu; Hauck, Cory D., E-mail: hauckc@ornl.gov

2016-09-15

In this work, we provide a fully-implicit implementation of the time-dependent, filtered spherical harmonics (FP{sub N}) equations for non-linear, thermal radiative transfer. We investigate local filtering strategies and analyze the effect of the filter on the conditioning of the system, showing in particular that the filter improves the convergence properties of the iterative solver. We also investigate numerically the rigorous error estimates derived in the linear setting, to determine whether they hold also for the non-linear case. Finally, we simulate a standard test problem on an unstructured mesh and make comparisons with implicit Monte Carlo (IMC) calculations.

A FORTRAN program for calculating nonlinear seismic ground response

USGS Publications Warehouse

Joyner, William B.

1977-01-01

The program described here was designed for calculating the nonlinear seismic response of a system of horizontal soil layers underlain by a semi-infinite elastic medium representing bedrock. Excitation is a vertically incident shear wave in the underlying medium. The nonlinear hysteretic behavior of the soil is represented by a model consisting of simple linear springs and Coulomb friction elements arranged as shown. A boundary condition is used which takes account of finite rigidity in the elastic substratum. The computations are performed by an explicit finite-difference scheme that proceeds step by step in space and time. A brief program description is provided here with instructions for preparing the input and a source listing. A more detailed discussion of the method is presented elsewhere as is the description of a different program employing implicit integration.

Computation of airfoil buffet boundaries

NASA Technical Reports Server (NTRS)

Levy, L. L., Jr.; Bailey, H. E.

1981-01-01

The ILLIAC IV computer has been programmed with an implicit, finite-difference code for solving the thin layer compressible Navier-Stokes equation. Results presented for the case of the buffet boundaries of a conventional and a supercritical airfoil section at high Reynolds numbers are found to be in agreement with experimentally determined buffet boundaries, especially at the higher freestream Mach numbers and lower lift coefficients where the onset of unsteady flows is associated with shock wave-induced boundary layer separation.

FINIFLUX: An implicit finite element model for quantification of groundwater fluxes and hyporheic exchange in streams and rivers using radon

NASA Astrophysics Data System (ADS)

Frei, S.; Gilfedder, B. S.

2015-08-01

A quantitative understanding of groundwater-surface water interactions is vital for sustainable management of water quantity and quality. The noble gas radon-222 (Rn) is becoming increasingly used as a sensitive tracer to quantify groundwater discharge to wetlands, lakes, and rivers: a development driven by technical and methodological advances in Rn measurement. However, quantitative interpretation of these data is not trivial, and the methods used to date are based on the simplest solutions to the mass balance equation (e.g., first-order finite difference and inversion). Here we present a new implicit numerical model (FINIFLUX) based on finite elements for quantifying groundwater discharge to streams and rivers using Rn surveys at the reach scale (1-50 km). The model is coupled to a state-of-the-art parameter optimization code Parallel-PEST to iteratively solve the mass balance equation for groundwater discharge and hyporheic exchange. The major benefit of this model is that it is programed to be very simple to use, reduces nonuniqueness, and provides numerically stable estimates of groundwater fluxes and hyporheic residence times from field data. FINIFLUX was tested against an analytical solution and then implemented on two German rivers of differing magnitude, the Salzach (˜112 m3 s-1) and the Rote Main (˜4 m3 s-1). We show that using previous inversion techniques numerical instability can lead to physically impossible negative values, whereas the new model provides stable positive values for all scenarios. We hope that by making FINIFLUX freely available to the community that Rn might find wider application in quantifying groundwater discharge to streams and rivers and thus assist in a combined management of surface and groundwater systems.

An optimal implicit staggered-grid finite-difference scheme based on the modified Taylor-series expansion with minimax approximation method for elastic modeling

NASA Astrophysics Data System (ADS)

Yang, Lei; Yan, Hongyong; Liu, Hong

2017-03-01

Implicit staggered-grid finite-difference (ISFD) scheme is competitive for its great accuracy and stability, whereas its coefficients are conventionally determined by the Taylor-series expansion (TE) method, leading to a loss in numerical precision. In this paper, we modify the TE method using the minimax approximation (MA), and propose a new optimal ISFD scheme based on the modified TE (MTE) with MA method. The new ISFD scheme takes the advantage of the TE method that guarantees great accuracy at small wavenumbers, and keeps the property of the MA method that keeps the numerical errors within a limited bound at the same time. Thus, it leads to great accuracy for numerical solution of the wave equations. We derive the optimal ISFD coefficients by applying the new method to the construction of the objective function, and using a Remez algorithm to minimize its maximum. Numerical analysis is made in comparison with the conventional TE-based ISFD scheme, indicating that the MTE-based ISFD scheme with appropriate parameters can widen the wavenumber range with high accuracy, and achieve greater precision than the conventional ISFD scheme. The numerical modeling results also demonstrate that the MTE-based ISFD scheme performs well in elastic wave simulation, and is more efficient than the conventional ISFD scheme for elastic modeling.

Hamiltonian approaches to spatial and temporal discretization of fully compressible equations

NASA Astrophysics Data System (ADS)

Dubos, Thomas; Dubey, Sarvesh

2017-04-01

The fully compressible Euler (FCE) equations are the most accurate for representing atmospheric motion, compared to approximate systems like the hydrostatic, anelastic or pseudo-incompressible systems. The price to pay for this accuracy is the presence of additional degrees of freedom and high-frequency acoustic waves that must be treated implicitly. In this work we explore a Hamiltonian approach to the issue of stable spatial and temporal discretization of the FCE using a non-Eulerian vertical coordinate. For scalability, a horizontally-explicit, vertically-implicit (HEVI) time discretization is adopted. The Hamiltonian structure of the equations is used to obtain the spatial finite-difference discretization and also in order to identify those terms of the equations of motion that need to be treated implicitly. A novel treatment of the lower boundary condition in the presence of orography is introduced: rather than enforcing a no-normal-flow boundary condition, which couples the horizontal and vertical velocity components and interferes with the HEVI structure, the ground is treated as a flexible surface with arbitrarily large stiffness, resulting in a decoupling of the horizontal and vertical dynamics and yielding a simple implicit problem which can be solved efficiently. Standard test cases performed in a vertical slice configuration suggest that an effective horizontal acoustic Courant number close to 1 can be achieved.

Two-level schemes for the advection equation

NASA Astrophysics Data System (ADS)

Vabishchevich, Petr N.

2018-06-01

The advection equation is the basis for mathematical models of continuum mechanics. In the approximate solution of nonstationary problems it is necessary to inherit main properties of the conservatism and monotonicity of the solution. In this paper, the advection equation is written in the symmetric form, where the advection operator is the half-sum of advection operators in conservative (divergent) and non-conservative (characteristic) forms. The advection operator is skew-symmetric. Standard finite element approximations in space are used. The standard explicit two-level scheme for the advection equation is absolutely unstable. New conditionally stable regularized schemes are constructed, on the basis of the general theory of stability (well-posedness) of operator-difference schemes, the stability conditions of the explicit Lax-Wendroff scheme are established. Unconditionally stable and conservative schemes are implicit schemes of the second (Crank-Nicolson scheme) and fourth order. The conditionally stable implicit Lax-Wendroff scheme is constructed. The accuracy of the investigated explicit and implicit two-level schemes for an approximate solution of the advection equation is illustrated by the numerical results of a model two-dimensional problem.

Analysis of rotary engine combustion processes based on unsteady, three-dimensional computations

NASA Technical Reports Server (NTRS)

Raju, M. S.; Willis, E. A.

1990-01-01

A new computer code was developed for predicting the turbulent and chemically reacting flows with sprays occurring inside of a stratified charge rotary engine. The solution procedure is based on an Eulerian Lagrangian approach where the unsteady, three-dimensional Navier-Stokes equations for a perfect gas mixture with variable properties are solved in generalized, Eulerian coordinates on a moving grid by making use of an implicit finite volume, Steger-Warming flux vector splitting scheme, and the liquid phase equations are solved in Lagrangian coordinates. Both the details of the numerical algorithm and the finite difference predictions of the combustor flow field during the opening of exhaust and/or intake, and also during fuel vaporization and combustion, are presented.

Analysis of rotary engine combustion processes based on unsteady, three-dimensional computations

NASA Technical Reports Server (NTRS)

Raju, M. S.; Willis, E. A.

1989-01-01

A new computer code was developed for predicting the turbulent, and chemically reacting flows with sprays occurring inside of a stratified charge rotary engine. The solution procedure is based on an Eulerian Lagrangian approach where the unsteady, 3-D Navier-Stokes equations for a perfect gas mixture with variable properties are solved in generalized, Eulerian coordinates on a moving grid by making use of an implicit finite volume, Steger-Warming flux vector splitting scheme, and the liquid phase equations are solved in Lagrangian coordinates. Both the details of the numerical algorithm and the finite difference predictions of the combustor flow field during the opening of exhaust and/or intake, and also during fuel vaporization and combustion, are presented.

An implicit time-marching method for the three-dimensional Navier-Stokes equations of contravariant velocity components

NASA Astrophysics Data System (ADS)

Daiguji, Hisaaki; Yamamoto, Satoru

1988-12-01

The implicit time-marching finite-difference method for solving the three-dimensional compressible Euler equations developed by the authors is extended to the Navier-Stokes equations. The distinctive features of this method are to make use of momentum equations of contravariant velocities instead of physical boundaries, and to be able to treat the periodic boundary condition for the three-dimensional impeller flow easily. These equations can be solved by using the same techniques as the Euler equations, such as the delta-form approximate factorization, diagonalization and upstreaming. In addition to them, a simplified total variation diminishing scheme by the authors is applied to the present method in order to capture strong shock waves clearly. Finally, the computed results of the three-dimensional flow through a transonic compressor rotor with tip clearance are shown.

Application of the Hughes-LIU algorithm to the 2-dimensional heat equation

NASA Technical Reports Server (NTRS)

Malkus, D. S.; Reichmann, P. I.; Haftka, R. T.

1982-01-01

An implicit explicit algorithm for the solution of transient problems in structural dynamics is described. The method involved dividing the finite elements into implicit and explicit groups while automatically satisfying the conditions. This algorithm is applied to the solution of the linear, transient, two dimensional heat equation subject to an initial condition derived from the soluton of a steady state problem over an L-shaped region made up of a good conductor and an insulating material. Using the IIT/PRIME computer with virtual memory, a FORTRAN computer program code was developed to make accuracy, stability, and cost comparisons among the fully explicit Euler, the Hughes-Liu, and the fully implicit Crank-Nicholson algorithms. The Hughes-Liu claim that the explicit group governs the stability of the entire region while maintaining the unconditional stability of the implicit group is illustrated.

Spillover, nonlinearity, and flexible structures

NASA Technical Reports Server (NTRS)

Bass, Robert W.; Zes, Dean

1991-01-01

Many systems whose evolution in time is governed by Partial Differential Equations (PDEs) are linearized around a known equilibrium before Computer Aided Control Engineering (CACE) is considered. In this case, there are infinitely many independent vibrational modes, and it is intuitively evident on physical grounds that infinitely many actuators would be needed in order to control all modes. A more precise, general formulation of this grave difficulty (spillover problem) is due to A.V. Balakrishnan. A possible route to circumvention of this difficulty lies in leaving the PDE in its original nonlinear form, and adding the essentially finite dimensional control action prior to linearization. One possibly applicable technique is the Liapunov Schmidt rigorous reduction of singular infinite dimensional implicit function problems to finite dimensional implicit function problems. Omitting details of Banach space rigor, the formalities of this approach are given.

Characteristics of the Shuttle Orbiter Leeside Flow During A Reentry Condition

NASA Technical Reports Server (NTRS)

Kleb, William L.; Weilmuenster, K. James

1992-01-01

A study of the leeside flow characteristics of the Shuttle Orbiter is presented for a reentry flight condition. The flow is computed using a point-implicit, finite-volume scheme known as the Langley Aerothermodynamic Upwind Relaxation Algorithm (LAURA). LAURA is a second-order accurate, laminar Navier-Stokes solver, incorporating finite-rate chemistry with a radiative equilibrium wall temperature distribution and finite-rate wall catalysis. The resulting computational solution is analyzed in terms of salient flow features and the surface quantities are compared with flight data.

Steady potential solver for unsteady aerodynamic analyses

NASA Technical Reports Server (NTRS)

Hoyniak, Dan

1994-01-01

Development of a steady flow solver for use with LINFLO was the objective of this report. The solver must be compatible with LINFLO, be composed of composite mesh, and have transonic capability. The approaches used were: (1) steady flow potential equations written in nonconservative form; (2) Newton's Method; (3) implicit, least-squares, interpolation method to obtain finite difference equations; and (4) matrix inversion routines from LINFLO. This report was given during the NASA LeRC Workshop on Forced Response in Turbomachinery in August of 1993.

Viscous-shock-layer solutions for turbulent flow of radiating gas mixtures in chemical equilibrium

NASA Technical Reports Server (NTRS)

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

1975-01-01

The viscous-shock-layer equations for hypersonic laminar and turbulent flows of radiating or nonradiating gas mixtures in chemical equilibrium are presented for two-dimensional and axially-symmetric flow fields. Solutions were obtained using an implicit finite-difference scheme and results are presented for hypersonic flow over spherically-blunted cone configurations at freestream conditions representative of entry into the atmosphere of Venus. These data are compared with solutions obtained using other methods of analysis.

Viscous shock layer solutions for turbulent flow of radiating gas mixtures in chemical equilibrium

NASA Technical Reports Server (NTRS)

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

1975-01-01

The viscous shock layer equations for hypersonic laminar and turbulent flows of radiating or nonradiating gas mixtures in chemical equilibrium are presented for two-dimensional and axially symmetric flow fields. Solutions are obtained using an implicit finite difference scheme and results are presented for hypersonic flow over spherically blunted cone configurations at free stream conditions representative of entry into the atmosphere of Venus. These data are compared with solutions obtained using other methods of analysis.

A New Discretization Method of Order Four for the Numerical Solution of One-Space Dimensional Second-Order Quasi-Linear Hyperbolic Equation

ERIC Educational Resources Information Center

Mohanty, R. K.; Arora, Urvashi

2002-01-01

Three level-implicit finite difference methods of order four are discussed for the numerical solution of the mildly quasi-linear second-order hyperbolic equation A(x, t, u)u[subscript xx] + 2B(x, t, u)u[subscript xt] + C(x, t, u)u[subscript tt] = f(x, t, u, u[subscript x], u[subscript t]), 0 less than x less than 1, t greater than 0 subject to…

Numerical solution of a coupled pair of elliptic equations from solid state electronics

NASA Technical Reports Server (NTRS)

Phillips, T. N.

1983-01-01

Iterative methods are considered for the solution of a coupled pair of second order elliptic partial differential equations which arise in the field of solid state electronics. A finite difference scheme is used which retains the conservative form of the differential equations. Numerical solutions are obtained in two ways, by multigrid and dynamic alternating direction implicit methods. Numerical results are presented which show the multigrid method to be an efficient way of solving this problem.

A Stable Finite-Difference Scheme for Population Growth and Diffusion on a Map

PubMed Central

Callegari, S.; Lake, G. R.; Tkachenko, N.; Weissmann, J. D.; Zollikofer, Ch. P. E.

2017-01-01

We describe a general Godunov-type splitting for numerical simulations of the Fisher–Kolmogorov–Petrovski–Piskunov growth and diffusion equation on a world map with Neumann boundary conditions. The procedure is semi-implicit, hence quite stable. Our principal application for this solver is modeling human population dispersal over geographical maps with changing paleovegetation and paleoclimate in the late Pleistocene. As a proxy for carrying capacity we use Net Primary Productivity (NPP) to predict times for human arrival in the Americas. PMID:28085882

Navier-Stokes computations for circulation control airfoils

NASA Technical Reports Server (NTRS)

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

1987-01-01

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

Navier-Stokes computations for circulation controlled airfoils

NASA Technical Reports Server (NTRS)

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

1986-01-01

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

Comparison of Implicit Collocation Methods for the Heat Equation

NASA Technical Reports Server (NTRS)

Kouatchou, Jules; Jezequel, Fabienne; Zukor, Dorothy (Technical Monitor)

2001-01-01

We combine a high-order compact finite difference scheme to approximate spatial derivatives arid collocation techniques for the time component to numerically solve the two dimensional heat equation. We use two approaches to implement the collocation methods. The first one is based on an explicit computation of the coefficients of polynomials and the second one relies on differential quadrature. We compare them by studying their merits and analyzing their numerical performance. All our computations, based on parallel algorithms, are carried out on the CRAY SV1.

Computation of the unsteady facilitated transport of oxygen in hemoglobin

NASA Technical Reports Server (NTRS)

Davis, Sanford

1990-01-01

The transport of a reacting permeant diffusing through a thin membrane is extended to more realistic dissociation models. A new nonlinear analysis of the reaction-diffusion equations, using implicit finite-difference methods and direct block solvers, is used to study the limits of linearized and equilibrium theories. Computed curves of molecular oxygen permeating through hemoglobin solution are used to illustrate higher-order reaction models, the effect of concentration boundary layers at the membrane interfaces, and the transient buildup of oxygen flux.

On the superconvergence of Galerkin methods for hyperbolic IBVP

NASA Technical Reports Server (NTRS)

Gottlieb, David; Gustafsson, Bertil; Olsson, Pelle; Strand, BO

1993-01-01

Finite element Galerkin methods for periodic first order hyperbolic equations exhibit superconvergence on uniform grids at the nodes, i.e., there is an error estimate 0(h(sup 2r)) instead of the expected approximation order 0(h(sup r)). It will be shown that no matter how the approximating subspace S(sup h) is chosen, the superconvergence property is lost if there are characteristics leaving the domain. The implications of this result when constructing compact implicit difference schemes is also discussed.

Numerical simulation of steady supersonic flow. [spatial marching

NASA Technical Reports Server (NTRS)

Schiff, L. B.; Steger, J. L.

1981-01-01

A noniterative, implicit, space-marching, finite-difference algorithm was developed for the steady thin-layer Navier-Stokes equations in conservation-law form. The numerical algorithm is applicable to steady supersonic viscous flow over bodies of arbitrary shape. In addition, the same code can be used to compute supersonic inviscid flow or three-dimensional boundary layers. Computed results from two-dimensional and three-dimensional versions of the numerical algorithm are in good agreement with those obtained from more costly time-marching techniques.

A Stable Finite-Difference Scheme for Population Growth and Diffusion on a Map.

PubMed

Petersen, W P; Callegari, S; Lake, G R; Tkachenko, N; Weissmann, J D; Zollikofer, Ch P E

2017-01-01

We describe a general Godunov-type splitting for numerical simulations of the Fisher-Kolmogorov-Petrovski-Piskunov growth and diffusion equation on a world map with Neumann boundary conditions. The procedure is semi-implicit, hence quite stable. Our principal application for this solver is modeling human population dispersal over geographical maps with changing paleovegetation and paleoclimate in the late Pleistocene. As a proxy for carrying capacity we use Net Primary Productivity (NPP) to predict times for human arrival in the Americas.

Calculation of transonic aileron buzz

NASA Technical Reports Server (NTRS)

Steger, J. L.; Bailey, H. E.

1979-01-01

An implicit finite-difference computer code that uses a two-layer algebraic eddy viscosity model and exact geometric specification of the airfoil has been used to simulate transonic aileron buzz. The calculated results, which were performed on both the Illiac IV parallel computer processor and the Control Data 7600 computer, are in essential agreement with the original expository wind-tunnel data taken in the Ames 16-Foot Wind Tunnel just after World War II. These results and a description of the pertinent numerical techniques are included.

Multiscale Failure Analysis of Laminated Composite Panels Subjected to Blast Loading Using FEAMAC/Explicit

NASA Technical Reports Server (NTRS)

Pineda, Evan J.; Waas, Anthony M.; Berdnarcyk, Brett A.; Arnold, Steven M.; Collier, Craig S.

2009-01-01

This preliminary report demonstrates the capabilities of the recently developed software implementation that links the Generalized Method of Cells to explicit finite element analysis by extending a previous development which tied the generalized method of cells to implicit finite elements. The multiscale framework, which uses explicit finite elements at the global-scale and the generalized method of cells at the microscale is detailed. This implementation is suitable for both dynamic mechanics problems and static problems exhibiting drastic and sudden changes in material properties, which often encounter convergence issues with commercial implicit solvers. Progressive failure analysis of stiffened and un-stiffened fiber-reinforced laminates subjected to normal blast pressure loads was performed and is used to demonstrate the capabilities of this framework. The focus of this report is to document the development of the software implementation; thus, no comparison between the results of the models and experimental data is drawn. However, the validity of the results are assessed qualitatively through the observation of failure paths, stress contours, and the distribution of system energies.

A nonlinear dynamic finite element approach for simulating muscular hydrostats.

PubMed

Vavourakis, V; Kazakidi, A; Tsakiris, D P; Ekaterinaris, J A

2014-01-01

An implicit nonlinear finite element model for simulating biological muscle mechanics is developed. The numerical method is suitable for dynamic simulations of three-dimensional, nonlinear, nearly incompressible, hyperelastic materials that undergo large deformations. These features characterise biological muscles, which consist of fibres and connective tissues. It can be assumed that the stress distribution inside the muscles is the superposition of stresses along the fibres and the connective tissues. The mechanical behaviour of the surrounding tissues is determined by adopting a Mooney-Rivlin constitutive model, while the mechanical description of fibres is considered to be the sum of active and passive stresses. Due to the nonlinear nature of the problem, evaluation of the Jacobian matrix is carried out in order to subsequently utilise the standard Newton-Raphson iterative procedure and to carry out time integration with an implicit scheme. The proposed methodology is implemented into our in-house, open source, finite element software, which is validated by comparing numerical results with experimental measurements and other numerical results. Finally, the numerical procedure is utilised to simulate primitive octopus arm manoeuvres, such as bending and reaching.

Modeling the absorption spectrum of the permanganate ion in vacuum and in aqueous solution

NASA Astrophysics Data System (ADS)

Olsen, Jógvan Magnus Haugaard; Hedegård, Erik Donovan

The absorption spectrum of the MnO$_{4}$$^{-}$ ion has been a test-bed for quantum-chemical methods over the last decades. Its correct description requires highly-correlated multiconfigurational methods, which are incompatible with the inclusion of finite-temperature and solvent effects due to their high computational demands. Therefore, implicit solvent models are usually employed. Here we show that implicit solvent models are not sufficiently accurate to model the solvent shift of MnO$_{4}$$^{-}$, and we analyze the origins of their failure. We obtain the correct solvent shift for MnO$_{4}$$^{-}$ in aqueous solution by employing the polarizable embedding (PE) model combined with a range-separated complete active space short-range density functional theory method (CAS-srDFT). Finite-temperature effects are taken into account by averaging over structures obtained from ab initio molecular dynamics simulations. The explicit treatment of finite-temperature and solvent effects facilitates the interpretation of the bands in the low-energy region of the MnO$_{4}$$^{-}$ absorption spectrum, whose assignment has been elusive.

A parallel algorithm for the two-dimensional time fractional diffusion equation with implicit difference method.

PubMed

Gong, Chunye; Bao, Weimin; Tang, Guojian; Jiang, Yuewen; Liu, Jie

2014-01-01

It is very time consuming to solve fractional differential equations. The computational complexity of two-dimensional fractional differential equation (2D-TFDE) with iterative implicit finite difference method is O(M(x)M(y)N(2)). In this paper, we present a parallel algorithm for 2D-TFDE and give an in-depth discussion about this algorithm. A task distribution model and data layout with virtual boundary are designed for this parallel algorithm. The experimental results show that the parallel algorithm compares well with the exact solution. The parallel algorithm on single Intel Xeon X5540 CPU runs 3.16-4.17 times faster than the serial algorithm on single CPU core. The parallel efficiency of 81 processes is up to 88.24% compared with 9 processes on a distributed memory cluster system. We do think that the parallel computing technology will become a very basic method for the computational intensive fractional applications in the near future.

Parallel Computing of Upwelling in a Rotating Stratified Flow

NASA Astrophysics Data System (ADS)

Cui, A.; Street, R. L.

1997-11-01

A code for the three-dimensional, unsteady, incompressible, and turbulent flow has been implemented on the IBM SP2, using message passing. The effects of rotation and variable density are included. A finite volume method is used to discretize the Navier-Stokes equations in general curvilinear coordinates on a non-staggered grid. All the spatial derivatives are approximated using second-order central differences with the exception of the convection terms, which are handled with special upwind-difference schemes. The semi-implicit, second-order accurate, time-advancement scheme employs the Adams-Bashforth method for the explicit terms and Crank-Nicolson for the implicit terms. A multigrid method, with the four-color ZEBRA as smoother, is used to solve the Poisson equation for pressure, while the momentum equations are solved with an approximate factorization technique. The code was successfully validated for a variety test cases. Simulations of a laboratory model of coastal upwelling in a rotating annulus are in progress and will be presented.

The mimetic finite difference method for the Landau–Lifshitz equation

DOE PAGES

Kim, Eugenia Hail; Lipnikov, Konstantin Nikolayevich

2017-01-01

The Landau–Lifshitz equation describes the dynamics of the magnetization inside ferromagnetic materials. This equation is highly nonlinear and has a non-convex constraint (the magnitude of the magnetization is constant) which poses interesting challenges in developing numerical methods. We develop and analyze explicit and implicit mimetic finite difference schemes for this equation. These schemes work on general polytopal meshes which provide enormous flexibility to model magnetic devices with various shapes. A projection on the unit sphere is used to preserve the magnitude of the magnetization. We also provide a proof that shows the exchange energy is decreasing in certain conditions. Themore » developed schemes are tested on general meshes that include distorted and randomized meshes. As a result, the numerical experiments include a test proposed by the National Institute of Standard and Technology and a test showing formation of domain wall structures in a thin film.« less

The mimetic finite difference method for the Landau–Lifshitz equation

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

Kim, Eugenia Hail; Lipnikov, Konstantin Nikolayevich

The Landau–Lifshitz equation describes the dynamics of the magnetization inside ferromagnetic materials. This equation is highly nonlinear and has a non-convex constraint (the magnitude of the magnetization is constant) which poses interesting challenges in developing numerical methods. We develop and analyze explicit and implicit mimetic finite difference schemes for this equation. These schemes work on general polytopal meshes which provide enormous flexibility to model magnetic devices with various shapes. A projection on the unit sphere is used to preserve the magnitude of the magnetization. We also provide a proof that shows the exchange energy is decreasing in certain conditions. Themore » developed schemes are tested on general meshes that include distorted and randomized meshes. As a result, the numerical experiments include a test proposed by the National Institute of Standard and Technology and a test showing formation of domain wall structures in a thin film.« less

Effect of absorption on nonlinear propagation of short ultrasound pulses generated by rectangular transducers

NASA Astrophysics Data System (ADS)

Khokhlova, Vera A.; Ponomaryov, Anatoly E.; Averkiou, Michalakis A.; Crum, Lawrence A.

2002-11-01

A numerical solution of the KZK-type parabolic nonlinear evolution equation is presented for finite-amplitude sound beams radiated by rectangular sources. The initial acoustic waveform is a short tone burst, similar to those used in diagnostic ultrasound. The generation of higher harmonic components and their spatial structure are investigated for media similar to tissue with various frequency dependent absorption properties. Nonlinear propagation in a thermoviscous fluid with a quadratic frequency law of absorption is compared to that in tissue with a nearly linear frequency law of absorption. The algorithm is based on that originally developed by Lee and Hamilton [J. Acoust. Soc. Am. 97, 906-917 (1995)] to model circular sources. The algorithm is generalized for two-dimensional sources without axial symmetry. The diffraction integral is adapted in the time-domain for two dimensions with the implicit backward finite difference (IBFD) scheme in the nearfield and with the alternate direction implicit (ADI) method at longer distances. Arbitrary frequency dependence of absorption is included in this model and solved in the frequency-domain using the FFT technique. The results of simulation may be used to better understand the nonlinear beam structure for tissue harmonic imaging in modern medical diagnostic scanners. [Work supported by CRDF and RFBR.

An Unstructured Finite Volume Approach for Structural Dynamics in Response to Fluid Motions.

PubMed

Xia, Guohua; Lin, Ching-Long

2008-04-01

A new cell-vortex unstructured finite volume method for structural dynamics is assessed for simulations of structural dynamics in response to fluid motions. A robust implicit dual-time stepping method is employed to obtain time accurate solutions. The resulting system of algebraic equations is matrix-free and allows solid elements to include structure thickness, inertia, and structural stresses for accurate predictions of structural responses and stress distributions. The method is coupled with a fluid dynamics solver for fluid-structure interaction, providing a viable alternative to the finite element method for structural dynamics calculations. A mesh sensitivity test indicates that the finite volume method is at least of second-order accuracy. The method is validated by the problem of vortex-induced vibration of an elastic plate with different initial conditions and material properties. The results are in good agreement with existing numerical data and analytical solutions. The method is then applied to simulate a channel flow with an elastic wall. The effects of wall inertia and structural stresses on the fluid flow are investigated.

Numerical simulation of hypersonic inlet flows with equilibrium or finite rate chemistry

NASA Technical Reports Server (NTRS)

Yu, Sheng-Tao; Hsieh, Kwang-Chung; Shuen, Jian-Shun; Mcbride, Bonnie J.

1988-01-01

An efficient numerical program incorporated with comprehensive high temperature gas property models has been developed to simulate hypersonic inlet flows. The computer program employs an implicit lower-upper time marching scheme to solve the two-dimensional Navier-Stokes equations with variable thermodynamic and transport properties. Both finite-rate and local-equilibrium approaches are adopted in the chemical reaction model for dissociation and ionization of the inlet air. In the finite rate approach, eleven species equations coupled with fluid dynamic equations are solved simultaneously. In the local-equilibrium approach, instead of solving species equations, an efficient chemical equilibrium package has been developed and incorporated into the flow code to obtain chemical compositions directly. Gas properties for the reaction products species are calculated by methods of statistical mechanics and fit to a polynomial form for C(p). In the present study, since the chemical reaction time is comparable to the flow residence time, the local-equilibrium model underpredicts the temperature in the shock layer. Significant differences of predicted chemical compositions in shock layer between finite rate and local-equilibrium approaches have been observed.

Further analytical study of hybrid rocket combustion

NASA Technical Reports Server (NTRS)

Hung, W. S. Y.; Chen, C. S.; Haviland, J. K.

1972-01-01

Analytical studies of the transient and steady-state combustion processes in a hybrid rocket system are discussed. The particular system chosen consists of a gaseous oxidizer flowing within a tube of solid fuel, resulting in a heterogeneous combustion. Finite rate chemical kinetics with appropriate reaction mechanisms were incorporated in the model. A temperature dependent Arrhenius type fuel surface regression rate equation was chosen for the current study. The governing mathematical equations employed for the reacting gas phase and for the solid phase are the general, two-dimensional, time-dependent conservation equations in a cylindrical coordinate system. Keeping the simplifying assumptions to a minimum, these basic equations were programmed for numerical computation, using two implicit finite-difference schemes, the Lax-Wendroff scheme for the gas phase, and, the Crank-Nicolson scheme for the solid phase.

Numerical Simulation of Combustion and Rotor-Stator Interaction in a Turbine Combustor

DOE PAGES

Isvoranu, Dragos D.; Cizmas, Paul G. A.

2003-01-01

This article presents the development of a numerical algorithm for the computation of flow and combustion in a turbine combustor. The flow and combustion are modeled by the Reynolds-averaged Navier-Stokes equations coupled with the species-conservation equations. The chemistry model used herein is a two-step, global, finite-rate combustion model for methane and combustion gases. The governing equations are written in the strong conservation form and solved using a fully implicit, finite-difference approximation. The gas dynamics and chemistry equations are fully decoupled. A correction technique has been developed to enforce the conservation of mass fractions. The numerical algorithm developed herein has beenmore » used to investigate the flow and combustion in a one-stage turbine combustor.« less

Design of a Variational Multiscale Method for Turbulent Compressible Flows

NASA Technical Reports Server (NTRS)

Diosady, Laslo Tibor; Murman, Scott M.

2013-01-01

A spectral-element framework is presented for the simulation of subsonic compressible high-Reynolds-number flows. The focus of the work is maximizing the efficiency of the computational schemes to enable unsteady simulations with a large number of spatial and temporal degrees of freedom. A collocation scheme is combined with optimized computational kernels to provide a residual evaluation with computational cost independent of order of accuracy up to 16th order. The optimized residual routines are used to develop a low-memory implicit scheme based on a matrix-free Newton-Krylov method. A preconditioner based on the finite-difference diagonalized ADI scheme is developed which maintains the low memory of the matrix-free implicit solver, while providing improved convergence properties. Emphasis on low memory usage throughout the solver development is leveraged to implement a coupled space-time DG solver which may offer further efficiency gains through adaptivity in both space and time.

A compatible high-order meshless method for the Stokes equations with applications to suspension flows

NASA Astrophysics Data System (ADS)

Trask, Nathaniel; Maxey, Martin; Hu, Xiaozhe

2018-02-01

A stable numerical solution of the steady Stokes problem requires compatibility between the choice of velocity and pressure approximation that has traditionally proven problematic for meshless methods. In this work, we present a discretization that couples a staggered scheme for pressure approximation with a divergence-free velocity reconstruction to obtain an adaptive, high-order, finite difference-like discretization that can be efficiently solved with conventional algebraic multigrid techniques. We use analytic benchmarks to demonstrate equal-order convergence for both velocity and pressure when solving problems with curvilinear geometries. In order to study problems in dense suspensions, we couple the solution for the flow to the equations of motion for freely suspended particles in an implicit monolithic scheme. The combination of high-order accuracy with fully-implicit schemes allows the accurate resolution of stiff lubrication forces directly from the solution of the Stokes problem without the need to introduce sub-grid lubrication models.

An implicit solution of the three-dimensional Navier-Stokes equations for an airfoil spanning a wind tunnel. Ph.D. Thesis

NASA Technical Reports Server (NTRS)

Moitra, A.

1982-01-01

An implicit finite-difference algorithm is developed for the numerical solution of the incompressible three dimensional Navier-Stokes equations in the non-conservative primitive-variable formulation. The flow field about an airfoil spanning a wind-tunnel is computed. The coordinate system is generated by an extension of the two dimensional body-fitted coordinate generation techniques of Thompson, as well as that of Sorenson, into three dimensions. Two dimensional grids are stacked along a spanwise coordinate defined by a simple analytical function. A Poisson pressure equation for advancing the pressure in time is arrived at by performing a divergence operation on the momentum equations. The pressure at each time-step is calculated on the assumption that continuity be unconditionally satisfied. An eddy viscosity coefficient, computed according to the algebraic turbulence formulation of Baldwin and Lomax, simulates the effects of turbulence.

An unstructured grid, three-dimensional model based on the shallow water equations

USGS Publications Warehouse

Casulli, V.; Walters, R.A.

2000-01-01

A semi-implicit finite difference model based on the three-dimensional shallow water equations is modified to use unstructured grids. There are obvious advantages in using unstructured grids in problems with a complicated geometry. In this development, the concept of unstructured orthogonal grids is introduced and applied to this model. The governing differential equations are discretized by means of a semi-implicit algorithm that is robust, stable and very efficient. The resulting model is relatively simple, conserves mass, can fit complicated boundaries and yet is sufficiently flexible to permit local mesh refinements in areas of interest. Moreover, the simulation of the flooding and drying is included in a natural and straightforward manner. These features are illustrated by a test case for studies of convergence rates and by examples of flooding on a river plain and flow in a shallow estuary. Copyright ?? 2000 John Wiley & Sons, Ltd.

Numerical simulation of flow path in the oxidizer side hot gas manifold of the Space Shuttle main engine

NASA Technical Reports Server (NTRS)

Lin, S. J.; Yang, R. J.; Chang, James L. C.; Kwak, D.

1987-01-01

The purpose of this study is to examine in detail incompressible laminar and turbulent flows inside the oxidizer side Hot Gas Manifold of the Space Shuttle Main Engine. To perform this study, an implicit finite difference code cast in general curvilinear coordinates is further developed. The code is based on the method of pseudo-compressibility and utilize ADI or implicit approximate factorization algorithm to achieve computational efficiency. A multiple-zone method is developed to overcome the complexity of the geometry. In the present study, the laminar and turbulent flows in the oxidizer side Hot Gas Manifold have been computed. The study reveals that: (1) there exists large recirculation zones inside the bowl if no vanes are present; (2) strong secondary flows are observed in the transfer tube; and (3) properly shaped and positioned guide vanes are effective in eliminating flow separation.

Calculation of flow about two-dimensional bodies by means of the velocity-vorticity formulation on a staggered grid

NASA Technical Reports Server (NTRS)

Stremel, Paul M.

1991-01-01

A method for calculating the incompressible viscous flow about two-dimensional bodies, utilizing the velocity-vorticity form of the Navier-Stokes equations using a staggered-grid formulation is presented. The solution is obtained by employing an alternative-direction implicit method for the solution of the block tridiagonal matrix resulting from the finite-difference representation of the governing equations. The boundary vorticity and the conservation of mass are calculated implicitly as a part of the solution. The mass conservation is calculated to machine zero for the duration of the computation. Calculations for the flow about a circular cylinder, a 2-pct thick flat plate at 90-deg incidence, an elliptic cylinder at 45-deg incidence, and a NACA 0012, with and without a deflected flap, at - 90-deg incidence are performed and compared with the results of other numerical investigations.

Complex-envelope alternating-direction-implicit FDTD method for simulating active photonic devices with semiconductor/solid-state media.

PubMed

Singh, Gurpreet; Ravi, Koustuban; Wang, Qian; Ho, Seng-Tiong

2012-06-15

A complex-envelope (CE) alternating-direction-implicit (ADI) finite-difference time-domain (FDTD) approach to treat light-matter interaction self-consistently with electromagnetic field evolution for efficient simulations of active photonic devices is presented for the first time (to our best knowledge). The active medium (AM) is modeled using an efficient multilevel system of carrier rate equations to yield the correct carrier distributions, suitable for modeling semiconductor/solid-state media accurately. To include the AM in the CE-ADI-FDTD method, a first-order differential system involving CE fields in the AM is first set up. The system matrix that includes AM parameters is then split into two time-dependent submatrices that are then used in an efficient ADI splitting formula. The proposed CE-ADI-FDTD approach with AM takes 22% of the time as the approach of the corresponding explicit FDTD, as validated by semiconductor microdisk laser simulations.

Finite-difference fluid dynamics computer mathematical models for the design and interpretation of experiments for space flight. [atmospheric general circulation experiment, convection in a float zone, and the Bridgman-Stockbarger crystal growing system

NASA Technical Reports Server (NTRS)

Roberts, G. O.; Fowlis, W. W.; Miller, T. L.

1984-01-01

Numerical methods are used to design a spherical baroclinic flow model experiment of the large scale atmosphere flow for Spacelab. The dielectric simulation of radial gravity is only dominant in a low gravity environment. Computer codes are developed to study the processes at work in crystal growing systems which are also candidates for space flight. Crystalline materials rarely achieve their potential properties because of imperfections and component concentration variations. Thermosolutal convection in the liquid melt can be the cause of these imperfections. Such convection is suppressed in a low gravity environment. Two and three dimensional finite difference codes are being used for this work. Nonuniform meshes and implicit iterative methods are used. The iterative method for steady solutions is based on time stepping but has the options of different time steps for velocity and temperature and of a time step varying smoothly with position according to specified powers of the mesh spacings. This allows for more rapid convergence. The code being developed for the crystal growth studies allows for growth of the crystal as the solid-liquid interface. The moving interface is followed using finite differences; shape variations are permitted. For convenience in applying finite differences in the solid and liquid, a time dependent coordinate transformation is used to make this interface a coordinate surface.

Finite element computation of compressible flows with the SUPG formulation

NASA Technical Reports Server (NTRS)

Le Beau, G. J.; Tezduyar, T. E.

1991-01-01

Finite element computation of compressible Euler equations is presented in the context of the streamline-upwind/Petrov-Galerkin (SUPG) formulation. The SUPG formulation, which is based on adding stabilizing terms to the Galerkin formulation, is further supplemented with a shock capturing operator which addresses the difficulty in maintaining a satisfactory solution near discontinuities in the solution field. The shock capturing operator, which has been derived from work done in entropy variables for a similar operator, is shown to lead to an appropriate level of additional stabilization near shocks, without resulting in excessive numerical diffusion. An implicit treatment of the impermeable wall boundary condition is also presented. This treatment of the no-penetration condition offers increased stability for large Courant numbers, and accelerated convergence of the computations for both implicit and explicit applications. Several examples are presented to demonstrate the ability of this method to solve the equations governing compressible fluid flow.

Numerical simulation of the solitary wave interacting with an elastic structure using MPS-FEM coupled method

NASA Astrophysics Data System (ADS)

Rao, Chengping; Zhang, Youlin; Wan, Decheng

2017-12-01

Fluid-Structure Interaction (FSI) caused by fluid impacting onto a flexible structure commonly occurs in naval architecture and ocean engineering. Research on the problem of wave-structure interaction is important to ensure the safety of offshore structures. This paper presents the Moving Particle Semi-implicit and Finite Element Coupled Method (MPS-FEM) to simulate FSI problems. The Moving Particle Semi-implicit (MPS) method is used to calculate the fluid domain, while the Finite Element Method (FEM) is used to address the structure domain. The scheme for the coupling of MPS and FEM is introduced first. Then, numerical validation and convergent study are performed to verify the accuracy of the solver for solitary wave generation and FSI problems. The interaction between the solitary wave and an elastic structure is investigated by using the MPS-FEM coupled method.

Finite difference model for aquifer simulation in two dimensions with results of numerical experiments

USGS Publications Warehouse

Trescott, Peter C.; Pinder, George Francis; Larson, S.P.

1976-01-01

The model will simulate ground-water flow in an artesian aquifer, a water-table aquifer, or a combined artesian and water-table aquifer. The aquifer may be heterogeneous and anisotropic and have irregular boundaries. The source term in the flow equation may include well discharge, constant recharge, leakage from confining beds in which the effects of storage are considered, and evapotranspiration as a linear function of depth to water. The theoretical development includes presentation of the appropriate flow equations and derivation of the finite-difference approximations (written for a variable grid). The documentation emphasizes the numerical techniques that can be used for solving the simultaneous equations and describes the results of numerical experiments using these techniques. Of the three numerical techniques available in the model, the strongly implicit procedure, in general, requires less computer time and has fewer numerical difficulties than do the iterative alternating direction implicit procedure and line successive overrelaxation (which includes a two-dimensional correction procedure to accelerate convergence). The documentation includes a flow chart, program listing, an example simulation, and sections on designing an aquifer model and requirements for data input. It illustrates how model results can be presented on the line printer and pen plotters with a program that utilizes the graphical display software available from the Geological Survey Computer Center Division. In addition the model includes options for reading input data from a disk and writing intermediate results on a disk.

A Semi-Implicit, Three-Dimensional Model for Estuarine Circulation

USGS Publications Warehouse

Smith, Peter E.

2006-01-01

A semi-implicit, finite-difference method for the numerical solution of the three-dimensional equations for circulation in estuaries is presented and tested. The method uses a three-time-level, leapfrog-trapezoidal scheme that is essentially second-order accurate in the spatial and temporal numerical approximations. The three-time-level scheme is shown to be preferred over a two-time-level scheme, especially for problems with strong nonlinearities. The stability of the semi-implicit scheme is free from any time-step limitation related to the terms describing vertical diffusion and the propagation of the surface gravity waves. The scheme does not rely on any form of vertical/horizontal mode-splitting to treat the vertical diffusion implicitly. At each time step, the numerical method uses a double-sweep method to transform a large number of small tridiagonal equation systems and then uses the preconditioned conjugate-gradient method to solve a single, large, five-diagonal equation system for the water surface elevation. The governing equations for the multi-level scheme are prepared in a conservative form by integrating them over the height of each horizontal layer. The layer-integrated volumetric transports replace velocities as the dependent variables so that the depth-integrated continuity equation that is used in the solution for the water surface elevation is linear. Volumetric transports are computed explicitly from the momentum equations. The resulting method is mass conservative, efficient, and numerically accurate.

A global multilevel atmospheric model using a vector semi-Lagrangian finite-difference scheme. I - Adiabatic formulation

NASA Technical Reports Server (NTRS)

Bates, J. R.; Moorthi, S.; Higgins, R. W.

1993-01-01

An adiabatic global multilevel primitive equation model using a two time-level, semi-Lagrangian semi-implicit finite-difference integration scheme is presented. A Lorenz grid is used for vertical discretization and a C grid for the horizontal discretization. The momentum equation is discretized in vector form, thus avoiding problems near the poles. The 3D model equations are reduced by a linear transformation to a set of 2D elliptic equations, whose solution is found by means of an efficient direct solver. The model (with minimal physics) is integrated for 10 days starting from an initialized state derived from real data. A resolution of 16 levels in the vertical is used, with various horizontal resolutions. The model is found to be stable and efficient, and to give realistic output fields. Integrations with time steps of 10 min, 30 min, and 1 h are compared, and the differences are found to be acceptable.

Analysis of turbulent free-jet hydrogen-air diffusion flames with finite chemical reaction rates

NASA Technical Reports Server (NTRS)

Sislian, J. P.; Glass, I. I.; Evans, J. S.

1979-01-01

A numerical analysis is presented of the nonequilibrium flow field resulting from the turbulent mixing and combustion of an axisymmetric hydrogen jet in a supersonic parallel ambient air stream. The effective turbulent transport properties are determined by means of a two-equation model of turbulence. The finite-rate chemistry model considers eight elementary reactions among six chemical species: H, O, H2O, OH, O2 and H2. The governing set of nonlinear partial differential equations was solved by using an implicit finite-difference procedure. Radial distributions were obtained at two downstream locations for some important variables affecting the flow development, such as the turbulent kinetic energy and its dissipation rate. The results show that these variables attain their peak values on the axis of symmetry. The computed distribution of velocity, temperature, and mass fractions of the chemical species gives a complete description of the flow field. The numerical predictions were compared with two sets of experimental data. Good qualitative agreement was obtained.

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

NASA Astrophysics Data System (ADS)

Otero, Evelyn; Eliasson, Peter

2015-03-01

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

A multi-dimensional, energy- and charge-conserving, nonlinearly implicit, electromagnetic Vlasov–Darwin particle-in-cell algorithm

DOE PAGES

Chen, G.; Chacón, L.

2015-08-11

For decades, the Vlasov–Darwin model has been recognized to be attractive for particle-in-cell (PIC) kinetic plasma simulations in non-radiative electromagnetic regimes, to avoid radiative noise issues and gain computational efficiency. However, the Darwin model results in an elliptic set of field equations that renders conventional explicit time integration unconditionally unstable. We explore a fully implicit PIC algorithm for the Vlasov–Darwin model in multiple dimensions, which overcomes many difficulties of traditional semi-implicit Darwin PIC algorithms. The finite-difference scheme for Darwin field equations and particle equations of motion is space–time-centered, employing particle sub-cycling and orbit-averaging. This algorithm conserves total energy, local charge,more » canonical-momentum in the ignorable direction, and preserves the Coulomb gauge exactly. An asymptotically well-posed fluid preconditioner allows efficient use of large cell sizes, which are determined by accuracy considerations, not stability, and can be orders of magnitude larger than required in a standard explicit electromagnetic PIC simulation. Finally, we demonstrate the accuracy and efficiency properties of the algorithm with various numerical experiments in 2D–3V.« less

Implicit Learning of Recursive Context-Free Grammars

PubMed Central

Rohrmeier, Martin; Fu, Qiufang; Dienes, Zoltan

2012-01-01

Context-free grammars are fundamental for the description of linguistic syntax. However, most artificial grammar learning experiments have explored learning of simpler finite-state grammars, while studies exploring context-free grammars have not assessed awareness and implicitness. This paper explores the implicit learning of context-free grammars employing features of hierarchical organization, recursive embedding and long-distance dependencies. The grammars also featured the distinction between left- and right-branching structures, as well as between centre- and tail-embedding, both distinctions found in natural languages. People acquired unconscious knowledge of relations between grammatical classes even for dependencies over long distances, in ways that went beyond learning simpler relations (e.g. n-grams) between individual words. The structural distinctions drawn from linguistics also proved important as performance was greater for tail-embedding than centre-embedding structures. The results suggest the plausibility of implicit learning of complex context-free structures, which model some features of natural languages. They support the relevance of artificial grammar learning for probing mechanisms of language learning and challenge existing theories and computational models of implicit learning. PMID:23094021

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

NASA Technical Reports Server (NTRS)

Radespiel, R.; Rossow, C.

1988-01-01

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

Given a one-step numerical scheme, on which ordinary differential equations is it exact?

NASA Astrophysics Data System (ADS)

Villatoro, Francisco R.

2009-01-01

A necessary condition for a (non-autonomous) ordinary differential equation to be exactly solved by a one-step, finite difference method is that the principal term of its local truncation error be null. A procedure to determine some ordinary differential equations exactly solved by a given numerical scheme is developed. Examples of differential equations exactly solved by the explicit Euler, implicit Euler, trapezoidal rule, second-order Taylor, third-order Taylor, van Niekerk's second-order rational, and van Niekerk's third-order rational methods are presented.

Numerical simulation of the control of the three-dimensional transition process in boundary layers

NASA Technical Reports Server (NTRS)

Kral, L. D.; Fasel, H. F.

1990-01-01

Surface heating techniques to control the three-dimensional laminar-turbulent transition process are numerically investigated for a water boundary layer. The Navier-Stokes and energy equations are solved using a fully implicit finite difference/spectral method. The spatially evolving boundary layer is simulated. Results of both passive and active methods of control are shown for small amplitude two-dimensional and three-dimensional disturbance waves. Control is also applied to the early stages of the secondary instability process using passive or active control techniques.

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

NASA Technical Reports Server (NTRS)

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

1977-01-01

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

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

NASA Technical Reports Server (NTRS)

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

1990-01-01

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

Development of the general interpolants method for the CYBER 200 series of supercomputers

NASA Technical Reports Server (NTRS)

Stalnaker, J. F.; Robinson, M. A.; Spradley, L. W.; Kurzius, S. C.; Thoenes, J.

1988-01-01

The General Interpolants Method (GIM) is a 3-D, time-dependent, hybrid procedure for generating numerical analogs of the conservation laws. This study is directed toward the development and application of the GIM computer code for fluid dynamic research applications as implemented for the Cyber 200 series of supercomputers. An elliptic and quasi-parabolic version of the GIM code are discussed. Turbulence models, algebraic and differential equations, were added to the basic viscous code. An equilibrium reacting chemistry model and an implicit finite difference scheme are also included.

Additional development of the XTRAN3S computer program

NASA Technical Reports Server (NTRS)

Borland, C. J.

1989-01-01

Additional developments and enhancements to the XTRAN3S computer program, a code for calculation of steady and unsteady aerodynamics, and associated aeroelastic solutions, for 3-D wings in the transonic flow regime are described. Algorithm improvements for the XTRAN3S program were provided including an implicit finite difference scheme to enhance the allowable time step and vectorization for improved computational efficiency. The code was modified to treat configurations with a fuselage, multiple stores/nacelles/pylons, and winglets. Computer program changes (updates) for error corrections and updates for version control are provided.

A finite-volume module for all-scale Earth-system modelling at ECMWF

NASA Astrophysics Data System (ADS)

Kühnlein, Christian; Malardel, Sylvie; Smolarkiewicz, Piotr

2017-04-01

We highlight recent advancements in the development of the finite-volume module (FVM) (Smolarkiewicz et al., 2016) for the IFS at ECMWF. FVM represents an alternative dynamical core that complements the operational spectral dynamical core of the IFS with new capabilities. Most notably, these include a compact-stencil finite-volume discretisation, flexible meshes, conservative non-oscillatory transport and all-scale governing equations. As a default, FVM solves the compressible Euler equations in a geospherical framework (Szmelter and Smolarkiewicz, 2010). The formulation incorporates a generalised terrain-following vertical coordinate. A hybrid computational mesh, fully unstructured in the horizontal and structured in the vertical, enables efficient global atmospheric modelling. Moreover, a centred two-time-level semi-implicit integration scheme is employed with 3D implicit treatment of acoustic, buoyant, and rotational modes. The associated 3D elliptic Helmholtz problem is solved using a preconditioned Generalised Conjugate Residual approach. The solution procedure employs the non-oscillatory finite-volume MPDATA advection scheme that is bespoke for the compressible dynamics on the hybrid mesh (Kühnlein and Smolarkiewicz, 2017). The recent progress of FVM is illustrated with results of benchmark simulations of intermediate complexity, and comparison to the operational spectral dynamical core of the IFS. C. Kühnlein, P.K. Smolarkiewicz: An unstructured-mesh finite-volume MPDATA for compressible atmospheric dynamics, J. Comput. Phys. (2017), in press. P.K. Smolarkiewicz, W. Deconinck, M. Hamrud, C. Kühnlein, G. Mozdzynski, J. Szmelter, N.P. Wedi: A finite-volume module for simulating global all-scale atmospheric flows, J. Comput. Phys. 314 (2016) 287-304. J. Szmelter, P.K. Smolarkiewicz: An edge-based unstructured mesh discretisation in geospherical framework, J. Comput. Phys. 229 (2010) 4980-4995.

LLNL contributions to ANL Report ANL/NE-16/6 "Sharp User Manual"

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

Solberg, J. M.

Diablo is a Multiphysics implicit finite element code with an emphasis on coupled structural/thermal analysis. In the SHARP framework, it is used as the structural solver, and may also be used as the mesh smoother.

Development and Verification of the Charring, Ablating Thermal Protection Implicit System Simulator

NASA Technical Reports Server (NTRS)

Amar, Adam J.; Calvert, Nathan; Kirk, Benjamin S.

2011-01-01

The development and verification of the Charring Ablating Thermal Protection Implicit System Solver (CATPISS) is presented. This work concentrates on the derivation and verification of the stationary grid terms in the equations that govern three-dimensional heat and mass transfer for charring thermal protection systems including pyrolysis gas flow through the porous char layer. The governing equations are discretized according to the Galerkin finite element method (FEM) with first and second order fully implicit time integrators. The governing equations are fully coupled and are solved in parallel via Newton s method, while the linear system is solved via the Generalized Minimum Residual method (GMRES). Verification results from exact solutions and Method of Manufactured Solutions (MMS) are presented to show spatial and temporal orders of accuracy as well as nonlinear convergence rates.

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.

Numerical solution of the wave equation with variable wave speed on nonconforming domains by high-order difference potentials

NASA Astrophysics Data System (ADS)

Britt, S.; Tsynkov, S.; Turkel, E.

2018-02-01

We solve the wave equation with variable wave speed on nonconforming domains with fourth order accuracy in both space and time. This is accomplished using an implicit finite difference (FD) scheme for the wave equation and solving an elliptic (modified Helmholtz) equation at each time step with fourth order spatial accuracy by the method of difference potentials (MDP). High-order MDP utilizes compact FD schemes on regular structured grids to efficiently solve problems on nonconforming domains while maintaining the design convergence rate of the underlying FD scheme. Asymptotically, the computational complexity of high-order MDP scales the same as that for FD.

Application of the θ-method to a telegraphic model of fluid flow in a dual-porosity medium

NASA Astrophysics Data System (ADS)

González-Calderón, Alfredo; Vivas-Cruz, Luis X.; Herrera-Hernández, Erik César

2018-01-01

This work focuses mainly on the study of numerical solutions, which are obtained using the θ-method, of a generalized Warren and Root model that includes a second-order wave-like equation in its formulation. The solutions approximately describe the single-phase hydraulic head in fractures by considering the finite velocity of propagation by means of a Cattaneo-like equation. The corresponding discretized model is obtained by utilizing a non-uniform grid and a non-uniform time step. A simple relationship is proposed to give the time-step distribution. Convergence is analyzed by comparing results from explicit, fully implicit, and Crank-Nicolson schemes with exact solutions: a telegraphic model of fluid flow in a single-porosity reservoir with relaxation dynamics, the Warren and Root model, and our studied model, which is solved with the inverse Laplace transform. We find that the flux and the hydraulic head have spurious oscillations that most often appear in small-time solutions but are attenuated as the solution time progresses. Furthermore, we show that the finite difference method is unable to reproduce the exact flux at time zero. Obtaining results for oilfield production times, which are in the order of months in real units, is only feasible using parallel implicit schemes. In addition, we propose simple parallel algorithms for the memory flux and for the explicit scheme.

An efficient semi-implicit method for three-dimensional non-hydrostatic flows in compliant arterial vessels.

PubMed

Fambri, Francesco; Dumbser, Michael; Casulli, Vincenzo

2014-11-01

Blood flow in arterial systems can be described by the three-dimensional Navier-Stokes equations within a time-dependent spatial domain that accounts for the elasticity of the arterial walls. In this article, blood is treated as an incompressible Newtonian fluid that flows through compliant vessels of general cross section. A three-dimensional semi-implicit finite difference and finite volume model is derived so that numerical stability is obtained at a low computational cost on a staggered grid. The key idea of the method consists in a splitting of the pressure into a hydrostatic and a non-hydrostatic part, where first a small quasi-one-dimensional nonlinear system is solved for the hydrostatic pressure and only in a second step the fully three-dimensional non-hydrostatic pressure is computed from a three-dimensional nonlinear system as a correction to the hydrostatic one. The resulting algorithm is robust, efficient, locally and globally mass conservative, and applies to hydrostatic and non-hydrostatic flows in one, two and three space dimensions. These features are illustrated on nontrivial test cases for flows in tubes with circular or elliptical cross section where the exact analytical solution is known. Test cases of steady and pulsatile flows in uniformly curved rigid and elastic tubes are presented. Wherever possible, axial velocity development and secondary flows are shown and compared with previously published results. Copyright © 2014 John Wiley & Sons, Ltd.

Unmitigated numerical solution to the diffraction term in the parabolic nonlinear ultrasound wave equation.

PubMed

Hasani, Mojtaba H; Gharibzadeh, Shahriar; Farjami, Yaghoub; Tavakkoli, Jahan

2013-09-01

Various numerical algorithms have been developed to solve the Khokhlov-Kuznetsov-Zabolotskaya (KZK) parabolic nonlinear wave equation. In this work, a generalized time-domain numerical algorithm is proposed to solve the diffraction term of the KZK equation. This algorithm solves the transverse Laplacian operator of the KZK equation in three-dimensional (3D) Cartesian coordinates using a finite-difference method based on the five-point implicit backward finite difference and the five-point Crank-Nicolson finite difference discretization techniques. This leads to a more uniform discretization of the Laplacian operator which in turn results in fewer calculation gridding nodes without compromising accuracy in the diffraction term. In addition, a new empirical algorithm based on the LU decomposition technique is proposed to solve the system of linear equations obtained from this discretization. The proposed empirical algorithm improves the calculation speed and memory usage, while the order of computational complexity remains linear in calculation of the diffraction term in the KZK equation. For evaluating the accuracy of the proposed algorithm, two previously published algorithms are used as comparison references: the conventional 2D Texas code and its generalization for 3D geometries. The results show that the accuracy/efficiency performance of the proposed algorithm is comparable with the established time-domain methods.

Comparison of Accuracy and Performance for Lattice Boltzmann and Finite Difference Simulations of Steady Viscous Flow

NASA Astrophysics Data System (ADS)

Noble, David R.; Georgiadis, John G.; Buckius, Richard O.

1996-07-01

The lattice Boltzmann method (LBM) is used to simulate flow in an infinite periodic array of octagonal cylinders. Results are compared with those obtained by a finite difference (FD) simulation solved in terms of streamfunction and vorticity using an alternating direction implicit scheme. Computed velocity profiles are compared along lines common to both the lattice Boltzmann and finite difference grids. Along all such slices, both streamwise and transverse velocity predictions agree to within 05% of the average streamwise velocity. The local shear on the surface of the cylinders also compares well, with the only deviations occurring in the vicinity of the corners of the cylinders, where the slope of the shear is discontinuous. When a constant dimensionless relaxation time is maintained, LBM exhibits the same convergence behaviour as the FD algorithm, with the time step increasing as the square of the grid size. By adjusting the relaxation time such that a constant Mach number is achieved, the time step of LBM varies linearly with the grid size. The efficiency of LBM on the CM-5 parallel computer at the National Center for Supercomputing Applications (NCSA) is evaluated by examining each part of the algorithm. Overall, a speed of 139 GFLOPS is obtained using 512 processors for a domain size of 2176×2176.

P1 Nonconforming Finite Element Method for the Solution of Radiation Transport Problems

NASA Technical Reports Server (NTRS)

Kang, Kab S.

2002-01-01

The simulation of radiation transport in the optically thick flux-limited diffusion regime has been identified as one of the most time-consuming tasks within large simulation codes. Due to multimaterial complex geometry, the radiation transport system must often be solved on unstructured grids. In this paper, we investigate the behavior and the benefits of the unstructured P(sub 1) nonconforming finite element method, which has proven to be flexible and effective on related transport problems, in solving unsteady implicit nonlinear radiation diffusion problems using Newton and Picard linearization methods. Key words. nonconforrning finite elements, radiation transport, inexact Newton linearization, multigrid preconditioning

magnum.fe: A micromagnetic finite-element simulation code based on FEniCS

NASA Astrophysics Data System (ADS)

Abert, Claas; Exl, Lukas; Bruckner, Florian; Drews, André; Suess, Dieter

2013-11-01

We have developed a finite-element micromagnetic simulation code based on the FEniCS package called magnum.fe. Here we describe the numerical methods that are applied as well as their implementation with FEniCS. We apply a transformation method for the solution of the demagnetization-field problem. A semi-implicit weak formulation is used for the integration of the Landau-Lifshitz-Gilbert equation. Numerical experiments show the validity of simulation results. magnum.fe is open source and well documented. The broad feature range of the FEniCS package makes magnum.fe a good choice for the implementation of novel micromagnetic finite-element algorithms.

Fully-Implicit Navier-Stokes (FIN-S)

NASA Technical Reports Server (NTRS)

Kirk, Benjamin S.

2010-01-01

FIN-S is a SUPG finite element code for flow problems under active development at NASA Lyndon B. Johnson Space Center and within PECOS: a) The code is built on top of the libMesh parallel, adaptive finite element library. b) The initial implementation of the code targeted supersonic/hypersonic laminar calorically perfect gas flows & conjugate heat transfer. c) Initial extension to thermochemical nonequilibrium about 9 months ago. d) The technologies in FIN-S have been enhanced through a strongly collaborative research effort with Sandia National Labs.

Finite Deformations and Internal Forces in Elastic-Plastic Crystals: Interpretations From Nonlinear Elasticity and Anharmonic Lattice Statics

DTIC Science & Technology

2009-09-01

Sec. 2, while the latter ase—which implicitly includes the effects of image forces of efects in neighboring volume elements—may be more practical rom...versetzungen und eigenspannungen,” Arch . Ration. Mech. Anal., 4, pp. 273–334. 25 Lee, E. H., 1969, “Elastic-Plastic Deformation at Finite Strains,” ASME J...Rev., 73, pp. 373–382. 27 Kroner, E., and Seeger, A., 1959, “Nicht-Lineare Elastizitatstheorie der Verset- zungen und Eigenspannungen,” Arch . Ration

Finite Element Analysis of M15 and M19 Mines Under Wheeled Vehicle Load

DTIC Science & Technology

2008-03-01

the plate statically. An implicit finite element option in a code called LSDYNA was used to model the pressure generated in the explosive by the...figure 4 for the M19 mines. Maximum pressure in the explosive for each mine calculated by LSDYNA code shown for a variety of plate sizes and weights...Director U.S. Army TRADOC Analysis Center-WSMR ATTN: ATRC-WSS-R White Sands Missile Range, NM 88002 Chemical Propulsion Information Agency ATTN

An energy- and charge-conserving, nonlinearly implicit, electromagnetic 1D-3V Vlasov-Darwin particle-in-cell algorithm

NASA Astrophysics Data System (ADS)

Chen, G.; Chacón, L.

2014-10-01

A recent proof-of-principle study proposes a nonlinear electrostatic implicit particle-in-cell (PIC) algorithm in one dimension (Chen et al., 2011). The algorithm employs a kinetically enslaved Jacobian-free Newton-Krylov (JFNK) method, and conserves energy and charge to numerical round-off. In this study, we generalize the method to electromagnetic simulations in 1D using the Darwin approximation to Maxwell's equations, which avoids radiative noise issues by ordering out the light wave. An implicit, orbit-averaged, time-space-centered finite difference scheme is employed in both the 1D Darwin field equations (in potential form) and the 1D-3V particle orbit equations to produce a discrete system that remains exactly charge- and energy-conserving. Furthermore, enabled by the implicit Darwin equations, exact conservation of the canonical momentum per particle in any ignorable direction is enforced via a suitable scattering rule for the magnetic field. We have developed a simple preconditioner that targets electrostatic waves and skin currents, and allows us to employ time steps O(√{mi /me } c /veT) larger than the explicit CFL. Several 1D numerical experiments demonstrate the accuracy, performance, and conservation properties of the algorithm. In particular, the scheme is shown to be second-order accurate, and CPU speedups of more than three orders of magnitude vs. an explicit Vlasov-Maxwell solver are demonstrated in the "cold" plasma regime (where kλD ≪ 1).

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

NASA Technical Reports Server (NTRS)

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

1979-01-01

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

Unsteady solute-transport simulation in streamflow using a finite-difference model

USGS Publications Warehouse

Land, Larry F.

1978-01-01

This report documents a rather simple, general purpose, one-dimensional, one-parameter, mass-transport model for field use. The model assumes a well-mixed conservative solute that may be coming from an unsteady source and is moving in unsteady streamflow. The quantity of solute being transported is in the units of concentration. Results are reported as such. An implicit finite-difference technique is used to solve the mass transport equation. It consists of creating a tridiagonal matrix and using the Thomas algorithm to solve the matrix for the unknown concentrations at the new time step. The computer program pesented is designed to compute the concentration of a water-quality constituent at any point and at any preselected time in a one-dimensional stream. The model is driven by the inflowing concentration of solute at the upstream boundary and is influenced by the solute entering the stream from tributaries and lateral ground-water inflow and from a source or sink. (Woodard-USGS)

Transpiration and film cooling boundary layer computer program. Volume 2: Computer program and user's manual

NASA Technical Reports Server (NTRS)

Gloss, R. J.

1971-01-01

A finite difference turbulent boundary layer computer program which allows for mass transfer wall cooling and equilibrium chemistry effects is presented. The program is capable of calculating laminar or turbulent boundary layer solutions for an arbitrary ideal gas or an equilibrium hydrogen oxygen system. Either two dimensional or axisymmetric geometric configurations may be considered. The equations are solved, in nondimension-alized physical coordinates, using the implicit Crank-Nicolson technique. The finite difference forms of the conservation of mass, momentum, total enthalpy and elements equations are linearized and uncoupled, thereby generating easily solvable tridiagonal sets of algebraic equations. A detailed description of the computer program, as well as a program user's manual is provided. Detailed descriptions of all boundary layer subroutines are included, as well as a section defining all program symbols of principal importance. Instructions are then given for preparing card input to the program and for interpreting the printed output. Finally, two sample cases are included to illustrate the use of the program.

Improved Boundary Layer Module (BLM) for the Solid Performance Program (SPP)

NASA Astrophysics Data System (ADS)

Coats, D. E.; Cebeci, T.

1982-03-01

The requirements for a replacement to the Bartz boundary layer code, the standard method of computing the performance loss due to viscous effects by the solid performance program, were discussed by the propulsion community along with four nationally recognized boundary layer experts. A consensus was reached regarding the preferred features for the analysis of the replacement code. The major points that were agreed upon are: (1) finite difference methods are preferred over integral methods; (2) a single equation eddy viscosity model was considered to be adequate for the purpose of computing performance loss; (3) a variable grid capability in both coordinate directions would be required; (4) a proven finite difference algorithm which is not stability restricted should be used, that is, an implicit numerical scheme would be required; and (5) the replacement code should be able to compute both turbulent and laminar flows. The program should treat mass addition at the wall as well as being able to calculate a stagnation point starting line.

Radiative interactions in chemically reacting supersonic internal flows

NASA Technical Reports Server (NTRS)

Tiwari, S. N.; Chandrasekhar, R.

1991-01-01

The two-dimensional, elliptic Navier-Stokes equations are used to investigate supersonic flows with finite-rate chemistry and radiation for hydrogen-air systems. The chemistry source terms in the species equation is treated implicitly to alleviate the stiffness associated with fast reactions. The explicit, unsplit MacCormack finite-difference scheme is used to advance the governing equations in time, until convergence is achieved. The specific problem considered is the premixed flow in a channel with a ten-degree compression ramp. Three different chemistry models are used, accounting for increasing number of reactions and participating species. Two chemistry models assure nitrogen as inert, while the third model accounts for nitrogen reactions and NO(x) formation. The tangent slab approximation is used in the radiative flux formulation. A pseudo-gray model is used to represent the absorption-emission characteristics of the participating species. Results obtained for specific conditions indicate that the radiative interactions vary substantially, depending on reactions involving HO2 and NO species and that this can have a significant influence on the flowfield.

Finite T spectral function of a single carrier injected into an Ising chain: a comparison of 3 different models

NASA Astrophysics Data System (ADS)

Moeller, Mirko; Berciu, Mona

2015-03-01

When studying the properties of complex, magnetic materials it is often necessary to work with effective Hamiltonians. In many cases the effective Hamiltonian is obtained by mapping the full, multiband Hamiltonian onto a simpler, single band model. A prominent example is the use of Zhang-Rice singlets to map the multiband Emery model for cuprates onto the single band t - J -model. Such mappings are usually done at zero temperature (T) and it is implicitly assumed that they are justified at finite T, as well. We present results on 3 different models of a single charge carrier (electron or hole) injected into a ferromagnetic Ising chain. Model I is a two band, two sublattice model, Model II is a two band, single sublattice model, and Model III is a single band model, the so called t -Jz -model. Due to the absence of spin-flip terms, a numerically exact solution of all 3 Models is possible, even at finite T. At zero T a mapping between all 3 models results in the same low energy physics. However, this is no longer true at finite T. Here the low energy behavior of Model III is significantly different from that of Models I and II. The reasons for this discrepancy and its implications for more realistic models (higher dimension, inclusion of spin-flip terms) are discussed. This work was supported by NSERC, QMI and the UBC 4YF (M.M.).

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

NASA Astrophysics Data System (ADS)

Zhu, Yajun; Zhong, Chengwen; Xu, Kun

2017-09-01

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

Modelling multiple cycles of static and dynamic recrystallisation using a fully implicit isotropic material model based on dislocation density

NASA Astrophysics Data System (ADS)

Jansen van Rensburg, Gerhardus J.; Kok, Schalk; Wilke, Daniel N.

2018-03-01

This paper presents the development and numerical implementation of a state variable based thermomechanical material model, intended for use within a fully implicit finite element formulation. Plastic hardening, thermal recovery and multiple cycles of recrystallisation can be tracked for single peak as well as multiple peak recrystallisation response. The numerical implementation of the state variable model extends on a J2 isotropic hypo-elastoplastic modelling framework. The complete numerical implementation is presented as an Abaqus UMAT and linked subroutines. Implementation is discussed with detailed explanation of the derivation and use of various sensitivities, internal state variable management and multiple recrystallisation cycle contributions. A flow chart explaining the proposed numerical implementation is provided as well as verification on the convergence of the material subroutine. The material model is characterised using two high temperature data sets for cobalt and copper. The results of finite element analyses using the material parameter values characterised on the copper data set are also presented.

Toward textbook multigrid efficiency for fully implicit resistive magnetohydrodynamics

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

Adams, Mark F.; Samtaney, Ravi, E-mail: samtaney@pppl.go; Brandt, Achi

2010-09-01

Multigrid methods can solve some classes of elliptic and parabolic equations to accuracy below the truncation error with a work-cost equivalent to a few residual calculations - so-called 'textbook' multigrid efficiency. We investigate methods to solve the system of equations that arise in time dependent magnetohydrodynamics (MHD) simulations with textbook multigrid efficiency. We apply multigrid techniques such as geometric interpolation, full approximate storage, Gauss-Seidel smoothers, and defect correction for fully implicit, nonlinear, second-order finite volume discretizations of MHD. We apply these methods to a standard resistive MHD benchmark problem, the GEM reconnection problem, and add a strong magnetic guide field,more » which is a critical characteristic of magnetically confined fusion plasmas. We show that our multigrid methods can achieve near textbook efficiency on fully implicit resistive MHD simulations.« less

Toward textbook multigrid efficiency for fully implicit resistive magnetohydrodynamics

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

Adams, Mark F.; Samtaney, Ravi; Brandt, Achi

2010-09-01

Multigrid methods can solve some classes of elliptic and parabolic equations to accuracy below the truncation error with a work-cost equivalent to a few residual calculations – so-called ‘‘textbook” multigrid efficiency. We investigate methods to solve the system of equations that arise in time dependent magnetohydrodynamics (MHD) simulations with textbook multigrid efficiency. We apply multigrid techniques such as geometric interpolation, full approximate storage, Gauss–Seidel smoothers, and defect correction for fully implicit, nonlinear, second-order finite volume discretizations of MHD. We apply these methods to a standard resistive MHD benchmark problem, the GEM reconnection problem, and add a strong magnetic guide field,more » which is a critical characteristic of magnetically confined fusion plasmas. We show that our multigrid methods can achieve near textbook efficiency on fully implicit resistive MHD simulations.« less

Toward textbook multigrid efficiency for fully implicit resistive magnetohydrodynamics

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

Adams, Mark F.; Samtaney, Ravi; Brandt, Achi

2013-12-14

Multigrid methods can solve some classes of elliptic and parabolic equations to accuracy below the truncation error with a work-cost equivalent to a few residual calculations – so-called “textbook” multigrid efficiency. We investigate methods to solve the system of equations that arise in time dependent magnetohydrodynamics (MHD) simulations with textbook multigrid efficiency. We apply multigrid techniques such as geometric interpolation, full approximate storage, Gauss-Seidel smoothers, and defect correction for fully implicit, nonlinear, second-order finite volume discretizations of MHD. We apply these methods to a standard resistive MHD benchmark problem, the GEM reconnection problem, and add a strong magnetic guide field,more » which is a critical characteristic of magnetically confined fusion plasmas. We show that our multigrid methods can achieve near textbook efficiency on fully implicit resistive MHD simulations.« less

A Numerical Model for Trickle Bed Reactors

NASA Astrophysics Data System (ADS)

Propp, Richard M.; Colella, Phillip; Crutchfield, William Y.; Day, Marcus S.

2000-12-01

Trickle bed reactors are governed by equations of flow in porous media such as Darcy's law and the conservation of mass. Our numerical method for solving these equations is based on a total-velocity splitting, sequential formulation which leads to an implicit pressure equation and a semi-implicit mass conservation equation. We use high-resolution finite-difference methods to discretize these equations. Our solution scheme extends previous work in modeling porous media flows in two ways. First, we incorporate physical effects due to capillary pressure, a nonlinear inlet boundary condition, spatial porosity variations, and inertial effects on phase mobilities. In particular, capillary forces introduce a parabolic component into the recast evolution equation, and the inertial effects give rise to hyperbolic nonconvexity. Second, we introduce a modification of the slope-limiting algorithm to prevent our numerical method from producing spurious shocks. We present a numerical algorithm for accommodating these difficulties, show the algorithm is second-order accurate, and demonstrate its performance on a number of simplified problems relevant to trickle bed reactor modeling.

The NCOREL computer program for 3D nonlinear supersonic potential flow computations

NASA Technical Reports Server (NTRS)

Siclari, M. J.

1983-01-01

An innovative computational technique (NCOREL) was established for the treatment of three dimensional supersonic flows. The method is nonlinear in that it solves the nonconservative finite difference analog of the full potential equation and can predict the formation of supercritical cross flow regions, embedded and bow shocks. The method implicitly computes a conical flow at the apex (R = 0) of a spherical coordinate system and uses a fully implicit marching technique to obtain three dimensional cross flow solutions. This implies that the radial Mach number must remain supersonic. The cross flow solutions are obtained by using type dependent transonic relaxation techniques with the type dependency linked to the character of the cross flow velocity (i.e., subsonic/supersonic). The spherical coordinate system and marching on spherical surfaces is ideally suited to the computation of wing flows at low supersonic Mach numbers due to the elimination of the subsonic axial Mach number problems that exist in other marching codes that utilize Cartesian transverse marching planes.

A parallel domain decomposition-based implicit method for the Cahn–Hilliard–Cook phase-field equation in 3D

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

Zheng, Xiang; Yang, Chao; State Key Laboratory of Computer Science, Chinese Academy of Sciences, Beijing 100190

2015-03-15

We present a numerical algorithm for simulating the spinodal decomposition described by the three dimensional Cahn–Hilliard–Cook (CHC) equation, which is a fourth-order stochastic partial differential equation with a noise term. The equation is discretized in space and time based on a fully implicit, cell-centered finite difference scheme, with an adaptive time-stepping strategy designed to accelerate the progress to equilibrium. At each time step, a parallel Newton–Krylov–Schwarz algorithm is used to solve the nonlinear system. We discuss various numerical and computational challenges associated with the method. The numerical scheme is validated by a comparison with an explicit scheme of high accuracymore » (and unreasonably high cost). We present steady state solutions of the CHC equation in two and three dimensions. The effect of the thermal fluctuation on the spinodal decomposition process is studied. We show that the existence of the thermal fluctuation accelerates the spinodal decomposition process and that the final steady morphology is sensitive to the stochastic noise. We also show the evolution of the energies and statistical moments. In terms of the parallel performance, it is found that the implicit domain decomposition approach scales well on supercomputers with a large number of processors.« less

A high-order Lagrangian-decoupling method for the incompressible Navier-Stokes equations

NASA Technical Reports Server (NTRS)

Ho, Lee-Wing; Maday, Yvon; Patera, Anthony T.; Ronquist, Einar M.

1989-01-01

A high-order Lagrangian-decoupling method is presented for the unsteady convection-diffusion and incompressible Navier-Stokes equations. The method is based upon: (1) Lagrangian variational forms that reduce the convection-diffusion equation to a symmetric initial value problem; (2) implicit high-order backward-differentiation finite-difference schemes for integration along characteristics; (3) finite element or spectral element spatial discretizations; and (4) mesh-invariance procedures and high-order explicit time-stepping schemes for deducing function values at convected space-time points. The method improves upon previous finite element characteristic methods through the systematic and efficient extension to high order accuracy, and the introduction of a simple structure-preserving characteristic-foot calculation procedure which is readily implemented on modern architectures. The new method is significantly more efficient than explicit-convection schemes for the Navier-Stokes equations due to the decoupling of the convection and Stokes operators and the attendant increase in temporal stability. Numerous numerical examples are given for the convection-diffusion and Navier-Stokes equations for the particular case of a spectral element spatial discretization.

Development of the US3D Code for Advanced Compressible and Reacting Flow Simulations

NASA Technical Reports Server (NTRS)

Candler, Graham V.; Johnson, Heath B.; Nompelis, Ioannis; Subbareddy, Pramod K.; Drayna, Travis W.; Gidzak, Vladimyr; Barnhardt, Michael D.

2015-01-01

Aerothermodynamics and hypersonic flows involve complex multi-disciplinary physics, including finite-rate gas-phase kinetics, finite-rate internal energy relaxation, gas-surface interactions with finite-rate oxidation and sublimation, transition to turbulence, large-scale unsteadiness, shock-boundary layer interactions, fluid-structure interactions, and thermal protection system ablation and thermal response. Many of the flows have a large range of length and time scales, requiring large computational grids, implicit time integration, and large solution run times. The University of Minnesota NASA US3D code was designed for the simulation of these complex, highly-coupled flows. It has many of the features of the well-established DPLR code, but uses unstructured grids and has many advanced numerical capabilities and physical models for multi-physics problems. The main capabilities of the code are described, the physical modeling approaches are discussed, the different types of numerical flux functions and time integration approaches are outlined, and the parallelization strategy is overviewed. Comparisons between US3D and the NASA DPLR code are presented, and several advanced simulations are presented to illustrate some of novel features of the code.

Analysis of turbulent free jet hydrogen-air diffusion flames with finite chemical reaction rates

NASA Technical Reports Server (NTRS)

Sislian, J. P.

1978-01-01

The nonequilibrium flow field resulting from the turbulent mixing and combustion of a supersonic axisymmetric hydrogen jet in a supersonic parallel coflowing air stream is analyzed. Effective turbulent transport properties are determined using the (K-epsilon) model. The finite-rate chemistry model considers eight reactions between six chemical species, H, O, H2O, OH, O2, and H2. The governing set of nonlinear partial differential equations is solved by an implicit finite-difference procedure. Radial distributions are obtained at two downstream locations of variables such as turbulent kinetic energy, turbulent dissipation rate, turbulent scale length, and viscosity. The results show that these variables attain peak values at the axis of symmetry. Computed distributions of velocity, temperature, and mass fraction are also given. A direct analytical approach to account for the effect of species concentration fluctuations on the mean production rate of species (the phenomenon of unmixedness) is also presented. However, the use of the method does not seem justified in view of the excessive computer time required to solve the resulting system of equations.

A Penalty Method for the Numerical Solution of Hamilton-Jacobi-Bellman (HJB) Equations in Finance

NASA Astrophysics Data System (ADS)

Witte, J. H.; Reisinger, C.

2010-09-01

We present a simple and easy to implement method for the numerical solution of a rather general class of Hamilton-Jacobi-Bellman (HJB) equations. In many cases, the considered problems have only a viscosity solution, to which, fortunately, many intuitive (e.g. finite difference based) discretisations can be shown to converge. However, especially when using fully implicit time stepping schemes with their desireable stability properties, one is still faced with the considerable task of solving the resulting nonlinear discrete system. In this paper, we introduce a penalty method which approximates the nonlinear discrete system to an order of O(1/ρ), where ρ>0 is the penalty parameter, and we show that an iterative scheme can be used to solve the penalised discrete problem in finitely many steps. We include a number of examples from mathematical finance for which the described approach yields a rigorous numerical scheme and present numerical results.

Diffusion of test particles in stochastic magnetic fields for small Kubo numbers.

PubMed

Neuer, Marcus; Spatschek, Karl H

2006-02-01

Motion of charged particles in a collisional plasma with stochastic magnetic field lines is investigated on the basis of the so-called A-Langevin equation. Compared to the previously used A-Langevin model, here finite Larmor radius effects are taken into account. The A-Langevin equation is solved under the assumption that the Lagrangian correlation function for the magnetic field fluctuations is related to the Eulerian correlation function (in Gaussian form) via the Corrsin approximation. The latter is justified for small Kubo numbers. The velocity correlation function, being averaged with respect to the stochastic variables including collisions, leads to an implicit differential equation for the mean square displacement. From the latter, different transport regimes, including the well-known Rechester-Rosenbluth diffusion coefficient, are derived. Finite Larmor radius contributions show a decrease of the diffusion coefficient compared to the guiding center limit. The case of small (or vanishing) mean fields is also discussed.

Topology optimization of finite strain viscoplastic systems under transient loads [Dynamic topology optimization based on finite strain visco-plasticity

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

Ivarsson, Niklas; Wallin, Mathias; Tortorelli, Daniel

In this paper, a transient finite strain viscoplastic model is implemented in a gradient-based topology optimization framework to design impact mitigating structures. The model's kinematics relies on the multiplicative split of the deformation gradient, and the constitutive response is based on isotropic hardening viscoplasticity. To solve the mechanical balance laws, the implicit Newmark-beta method is used together with a total Lagrangian finite element formulation. The optimization problem is regularized using a partial differential equation filter and solved using the method of moving asymptotes. Sensitivities required to solve the optimization problem are derived using the adjoint method. To demonstrate the capabilitymore » of the algorithm, several protective systems are designed, in which the absorbed viscoplastic energy is maximized. Finally, the numerical examples demonstrate that transient finite strain viscoplastic effects can successfully be combined with topology optimization.« less

Topology optimization of finite strain viscoplastic systems under transient loads [Dynamic topology optimization based on finite strain visco-plasticity

DOE PAGES

Ivarsson, Niklas; Wallin, Mathias; Tortorelli, Daniel

2018-02-08

In this paper, a transient finite strain viscoplastic model is implemented in a gradient-based topology optimization framework to design impact mitigating structures. The model's kinematics relies on the multiplicative split of the deformation gradient, and the constitutive response is based on isotropic hardening viscoplasticity. To solve the mechanical balance laws, the implicit Newmark-beta method is used together with a total Lagrangian finite element formulation. The optimization problem is regularized using a partial differential equation filter and solved using the method of moving asymptotes. Sensitivities required to solve the optimization problem are derived using the adjoint method. To demonstrate the capabilitymore » of the algorithm, several protective systems are designed, in which the absorbed viscoplastic energy is maximized. Finally, the numerical examples demonstrate that transient finite strain viscoplastic effects can successfully be combined with topology optimization.« less

A Fourier collocation time domain method for numerically solving Maxwell's equations

NASA Technical Reports Server (NTRS)

Shebalin, John V.

1991-01-01

A new method for solving Maxwell's equations in the time domain for arbitrary values of permittivity, conductivity, and permeability is presented. Spatial derivatives are found by a Fourier transform method and time integration is performed using a second order, semi-implicit procedure. Electric and magnetic fields are collocated on the same grid points, rather than on interleaved points, as in the Finite Difference Time Domain (FDTD) method. Numerical results are presented for the propagation of a 2-D Transverse Electromagnetic (TEM) mode out of a parallel plate waveguide and into a dielectric and conducting medium.

A preliminary study of numerical simulation of thermosolutal convection of interest to crystal growth

NASA Technical Reports Server (NTRS)

Miller, T. L.

1984-01-01

Calculations were performed with computer models using three types of finite difference methods of thermosolutal convection: horizontal heating of a container filled with a stably stratified solution, finger convection in a container, and finger convection in a horizontally infinite channel. The importance of including thermosolutal convection in models of crystal growth is emphasized, and the difficulties in doing so are demonstrated. It is pointed out that these difficulties, due primarily to the fine structure of the convection, may be partly overcome by the use of fine grids and implicit time stepping methods.

Longitudinal curvature and displacement speed effects on incompressible laminar boundary layers.

NASA Technical Reports Server (NTRS)

Werle, M. J.; Wornom, S. F.

1972-01-01

The title problem is considered for the case of flow past a circular cylinder placed normal to a uniform mainstream with Reynolds numbers from 40 to 200. Implicit finite difference numerical solutions are obtained for a set of boundary-layer equations that account for the second order effects associated with surface curvature and displacement speed. It was found that both of these contributors have a significant influence on the internal structure of the viscous region and that an accurate estimate of the surface pressure distribution is essential for estimating the surface shear stress.

Computation of the shock-wave boundary layer interaction with flow separation

NASA Technical Reports Server (NTRS)

Ardonceau, P.; Alziary, T.; Aymer, D.

1980-01-01

The boundary layer concept is used to describe the flow near the wall. The external flow is approximated by a pressure displacement relationship (tangent wedge in linearized supersonic flow). The boundary layer equations are solved in finite difference form and the question of the presence and unicity of the solution is considered for the direct problem (assumed pressure) or converse problem (assumed displacement thickness, friction ratio). The coupling algorithm presented implicitly processes the downstream boundary condition necessary to correctly define the interacting boundary layer problem. The algorithm uses a Newton linearization technique to provide a fast convergence.

Direct Coupling Method for Time-Accurate Solution of Incompressible Navier-Stokes Equations

NASA Technical Reports Server (NTRS)

Soh, Woo Y.

1992-01-01

A noniterative finite difference numerical method is presented for the solution of the incompressible Navier-Stokes equations with second order accuracy in time and space. Explicit treatment of convection and diffusion terms and implicit treatment of the pressure gradient give a single pressure Poisson equation when the discretized momentum and continuity equations are combined. A pressure boundary condition is not needed on solid boundaries in the staggered mesh system. The solution of the pressure Poisson equation is obtained directly by Gaussian elimination. This method is tested on flow problems in a driven cavity and a curved duct.

IRMHD: an implicit radiative and magnetohydrodynamical solver for self-gravitating systems

NASA Astrophysics Data System (ADS)

Hujeirat, A.

1998-07-01

The 2D implicit hydrodynamical solver developed by Hujeirat & Rannacher is now modified to include the effects of radiation, magnetic fields and self-gravity in different geometries. The underlying numerical concept is based on the operator splitting approach, and the resulting 2D matrices are inverted using different efficient preconditionings such as ADI (alternating direction implicit), the approximate factorization method and Line-Gauss-Seidel or similar iteration procedures. Second-order finite volume with third-order upwinding and second-order time discretization is used. To speed up convergence and enhance efficiency we have incorporated an adaptive time-step control and monotonic multilevel grid distributions as well as vectorizing the code. Test calculations had shown that it requires only 38 per cent more computational effort than its explicit counterpart, whereas its range of application to astrophysical problems is much larger. For example, strongly time-dependent, quasi-stationary and steady-state solutions for the set of Euler and Navier-Stokes equations can now be sought on a non-linearly distributed and strongly stretched mesh. As most of the numerical techniques used to build up this algorithm have been described by Hujeirat & Rannacher in an earlier paper, we focus in this paper on the inclusion of self-gravity, radiation and magnetic fields. Strategies for satisfying the condition ∇.B=0 in the implicit evolution of MHD flows are given. A new discretization strategy for the vector potential which allows alternating use of the direct method is prescribed. We investigate the efficiencies of several 2D solvers for a Poisson-like equation and compare their convergence rates. We provide a splitting approach for the radiative flux within the FLD (flux-limited diffusion) approximation to enhance consistency and accuracy between regions of different optical depths. The results of some test problems are presented to demonstrate the accuracy and robustness of the code.

Analysis of Transformation Plasticity in Steel Using a Finite Element Method Coupled with a Phase Field Model

PubMed Central

Cho, Yi-Gil; Kim, Jin-You; Cho, Hoon-Hwe; Cha, Pil-Ryung; Suh, Dong-Woo; Lee, Jae Kon; Han, Heung Nam

2012-01-01

An implicit finite element model was developed to analyze the deformation behavior of low carbon steel during phase transformation. The finite element model was coupled hierarchically with a phase field model that could simulate the kinetics and micro-structural evolution during the austenite-to-ferrite transformation of low carbon steel. Thermo-elastic-plastic constitutive equations for each phase were adopted to confirm the transformation plasticity due to the weaker phase yielding that was proposed by Greenwood and Johnson. From the simulations under various possible plastic properties of each phase, a more quantitative understanding of the origin of transformation plasticity was attempted by a comparison with the experimental observation. PMID:22558295

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.

HYDRODYNAMIC SIMULATION OF THE UPPER POTOMAC ESTUARY.

USGS Publications Warehouse

Schaffranck, Raymond W.

1986-01-01

Hydrodynamics of the upper extent of the Potomac Estuary between Indian Head and Morgantown, Md. , are simulated using a two-dimensional model. The model computes water-surface elevations and depth-averaged velocities by numerically integrating finite-difference forms of the equations of mass and momentum conservation using the alternating direction implicit method. The fundamental, non-linear, unsteady-flow equations, upon which the model is formulated, include additional terms to account for Coriolis acceleration and meteorological influences. Preliminary model/prototype data comparisons show agreement to within 9% for tidal flow volumes and phase differences within the measured-data-recording interval. Use of the model to investigate the hydrodynamics and certain aspects of transport within this Potomac Estuary reach is demonstrated. Refs.

Numerical simulation of weakly ionized hypersonic flow over reentry capsules

NASA Astrophysics Data System (ADS)

Scalabrin, Leonardo C.

The mathematical and numerical formulation employed in the development of a new multi-dimensional Computational Fluid Dynamics (CFD) code for the simulation of weakly ionized hypersonic flows in thermo-chemical non-equilibrium over reentry configurations is presented. The flow is modeled using the Navier-Stokes equations modified to include finite-rate chemistry and relaxation rates to compute the energy transfer between different energy modes. The set of equations is solved numerically by discretizing the flowfield using unstructured grids made of any mixture of quadrilaterals and triangles in two-dimensions or hexahedra, tetrahedra, prisms and pyramids in three-dimensions. The partial differential equations are integrated on such grids using the finite volume approach. The fluxes across grid faces are calculated using a modified form of the Steger-Warming Flux Vector Splitting scheme that has low numerical dissipation inside boundary layers. The higher order extension of inviscid fluxes in structured grids is generalized in this work to be used in unstructured grids. Steady state solutions are obtained by integrating the solution over time implicitly. The resulting sparse linear system is solved by using a point implicit or by a line implicit method in which a tridiagonal matrix is assembled by using lines of cells that are formed starting at the wall. An algorithm that assembles these lines using completely general unstructured grids is developed. The code is parallelized to allow simulation of computationally demanding problems. The numerical code is successfully employed in the simulation of several hypersonic entry flows over space capsules as part of its validation process. Important quantities for the aerothermodynamics design of capsules such as aerodynamic coefficients and heat transfer rates are compared to available experimental and flight test data and other numerical results yielding very good agreement. A sensitivity analysis of predicted radiative heating of a space capsule to several thermo-chemical non-equilibrium models is also performed.

An interacting boundary layer model for cascades

NASA Technical Reports Server (NTRS)

Davis, R. T.; Rothmayer, A. P.

1983-01-01

A laminar, incompressible interacting boundary layer model is developed for two-dimensional cascades. In the limit of large cascade spacing these equations reduce to the interacting boundary layer equations for a single body immersed in an infinite stream. A fully implicit numerical method is used to solve the governing equations, and is found to be at least as efficient as the same technique applied to the single body problem. Solutions are then presented for a cascade of finite flat plates and a cascade of finite sine-waves, with cusped leading and trailing edges.

Computational simulation of laser heat processing of materials

NASA Astrophysics Data System (ADS)

Shankar, Vijaya; Gnanamuthu, Daniel

1987-04-01

A computational model simulating the laser heat treatment of AISI 4140 steel plates with a CW CO2 laser beam has been developed on the basis of the three-dimensional, time-dependent heat equation (subject to the appropriate boundary conditions). The solution method is based on Newton iteration applied to a triple-approximate factorized form of the equation. The method is implicit and time-accurate; the maintenance of time-accuracy in the numerical formulation is noted to be critical for the simulation of finite length workpieces with a finite laser beam dwell time.

The Crank Nicolson Time Integrator for EMPHASIS.

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

McGregor, Duncan Alisdair Odum; Love, Edward; Kramer, Richard Michael Jack

2018-03-01

We investigate the use of implicit time integrators for finite element time domain approxi- mations of Maxwell's equations in vacuum. We discretize Maxwell's equations in time using Crank-Nicolson and in 3D space using compatible finite elements. We solve the system by taking a single step of Newton's method and inverting the Eddy-Current Schur complement allowing for the use of standard preconditioning techniques. This approach also generalizes to more complex material models that can include the Unsplit PML. We present verification results and demonstrate performance at CFL numbers up to 1000.

Application of a lower-upper implicit scheme and an interactive grid generation for turbomachinery flow field simulations

NASA Technical Reports Server (NTRS)

Choo, Yung K.; Soh, Woo-Yung; Yoon, Seokkwan

1989-01-01

A finite-volume lower-upper (LU) implicit scheme is used to simulate an inviscid flow in a tubine cascade. This approximate factorization scheme requires only the inversion of sparse lower and upper triangular matrices, which can be done efficiently without extensive storage. As an implicit scheme it allows a large time step to reach the steady state. An interactive grid generation program (TURBO), which is being developed, is used to generate grids. This program uses the control point form of algebraic grid generation which uses a sparse collection of control points from which the shape and position of coordinate curves can be adjusted. A distinct advantage of TURBO compared with other grid generation programs is that it allows the easy change of local mesh structure without affecting the grid outside the domain of independence. Sample grids are generated by TURBO for a compressor rotor blade and a turbine cascade. The turbine cascade flow is simulated by using the LU implicit scheme on the grid generated by TURBO.

A finite deformation viscoelastic-viscoplastic constitutive model for self-healing materials

NASA Astrophysics Data System (ADS)

Shahsavari, H.; Naghdabadi, R.; Baghani, M.; Sohrabpour, S.

2016-12-01

In this paper, employing the Hencky strain, viscoelastic-viscoplastic response of self-healing materials is investigated. Considering the irreversible thermodynamics and using the effective configuration in the Continuum Damage-Healing Mechanics (CDHM), a phenomenological finite strain viscoelastic-viscoplastic constitutive model is presented. Considering finite viscoelastic and viscoplastic deformations, total deformation gradient is multiplicatively decomposed into viscoelastic and viscoplastic parts. Due to mathematical advantages and physical meaning of Hencky strain, this measure of strain is employed in the constitutive model development. In this regard, defining the damage and healing variables and employing the strain equivalence hypothesis, the strain tensor is determined in the effective configuration. Satisfying the Clausius-Duhem inequality, the evolution equations are introduced for the viscoelastic and viscoplastic strains. The damage and healing variables also evolve according to two different prescribed functions. To employ the proposed model in different loading conditions, the model is discretized in the semi-implicit form. Material parameters of the model are identified employing experimental tests on asphalt mixes available in the literature. Finally, capability of the model is demonstrated comparing the model predictions in the creep-recovery and repeated creep-recovery with the experimental results available in the literature and a good agreement between predicted and test results is revealed.

Sierra/Solid Mechanics 4.48 User's Guide.

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

Merewether, Mark Thomas; Crane, Nathan K; de Frias, Gabriel Jose

Sierra/SolidMechanics (Sierra/SM) is a Lagrangian, three-dimensional code for finite element analysis of solids and structures. It provides capabilities for explicit dynamic, implicit quasistatic and dynamic analyses. The explicit dynamics capabilities allow for the efficient and robust solution of models with extensive contact subjected to large, suddenly applied loads. For implicit problems, Sierra/SM uses a multi-level iterative solver, which enables it to effectively solve problems with large deformations, nonlinear material behavior, and contact. Sierra/SM has a versatile library of continuum and structural elements, and a large library of material models. The code is written for parallel computing environments enabling scalable solutionsmore » of extremely large problems for both implicit and explicit analyses. It is built on the SIERRA Framework, which facilitates coupling with other SIERRA mechanics codes. This document describes the functionality and input syntax for Sierra/SM.« less

Investigation of supersonic chemically reacting and radiating channel flow

NASA Technical Reports Server (NTRS)

Mani, Mortaza; Tiwari, Surendra N.

1988-01-01

The 2-D time-dependent Navier-Stokes equations are used to investigate supersonic flows undergoing finite rate chemical reaction and radiation interaction for a hydrogen-air system. The explicit multistage finite volume technique of Jameson is used to advance the governing equations in time until convergence is achieved. The chemistry source term in the species equation is treated implicitly to alleviate the stiffness associated with fast reactions. The multidimensional radiative transfer equations for a nongray model are provided for a general configuration and then reduced for a planar geometry. Both pseudo-gray and nongray models are used to represent the absorption-emission characteristics of the participating species. The supersonic inviscid and viscous, nonreacting flows are solved by employing the finite volume technique of Jameson and the unsplit finite difference scheme of MacCormack. The specified problem considered is of the flow in a channel with a 10 deg compression-expansion ramp. The calculated results are compared with those of an upwind scheme. The problem of chemically reacting and radiating flows are solved for the flow of premixed hydrogen-air through a channel with parallel boundaries, and a channel with a compression corner. Results obtained for specific conditions indicate that the radiative interaction can have a significant influence on the entire flow field.

Finite element structural redesign by large admissible perturbations

NASA Technical Reports Server (NTRS)

Bernitsas, Michael M.; Beyko, E.; Rim, C. W.; Alzahabi, B.

1991-01-01

In structural redesign, two structural states are involved; the baseline (known) State S1 with unacceptable performance, and the objective (unknown) State S2 with given performance specifications. The difference between the two states in performance and design variables may be as high as 100 percent or more depending on the scale of the structure. A Perturbation Approach to Redesign (PAR) is presented to relate any two structural states S1 and S2 that are modeled by the same finite element model and represented by different values of the design variables. General perturbation equations are derived expressing implicitly the natural frequencies, dynamic modes, static deflections, static stresses, Euler buckling loads, and buckling modes of the objective S2 in terms of its performance specifications, and S1 data and Finite Element Analysis (FEA) results. Large Admissible Perturbation (LEAP) algorithms are implemented in code RESTRUCT to define the objective S2 incrementally without trial and error by postprocessing FEA results of S1 with no additional FEAs. Systematic numerical applications in redesign of a 10 element 48 degree of freedom (dof) beam, a 104 element 192 dof offshore tower, a 64 element 216 dof plate, and a 144 element 896 dof cylindrical shell show the accuracy, efficiency, and potential of PAR to find an objective state that may differ 100 percent from the baseline design.

How to choose a subset of frequencies in frequency-domain finite-difference migration

NASA Astrophysics Data System (ADS)

Mulder, W. A.; Plessix, R.-E.

2004-09-01

Finite-difference migration with the two-way wave equation can be accelerated by an order of magnitude if the frequency domain rather than the time domain is used. This gain is mainly accomplished by using a subset of the available frequencies. The implicit assumption is that the data have a certain amount of redundancy in the frequency domain. The choice of frequencies cannot be arbitrary. If the frequencies are chosen with a constant increment and their spacing is too large, the well-known wrap-around that occurs when transforming back to the time domain will also show up in the migration to the depth domain, albeit in a more subtle way. Because migration involves propagation in a given background velocity model and summation over shots and receivers, the effects of wrap-around may disappear even when the Nyquist theorem is not obeyed. We have studied these effects analytically for the constant-velocity case and determined sampling conditions that avoid wrap-around artefacts. The conditions depend on the velocity, depth of the migration grid and offset range. They show that the spacing between subsequent frequencies can be larger than the inverse of the time range prescribed by the Nyquist theorem. A 2-D example has been used to test the validity of these conditions for a more realistic velocity model. Finite-difference migration with the one-way wave equation shows a similar behaviour.

Topology optimization of finite strain viscoplastic systems under transient loads

DOE PAGES

Ivarsson, Niklas; Wallin, Mathias; Tortorelli, Daniel

2018-02-08

In this paper, a transient finite strain viscoplastic model is implemented in a gradient-based topology optimization framework to design impact mitigating structures. The model's kinematics relies on the multiplicative split of the deformation gradient, and the constitutive response is based on isotropic hardening viscoplasticity. To solve the mechanical balance laws, the implicit Newmark-beta method is used together with a total Lagrangian finite element formulation. The optimization problem is regularized using a partial differential equation filter and solved using the method of moving asymptotes. Sensitivities required to solve the optimization problem are derived using the adjoint method. To demonstrate the capabilitymore » of the algorithm, several protective systems are designed, in which the absorbed viscoplastic energy is maximized. Finally, the numerical examples demonstrate that transient finite strain viscoplastic effects can successfully be combined with topology optimization.« less

On finite element implementation and computational techniques for constitutive modeling of high temperature composites

NASA Technical Reports Server (NTRS)

Saleeb, A. F.; Chang, T. Y. P.; Wilt, T.; Iskovitz, I.

1989-01-01

The research work performed during the past year on finite element implementation and computational techniques pertaining to high temperature composites is outlined. In the present research, two main issues are addressed: efficient geometric modeling of composite structures and expedient numerical integration techniques dealing with constitutive rate equations. In the first issue, mixed finite elements for modeling laminated plates and shells were examined in terms of numerical accuracy, locking property and computational efficiency. Element applications include (currently available) linearly elastic analysis and future extension to material nonlinearity for damage predictions and large deformations. On the material level, various integration methods to integrate nonlinear constitutive rate equations for finite element implementation were studied. These include explicit, implicit and automatic subincrementing schemes. In all cases, examples are included to illustrate the numerical characteristics of various methods that were considered.

High-Order Finite-Difference Schemes for Numerical Simulation of Hypersonic Boundary-Layer Transition

NASA Astrophysics Data System (ADS)

Zhong, Xiaolin

1998-08-01

Direct numerical simulation (DNS) has become a powerful tool in studying fundamental phenomena of laminar-turbulent transition of high-speed boundary layers. Previous DNS studies of supersonic and hypersonic boundary layer transition have been limited to perfect-gas flow over flat-plate boundary layers without shock waves. For hypersonic boundary layers over realistic blunt bodies, DNS studies of transition need to consider the effects of bow shocks, entropy layers, surface curvature, and finite-rate chemistry. It is necessary that numerical methods for such studies are robust and high-order accurate both in resolving wide ranges of flow time and length scales and in resolving the interaction between the bow shocks and flow disturbance waves. This paper presents a new high-order shock-fitting finite-difference method for the DNS of the stability and transition of hypersonic boundary layers over blunt bodies with strong bow shocks and with (or without) thermo-chemical nonequilibrium. The proposed method includes a set of new upwind high-order finite-difference schemes which are stable and are less dissipative than a straightforward upwind scheme using an upwind-bias grid stencil, a high-order shock-fitting formulation, and third-order semi-implicit Runge-Kutta schemes for temporal discretization of stiff reacting flow equations. The accuracy and stability of the new schemes are validated by numerical experiments of the linear wave equation and nonlinear Navier-Stokes equations. The algorithm is then applied to the DNS of the receptivity of hypersonic boundary layers over a parabolic leading edge to freestream acoustic disturbances.

Evaluation of the UnTRIM model for 3-D tidal circulation

USGS Publications Warehouse

Cheng, R.T.; Casulli, V.; ,

2001-01-01

A family of numerical models, known as the TRIM models, shares the same modeling philosophy for solving the shallow water equations. A characteristic analysis of the shallow water equations points out that the numerical instability is controlled by the gravity wave terms in the momentum equations and by the transport terms in the continuity equation. A semi-implicit finite-difference scheme has been formulated so that these terms and the vertical diffusion terms are treated implicitly and the remaining terms explicitly to control the numerical stability and the computations are carried out over a uniform finite-difference computational mesh without invoking horizontal or vertical coordinate transformations. An unstructured grid version of TRIM model is introduced, or UnTRIM (pronounces as "you trim"), which preserves these basic numerical properties and modeling philosophy, only the computations are carried out over an unstructured orthogonal grid. The unstructured grid offers the flexibilities in representing complex study areas so that fine grid resolution can be placed in regions of interest, and coarse grids are used to cover the remaining domain. Thus, the computational efforts are concentrated in areas of importance, and an overall computational saving can be achieved because the total number of grid-points is dramatically reduced. To use this modeling approach, an unstructured grid mesh must be generated to properly reflect the properties of the domain of the investigation. The new modeling flexibility in grid structure is accompanied by new challenges associated with issues of grid generation. To take full advantage of this new model flexibility, the model grid generation should be guided by insights into the physics of the problems; and the insights needed may require a higher degree of modeling skill.

PIXIE3D: A Parallel, Implicit, eXtended MHD 3D Code.

NASA Astrophysics Data System (ADS)

Chacon, L.; Knoll, D. A.

2004-11-01

We report on the development of PIXIE3D, a 3D parallel, fully implicit Newton-Krylov extended primitive-variable MHD code in general curvilinear geometry. PIXIE3D employs a second-order, finite-volume-based spatial discretization that satisfies remarkable properties such as being conservative, solenoidal in the magnetic field, non-dissipative, and stable in the absence of physical dissipation.(L. Chacón , phComput. Phys. Comm.) submitted (2004) PIXIE3D employs fully-implicit Newton-Krylov methods for the time advance. Currently, first and second-order implicit schemes are available, although higher-order temporal implicit schemes can be effortlessly implemented within the Newton-Krylov framework. A successful, scalable, MG physics-based preconditioning strategy, similar in concept to previous 2D MHD efforts,(L. Chacón et al., phJ. Comput. Phys). 178 (1), 15- 36 (2002); phJ. Comput. Phys., 188 (2), 573-592 (2003) has been developed. We are currently in the process of parallelizing the code using the PETSc library, and a Newton-Krylov-Schwarz approach for the parallel treatment of the preconditioner. In this poster, we will report on both the serial and parallel performance of PIXIE3D, focusing primarily on scalability and CPU speedup vs. an explicit approach.

Benchmark solution of the dynamic response of a spherical shell at finite strain

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

Versino, Daniele; Brock, Jerry S.

2016-09-28

Our paper describes the development of high fidelity solutions for the study of homogeneous (elastic and inelastic) spherical shells subject to dynamic loading and undergoing finite deformations. The goal of the activity is to provide high accuracy results that can be used as benchmark solutions for the verification of computational physics codes. Furthermore, the equilibrium equations for the geometrically non-linear problem are solved through mode expansion of the displacement field and the boundary conditions are enforced in a strong form. Time integration is performed through high-order implicit Runge–Kutta schemes. Finally, we evaluate accuracy and convergence of the proposed method bymore » means of numerical examples with finite deformations and material non-linearities and inelasticity.« less

SMAUMAT_ITI

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

Jannetti, C.; Becker, R.

The software is an ABAQUS/Standard UMAT (user defined material behavior subroutine) that implements the constitutive model for shape-memory alloy materials developed by Jannetti et. al. (2003a) using a fully implicit time integration scheme to integrate the constitutive equations. The UMAT is used in conjunction with ABAQUS/Standard to perform a finite-element analysis of SMA materials.

A fully implicit finite element method for bidomain models of cardiac electromechanics

PubMed Central

Dal, Hüsnü; Göktepe, Serdar; Kaliske, Michael; Kuhl, Ellen

2012-01-01

We propose a novel, monolithic, and unconditionally stable finite element algorithm for the bidomain-based approach to cardiac electromechanics. We introduce the transmembrane potential, the extracellular potential, and the displacement field as independent variables, and extend the common two-field bidomain formulation of electrophysiology to a three-field formulation of electromechanics. The intrinsic coupling arises from both excitation-induced contraction of cardiac cells and the deformation-induced generation of intra-cellular currents. The coupled reaction-diffusion equations of the electrical problem and the momentum balance of the mechanical problem are recast into their weak forms through a conventional isoparametric Galerkin approach. As a novel aspect, we propose a monolithic approach to solve the governing equations of excitation-contraction coupling in a fully coupled, implicit sense. We demonstrate the consistent linearization of the resulting set of non-linear residual equations. To assess the algorithmic performance, we illustrate characteristic features by means of representative three-dimensional initial-boundary value problems. The proposed algorithm may open new avenues to patient specific therapy design by circumventing stability and convergence issues inherent to conventional staggered solution schemes. PMID:23175588

An analysis for high Reynolds number inviscid/viscid interactions in cascades

NASA Technical Reports Server (NTRS)

Barnett, Mark; Verdon, Joseph M.; Ayer, Timothy C.

1993-01-01

An efficient steady analysis for predicting strong inviscid/viscid interaction phenomena such as viscous-layer separation, shock/boundary-layer interaction, and trailing-edge/near-wake interaction in turbomachinery blade passages is needed as part of a comprehensive analytical blade design prediction system. Such an analysis is described. It uses an inviscid/viscid interaction approach, in which the flow in the outer inviscid region is assumed to be potential, and that in the inner or viscous-layer region is governed by Prandtl's equations. The inviscid solution is determined using an implicit, least-squares, finite-difference approximation, the viscous-layer solution using an inverse, finite-difference, space-marching method which is applied along the blade surfaces and wake streamlines. The inviscid and viscid solutions are coupled using a semi-inverse global iteration procedure, which permits the prediction of boundary-layer separation and other strong-interaction phenomena. Results are presented for three cascades, with a range of inlet flow conditions considered for one of them, including conditions leading to large-scale flow separations. Comparisons with Navier-Stokes solutions and experimental data are also given.

Transpiration and film cooling boundary layer computer program. Volume 1: Numerical solutions of the turbulent boundary layer equations with equilibrium chemistry

NASA Technical Reports Server (NTRS)

Levine, J. N.

1971-01-01

A finite difference turbulent boundary layer computer program has been developed. The program is primarily oriented towards the calculation of boundary layer performance losses in rocket engines; however, the solution is general, and has much broader applicability. The effects of transpiration and film cooling as well as the effect of equilibrium chemical reactions (currently restricted to the H2-O2 system) can be calculated. The turbulent transport terms are evaluated using the phenomenological mixing length - eddy viscosity concept. The equations of motion are solved using the Crank-Nicolson implicit finite difference technique. The analysis and computer program have been checked out by solving a series of both laminar and turbulent test cases and comparing the results to data or other solutions. These comparisons have shown that the program is capable of producing very satisfactory results for a wide range of flows. Further refinements to the analysis and program, especially as applied to film cooling solutions, would be aided by the acquisition of a firm data base.

Unconditionally stable finite-difference time-domain methods for modeling the Sagnac effect

NASA Astrophysics Data System (ADS)

Novitski, Roman; Scheuer, Jacob; Steinberg, Ben Z.

2013-02-01

We present two unconditionally stable finite-difference time-domain (FDTD) methods for modeling the Sagnac effect in rotating optical microsensors. The methods are based on the implicit Crank-Nicolson scheme, adapted to hold in the rotating system reference frame—the rotating Crank-Nicolson (RCN) methods. The first method (RCN-2) is second order accurate in space whereas the second method (RCN-4) is fourth order accurate. Both methods are second order accurate in time. We show that the RCN-4 scheme is more accurate and has better dispersion isotropy. The numerical results show good correspondence with the expression for the classical Sagnac resonant frequency splitting when using group refractive indices of the resonant modes of a microresonator. Also we show that the numerical results are consistent with the perturbation theory for the rotating degenerate microcavities. We apply our method to simulate the effect of rotation on an entire Coupled Resonator Optical Waveguide (CROW) consisting of a set of coupled microresonators. Preliminary results validate the formation of a rotation-induced gap at the center of a transfer function of a CROW.

Assessment of a 3-D boundary layer code to predict heat transfer and flow losses in a turbine

NASA Technical Reports Server (NTRS)

Anderson, O. L.

1984-01-01

Zonal concepts are utilized to delineate regions of application of three-dimensional boundary layer (DBL) theory. The zonal approach requires three distinct analyses. A modified version of the 3-DBL code named TABLET is used to analyze the boundary layer flow. This modified code solves the finite difference form of the compressible 3-DBL equations in a nonorthogonal surface coordinate system which includes coriolis forces produced by coordinate rotation. These equations are solved using an efficient, implicit, fully coupled finite difference procedure. The nonorthogonal surface coordinate system is calculated using a general analysis based on the transfinite mapping of Gordon which is valid for any arbitrary surface. Experimental data is used to determine the boundary layer edge conditions. The boundary layer edge conditions are determined by integrating the boundary layer edge equations, which are the Euler equations at the edge of the boundary layer, using the known experimental wall pressure distribution. Starting solutions along the inflow boundaries are estimated by solving the appropriate limiting form of the 3-DBL equations.

Assessing a mini-application as a performance proxy for a finite element method engineering application

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

Lin, Paul T.; Heroux, Michael A.; Barrett, Richard F.

The performance of a large-scale, production-quality science and engineering application (‘app’) is often dominated by a small subset of the code. Even within that subset, computational and data access patterns are often repeated, so that an even smaller portion can represent the performance-impacting features. If application developers, parallel computing experts, and computer architects can together identify this representative subset and then develop a small mini-application (‘miniapp’) that can capture these primary performance characteristics, then this miniapp can be used to both improve the performance of the app as well as provide a tool for co-design for the high-performance computing community.more » However, a critical question is whether a miniapp can effectively capture key performance behavior of an app. This study provides a comparison of an implicit finite element semiconductor device modeling app on unstructured meshes with an implicit finite element miniapp on unstructured meshes. The goal is to assess whether the miniapp is predictive of the performance of the app. Finally, single compute node performance will be compared, as well as scaling up to 16,000 cores. Results indicate that the miniapp can be reasonably predictive of the performance characteristics of the app for a single iteration of the solver on a single compute node.« less

Assessing a mini-application as a performance proxy for a finite element method engineering application

DOE PAGES

Lin, Paul T.; Heroux, Michael A.; Barrett, Richard F.; ...

2015-07-30

The performance of a large-scale, production-quality science and engineering application (‘app’) is often dominated by a small subset of the code. Even within that subset, computational and data access patterns are often repeated, so that an even smaller portion can represent the performance-impacting features. If application developers, parallel computing experts, and computer architects can together identify this representative subset and then develop a small mini-application (‘miniapp’) that can capture these primary performance characteristics, then this miniapp can be used to both improve the performance of the app as well as provide a tool for co-design for the high-performance computing community.more » However, a critical question is whether a miniapp can effectively capture key performance behavior of an app. This study provides a comparison of an implicit finite element semiconductor device modeling app on unstructured meshes with an implicit finite element miniapp on unstructured meshes. The goal is to assess whether the miniapp is predictive of the performance of the app. Finally, single compute node performance will be compared, as well as scaling up to 16,000 cores. Results indicate that the miniapp can be reasonably predictive of the performance characteristics of the app for a single iteration of the solver on a single compute node.« less

Finite time step and spatial grid effects in δf simulation of warm plasmas

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

Sturdevant, Benjamin J., E-mail: benjamin.j.sturdevant@gmail.com; Department of Applied Mathematics, University of Colorado at Boulder, Boulder, CO 80309; Parker, Scott E.

2016-01-15

This paper introduces a technique for analyzing time integration methods used with the particle weight equations in δf method particle-in-cell (PIC) schemes. The analysis applies to the simulation of warm, uniform, periodic or infinite plasmas in the linear regime and considers the collective behavior similar to the analysis performed by Langdon for full-f PIC schemes [1,2]. We perform both a time integration analysis and spatial grid analysis for a kinetic ion, adiabatic electron model of ion acoustic waves. An implicit time integration scheme is studied in detail for δf simulations using our weight equation analysis and for full-f simulations usingmore » the method of Langdon. It is found that the δf method exhibits a CFL-like stability condition for low temperature ions, which is independent of the parameter characterizing the implicitness of the scheme. The accuracy of the real frequency and damping rate due to the discrete time and spatial schemes is also derived using a perturbative method. The theoretical analysis of numerical error presented here may be useful for the verification of simulations and for providing intuition for the design of new implicit time integration schemes for the δf method, as well as understanding differences between δf and full-f approaches to plasma simulation.« less

A modified dodge algorithm for the parabolized Navier-Stokes equations and compressible duct flows

NASA Technical Reports Server (NTRS)

Cooke, C. H.

1981-01-01

A revised version of a split-velocity method for numerical calculation of compressible duct flow was developed. The revision incorporates balancing of mass flow rates on each marching step in order to maintain front-to-back continuity during the calculation. The (checkerboard) zebra algorithm is applied to solution of the three-dimensional continuity equation in conservative form. A second-order A-stable linear multistep method is employed in effecting a marching solution of the parabolized momentum equations. A checkerboard successive overrelaxation iteration is used to solve the resulting implicit nonlinear systems of finite-difference equations which govern stepwise transition.

Numerical solutions of 2-D multi-stage rotor/stator unsteady flow interactions

NASA Astrophysics Data System (ADS)

Yang, R.-J.; Lin, S.-J.

1991-01-01

The Rai method of single-stage rotor/stator flow interaction is extended to handle multistage configurations. In this study, a two-dimensional Navier-Stokes multi-zone approach was used to investigate unsteady flow interactions within two multistage axial turbines. The governing equations are solved by an iterative, factored, implicit finite-difference, upwind algorithm. Numerical accuracy is checked by investigating the effect of time step size, the effect of subiteration in the Newton-Raphson technique, and the effect of full viscous versus thin-layer approximation. Computer results compared well with experimental data. Unsteady flow interactions, wake cutting, and the associated evolution of vortical entities are discussed.

Aerothermodynamic shape optimization of hypersonic blunt bodies

NASA Astrophysics Data System (ADS)

Eyi, Sinan; Yumuşak, Mine

2015-07-01

The aim of this study is to develop a reliable and efficient design tool that can be used in hypersonic flows. The flow analysis is based on the axisymmetric Euler/Navier-Stokes and finite-rate chemical reaction equations. The equations are coupled simultaneously and solved implicitly using Newton's method. The Jacobian matrix is evaluated analytically. A gradient-based numerical optimization is used. The adjoint method is utilized for sensitivity calculations. The objective of the design is to generate a hypersonic blunt geometry that produces the minimum drag with low aerodynamic heating. Bezier curves are used for geometry parameterization. The performances of the design optimization method are demonstrated for different hypersonic flow conditions.

Supersonic quasi-axisymmetric vortex breakdown

NASA Technical Reports Server (NTRS)

Kandil, Osama A.; Kandil, Hamdy A.; Liu, C. H.

1991-01-01

An extensive computational study of supersonic quasi-axisymmetric vortex breakdown in a configured circular duct is presented. The unsteady, compressible, full Navier-Stokes (NS) equations are used. The NS equations are solved for the quasi-axisymmetric flows using an implicit, upwind, flux difference splitting, finite volume scheme. The quasi-axisymmetric solutions are time accurate and are obtained by forcing the components of the flowfield vector to be equal on two axial planes, which are in close proximity of each other. The effect of Reynolds number, for laminar flows, on the evolution and persistence of vortex breakdown, is studied. Finally, the effect of swirl ration at the duct inlet is investigated.

Analysis of viscous transonic flow over airfoil sections

NASA Technical Reports Server (NTRS)

Huff, Dennis L.; Wu, Jiunn-Chi; Sankar, L. N.

1987-01-01

A full Navier-Stokes solver has been used to model transonic flow over three airfoil sections. The method uses a two-dimensional, implicit, conservative finite difference scheme for solving the compressible Navier-Stokes equations. Results are presented as prescribed for the Viscous Transonic Airfoil Workshop to be held at the AIAA 25th Aerospace Sciences Meeting. The NACA 0012, RAE 2822 and Jones airfoils have been investigated for both attached and separated transonic flows. Predictions for pressure distributions, loads, skin friction coefficients, boundary layer displacement thickness and velocity profiles are included and compared with experimental data when possible. Overall, the results are in good agreement with experimental data.

Aerodynamic Design on Unstructured Grids for Turbulent Flows

NASA Technical Reports Server (NTRS)

Anderson, W. Kyle; Bonhaus, Daryl L.

1997-01-01

An aerodynamic design algorithm for turbulent flows using unstructured grids is described. The current approach uses adjoint (costate) variables for obtaining derivatives of the cost function. The solution of the adjoint equations is obtained using an implicit formulation in which the turbulence model is fully coupled with the flow equations when solving for the costate variables. The accuracy of the derivatives is demonstrated by comparison with finite-difference gradients and a few example computations are shown. In addition, a user interface is described which significantly reduces the time required for setting up the design problems. Recommendations on directions of further research into the Navier Stokes design process are made.

Three-Dimensional Flow of Nanofluid Induced by an Exponentially Stretching Sheet: An Application to Solar Energy

PubMed Central

Khan, Junaid Ahmad; Mustafa, M.; Hayat, T.; Sheikholeslami, M.; Alsaedi, A.

2015-01-01

This work deals with the three-dimensional flow of nanofluid over a bi-directional exponentially stretching sheet. The effects of Brownian motion and thermophoretic diffusion of nanoparticles are considered in the mathematical model. The temperature and nanoparticle volume fraction at the sheet are also distributed exponentially. Local similarity solutions are obtained by an implicit finite difference scheme known as Keller-box method. The results are compared with the existing studies in some limiting cases and found in good agreement. The results reveal the existence of interesting Sparrow-Gregg-type hills for temperature distribution corresponding to some range of parametric values. PMID:25785857

MagIC: Fluid dynamics in a spherical shell simulator

NASA Astrophysics Data System (ADS)

Wicht, J.; Gastine, T.; Barik, A.; Putigny, B.; Yadav, R.; Duarte, L.; Dintrans, B.

2017-09-01

MagIC simulates fluid dynamics in a spherical shell. It solves for the Navier-Stokes equation including Coriolis force, optionally coupled with an induction equation for Magneto-Hydro Dynamics (MHD), a temperature (or entropy) equation and an equation for chemical composition under both the anelastic and the Boussinesq approximations. MagIC uses either Chebyshev polynomials or finite differences in the radial direction and spherical harmonic decomposition in the azimuthal and latitudinal directions. The time-stepping scheme relies on a semi-implicit Crank-Nicolson for the linear terms of the MHD equations and a Adams-Bashforth scheme for the non-linear terms and the Coriolis force.

Numerical simulation of two-dimensional heat transfer in composite bodies with application to de-icing of aircraft components. Ph.D. Thesis. Final Report

NASA Technical Reports Server (NTRS)

Chao, D. F. K.

1983-01-01

Transient, numerical simulations of the de-icing of composite aircraft components by electrothermal heating were performed for a two dimensional rectangular geometry. The implicit Crank-Nicolson formulation was used to insure stability of the finite-difference heat conduction equations and the phase change in the ice layer was simulated using the Enthalpy method. The Gauss-Seidel point iterative method was used to solve the system of difference equations. Numerical solutions illustrating de-icer performance for various composite aircraft structures and environmental conditions are presented. Comparisons are made with previous studies. The simulation can also be used to solve a variety of other heat conduction problems involving composite bodies.

On a phase field approach for martensitic transformations in a crystal plastic material at a loaded surface

NASA Astrophysics Data System (ADS)

Schmitt, Regina; Kuhn, Charlotte; Müller, Ralf

2017-07-01

A continuum phase field model for martensitic transformations is introduced, including crystal plasticity with different slip systems for the different phases. In a 2D setting, the transformation-induced eigenstrain is taken into account for two martensitic orientation variants. With aid of the model, the phase transition and its dependence on the volume change, crystal plastic material behavior, and the inheritance of plastic deformations from austenite to martensite are studied in detail. The numerical setup is motivated by the process of cryogenic turning. The resulting microstructure qualitatively coincides with an experimentally obtained martensite structure. For the numerical calculations, finite elements together with global and local implicit time integration scheme are employed.

Aerothermodynamic environment of a Titan aerocapture vehicle

NASA Technical Reports Server (NTRS)

Tiwari, S. N.; Chow, H.

1982-01-01

The extent of convective and radiative heating for a Titan aerocapture vehicle is investigated. The flow in the shock layer is assumed to be axisymmetric, steady, viscous, and compressible. It is further assumed that the gas is in chemical and local thermodynamic equilibrium and tangent slab approximation is used for the radiative transport. The effect of the slip boundary conditions on the body surface and at the shock wave are included in the analysis of high-altitude entry conditions. The implicit finite difference techniques is used to solve the viscous shock-layer equations for a 45 degree sphere cone at zero angle of attack. Different compositions for the Titan atmosphere are assumed, and results are obtained for the entry conditions specified by the Jet Propulsion Laboratory.

Adaptive macro finite elements for the numerical solution of monodomain equations in cardiac electrophysiology.

PubMed

Heidenreich, Elvio A; Ferrero, José M; Doblaré, Manuel; Rodríguez, José F

2010-07-01

Many problems in biology and engineering are governed by anisotropic reaction-diffusion equations with a very rapidly varying reaction term. This usually implies the use of very fine meshes and small time steps in order to accurately capture the propagating wave while avoiding the appearance of spurious oscillations in the wave front. This work develops a family of macro finite elements amenable for solving anisotropic reaction-diffusion equations with stiff reactive terms. The developed elements are incorporated on a semi-implicit algorithm based on operator splitting that includes adaptive time stepping for handling the stiff reactive term. A linear system is solved on each time step to update the transmembrane potential, whereas the remaining ordinary differential equations are solved uncoupled. The method allows solving the linear system on a coarser mesh thanks to the static condensation of the internal degrees of freedom (DOF) of the macroelements while maintaining the accuracy of the finer mesh. The method and algorithm have been implemented in parallel. The accuracy of the method has been tested on two- and three-dimensional examples demonstrating excellent behavior when compared to standard linear elements. The better performance and scalability of different macro finite elements against standard finite elements have been demonstrated in the simulation of a human heart and a heterogeneous two-dimensional problem with reentrant activity. Results have shown a reduction of up to four times in computational cost for the macro finite elements with respect to equivalent (same number of DOF) standard linear finite elements as well as good scalability properties.

Time-independent hybrid enrichment for finite element solution of transient conduction–radiation in diffusive grey media

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

Mohamed, M. Shadi, E-mail: m.s.mohamed@durham.ac.uk; Seaid, Mohammed; Trevelyan, Jon

2013-10-15

We investigate the effectiveness of the partition-of-unity finite element method for transient conduction–radiation problems in diffusive grey media. The governing equations consist of a semi-linear transient heat equation for the temperature field and a stationary diffusion approximation to the radiation in grey media. The coupled equations are integrated in time using a semi-implicit method in the finite element framework. We show that for the considered problems, a combination of hyperbolic and exponential enrichment functions based on an approximation of the boundary layer leads to improved accuracy compared to the conventional finite element method. It is illustrated that this approach canmore » be more efficient than using h adaptivity to increase the accuracy of the finite element method near the boundary walls. The performance of the proposed partition-of-unity method is analyzed on several test examples for transient conduction–radiation problems in two space dimensions.« less

Processing implicit control: evidence from reading times

PubMed Central

McCourt, Michael; Green, Jeffrey J.; Lau, Ellen; Williams, Alexander

2015-01-01

Sentences such as “The ship was sunk to collect the insurance” exhibit an unusual form of anaphora, implicit control, where neither anaphor nor antecedent is audible. The non-finite reason clause has an understood subject, PRO, that is anaphoric; here it may be understood as naming the agent of the event of the host clause. Yet since the host is a short passive, this agent is realized by no audible dependent. The putative antecedent to PRO is therefore implicit, which it normally cannot be. What sorts of representations subserve the comprehension of this dependency? Here we present four self-paced reading time studies directed at this question. Previous work showed no processing cost for implicit vs. explicit control, and took this to support the view that PRO is linked syntactically to a silent argument in the passive. We challenge this conclusion by reporting that we also find no processing cost for remote implicit control, as in: “The ship was sunk. The reason was to collect the insurance.” Here the dependency crosses two independent sentences, and so cannot, we argue, be mediated by syntax. Our Experiments 1–4 examined the processing of both implicit (short passive) and explicit (active or long passive) control in both local and remote configurations. Experiments 3 and 4 added either “3 days ago” or “just in order” to the local conditions, to control for the distance between the passive and infinitival verbs, and for the predictability of the reason clause, respectively. We replicate the finding that implicit control does not impose an additional processing cost. But critically we show that remote control does not impose a processing cost either. Reading times at the reason clause were never slower when control was remote. In fact they were always faster. Thus, efficient processing of local implicit control cannot show that implicit control is mediated by syntax; nor, in turn, that there is a silent but grammatically active argument in passives. PMID:26579016

Construction and comparison of parallel implicit kinetic solvers in three spatial dimensions

NASA Astrophysics Data System (ADS)

Titarev, Vladimir; Dumbser, Michael; Utyuzhnikov, Sergey

2014-01-01

The paper is devoted to the further development and systematic performance evaluation of a recent deterministic framework Nesvetay-3D for modelling three-dimensional rarefied gas flows. Firstly, a review of the existing discretization and parallelization strategies for solving numerically the Boltzmann kinetic equation with various model collision integrals is carried out. Secondly, a new parallelization strategy for the implicit time evolution method is implemented which improves scaling on large CPU clusters. Accuracy and scalability of the methods are demonstrated on a pressure-driven rarefied gas flow through a finite-length circular pipe as well as an external supersonic flow over a three-dimensional re-entry geometry of complicated aerodynamic shape.

Application of viscous-inviscid interaction methods to transonic turbulent flows

NASA Technical Reports Server (NTRS)

Lee, D.; Pletcher, R. H.

1986-01-01

Two different viscous-inviscid interaction schemes were developed for the analysis of steady, turbulent, transonic, separated flows over axisymmetric bodies. The viscous and inviscid solutions are coupled through the displacement concept using a transpiration velocity approach. In the semi-inverse interaction scheme, the viscous and inviscid equations are solved in an explicitly separate manner and the displacement thickness distribution is iteratively updated by a simple coupling algorithm. In the simultaneous interaction method, local solutions of viscous and inviscid equations are treated simultaneously, and the displacement thickness is treated as an unknown and is obtained as a part of the solution through a global iteration procedure. The inviscid flow region is described by a direct finite-difference solution of a velocity potential equation in conservative form. The potential equation is solved on a numerically generated mesh by an approximate factorization (AF2) scheme in the semi-inverse interaction method and by a successive line overrelaxation (SLOR) scheme in the simultaneous interaction method. The boundary-layer equations are used for the viscous flow region. The continuity and momentum equations are solved inversely in a coupled manner using a fully implicit finite-difference scheme.

Algorithm and code development for unsteady three-dimensional Navier-Stokes equations

NASA Technical Reports Server (NTRS)

Obayashi, Shigeru

1991-01-01

A streamwise upwind algorithm for solving the unsteady 3-D Navier-Stokes equations was extended to handle the moving grid system. It is noted that the finite volume concept is essential to extend the algorithm. The resulting algorithm is conservative for any motion of the coordinate system. Two extensions to an implicit method were considered and the implicit extension that makes the algorithm computationally efficient is implemented into Ames's aeroelasticity code, ENSAERO. The new flow solver has been validated through the solution of test problems. Test cases include three-dimensional problems with fixed and moving grids. The first test case shown is an unsteady viscous flow over an F-5 wing, while the second test considers the motion of the leading edge vortex as well as the motion of the shock wave for a clipped delta wing. The resulting algorithm has been implemented into ENSAERO. The upwind version leads to higher accuracy in both steady and unsteady computations than the previously used central-difference method does, while the increase in the computational time is small.

CPDES3: A preconditioned conjugate gradient solver for linear asymmetric matrix equations arising from coupled partial differential equations in three dimensions

NASA Astrophysics Data System (ADS)

Anderson, D. V.; Koniges, A. E.; Shumaker, D. E.

1988-11-01

Many physical problems require the solution of coupled partial differential equations on three-dimensional domains. When the time scales of interest dictate an implicit discretization of the equations a rather complicated global matrix system needs solution. The exact form of the matrix depends on the choice of spatial grids and on the finite element or finite difference approximations employed. CPDES3 allows each spatial operator to have 7, 15, 19, or 27 point stencils and allows for general couplings between all of the component PDE's and it automatically generates the matrix structures needed to perform the algorithm. The resulting sparse matrix equation is solved by either the preconditioned conjugate gradient (CG) method or by the preconditioned biconjugate gradient (BCG) algorithm. An arbitrary number of component equations are permitted only limited by available memory. In the sub-band representation used, we generate an algorithm that is written compactly in terms of indirect induces which is vectorizable on some of the newer scientific computers.

CPDES2: A preconditioned conjugate gradient solver for linear asymmetric matrix equations arising from coupled partial differential equations in two dimensions

NASA Astrophysics Data System (ADS)

Anderson, D. V.; Koniges, A. E.; Shumaker, D. E.

1988-11-01

Many physical problems require the solution of coupled partial differential equations on two-dimensional domains. When the time scales of interest dictate an implicit discretization of the equations a rather complicated global matrix system needs solution. The exact form of the matrix depends on the choice of spatial grids and on the finite element or finite difference approximations employed. CPDES2 allows each spatial operator to have 5 or 9 point stencils and allows for general couplings between all of the component PDE's and it automatically generates the matrix structures needed to perform the algorithm. The resulting sparse matrix equation is solved by either the preconditioned conjugate gradient (CG) method or by the preconditioned biconjugate gradient (BCG) algorithm. An arbitrary number of component equations are permitted only limited by available memory. In the sub-band representation used, we generate an algorithm that is written compactly in terms of indirect indices which is vectorizable on some of the newer scientific computers.

An analysis of a charring ablator with thermal nonequilibrium, chemical kinetics, and mass transfer

NASA Technical Reports Server (NTRS)

Clark, R. K.

1973-01-01

The differential equations governing the transient response of a one-dimensional ablative thermal protection system are presented for thermal nonequilibrium between the pyrolysis gases and the char layer and with finite rate chemical reactions occurring. The system consists of three layers (the char layer, the uncharred layer, and an optical insulation layer) with concentrated heat sinks at the back surface and between the second and third layers. The equations are solved numerically by using a modified implicit finite difference scheme to obtain solutions for the thickness of the charred and uncharred layers, surface recession and pyrolysis rates, solid temperatures, porosity profiles, and profiles of pyrolysis-gas temperature, pressure, composition, and flow rate. Good agreement is obtained between numerical results and exact solutions for a number of simplified cases. The complete numerical analysis is used to obtain solutions for an ablative system subjected to a constant heating environment. Effects of thermal, chemical, and mass transfer processes are shown.

A three-dimensional multiphase flow model for assesing NAPL contamination in porous and fractured media, 1. Formulation

NASA Astrophysics Data System (ADS)

Huyakorn, P. S.; Panday, S.; Wu, Y. S.

1994-06-01

A three-dimensional, three-phase numerical model is presented for stimulating the movement on non-aqueous-phase liquids (NAPL's) through porous and fractured media. The model is designed for practical application to a wide variety of contamination and remediation scenarios involving light or dense NAPL's in heterogeneous subsurface systems. The model formulation is first derived for three-phase flow of water, NAPL and air (or vapor) in porous media. The formulation is then extended to handle fractured systems using the dual-porosity and discrete-fracture modeling approaches The model accommodates a wide variety of boundary conditions, including withdrawal and injection well conditions which are treated rigorously using fully implicit schemes. The three-phase of formulation collapses to its simpler forms when air-phase dynamics are neglected, capillary effects are neglected, or two-phase-air-liquid, liquid-liquid systems with one or two active phases are considered. A Galerkin procedure with upstream weighting of fluid mobilities, storage matrix lumping, and fully implicit treatment of nonlinear coefficients and well conditions is used. A variety of nodal connectivity schemes leading to finite-difference, finite-element and hybrid spatial approximations in three dimensions are incorporated in the formulation. Selection of primary variables and evaluation of the terms of the Jacobian matrix for the Newton-Raphson linearized equations is discussed. The various nodal lattice options, and their significance to the computational time and memory requirements with regards to the block-Orthomin solution scheme are noted. Aggressive time-stepping schemes and under-relaxation formulas implemented in the code further alleviate the computational burden.

Weak Galerkin method for the Biot’s consolidation model

DOE PAGES

Hu, Xiaozhe; Mu, Lin; Ye, Xiu

2017-08-23

In this study, we develop a weak Galerkin (WG) finite element method for the Biot’s consolidation model in the classical displacement–pressure two-field formulation. Weak Galerkin linear finite elements are used for both displacement and pressure approximations in spatial discretizations. Backward Euler scheme is used for temporal discretization in order to obtain an implicit fully discretized scheme. We study the well-posedness of the linear system at each time step and also derive the overall optimal-order convergence of the WG formulation. Such WG scheme is designed on general shape regular polytopal meshes and provides stable and oscillation-free approximation for the pressure withoutmore » special treatment. Lastlyl, numerical experiments are presented to demonstrate the efficiency and accuracy of the proposed weak Galerkin finite element method.« less

Weak Galerkin method for the Biot’s consolidation model

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

Hu, Xiaozhe; Mu, Lin; Ye, Xiu

In this study, we develop a weak Galerkin (WG) finite element method for the Biot’s consolidation model in the classical displacement–pressure two-field formulation. Weak Galerkin linear finite elements are used for both displacement and pressure approximations in spatial discretizations. Backward Euler scheme is used for temporal discretization in order to obtain an implicit fully discretized scheme. We study the well-posedness of the linear system at each time step and also derive the overall optimal-order convergence of the WG formulation. Such WG scheme is designed on general shape regular polytopal meshes and provides stable and oscillation-free approximation for the pressure withoutmore » special treatment. Lastlyl, numerical experiments are presented to demonstrate the efficiency and accuracy of the proposed weak Galerkin finite element method.« less

Time-domain simulation of constitutive relations for nonlinear acoustics including relaxation for frequency power law attenuation media modeling

NASA Astrophysics Data System (ADS)

Jiménez, Noé; Camarena, Francisco; Redondo, Javier; Sánchez-Morcillo, Víctor; Konofagou, Elisa E.

2015-10-01

We report a numerical method for solving the constitutive relations of nonlinear acoustics, where multiple relaxation processes are included in a generalized formulation that allows the time-domain numerical solution by an explicit finite differences scheme. Thus, the proposed physical model overcomes the limitations of the one-way Khokhlov-Zabolotskaya-Kuznetsov (KZK) type models and, due to the Lagrangian density is implicitly included in the calculation, the proposed method also overcomes the limitations of Westervelt equation in complex configurations for medical ultrasound. In order to model frequency power law attenuation and dispersion, such as observed in biological media, the relaxation parameters are fitted to both exact frequency power law attenuation/dispersion media and also empirically measured attenuation of a variety of tissues that does not fit an exact power law. Finally, a computational technique based on artificial relaxation is included to correct the non-negligible numerical dispersion of the finite difference scheme, and, on the other hand, improve stability trough artificial attenuation when shock waves are present. This technique avoids the use of high-order finite-differences schemes leading to fast calculations. The present algorithm is especially suited for practical configuration where spatial discontinuities are present in the domain (e.g. axisymmetric domains or zero normal velocity boundary conditions in general). The accuracy of the method is discussed by comparing the proposed simulation solutions to one dimensional analytical and k-space numerical solutions.

A new solution method for wheel/rail rolling contact.

PubMed

Yang, Jian; Song, Hua; Fu, Lihua; Wang, Meng; Li, Wei

2016-01-01

To solve the problem of wheel/rail rolling contact of nonlinear steady-state curving, a three-dimensional transient finite element (FE) model is developed by the explicit software ANSYS/LS-DYNA. To improve the solving speed and efficiency, an explicit-explicit order solution method is put forward based on analysis of the features of implicit and explicit algorithm. The solution method was first applied to calculate the pre-loading of wheel/rail rolling contact with explicit algorithm, and then the results became the initial conditions in solving the dynamic process of wheel/rail rolling contact with explicit algorithm as well. Simultaneously, the common implicit-explicit order solution method is used to solve the FE model. Results show that the explicit-explicit order solution method has faster operation speed and higher efficiency than the implicit-explicit order solution method while the solution accuracy is almost the same. Hence, the explicit-explicit order solution method is more suitable for the wheel/rail rolling contact model with large scale and high nonlinearity.

An Implicit Algorithm for the Numerical Simulation of Shape-Memory Alloys

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

Becker, R; Stolken, J; Jannetti, C

Shape-memory alloys (SMA) have the potential to be used in a variety of interesting applications due to their unique properties of pseudoelasticity and the shape-memory effect. However, in order to design SMA devices efficiently, a physics-based constitutive model is required to accurately simulate the behavior of shape-memory alloys. The scope of this work is to extend the numerical capabilities of the SMA constitutive model developed by Jannetti et. al. (2003), to handle large-scale polycrystalline simulations. The constitutive model is implemented within the finite-element software ABAQUS/Standard using a user defined material subroutine, or UMAT. To improve the efficiency of the numericalmore » simulations, so that polycrystalline specimens of shape-memory alloys can be modeled, a fully implicit algorithm has been implemented to integrate the constitutive equations. Using an implicit integration scheme increases the efficiency of the UMAT over the previously implemented explicit integration method by a factor of more than 100 for single crystal simulations.« less

Towards full-Braginskii implicit extended MHD

NASA Astrophysics Data System (ADS)

Chacon, Luis

2009-05-01

Recently, viable algorithms have been proposed for the scalable, fully-implicit temporal integration of 3D resistive MHD and cold-ion extended MHD models. While significant, these achievements must be tempered by the fact that such models lack predictive capabilities in regimes of interest for magnetic fusion. Short of including kinetic closures, a natural evolution path towards predictability starts by considering additional terms as described in Braginskii's fluid closures in the collisional regime. Here, we focus on the inclusion of two fundamental elements of relevance for fusion plasmas: anisotropic parallel electron transport, and warm-ion physics (i.e., ion finite Larmor radius effects, included via gyroviscosity). Both these elements introduce significant numerical difficulties, due to the strong anisotropy in the former, and the presence of dispersive waves in the latter. In this presentation, we will discuss progress in our fully implicit algorithmic formulation towards the inclusion of both these elements. L. Chac'on, Phys. Plasmas, 15, 056103 (2008) L. Chac'on, J. Physics: Conf. Series, 125, 012041 (2008)

Hybrid simulation combining two space-time discretization of the discrete-velocity Boltzmann equation

NASA Astrophysics Data System (ADS)

Horstmann, Jan Tobias; Le Garrec, Thomas; Mincu, Daniel-Ciprian; Lévêque, Emmanuel

2017-11-01

Despite the efficiency and low dissipation of the stream-collide scheme of the discrete-velocity Boltzmann equation, which is nowadays implemented in many lattice Boltzmann solvers, a major drawback exists over alternative discretization schemes, i.e. finite-volume or finite-difference, that is the limitation to Cartesian uniform grids. In this paper, an algorithm is presented that combines the positive features of each scheme in a hybrid lattice Boltzmann method. In particular, the node-based streaming of the distribution functions is coupled with a second-order finite-volume discretization of the advection term of the Boltzmann equation under the Bhatnagar-Gross-Krook approximation. The algorithm is established on a multi-domain configuration, with the individual schemes being solved on separate sub-domains and connected by an overlapping interface of at least 2 grid cells. A critical parameter in the coupling is the CFL number equal to unity, which is imposed by the stream-collide algorithm. Nevertheless, a semi-implicit treatment of the collision term in the finite-volume formulation allows us to obtain a stable solution for this condition. The algorithm is validated in the scope of three different test cases on a 2D periodic mesh. It is shown that the accuracy of the combined discretization schemes agrees with the order of each separate scheme involved. The overall numerical error of the hybrid algorithm in the macroscopic quantities is contained between the error of the two individual algorithms. Finally, we demonstrate how such a coupling can be used to adapt to anisotropic flows with some gradual mesh refinement in the FV domain.

A comparison of two closely-related approaches to aerodynamic design optimization

NASA Technical Reports Server (NTRS)

Shubin, G. R.; Frank, P. D.

1991-01-01

Two related methods for aerodynamic design optimization are compared. The methods, called the implicit gradient approach and the variational (or optimal control) approach, both attempt to obtain gradients necessary for numerical optimization at a cost significantly less than that of the usual black-box approach that employs finite difference gradients. While the two methods are seemingly quite different, they are shown to differ (essentially) in that the order of discretizing the continuous problem, and of applying calculus, is interchanged. Under certain circumstances, the two methods turn out to be identical. We explore the relationship between these methods by applying them to a model problem for duct flow that has many features in common with transonic flow over an airfoil. We find that the gradients computed by the variational method can sometimes be sufficiently inaccurate to cause the optimization to fail.

A robust, finite element model for hydrostatic surface water flows

USGS Publications Warehouse

Walters, R.A.; Casulli, V.

1998-01-01

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

On-the-fly Numerical Surface Integration for Finite-Difference Poisson-Boltzmann Methods.

PubMed

Cai, Qin; Ye, Xiang; Wang, Jun; Luo, Ray

2011-11-01

Most implicit solvation models require the definition of a molecular surface as the interface that separates the solute in atomic detail from the solvent approximated as a continuous medium. Commonly used surface definitions include the solvent accessible surface (SAS), the solvent excluded surface (SES), and the van der Waals surface. In this study, we present an efficient numerical algorithm to compute the SES and SAS areas to facilitate the applications of finite-difference Poisson-Boltzmann methods in biomolecular simulations. Different from previous numerical approaches, our algorithm is physics-inspired and intimately coupled to the finite-difference Poisson-Boltzmann methods to fully take advantage of its existing data structures. Our analysis shows that the algorithm can achieve very good agreement with the analytical method in the calculation of the SES and SAS areas. Specifically, in our comprehensive test of 1,555 molecules, the average unsigned relative error is 0.27% in the SES area calculations and 1.05% in the SAS area calculations at the grid spacing of 1/2Å. In addition, a systematic correction analysis can be used to improve the accuracy for the coarse-grid SES area calculations, with the average unsigned relative error in the SES areas reduced to 0.13%. These validation studies indicate that the proposed algorithm can be applied to biomolecules over a broad range of sizes and structures. Finally, the numerical algorithm can also be adapted to evaluate the surface integral of either a vector field or a scalar field defined on the molecular surface for additional solvation energetics and force calculations.

Computation of viscous blast wave flowfields

NASA Technical Reports Server (NTRS)

Atwood, Christopher A.

1991-01-01

A method to determine unsteady solutions of the Navier-Stokes equations was developed and applied. The structural finite-volume, approximately factored implicit scheme uses Newton subiterations to obtain the spatially and temporally second-order accurate time history of the interaction of blast-waves with stationary targets. The inviscid flux is evaluated using MacCormack's modified Steger-Warming flux or Roe flux difference splittings with total variation diminishing limiters, while the viscous flux is computed using central differences. The use of implicit boundary conditions in conjunction with a telescoping in time and space method permitted solutions to this strongly unsteady class of problems. Comparisons of numerical, analytical, and experimental results were made in two and three dimensions. These comparisons revealed accurate wave speed resolution with nonoscillatory discontinuity capturing. The purpose of this effort was to address the three-dimensional, viscous blast-wave problem. Test cases were undertaken to reveal these methods' weaknesses in three regimes: (1) viscous-dominated flow; (2) complex unsteady flow; and (3) three-dimensional flow. Comparisons of these computations to analytic and experimental results provided initial validation of the resultant code. Addition details on the numerical method and on the validation can be found in the appendix. Presently, the code is capable of single zone computations with selection of any permutation of solid wall or flow-through boundaries.

A New Cell-Centered Implicit Numerical Scheme for Ions in the 2-D Axisymmetric Code Hall2de

NASA Technical Reports Server (NTRS)

Lopez Ortega, Alejandro; Mikellides, Ioannis G.

2014-01-01

We present a new algorithm in the Hall2De code to simulate the ion hydrodynamics in the acceleration channel and near plume regions of Hall-effect thrusters. This implementation constitutes an upgrade of the capabilities built in the Hall2De code. The equations of mass conservation and momentum for unmagnetized ions are solved using a conservative, finite-volume, cell-centered scheme on a magnetic-field-aligned grid. Major computational savings are achieved by making use of an implicit predictor/multi-corrector algorithm for time evolution. Inaccuracies in the prediction of the motion of low-energy ions in the near plume in hydrodynamics approaches are addressed by implementing a multi-fluid algorithm that tracks ions of different energies separately. A wide range of comparisons with measurements are performed to validate the new ion algorithms. Several numerical experiments with the location and value of the anomalous collision frequency are also presented. Differences in the plasma properties in the near-plume between the single fluid and multi-fluid approaches are discussed. We complete our validation by comparing predicted erosion rates at the channel walls of the thruster with measurements. Erosion rates predicted by the plasma properties obtained from simulations replicate accurately measured rates of erosion within the uncertainty range of the sputtering models employed.

Adult age differences in perceptually based, but not conceptually based implicit tests of memory.

PubMed

Small, B J; Hultsch, D F; Masson, M E

1995-05-01

Implicit tests of memory assess the influence of recent experience without requiring awareness of remembering. Evidence concerning age differences on implicit tests of memory suggests small age differences in favor of younger adults. However, the majority of research examining this issue has relied upon perceptually based implicit tests. Recently, a second type of implicit test, one that relies upon conceptually based processes, has been identified. The pattern of age differences on this second type of implicit test is less clear. In the present study, we examined the pattern of age differences on one conceptually based (fact completion) and one perceptually based (stem completion) implicit test of memory, as well as two explicit tests of memory (fact and word recall). Tasks were administered to 403 adults from three age groups (19-34 years, 58-73 years, 74-89 years). Significant age differences in favor of the young were found on stem completion but not fact completion. Age differences were present for both word and fast recall. Correlational analyses examining the relationship of memory performance to other cognitive variables indicated that the implicit tests were supported by different components than the explicit tests, as well as being different from each other.

An advanced probabilistic structural analysis method for implicit performance functions

NASA Technical Reports Server (NTRS)

Wu, Y.-T.; Millwater, H. R.; Cruse, T. A.

1989-01-01

In probabilistic structural analysis, the performance or response functions usually are implicitly defined and must be solved by numerical analysis methods such as finite element methods. In such cases, the most commonly used probabilistic analysis tool is the mean-based, second-moment method which provides only the first two statistical moments. This paper presents a generalized advanced mean value (AMV) method which is capable of establishing the distributions to provide additional information for reliability design. The method requires slightly more computations than the second-moment method but is highly efficient relative to the other alternative methods. In particular, the examples show that the AMV method can be used to solve problems involving non-monotonic functions that result in truncated distributions.

Co-simulation coupling spectral/finite elements for 3D soil/structure interaction problems

NASA Astrophysics Data System (ADS)

Zuchowski, Loïc; Brun, Michael; De Martin, Florent

2018-05-01

The coupling between an implicit finite elements (FE) code and an explicit spectral elements (SE) code has been explored for solving the elastic wave propagation in the case of soil/structure interaction problem. The coupling approach is based on domain decomposition methods in transient dynamics. The spatial coupling at the interface is managed by a standard coupling mortar approach, whereas the time integration is dealt with an hybrid asynchronous time integrator. An external coupling software, handling the interface problem, has been set up in order to couple the FE software Code_Aster with the SE software EFISPEC3D.

The SPAR thermal analyzer: Present and future

NASA Astrophysics Data System (ADS)

Marlowe, M. B.; Whetstone, W. D.; Robinson, J. C.

The SPAR thermal analyzer, a system of finite-element processors for performing steady-state and transient thermal analyses, is described. The processors communicate with each other through the SPAR random access data base. As each processor is executed, all pertinent source data is extracted from the data base and results are stored in the data base. Steady state temperature distributions are determined by a direct solution method for linear problems and a modified Newton-Raphson method for nonlinear problems. An explicit and several implicit methods are available for the solution of transient heat transfer problems. Finite element plotting capability is available for model checkout and verification.

The SPAR thermal analyzer: Present and future

NASA Technical Reports Server (NTRS)

Marlowe, M. B.; Whetstone, W. D.; Robinson, J. C.

1982-01-01

The SPAR thermal analyzer, a system of finite-element processors for performing steady-state and transient thermal analyses, is described. The processors communicate with each other through the SPAR random access data base. As each processor is executed, all pertinent source data is extracted from the data base and results are stored in the data base. Steady state temperature distributions are determined by a direct solution method for linear problems and a modified Newton-Raphson method for nonlinear problems. An explicit and several implicit methods are available for the solution of transient heat transfer problems. Finite element plotting capability is available for model checkout and verification.

On numerical model of time-dependent processes in three-dimensional porous heat-releasing objects

NASA Astrophysics Data System (ADS)

Lutsenko, Nickolay A.

2016-10-01

The gas flows in the gravity field through porous objects with heat-releasing sources are investigated when the self-regulation of the flow rate of the gas passing through the porous object takes place. Such objects can appear after various natural or man-made disasters (like the exploded unit of the Chernobyl NPP). The mathematical model and the original numerical method, based on a combination of explicit and implicit finite difference schemes, are developed for investigating the time-dependent processes in 3D porous energy-releasing objects. The advantage of the numerical model is its ability to describe unsteady processes under both natural convection and forced filtration. The gas cooling of 3D porous objects with different distribution of heat sources is studied using computational experiment.

Coastal Modeling System: Mathematical Formulations and Numerical Methods

DTIC Science & Technology

2014-03-01

sediment transport , and morphology change. The CMS was designed and developed for coastal inlets and navigation applications, including channel...numerical methods of hydrodynamic, salinity and sediment transport , and morphology change model CMS-Flow. The CMS- Flow uses the Finite Volume...and the influence of coastal structures. The implicit hydrodynamic model is coupled to a nonequilibrium transport model of multiple-sized total

Finite element solution to passive scalar transport behind line sources under neutral and unstable stratification

NASA Astrophysics Data System (ADS)

Liu, Chun-Ho; Leung, Dennis Y. C.

2006-02-01

This study employed a direct numerical simulation (DNS) technique to contrast the plume behaviours and mixing of passive scalar emitted from line sources (aligned with the spanwise direction) in neutrally and unstably stratified open-channel flows. The DNS model was developed using the Galerkin finite element method (FEM) employing trilinear brick elements with equal-order interpolating polynomials that solved the momentum and continuity equations, together with conservation of energy and mass equations in incompressible flow. The second-order accurate fractional-step method was used to handle the implicit velocity-pressure coupling in incompressible flow. It also segregated the solution to the advection and diffusion terms, which were then integrated in time, respectively, by the explicit third-order accurate Runge-Kutta method and the implicit second-order accurate Crank-Nicolson method. The buoyancy term under unstable stratification was integrated in time explicitly by the first-order accurate Euler method. The DNS FEM model calculated the scalar-plume development and the mean plume path. In particular, it calculated the plume meandering in the wall-normal direction under unstable stratification that agreed well with the laboratory and field measurements, as well as previous modelling results available in literature.

Dynamic Relaxation: A Technique for Detailed Thermo-Elastic Structural Analysis of Transportation Structures

NASA Astrophysics Data System (ADS)

Shoukry, Samir N.; William, Gergis W.; Riad, Mourad Y.; McBride, Kevyn C.

2006-08-01

Dynamic relaxation is a technique developed to solve static problems through an explicit integration in finite element. The main advantage of such a technique is the ability to solve a large problem in a relatively short time compared with the traditional implicit techniques, especially when using nonlinear material models. This paper describes the use of such a technique in analyzing large transportation structures as dowel jointed concrete pavements and 306-m-long, reinforced concrete bridge superstructure under the effect of temperature variations. The main feature of the pavement model is the detailed modeling of dowel bars and their interfaces with the surrounding concrete using extremely fine mesh of solid elements, while in the bridge structure it is the detailed modeling of the girder-deck interface as well as the bracing members between the girders. The 3DFE results were found to be in a good agreement with experimentally measured data obtained from an instrumented pavements sections and a highway bridge constructed in West Virginia. Thus, such a technique provides a good tool for analyzing the response of large structures to static loads in a fraction of the time required by traditional, implicit finite element methods.

An efficient numerical model for multicomponent compressible flow in fractured porous media

NASA Astrophysics Data System (ADS)

Zidane, Ali; Firoozabadi, Abbas

2014-12-01

An efficient and accurate numerical model for multicomponent compressible single-phase flow in fractured media is presented. The discrete-fracture approach is used to model the fractures where the fracture entities are described explicitly in the computational domain. We use the concept of cross flow equilibrium in the fractures. This will allow large matrix elements in the neighborhood of the fractures and considerable speed up of the algorithm. We use an implicit finite volume (FV) scheme to solve the species mass balance equation in the fractures. This step avoids the use of Courant-Freidricks-Levy (CFL) condition and contributes to significant speed up of the code. The hybrid mixed finite element method (MFE) is used to solve for the velocity in both the matrix and the fractures coupled with the discontinuous Galerkin (DG) method to solve the species transport equations in the matrix. Four numerical examples are presented to demonstrate the robustness and efficiency of the proposed model. We show that the combination of the fracture cross-flow equilibrium and the implicit composition calculation in the fractures increase the computational speed 20-130 times in 2D. In 3D, one may expect even a higher computational efficiency.

Application of adaptive gridding to magnetohydrodynamic flows

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

Schnack, D.D.; Lotatti, I.; Satyanarayana, P.

1996-12-31

The numerical simulation of the primitive, three-dimensional, time-dependent, resistive MHD equations on an unstructured, adaptive poloidal mesh using the TRIM code has been reported previously. The toroidal coordinate is approximated pseudo-spectrally with finite Fourier series and Fast-Fourier Transforms. The finite-volume algorithm preserves the magnetic field as solenoidal to round-off error, and also conserves mass, energy, and magnetic flux exactly. A semi-implicit method is used to allow for large time steps on the unstructured mesh. This is important for tokamak calculations where the relevant time scale is determined by the poloidal Alfven time. This also allows the viscosity to be treatedmore » implicitly. A conjugate-gradient method with pre-conditioning is used for matrix inversion. Applications to the growth and saturation of ideal instabilities in several toroidal fusion systems has been demonstrated. Recently we have concentrated on the details of the mesh adaption algorithm used in TRIM. We present several two-dimensional results relating to the use of grid adaptivity to track the evolution of hydrodynamic and MHD structures. Examples of plasma guns, opening switches, and supersonic flow over a magnetized sphere are presented. Issues relating to mesh adaption criteria are discussed.« less

A solution to the Navier-Stokes equations based upon the Newton Kantorovich method

NASA Technical Reports Server (NTRS)

Davis, J. E.; Gabrielsen, R. E.; Mehta, U. B.

1977-01-01

An implicit finite difference scheme based on the Newton-Kantorovich technique was developed for the numerical solution of the nonsteady, incompressible, two-dimensional Navier-Stokes equations in conservation-law form. The algorithm was second-order-time accurate, noniterative with regard to the nonlinear terms in the vorticity transport equation except at the earliest few time steps, and spatially factored. Numerical results were obtained with the technique for a circular cylinder at Reynolds number 15. Results indicate that the technique is in excellent agreement with other numerical techniques for all geometries and Reynolds numbers investigated, and indicates a potential for significant reduction in computation time over current iterative techniques.

An efficient coordinate transformation technique for unsteady, transonic aerodynamic analysis of low aspect-ratio wings

NASA Technical Reports Server (NTRS)

Guruswamy, G. P.; Goorjian, P. M.

1984-01-01

An efficient coordinate transformation technique is presented for constructing grids for unsteady, transonic aerodynamic computations for delta-type wings. The original shearing transformation yielded computations that were numerically unstable and this paper discusses the sources of those instabilities. The new shearing transformation yields computations that are stable, fast, and accurate. Comparisons of those two methods are shown for the flow over the F5 wing that demonstrate the new stability. Also, comparisons are made with experimental data that demonstrate the accuracy of the new method. The computations were made by using a time-accurate, finite-difference, alternating-direction-implicit (ADI) algorithm for the transonic small-disturbance potential equation.

Radiative Effects on a Free Convective MHD Flow past a Vertically Inclined Plate with with Heat Source and Sink

NASA Astrophysics Data System (ADS)

Sambath, P.; Pullepu, Bapuji; Kannan, R. M.

2018-04-01

The impact of thermal radiation on unsteady laminar free convective MHD flow of a incompressible viscous fluid passes through a vertically inclined plate under the persuade of heat source and sink is presented here.Plate surface is considered to have variable wall temperature. The fluid regarded as gray absorbing / emitting, but non dispersing medium. The periphery layer dimensionless equations that administer the flow are evaluated by a finite difference implicit method called Crank Nicolson method. Numerical solutions are carried out for velocity, temperature, local shear stress, heat transfer rate for various values of the parameters (Pr, λ, Δ M, Rd ) are presented.

A computational/experimental study of the flow around a body of revolution at angle of attack

NASA Technical Reports Server (NTRS)

Zilliac, Gregory G.

1986-01-01

The incompressible Navier-Stokes equations are numerically solved for steady flow around an ogive-cylinder (fineness ration 4.5) at angle of attack. The three-dimensional vortical flow is investigated with emphasis on the tip and the near wake region. The implicit, finite-difference computation is performed on the CRAY X-MP computer using the method of pseudo-compressibility. Comparisons of computational results with results of a companion towing tank experiment are presented for two symmetric leeside flow cases of moderate angles of attack. The topology of the flow is discussed and conclusions are drawn concerning the growth and stability of the primary vortices.

Effects of using a posteriori methods for the conservation of integral invariants. [for weather forecasting

NASA Technical Reports Server (NTRS)

Takacs, Lawrence L.

1988-01-01

The nature and effect of using a posteriori adjustments to nonconservative finite-difference schemes to enforce integral invariants of the corresponding analytic system are examined. The method of a posteriori integral constraint restoration is analyzed for the case of linear advection, and the harmonic response associated with the a posteriori adjustments is examined in detail. The conservative properties of the shallow water system are reviewed, and the constraint restoration algorithm applied to the shallow water equations are described. A comparison is made between forecasts obtained using implicit and a posteriori methods for the conservation of mass, energy, and potential enstrophy in the complete nonlinear shallow-water system.

An efficient three-dimensional Poisson solver for SIMD high-performance-computing architectures

NASA Technical Reports Server (NTRS)

Cohl, H.

1994-01-01

We present an algorithm that solves the three-dimensional Poisson equation on a cylindrical grid. The technique uses a finite-difference scheme with operator splitting. This splitting maps the banded structure of the operator matrix into a two-dimensional set of tridiagonal matrices, which are then solved in parallel. Our algorithm couples FFT techniques with the well-known ADI (Alternating Direction Implicit) method for solving Elliptic PDE's, and the implementation is extremely well suited for a massively parallel environment like the SIMD architecture of the MasPar MP-1. Due to the highly recursive nature of our problem, we believe that our method is highly efficient, as it avoids excessive interprocessor communication.

Solution of Poisson equations for 3-dimensional grid generations. [computations of a flow field over a thin delta wing

NASA Technical Reports Server (NTRS)

Fujii, K.

1983-01-01

A method for generating three dimensional, finite difference grids about complicated geometries by using Poisson equations is developed. The inhomogenous terms are automatically chosen such that orthogonality and spacing restrictions at the body surface are satisfied. Spherical variables are used to avoid the axis singularity, and an alternating-direction-implicit (ADI) solution scheme is used to accelerate the computations. Computed results are presented that show the capability of the method. Since most of the results presented have been used as grids for flow-field computations, this is indicative that the method is a useful tool for generating three-dimensional grids about complicated geometries.

Numerical solution of Euler's equation by perturbed functionals

NASA Technical Reports Server (NTRS)

Dey, S. K.

1985-01-01

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

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

NASA Technical Reports Server (NTRS)

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

1999-01-01

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

Incompressible viscous flow computations for the pump components and the artificial heart

NASA Technical Reports Server (NTRS)

Kiris, Cetin

1992-01-01

A finite difference, three dimensional incompressible Navier-Stokes formulation to calculate the flow through turbopump components is utilized. The solution method is based on the pseudo compressibility approach and uses an implicit upwind differencing scheme together with the Gauss-Seidel line relaxation method. Both steady and unsteady flow calculations can be performed using the current algorithm. Here, equations are solved in steadily rotating reference frames by using the steady state formulation in order to simulate the flow through a turbopump inducer. Eddy viscosity is computed by using an algebraic mixing-length turbulence model. Numerical results are compared with experimental measurements and a good agreement is found between the two.

Inverse boundary-layer theory and comparison with experiment

NASA Technical Reports Server (NTRS)

Carter, J. E.

1978-01-01

Inverse boundary layer computational procedures, which permit nonsingular solutions at separation and reattachment, are presented. In the first technique, which is for incompressible flow, the displacement thickness is prescribed; in the second technique, for compressible flow, a perturbation mass flow is the prescribed condition. The pressure is deduced implicitly along with the solution in each of these techniques. Laminar and turbulent computations, which are typical of separated flow, are presented and comparisons are made with experimental data. In both inverse procedures, finite difference techniques are used along with Newton iteration. The resulting procedure is no more complicated than conventional boundary layer computations. These separated boundary layer techniques appear to be well suited for complete viscous-inviscid interaction computations.

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.

TAP 2: A finite element program for thermal analysis of convectively cooled structures

NASA Technical Reports Server (NTRS)

Thornton, E. A.

1980-01-01

A finite element computer program (TAP 2) for steady-state and transient thermal analyses of convectively cooled structures is presented. The program has a finite element library of six elements: two conduction/convection elements to model heat transfer in a solid, two convection elements to model heat transfer in a fluid, and two integrated conduction/convection elements to represent combined heat transfer in tubular and plate/fin fluid passages. Nonlinear thermal analysis due to temperature-dependent thermal parameters is performed using the Newton-Raphson iteration method. Transient analyses are performed using an implicit Crank-Nicolson time integration scheme with consistent or lumped capacitance matrices as an option. Program output includes nodal temperatures and element heat fluxes. Pressure drops in fluid passages may be computed as an option. User instructions and sample problems are presented in appendixes.

Iterative methods for 3D implicit finite-difference migration using the complex Padé approximation

NASA Astrophysics Data System (ADS)

Costa, Carlos A. N.; Campos, Itamara S.; Costa, Jessé C.; Neto, Francisco A.; Schleicher, Jörg; Novais, Amélia

2013-08-01

Conventional implementations of 3D finite-difference (FD) migration use splitting techniques to accelerate performance and save computational cost. However, such techniques are plagued with numerical anisotropy that jeopardises the correct positioning of dipping reflectors in the directions not used for the operator splitting. We implement 3D downward continuation FD migration without splitting using a complex Padé approximation. In this way, the numerical anisotropy is eliminated at the expense of a computationally more intensive solution of a large-band linear system. We compare the performance of the iterative stabilized biconjugate gradient (BICGSTAB) and that of the multifrontal massively parallel direct solver (MUMPS). It turns out that the use of the complex Padé approximation not only stabilizes the solution, but also acts as an effective preconditioner for the BICGSTAB algorithm, reducing the number of iterations as compared to the implementation using the real Padé expansion. As a consequence, the iterative BICGSTAB method is more efficient than the direct MUMPS method when solving a single term in the Padé expansion. The results of both algorithms, here evaluated by computing the migration impulse response in the SEG/EAGE salt model, are of comparable quality.

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.

Reprint of Solution of Ambrosio-Tortorelli model for image segmentation by generalized relaxation method

NASA Astrophysics Data System (ADS)

D'Ambra, Pasqua; Tartaglione, Gaetano

2015-04-01

Image segmentation addresses the problem to partition a given image into its constituent objects and then to identify the boundaries of the objects. This problem can be formulated in terms of a variational model aimed to find optimal approximations of a bounded function by piecewise-smooth functions, minimizing a given functional. The corresponding Euler-Lagrange equations are a set of two coupled elliptic partial differential equations with varying coefficients. Numerical solution of the above system often relies on alternating minimization techniques involving descent methods coupled with explicit or semi-implicit finite-difference discretization schemes, which are slowly convergent and poorly scalable with respect to image size. In this work we focus on generalized relaxation methods also coupled with multigrid linear solvers, when a finite-difference discretization is applied to the Euler-Lagrange equations of Ambrosio-Tortorelli model. We show that non-linear Gauss-Seidel, accelerated by inner linear iterations, is an effective method for large-scale image analysis as those arising from high-throughput screening platforms for stem cells targeted differentiation, where one of the main goal is segmentation of thousand of images to analyze cell colonies morphology.

Solution of Ambrosio-Tortorelli model for image segmentation by generalized relaxation method

NASA Astrophysics Data System (ADS)

D'Ambra, Pasqua; Tartaglione, Gaetano

2015-03-01

Image segmentation addresses the problem to partition a given image into its constituent objects and then to identify the boundaries of the objects. This problem can be formulated in terms of a variational model aimed to find optimal approximations of a bounded function by piecewise-smooth functions, minimizing a given functional. The corresponding Euler-Lagrange equations are a set of two coupled elliptic partial differential equations with varying coefficients. Numerical solution of the above system often relies on alternating minimization techniques involving descent methods coupled with explicit or semi-implicit finite-difference discretization schemes, which are slowly convergent and poorly scalable with respect to image size. In this work we focus on generalized relaxation methods also coupled with multigrid linear solvers, when a finite-difference discretization is applied to the Euler-Lagrange equations of Ambrosio-Tortorelli model. We show that non-linear Gauss-Seidel, accelerated by inner linear iterations, is an effective method for large-scale image analysis as those arising from high-throughput screening platforms for stem cells targeted differentiation, where one of the main goal is segmentation of thousand of images to analyze cell colonies morphology.

Implicit Attitudes toward the Self Over Time in Chinese Undergraduates

PubMed Central

Yang, Qing; Zhao, Yufang; Guan, Lili; Huang, Xiting

2017-01-01

Although the explicit attitudes of Chinese people toward the self over time are known (i.e., past = present < future), little is known about their implicit attitudes. Two studies were conducted to measure the implicit subjective temporal trajectory (STT) of Chinese undergraduates. Study 1 used a Go/No-go association task to measure participants’ implicit attitudes toward their past, present, and future selves. The obtained implicit STT was different from the explicit pattern found in former research. It showed that the future self was viewed to be identical to the present self and participants implicitly evaluated their present self as better than the past self. Since this comparison of the past and present selves suggested a cultural difference, we aimed to replicate this finding in Study 2. Using an implicit association test, we again found that the present self was more easily associated with positive valence than the past self. Overall, both studies reveal an implicitly inclining-flat STT (i.e., past < present = future) for Chinese undergraduates. Implications of this difference in explicit-implicit measures and the cultural differences of temporal self appraisals are discussed. PMID:29163291

Discontinuous dual-primal mixed finite elements for elliptic problems

NASA Technical Reports Server (NTRS)

Bottasso, Carlo L.; Micheletti, Stefano; Sacco, Riccardo

2000-01-01

We propose a novel discontinuous mixed finite element formulation for the solution of second-order elliptic problems. Fully discontinuous piecewise polynomial finite element spaces are used for the trial and test functions. The discontinuous nature of the test functions at the element interfaces allows to introduce new boundary unknowns that, on the one hand enforce the weak continuity of the trial functions, and on the other avoid the need to define a priori algorithmic fluxes as in standard discontinuous Galerkin methods. Static condensation is performed at the element level, leading to a solution procedure based on the sole interface unknowns. The resulting family of discontinuous dual-primal mixed finite element methods is presented in the one and two-dimensional cases. In the one-dimensional case, we show the equivalence of the method with implicit Runge-Kutta schemes of the collocation type exhibiting optimal behavior. Numerical experiments in one and two dimensions demonstrate the order accuracy of the new method, confirming the results of the analysis.

An efficicient data structure for three-dimensional vertex based finite volume method

NASA Astrophysics Data System (ADS)

Akkurt, Semih; Sahin, Mehmet

2017-11-01

A vertex based three-dimensional finite volume algorithm has been developed using an edge based data structure.The mesh data structure of the given algorithm is similar to ones that exist in the literature. However, the data structures are redesigned and simplied in order to fit requirements of the vertex based finite volume method. In order to increase the cache efficiency, the data access patterns for the vertex based finite volume method are investigated and these datas are packed/allocated in a way that they are close to each other in the memory. The present data structure is not limited with tetrahedrons, arbitrary polyhedrons are also supported in the mesh without putting any additional effort. Furthermore, the present data structure also supports adaptive refinement and coarsening. For the implicit and parallel implementation of the FVM algorithm, PETSc and MPI libraries are employed. The performance and accuracy of the present algorithm are tested for the classical benchmark problems by comparing the CPU time for the open source algorithms.

Time integration algorithms for the two-dimensional Euler equations on unstructured meshes

NASA Technical Reports Server (NTRS)

Slack, David C.; Whitaker, D. L.; Walters, Robert W.

1994-01-01

Explicit and implicit time integration algorithms for the two-dimensional Euler equations on unstructured grids are presented. Both cell-centered and cell-vertex finite volume upwind schemes utilizing Roe's approximate Riemann solver are developed. For the cell-vertex scheme, a four-stage Runge-Kutta time integration, a fourstage Runge-Kutta time integration with implicit residual averaging, a point Jacobi method, a symmetric point Gauss-Seidel method and two methods utilizing preconditioned sparse matrix solvers are presented. For the cell-centered scheme, a Runge-Kutta scheme, an implicit tridiagonal relaxation scheme modeled after line Gauss-Seidel, a fully implicit lower-upper (LU) decomposition, and a hybrid scheme utilizing both Runge-Kutta and LU methods are presented. A reverse Cuthill-McKee renumbering scheme is employed for the direct solver to decrease CPU time by reducing the fill of the Jacobian matrix. A comparison of the various time integration schemes is made for both first-order and higher order accurate solutions using several mesh sizes, higher order accuracy is achieved by using multidimensional monotone linear reconstruction procedures. The results obtained for a transonic flow over a circular arc suggest that the preconditioned sparse matrix solvers perform better than the other methods as the number of elements in the mesh increases.

Parallelized modelling and solution scheme for hierarchically scaled simulations

NASA Technical Reports Server (NTRS)

Padovan, Joe

1995-01-01

This two-part paper presents the results of a benchmarked analytical-numerical investigation into the operational characteristics of a unified parallel processing strategy for implicit fluid mechanics formulations. This hierarchical poly tree (HPT) strategy is based on multilevel substructural decomposition. The Tree morphology is chosen to minimize memory, communications and computational effort. The methodology is general enough to apply to existing finite difference (FD), finite element (FEM), finite volume (FV) or spectral element (SE) based computer programs without an extensive rewrite of code. In addition to finding large reductions in memory, communications, and computational effort associated with a parallel computing environment, substantial reductions are generated in the sequential mode of application. Such improvements grow with increasing problem size. Along with a theoretical development of general 2-D and 3-D HPT, several techniques for expanding the problem size that the current generation of computers are capable of solving, are presented and discussed. Among these techniques are several interpolative reduction methods. It was found that by combining several of these techniques that a relatively small interpolative reduction resulted in substantial performance gains. Several other unique features/benefits are discussed in this paper. Along with Part 1's theoretical development, Part 2 presents a numerical approach to the HPT along with four prototype CFD applications. These demonstrate the potential of the HPT strategy.

A Numerical Study of Scalable Cardiac Electro-Mechanical Solvers on HPC Architectures

PubMed Central

Colli Franzone, Piero; Pavarino, Luca F.; Scacchi, Simone

2018-01-01

We introduce and study some scalable domain decomposition preconditioners for cardiac electro-mechanical 3D simulations on parallel HPC (High Performance Computing) architectures. The electro-mechanical model of the cardiac tissue is composed of four coupled sub-models: (1) the static finite elasticity equations for the transversely isotropic deformation of the cardiac tissue; (2) the active tension model describing the dynamics of the intracellular calcium, cross-bridge binding and myofilament tension; (3) the anisotropic Bidomain model describing the evolution of the intra- and extra-cellular potentials in the deforming cardiac tissue; and (4) the ionic membrane model describing the dynamics of ionic currents, gating variables, ionic concentrations and stretch-activated channels. This strongly coupled electro-mechanical model is discretized in time with a splitting semi-implicit technique and in space with isoparametric finite elements. The resulting scalable parallel solver is based on Multilevel Additive Schwarz preconditioners for the solution of the Bidomain system and on BDDC preconditioned Newton-Krylov solvers for the non-linear finite elasticity system. The results of several 3D parallel simulations show the scalability of both linear and non-linear solvers and their application to the study of both physiological excitation-contraction cardiac dynamics and re-entrant waves in the presence of different mechano-electrical feedbacks. PMID:29674971

Finite Volume Element (FVE) discretization and multilevel solution of the axisymmetric heat equation

NASA Astrophysics Data System (ADS)

Litaker, Eric T.

1994-12-01

The axisymmetric heat equation, resulting from a point-source of heat applied to a metal block, is solved numerically; both iterative and multilevel solutions are computed in order to compare the two processes. The continuum problem is discretized in two stages: finite differences are used to discretize the time derivatives, resulting is a fully implicit backward time-stepping scheme, and the Finite Volume Element (FVE) method is used to discretize the spatial derivatives. The application of the FVE method to a problem in cylindrical coordinates is new, and results in stencils which are analyzed extensively. Several iteration schemes are considered, including both Jacobi and Gauss-Seidel; a thorough analysis of these schemes is done, using both the spectral radii of the iteration matrices and local mode analysis. Using this discretization, a Gauss-Seidel relaxation scheme is used to solve the heat equation iteratively. A multilevel solution process is then constructed, including the development of intergrid transfer and coarse grid operators. Local mode analysis is performed on the components of the amplification matrix, resulting in the two-level convergence factors for various combinations of the operators. A multilevel solution process is implemented by using multigrid V-cycles; the iterative and multilevel results are compared and discussed in detail. The computational savings resulting from the multilevel process are then discussed.

A mixed finite-element method for solving the poroelastic Biot equations with electrokinetic coupling

NASA Astrophysics Data System (ADS)

Pain, C. C.; Saunders, J. H.; Worthington, M. H.; Singer, J. M.; Stuart-Bruges, W.; Mason, G.; Goddard, A.

2005-02-01

In this paper, a numerical method for solving the Biot poroelastic equations is developed. These equations comprise acoustic (typically water) and elastic (porous medium frame) equations, which are coupled mainly through fluid/solid drag terms. This wave solution is coupled to a simplified form of Maxwell's equations, which is solved for the streaming potential resulting from electrokinesis. The ultimate aim is to use the generated electrical signals to provide porosity, permeability and other information about the formation surrounding a borehole. The electrical signals are generated through electrokinesis by seismic waves causing movement of the fluid through pores or fractures of a porous medium. The focus of this paper is the numerical solution of the Biot equations in displacement form, which is achieved using a mixed finite-element formulation with a different finite-element representation for displacements and stresses. The mixed formulation is used in order to reduce spurious displacement modes and fluid shear waves in the numerical solutions. These equations are solved in the time domain using an implicit unconditionally stable time-stepping method using iterative solution methods amenable to solving large systems of equations. The resulting model is embodied in the MODELLING OF ACOUSTICS, POROELASTICS AND ELECTROKINETICS (MAPEK) computer model for electroseismic analysis.

Design of a Modular Monolithic Implicit Solver for Multi-Physics Applications

NASA Technical Reports Server (NTRS)

Carton De Wiart, Corentin; Diosady, Laslo T.; Garai, Anirban; Burgess, Nicholas; Blonigan, Patrick; Ekelschot, Dirk; Murman, Scott M.

2018-01-01

The design of a modular multi-physics high-order space-time finite-element framework is presented together with its extension to allow monolithic coupling of different physics. One of the main objectives of the framework is to perform efficient high- fidelity simulations of capsule/parachute systems. This problem requires simulating multiple physics including, but not limited to, the compressible Navier-Stokes equations, the dynamics of a moving body with mesh deformations and adaptation, the linear shell equations, non-re effective boundary conditions and wall modeling. The solver is based on high-order space-time - finite element methods. Continuous, discontinuous and C1-discontinuous Galerkin methods are implemented, allowing one to discretize various physical models. Tangent and adjoint sensitivity analysis are also targeted in order to conduct gradient-based optimization, error estimation, mesh adaptation, and flow control, adding another layer of complexity to the framework. The decisions made to tackle these challenges are presented. The discussion focuses first on the "single-physics" solver and later on its extension to the monolithic coupling of different physics. The implementation of different physics modules, relevant to the capsule/parachute system, are also presented. Finally, examples of coupled computations are presented, paving the way to the simulation of the full capsule/parachute system.

FY07 NRL DoD High Performance Computing Modernization Program Annual Reports

DTIC Science & Technology

2008-09-05

performed. Implicit and explicit solutions methods are used as appropriate. The primary finite element codes used are ABAQUS and ANSYS. User subroutines ...geometric complexities, loading path dependence, rate dependence, and interaction between loading types (electrical, thermal and mechanical). Work is not...are used for specialized material constitutive response. Coupled material responses, such as electrical- thermal for capacitor materials or electrical

Predictive Flow Control to Minimize Convective Time Delays

DTIC Science & Technology

2013-08-19

simulation. The CFO solver used is Cobalt, an unstructured finite-volume code developed for the solution of the compress- ible Navier-Stokes...cell-centered fin ite volume approach applicable to arbitrary cell topologies (e.g, hexahedra, prisms, tetrahedra). The spatial operator uses a Riemann ... solver , least squares gradient calculations using QR factorizati on to provide second order accuracy in space. A point implicit method using

A weak-coupling immersed boundary method for fluid-structure interaction with low density ratio of solid to fluid

NASA Astrophysics Data System (ADS)

Kim, Woojin; Lee, Injae; Choi, Haecheon

2018-04-01

We present a weak-coupling approach for fluid-structure interaction with low density ratio (ρ) of solid to fluid. For accurate and stable solutions, we introduce predictors, an explicit two-step method and the implicit Euler method, to obtain provisional velocity and position of fluid-structure interface at each time step, respectively. The incompressible Navier-Stokes equations, together with these provisional velocity and position at the fluid-structure interface, are solved in an Eulerian coordinate using an immersed-boundary finite-volume method on a staggered mesh. The dynamic equation of an elastic solid-body motion, together with the hydrodynamic force at the provisional position of the interface, is solved in a Lagrangian coordinate using a finite element method. Each governing equation for fluid and structure is implicitly solved using second-order time integrators. The overall second-order temporal accuracy is preserved even with the use of lower-order predictors. A linear stability analysis is also conducted for an ideal case to find the optimal explicit two-step method that provides stable solutions down to the lowest density ratio. With the present weak coupling, three different fluid-structure interaction problems were simulated: flows around an elastically mounted rigid circular cylinder, an elastic beam attached to the base of a stationary circular cylinder, and a flexible plate, respectively. The lowest density ratios providing stable solutions are searched for the first two problems and they are much lower than 1 (ρmin = 0.21 and 0.31, respectively). The simulation results agree well with those from strong coupling suggested here and also from previous numerical and experimental studies, indicating the efficiency and accuracy of the present weak coupling.

Social intuition as a form of implicit learning: Sequences of body movements are learned less explicitly than letter sequences

PubMed Central

Norman, Elisabeth; Price, Mark C.

2012-01-01

In the current paper, we first evaluate the suitability of traditional serial reaction time (SRT) and artificial grammar learning (AGL) experiments for measuring implicit learning of social signals. We then report the results of a novel sequence learning task which combines aspects of the SRT and AGL paradigms to meet our suggested criteria for how implicit learning experiments can be adapted to increase their relevance to situations of social intuition. The sequences followed standard finite-state grammars. Sequence learning and consciousness of acquired knowledge were compared between 2 groups of 24 participants viewing either sequences of individually presented letters or sequences of body-posture pictures, which were described as series of yoga movements. Participants in both conditions showed above-chance classification accuracy, indicating that sequence learning had occurred in both stimulus conditions. This shows that sequence learning can still be found when learning procedures reflect the characteristics of social intuition. Rule awareness was measured using trial-by-trial evaluation of decision strategy (Dienes & Scott, 2005; Scott & Dienes, 2008). For letters, sequence classification was best on trials where participants reported responding on the basis of explicit rules or memory, indicating some explicit learning in this condition. For body-posture, classification was not above chance on these types of trial, but instead showed a trend to be best on those trials where participants reported that their responses were based on intuition, familiarity, or random choice, suggesting that learning was more implicit. Results therefore indicate that the use of traditional stimuli in research on sequence learning might underestimate the extent to which learning is implicit in domains such as social learning, contributing to ongoing debate about levels of conscious awareness in implicit learning. PMID:22679467

Numerical solution of transport equation for applications in environmental hydraulics and hydrology

NASA Astrophysics Data System (ADS)

Rashidul Islam, M.; Hanif Chaudhry, M.

1997-04-01

The advective term in the one-dimensional transport equation, when numerically discretized, produces artificial diffusion. To minimize such artificial diffusion, which vanishes only for Courant number equal to unity, transport owing to advection has been modeled separately. The numerical solution of the advection equation for a Gaussian initial distribution is well established; however, large oscillations are observed when applied to an initial distribution with sleep gradients, such as trapezoidal distribution of a constituent or propagation of mass from a continuous input. In this study, the application of seven finite-difference schemes and one polynomial interpolation scheme is investigated to solve the transport equation for both Gaussian and non-Gaussian (trapezoidal) initial distributions. The results obtained from the numerical schemes are compared with the exact solutions. A constant advective velocity is assumed throughout the transport process. For a Gaussian distribution initial condition, all eight schemes give excellent results, except the Lax scheme which is diffusive. In application to the trapezoidal initial distribution, explicit finite-difference schemes prove to be superior to implicit finite-difference schemes because the latter produce large numerical oscillations near the steep gradients. The Warming-Kutler-Lomax (WKL) explicit scheme is found to be better among this group. The Hermite polynomial interpolation scheme yields the best result for a trapezoidal distribution among all eight schemes investigated. The second-order accurate schemes are sufficiently accurate for most practical problems, but the solution of unusual problems (concentration with steep gradient) requires the application of higher-order (e.g. third- and fourth-order) accurate schemes.

An improved 3D MoF method based on analytical partial derivatives

NASA Astrophysics Data System (ADS)

Chen, Xiang; Zhang, Xiong

2016-12-01

MoF (Moment of Fluid) method is one of the most accurate approaches among various surface reconstruction algorithms. As other second order methods, MoF method needs to solve an implicit optimization problem to obtain the optimal approximate surface. Therefore, the partial derivatives of the objective function have to be involved during the iteration for efficiency and accuracy. However, to the best of our knowledge, the derivatives are currently estimated numerically by finite difference approximation because it is very difficult to obtain the analytical derivatives of the object function for an implicit optimization problem. Employing numerical derivatives in an iteration not only increase the computational cost, but also deteriorate the convergence rate and robustness of the iteration due to their numerical error. In this paper, the analytical first order partial derivatives of the objective function are deduced for 3D problems. The analytical derivatives can be calculated accurately, so they are incorporated into the MoF method to improve its accuracy, efficiency and robustness. Numerical studies show that by using the analytical derivatives the iterations are converged in all mixed cells with the efficiency improvement of 3 to 4 times.

Implicit time-marching solution of the Navier-Stokes equations for thrust reversing and thrust vectoring nozzle flows

NASA Technical Reports Server (NTRS)

Imlay, S. T.

1986-01-01

An implicit finite volume method is investigated for the solution of the compressible Navier-Stokes equations for flows within thrust reversing and thrust vectoring nozzles. Thrust reversing nozzles typically have sharp corners, and the rapid expansion and large turning angles near these corners are shown to cause unacceptable time step restrictions when conventional approximate factorization methods are used. In this investigation these limitations are overcome by using second-order upwind differencing and line Gauss-Siedel relaxation. This method is implemented with a zonal mesh so that flows through complex nozzle geometries may be efficiently calculated. Results are presented for five nozzle configurations including two with time varying geometries. Three cases are compared with available experimental data and the results are generally acceptable.

Semi-automatic sparse preconditioners for high-order finite element methods on non-uniform meshes

NASA Astrophysics Data System (ADS)

Austin, Travis M.; Brezina, Marian; Jamroz, Ben; Jhurani, Chetan; Manteuffel, Thomas A.; Ruge, John

2012-05-01

High-order finite elements often have a higher accuracy per degree of freedom than the classical low-order finite elements. However, in the context of implicit time-stepping methods, high-order finite elements present challenges to the construction of efficient simulations due to the high cost of inverting the denser finite element matrix. There are many cases where simulations are limited by the memory required to store the matrix and/or the algorithmic components of the linear solver. We are particularly interested in preconditioned Krylov methods for linear systems generated by discretization of elliptic partial differential equations with high-order finite elements. Using a preconditioner like Algebraic Multigrid can be costly in terms of memory due to the need to store matrix information at the various levels. We present a novel method for defining a preconditioner for systems generated by high-order finite elements that is based on a much sparser system than the original high-order finite element system. We investigate the performance for non-uniform meshes on a cube and a cubed sphere mesh, showing that the sparser preconditioner is more efficient and uses significantly less memory. Finally, we explore new methods to construct the sparse preconditioner and examine their effectiveness for non-uniform meshes. We compare results to a direct use of Algebraic Multigrid as a preconditioner and to a two-level additive Schwarz method.

Progress on a Taylor weak statement finite element algorithm for high-speed aerodynamic flows

NASA Technical Reports Server (NTRS)

Baker, A. J.; Freels, J. D.

1989-01-01

A new finite element numerical Computational Fluid Dynamics (CFD) algorithm has matured to the point of efficiently solving two-dimensional high speed real-gas compressible flow problems in generalized coordinates on modern vector computer systems. The algorithm employs a Taylor Weak Statement classical Galerkin formulation, a variably implicit Newton iteration, and a tensor matrix product factorization of the linear algebra Jacobian under a generalized coordinate transformation. Allowing for a general two-dimensional conservation law system, the algorithm has been exercised on the Euler and laminar forms of the Navier-Stokes equations. Real-gas fluid properties are admitted, and numerical results verify solution accuracy, efficiency, and stability over a range of test problem parameters.

Accuracy of a class of concurrent algorithms for transient finite element analysis

NASA Technical Reports Server (NTRS)

Ortiz, Michael; Sotelino, Elisa D.; Nour-Omid, Bahram

1988-01-01

The accuracy of a new class of concurrent procedures for transient finite element analysis is examined. A phase error analysis is carried out which shows that wave retardation leading to unacceptable loss of accuracy may occur if a Courant condition based on the dimensions of the subdomains is violated. Numerical tests suggest that this Courant condition is conservative for typical structural applications and may lead to a marked increase in accuracy as the number of subdomains is increased. Theoretical speed-up ratios are derived which suggest that the algorithms under consideration can be expected to exhibit a performance superior to that of globally implicit methods when implemented on parallel machines.

A hybrid incremental projection method for thermal-hydraulics applications

NASA Astrophysics Data System (ADS)

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

2016-07-01

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

A hybrid incremental projection method for thermal-hydraulics applications

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

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

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

A hybrid incremental projection method for thermal-hydraulics applications

DOE PAGES

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

2016-07-01

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

The Pivotal Role of Effort Beliefs in Mediating Implicit Theories of Intelligence and Achievement Goals and Academic Motivations

ERIC Educational Resources Information Center

Tempelaar, Dirk T.; Rienties, Bart; Giesbers, Bas; Gijselaers, Wim H.

2015-01-01

Empirical studies into meaning systems surrounding implicit theories of intelligence typically entail two stringent assumptions: that different implicit theories and different effort beliefs represent opposite poles on a single scale, and that implicit theories directly impact the constructs as achievement goals and academic motivations. Through…

Documentation of a numerical code for the simulation of variable density ground-water flow in three dimensions

USGS Publications Warehouse

Kuiper, L.K.

1985-01-01

A numerical code is documented for the simulation of variable density time dependent groundwater flow in three dimensions. The groundwater density, although variable with distance, is assumed to be constant in time. The Integrated Finite Difference grid elements in the code follow the geologic strata in the modeled area. If appropriate, the determination of hydraulic head in confining beds can be deleted to decrease computation time. The strongly implicit procedure (SIP), successive over-relaxation (SOR), and eight different preconditioned conjugate gradient (PCG) methods are used to solve the approximating equations. The use of the computer program that performs the calculations in the numerical code is emphasized. Detailed instructions are given for using the computer program, including input data formats. An example simulation and the Fortran listing of the program are included. (USGS)

A monolithic homotopy continuation algorithm with application to computational fluid dynamics

NASA Astrophysics Data System (ADS)

Brown, David A.; Zingg, David W.

2016-09-01

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

Changes of Explicit and Implicit Stigma in Medical Students during Psychiatric Clerkship.

PubMed

Wang, Peng-Wei; Ko, Chih-Hung; Chen, Cheng-Sheng; Yang, Yi-Hsin Connine; Lin, Huang-Chi; Cheng, Cheng-Chung; Tsang, Hin-Yeung; Wu, Ching-Kuan; Yen, Cheng-Fang

2016-04-01

This study examines the differences in explicit and implicit stigma between medical and non-medical undergraduate students at baseline; the changes of explicit and implicit stigma in medical undergraduate and non-medical undergraduate students after a 1-month psychiatric clerkship and 1-month follow-up period; and the differences in the changes of explicit and implicit stigma between medical and non-medical undergraduate students. Seventy-two medical undergraduate students and 64 non-medical undergraduate students were enrolled. All participants were interviewed at intake and after 1 month. The Taiwanese version of the Stigma Assessment Scale and the Implicit Association Test were used to measure the participants' explicit and implicit stigma. Neither explicit nor implicit stigma differed between two groups at baseline. The medical, but not the non-medical, undergraduate students had a significant decrease in explicit stigma during the 1-month period of follow-up. Neither the medical nor the non-medical undergraduate students exhibited a significant change in implicit stigma during the one-month of follow-up, however. There was an interactive effect between group and time on explicit stigma but not on implicit stigma. Explicit but not implicit stigma toward mental illness decreased in the medical undergraduate students after a psychiatric clerkship. Further study is needed to examine how to improve implicit stigma toward mental illness.

Parallel Semi-Implicit Spectral Element Atmospheric Model

NASA Astrophysics Data System (ADS)

Fournier, A.; Thomas, S.; Loft, R.

2001-05-01

The shallow-water equations (SWE) have long been used to test atmospheric-modeling numerical methods. The SWE contain essential wave-propagation and nonlinear effects of more complete models. We present a semi-implicit (SI) improvement of the Spectral Element Atmospheric Model to solve the SWE (SEAM, Taylor et al. 1997, Fournier et al. 2000, Thomas & Loft 2000). SE methods are h-p finite element methods combining the geometric flexibility of size-h finite elements with the accuracy of degree-p spectral methods. Our work suggests that exceptional parallel-computation performance is achievable by a General-Circulation-Model (GCM) dynamical core, even at modest climate-simulation resolutions (>1o). The code derivation involves weak variational formulation of the SWE, Gauss(-Lobatto) quadrature over the collocation points, and Legendre cardinal interpolators. Appropriate weak variation yields a symmetric positive-definite Helmholtz operator. To meet the Ladyzhenskaya-Babuska-Brezzi inf-sup condition and avoid spurious modes, we use a staggered grid. The SI scheme combines leapfrog and Crank-Nicholson schemes for the nonlinear and linear terms respectively. The localization of operations to elements ideally fits the method to cache-based microprocessor computer architectures --derivatives are computed as collections of small (8x8), naturally cache-blocked matrix-vector products. SEAM also has desirable boundary-exchange communication, like finite-difference models. Timings on on the IBM SP and Compaq ES40 supercomputers indicate that the SI code (20-min timestep) requires 1/3 the CPU time of the explicit code (2-min timestep) for T42 resolutions. Both codes scale nearly linearly out to 400 processors. We achieved single-processor performance up to 30% of peak for both codes on the 375-MHz IBM Power-3 processors. Fast computation and linear scaling lead to a useful climate-simulation dycore only if enough model time is computed per unit wall-clock time. An efficient SI solver is essential to substantially increase this rate. Parallel preconditioning for an iterative conjugate-gradient elliptic solver is described. We are building a GCM dycore capable of 200 GF% lOPS sustained performance on clustered RISC/cache architectures using hybrid MPI/OpenMP programming.

Tetrahedral Finite-Volume Solutions to the Navier-Stokes Equations on Complex Configurations

NASA Technical Reports Server (NTRS)

Frink, Neal T.; Pirzadeh, Shahyar Z.

1998-01-01

A review of the algorithmic features and capabilities of the unstructured-grid flow solver USM3Dns is presented. This code, along with the tetrahedral grid generator, VGRIDns, is being extensively used throughout the U.S. for solving the Euler and Navier-Stokes equations on complex aerodynamic problems. Spatial discretization is accomplished by a tetrahedral cell-centered finite-volume formulation using Roe's upwind flux difference splitting. The fluxes are limited by either a Superbee or MinMod limiter. Solution reconstruction within the tetrahedral cells is accomplished with a simple, but novel, multidimensional analytical formula. Time is advanced by an implicit backward-Euler time-stepping scheme. Flow turbulence effects are modeled by the Spalart-Allmaras one-equation model, which is coupled with a wall function to reduce the number of cells in the near-wall region of the boundary layer. The issues of accuracy and robustness of USM3Dns Navier-Stokes capabilities are addressed for a flat-plate boundary layer, and a full F-16 aircraft with external stores at transonic speed.

Assessment of implicit health attitudes: a multitrait-multimethod approach and a comparison between patients with hypochondriasis and patients with anxiety disorders.

PubMed

Weck, Florian; Höfling, Volkmar

2015-01-01

Two adaptations of the Implicit Association Task were used to assess implicit anxiety (IAT-Anxiety) and implicit health attitudes (IAT-Hypochondriasis) in patients with hypochondriasis (n = 58) and anxiety patients (n = 71). Explicit anxieties and health attitudes were assessed using questionnaires. The analysis of several multitrait-multimethod models indicated that the low correlation between explicit and implicit measures of health attitudes is due to the substantial methodological differences between the IAT and the self-report questionnaire. Patients with hypochondriasis displayed significantly more dysfunctional explicit and implicit health attitudes than anxiety patients, but no differences were found regarding explicit and implicit anxieties. The study demonstrates the specificity of explicit and implicit dysfunctional health attitudes among patients with hypochondriasis.

A modified Dodge algorithm for the parabolized Navier-Stokes equation and compressible duct flows

NASA Technical Reports Server (NTRS)

Cooke, C. H.

1981-01-01

A revised version of Dodge's split-velocity method for numerical calculation of compressible duct flow was developed. The revision incorporates balancing of mass flow rates on each marching step in order to maintain front-to-back continuity during the calculation. The (checkerboard) zebra algorithm is applied to solution of the three dimensional continuity equation in conservative form. A second-order A-stable linear multistep method is employed in effecting a marching solution of the parabolized momentum equations. A checkerboard iteration is used to solve the resulting implicit nonlinear systems of finite-difference equations which govern stepwise transition. Qualitive agreement with analytical predictions and experimental results was obtained for some flows with well-known solutions.

Numerical computation of space shuttle orbiter flow field

NASA Technical Reports Server (NTRS)

Tannehill, John C.

1988-01-01

A new parabolized Navier-Stokes (PNS) code has been developed to compute the hypersonic, viscous chemically reacting flow fields around 3-D bodies. The flow medium is assumed to be a multicomponent mixture of thermally perfect but calorically imperfect gases. The new PNS code solves the gas dynamic and species conservation equations in a coupled manner using a noniterative, implicit, approximately factored, finite difference algorithm. The space-marching method is made well-posed by special treatment of the streamwise pressure gradient term. The code has been used to compute hypersonic laminar flow of chemically reacting air over cones at angle of attack. The results of the computations are compared with the results of reacting boundary-layer computations and show excellent agreement.

Some problems of the calculation of three-dimensional boundary layer flows on general configurations

NASA Technical Reports Server (NTRS)

Cebeci, T.; Kaups, K.; Mosinskis, G. J.; Rehn, J. A.

1973-01-01

An accurate solution of the three-dimensional boundary layer equations over general configurations such as those encountered in aircraft and space shuttle design requires a very efficient, fast, and accurate numerical method with suitable turbulence models for the Reynolds stresses. The efficiency, speed, and accuracy of a three-dimensional numerical method together with the turbulence models for the Reynolds stresses are examined. The numerical method is the implicit two-point finite difference approach (Box Method) developed by Keller and applied to the boundary layer equations by Keller and Cebeci. In addition, a study of some of the problems that may arise in the solution of these equations for three-dimensional boundary layer flows over general configurations.

Verification of a neutronic code for transient analysis in reactors with Hex-z geometry

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

Gonzalez-Pintor, S.; Verdu, G.; Ginestar, D.

Due to the geometry of the fuel bundles, to simulate reactors such as VVER reactors it is necessary to develop methods that can deal with hexagonal prisms as basic elements of the spatial discretization. The main features of a code based on a high order finite element method for the spatial discretization of the neutron diffusion equation and an implicit difference method for the time discretization of this equation are presented and the performance of the code is tested solving the first exercise of the AER transient benchmark. The obtained results are compared with the reference results of the benchmarkmore » and with the results provided by PARCS code. (authors)« less

A Navier-Stokes Solution of Hull-Ring Wing-Thruster Interaction

NASA Technical Reports Server (NTRS)

Yang, C.-I.; Hartwich, P.; Sundaram, P.

1991-01-01

Navier-Stokes simulations of high Reynolds number flow around an axisymmetric body supported in a water tunnel were made. The numerical method is based on a finite-differencing high resolution second-order accurate implicit upwind scheme. Four different configurations were investigated, these are: (1) barebody; (2) body with an operating propeller; (3) body with a ring wing; and (4) body with a ring wing and an operating propeller. Pressure and velocity components near the stern region were obtained computationally and are shown to compare favorably with the experimental data. The method correctly predicts the existence and extent of stern flow separation for the barebody and the absence of flow separation for the three other configurations with ring wing and/or propeller.

BeamDyn: A High-Fidelity Wind Turbine Blade Solver in the FAST Modular Framework: Preprint

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

Wang, Q.; Sprague, M.; Jonkman, J.

2015-01-01

BeamDyn, a Legendre-spectral-finite-element implementation of geometrically exact beam theory (GEBT), was developed to meet the design challenges associated with highly flexible composite wind turbine blades. In this paper, the governing equations of GEBT are reformulated into a nonlinear state-space form to support its coupling within the modular framework of the FAST wind turbine computer-aided engineering (CAE) tool. Different time integration schemes (implicit and explicit) were implemented and examined for wind turbine analysis. Numerical examples are presented to demonstrate the capability of this new beam solver. An example analysis of a realistic wind turbine blade, the CX-100, is also presented asmore » validation.« less

Computation and analysis for a constrained entropy optimization problem in finance

NASA Astrophysics Data System (ADS)

He, Changhong; Coleman, Thomas F.; Li, Yuying

2008-12-01

In [T. Coleman, C. He, Y. Li, Calibrating volatility function bounds for an uncertain volatility model, Journal of Computational Finance (2006) (submitted for publication)], an entropy minimization formulation has been proposed to calibrate an uncertain volatility option pricing model (UVM) from market bid and ask prices. To avoid potential infeasibility due to numerical error, a quadratic penalty function approach is applied. In this paper, we show that the solution to the quadratic penalty problem can be obtained by minimizing an objective function which can be evaluated via solving a Hamilton-Jacobian-Bellman (HJB) equation. We prove that the implicit finite difference solution of this HJB equation converges to its viscosity solution. In addition, we provide computational examples illustrating accuracy of calibration.

Using implicit attitudes of exercise importance to predict explicit exercise dependence symptoms and exercise behaviors.

PubMed

Forrest, Lauren N; Smith, April R; Fussner, Lauren M; Dodd, Dorian R; Clerkin, Elise M

2016-01-01

"Fast" (i.e., implicit) processing is relatively automatic; "slow" (i.e., explicit) processing is relatively controlled and can override automatic processing. These different processing types often produce different responses that uniquely predict behaviors. In the present study, we tested if explicit, self-reported symptoms of exercise dependence and an implicit association of exercise as important predicted exercise behaviors and change in problematic exercise attitudes. We assessed implicit attitudes of exercise importance and self-reported symptoms of exercise dependence at Time 1. Participants reported daily exercise behaviors for approximately one month, and then completed a Time 2 assessment of self-reported exercise dependence symptoms. Undergraduate males and females (Time 1, N = 93; Time 2, N = 74) tracked daily exercise behaviors for one month and completed an Implicit Association Test assessing implicit exercise importance and subscales of the Exercise Dependence Questionnaire (EDQ) assessing exercise dependence symptoms. Implicit attitudes of exercise importance and Time 1 EDQ scores predicted Time 2 EDQ scores. Further, implicit exercise importance and Time 1 EDQ scores predicted daily exercise intensity while Time 1 EDQ scores predicted the amount of days exercised. Implicit and explicit processing appear to uniquely predict exercise behaviors and attitudes. Given that different implicit and explicit processes may drive certain exercise factors (e.g., intensity and frequency, respectively), these behaviors may contribute to different aspects of exercise dependence.

Using implicit attitudes of exercise importance to predict explicit exercise dependence symptoms and exercise behaviors

PubMed Central

Forrest, Lauren N.; Smith, April R.; Fussner, Lauren M.; Dodd, Dorian R.; Clerkin, Elise M.

2015-01-01

Objectives ”Fast” (i.e., implicit) processing is relatively automatic; “slow” (i.e., explicit) processing is relatively controlled and can override automatic processing. These different processing types often produce different responses that uniquely predict behaviors. In the present study, we tested if explicit, self-reported symptoms of exercise dependence and an implicit association of exercise as important predicted exercise behaviors and change in problematic exercise attitudes. Design We assessed implicit attitudes of exercise importance and self-reported symptoms of exercise dependence at Time 1. Participants reported daily exercise behaviors for approximately one month, and then completed a Time 2 assessment of self-reported exercise dependence symptoms. Method Undergraduate males and females (Time 1, N = 93; Time 2, N = 74) tracked daily exercise behaviors for one month and completed an Implicit Association Test assessing implicit exercise importance and subscales of the Exercise Dependence Questionnaire (EDQ) assessing exercise dependence symptoms. Results Implicit attitudes of exercise importance and Time 1 EDQ scores predicted Time 2 EDQ scores. Further, implicit exercise importance and Time 1 EDQ scores predicted daily exercise intensity while Time 1 EDQ scores predicted the amount of days exercised. Conclusion Implicit and explicit processing appear to uniquely predict exercise behaviors and attitudes. Given that different implicit and explicit processes may drive certain exercise factors (e.g., intensity and frequency, respectively), these behaviors may contribute to different aspects of exercise dependence. PMID:26195916

Analyse et caracterisation d'interactions fluide-structure instationnaires en grands deplacements

NASA Astrophysics Data System (ADS)

Cori, Jean-Francois

Flapping wings for flying and oscillating fins for swimming stand out as the most complex yet efficient propulsion methods found in nature. Understanding the phenomena involved is a great challenge generating significant interests, especially in the growing field of Micro Air Vehicles. The thrust and lift are induced by oscillating foils thanks to a complex phenomenon of unsteady fluid-structure interaction (FSI). The aim of the dissertation is to develop an efficient CFD framework for simulating the FSI process involved in the propulsion or the power extraction of an oscillating flexible airfoil in a viscous incompressible flow. The numerical method relies on direct implicit monolithic formulation using high-order implicit time integrators. We use an Arbitrary Lagrangian Eulerian (ALE) formulation of the equations designed to satisfy the Geometric Conservation Law (GCL) and to guarantee that the high order temporal accuracy of the time integrators observed on fixed meshes is preserved on ALE deforming meshes. Hyperelastic structural Saint-Venant Kirchhoff model, viscous incompressible Navier-Stokes equations for the flow, Newton's law for the point mass and equilibrium equations at the interface form one large monolithic system. The fully implicit FSI approach uses coincidents nodes on the fluid-structure interface, so that loads, velocities and displacements are evaluated at the same location and at the same time. The problem is solved in an implicit manner using a Newton-Raphson pseudo-solid finite element approach. High-order implicit Runge-Kutta time integrators are implemented (up to 5th order) to improve the accuracy and reduce the computational cost. In this context of stiff interaction problems, the highly stable fully implicit one-step approach is an original alternative to traditional multistep or explicit one-step finite element approaches. The methodology has been verified with three different test-cases. Thorough time-step refinement studies for a rigid oscillating airfoil on deforming meshes, for flow induced vibrations of a flexible strip and for a self-propulsed flapping airfoil indicate that the stability of the proposed approach is always observed even with large time steps, spurious oscillations on the structure are avoided without any damping and the high order accuracy of the IRK schemes is maintained. We have applied our powerful FSI framework on three interesting applications, with a detailed dimensional analysis to obtain their characteristic parameters. Firstly, we have studied the vibrational characteristics of a well-documented fluid-structure interaction case : a flexible strip fixed behind a rigid square cylinder. Our results compare favorably with previous works. The accuracy of the IRK time integrators (even for the pressure field of incompressible flow), their unconditional stability and their non-dissipative nature produced results revealing new, never previously reported, higher frequency structural forces weakly coupled with the fluid. Secondly, we have explored the propulsive and power extraction characteristics of rigid and flexible flapping airfoils. For the power extraction, we found an excellent agreement with literature results. A parametric study indicates the optimal motion parameters to get high propulsive efficiencies. An optimal flexibility seems to improve power extraction efficiency. Finally, a survey on flapping propulsion has given initial results for a self-propulsed airfoil and has opened a new way of studying propulsive efficiency. (Abstract shortened by UMI.)

HEATING 7. 1 user's manual

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

Childs, K.W.

1991-07-01

HEATING is a FORTRAN program designed to solve steady-state and/or transient heat conduction problems in one-, two-, or three- dimensional Cartesian, cylindrical, or spherical coordinates. A model may include multiple materials, and the thermal conductivity, density, and specific heat of each material may be both time- and temperature-dependent. The thermal conductivity may be anisotropic. Materials may undergo change of phase. Thermal properties of materials may be input or may be extracted from a material properties library. Heating generation rates may be dependent on time, temperature, and position, and boundary temperatures may be time- and position-dependent. The boundary conditions, which maymore » be surface-to-boundary or surface-to-surface, may be specified temperatures or any combination of prescribed heat flux, forced convection, natural convection, and radiation. The boundary condition parameters may be time- and/or temperature-dependent. General graybody radiation problems may be modeled with user-defined factors for radiant exchange. The mesh spacing may be variable along each axis. HEATING is variably dimensioned and utilizes free-form input. Three steady-state solution techniques are available: point-successive-overrelaxation iterative method with extrapolation, direct-solution (for one-dimensional or two-dimensional problems), and conjugate gradient. Transient problems may be solved using one of several finite-difference schemes: Crank-Nicolson implicit, Classical Implicit Procedure (CIP), Classical Explicit Procedure (CEP), or Levy explicit method (which for some circumstances allows a time step greater than the CEP stability criterion). The solution of the system of equations arising from the implicit techniques is accomplished by point-successive-overrelaxation iteration and includes procedures to estimate the optimum acceleration parameter.« less

The Use of Non-Standard Devices in Finite Element Analysis

NASA Technical Reports Server (NTRS)

Schur, Willi W.; Broduer, Steve (Technical Monitor)

2001-01-01

A general mathematical description of the response behavior of thin-skin pneumatic envelopes and many other membrane and cable structures produces under-constrained systems that pose severe difficulties to analysis. These systems are mobile, and the general mathematical description exposes the mobility. Yet the response behavior of special under-constrained structures under special loadings can be accurately predicted using a constrained mathematical description. The static response behavior of systems that are infinitesimally mobile, such as a non-slack membrane subtended from a rigid or elastic boundary frame, can be easily analyzed using such general mathematical description as afforded by the non-linear, finite element method using an implicit solution scheme if the incremental uploading is guided through a suitable path. Similarly, if such structures are assembled with structural lack of fit that provides suitable self-stress, then dynamic response behavior can be predicted by the non-linear, finite element method and an implicit solution scheme. An explicit solution scheme is available for evolution problems. Such scheme can be used via the method of dynamic relaxation to obtain the solution to a static problem. In some sense, pneumatic envelopes and many other compliant structures can be said to have destiny under a specified loading system. What that means to the analyst is that what happens on the evolution path of the solution is irrelevant as long as equilibrium is achieved at destiny under full load and that the equilibrium is stable in the vicinity of that load. The purpose of this paper is to alert practitioners to the fact that non-standard procedures in finite element analysis are useful and can be legitimate although they burden their users with the requirement to use special caution. Some interesting findings that are useful to the US Scientific Balloon Program and that could not be obtained without non-standard techniques are presented.

MPSalsa Version 1.5: A Finite Element Computer Program for Reacting Flow Problems: Part 1 - Theoretical Development

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

Devine, K.D.; Hennigan, G.L.; Hutchinson, S.A.

1999-01-01

The theoretical background for the finite element computer program, MPSalsa Version 1.5, is presented in detail. MPSalsa is designed to solve laminar or turbulent low Mach number, two- or three-dimensional incompressible and variable density reacting fluid flows on massively parallel computers, using a Petrov-Galerkin finite element formulation. The code has the capability to solve coupled fluid flow (with auxiliary turbulence equations), heat transport, multicomponent species transport, and finite-rate chemical reactions, and to solve coupled multiple Poisson or advection-diffusion-reaction equations. The program employs the CHEMKIN library to provide a rigorous treatment of multicomponent ideal gas kinetics and transport. Chemical reactions occurringmore » in the gas phase and on surfaces are treated by calls to CHEMKIN and SURFACE CHEMK3N, respectively. The code employs unstructured meshes, using the EXODUS II finite element database suite of programs for its input and output files. MPSalsa solves both transient and steady flows by using fully implicit time integration, an inexact Newton method and iterative solvers based on preconditioned Krylov methods as implemented in the Aztec. solver library.« less

Micromechanics based simulation of ductile fracture in structural steels

NASA Astrophysics Data System (ADS)

Yellavajjala, Ravi Kiran

The broader aim of this research is to develop fundamental understanding of ductile fracture process in structural steels, propose robust computational models to quantify the associated damage, and provide numerical tools to simplify the implementation of these computational models into general finite element framework. Mechanical testing on different geometries of test specimens made of ASTM A992 steels is conducted to experimentally characterize the ductile fracture at different stress states under monotonic and ultra-low cycle fatigue (ULCF) loading. Scanning electron microscopy studies of the fractured surfaces is conducted to decipher the underlying microscopic damage mechanisms that cause fracture in ASTM A992 steels. Detailed micromechanical analyses for monotonic and cyclic loading are conducted to understand the influence of stress triaxiality and Lode parameter on the void growth phase of ductile fracture. Based on monotonic analyses, an uncoupled micromechanical void growth model is proposed to predict ductile fracture. This model is then incorporated in to finite element program as a weakly coupled model to simulate the loss of load carrying capacity in the post microvoid coalescence regime for high triaxialities. Based on the cyclic analyses, an uncoupled micromechanics based cyclic void growth model is developed to predict the ULCF life of ASTM A992 steels subjected to high stress triaxialities. Furthermore, a computational fracture locus for ASTM A992 steels is developed and incorporated in to finite element program as an uncoupled ductile fracture model. This model can be used to predict the ductile fracture initiation under monotonic loading in a wide range of triaxiality and Lode parameters. Finally, a coupled microvoid elongation and dilation based continuum damage model is proposed, implemented, calibrated and validated. This model is capable of simulating the local softening caused by the various phases of ductile fracture process under monotonic loading for a wide range of stress states. Novel differentiation procedures based on complex analyses along with existing finite difference methods and automatic differentiation are extended using perturbation techniques to evaluate tensor derivatives. These tensor differentiation techniques are then used to automate nonlinear constitutive models into implicit finite element framework. Finally, the efficiency of these automation procedures is demonstrated using benchmark problems.

PIXIE3D: A Parallel, Implicit, eXtended MHD 3D Code

NASA Astrophysics Data System (ADS)

Chacon, Luis

2006-10-01

We report on the development of PIXIE3D, a 3D parallel, fully implicit Newton-Krylov extended MHD code in general curvilinear geometry. PIXIE3D employs a second-order, finite-volume-based spatial discretization that satisfies remarkable properties such as being conservative, solenoidal in the magnetic field to machine precision, non-dissipative, and linearly and nonlinearly stable in the absence of physical dissipation. PIXIE3D employs fully-implicit Newton-Krylov methods for the time advance. Currently, second-order implicit schemes such as Crank-Nicolson and BDF2 (2^nd order backward differentiation formula) are available. PIXIE3D is fully parallel (employs PETSc for parallelism), and exhibits excellent parallel scalability. A parallel, scalable, MG preconditioning strategy, based on physics-based preconditioning ideas, has been developed for resistive MHD, and is currently being extended to Hall MHD. In this poster, we will report on progress in the algorithmic formulation for extended MHD, as well as the the serial and parallel performance of PIXIE3D in a variety of problems and geometries. L. Chac'on, Comput. Phys. Comm., 163 (3), 143-171 (2004) L. Chac'on et al., J. Comput. Phys. 178 (1), 15- 36 (2002); J. Comput. Phys., 188 (2), 573-592 (2003) L. Chac'on, 32nd EPS Conf. Plasma Physics, Tarragona, Spain, 2005 L. Chac'on et al., 33rd EPS Conf. Plasma Physics, Rome, Italy, 2006

Ablation, Thermal Response, and Chemistry Program for Analysis of Thermal Protection Systems

NASA Technical Reports Server (NTRS)

Milos, Frank S.; Chen, Yih-Kanq

2010-01-01

In previous work, the authors documented the Multicomponent Ablation Thermochemistry (MAT) and Fully Implicit Ablation and Thermal response (FIAT) programs. In this work, key features from MAT and FIAT were combined to create the new Fully Implicit Ablation, Thermal response, and Chemistry (FIATC) program. FIATC is fully compatible with FIAT (version 2.5) but has expanded capabilities to compute the multispecies surface chemistry and ablation rate as part of the surface energy balance. This new methodology eliminates B' tables, provides blown species fractions as a function of time, and enables calculations that would otherwise be impractical (e.g. 4+ dimensional tables) such as pyrolysis and ablation with kinetic rates or unequal diffusion coefficients. Equations and solution procedures are presented, then representative calculations of equilibrium and finite-rate ablation in flight and ground-test environments are discussed.

User's manual for the one-dimensional hypersonic experimental aero-thermodynamic (1DHEAT) data reduction code

NASA Technical Reports Server (NTRS)

Hollis, Brian R.

1995-01-01

A FORTRAN computer code for the reduction and analysis of experimental heat transfer data has been developed. This code can be utilized to determine heat transfer rates from surface temperature measurements made using either thin-film resistance gages or coaxial surface thermocouples. Both an analytical and a numerical finite-volume heat transfer model are implemented in this code. The analytical solution is based on a one-dimensional, semi-infinite wall thickness model with the approximation of constant substrate thermal properties, which is empirically corrected for the effects of variable thermal properties. The finite-volume solution is based on a one-dimensional, implicit discretization. The finite-volume model directly incorporates the effects of variable substrate thermal properties and does not require the semi-finite wall thickness approximation used in the analytical model. This model also includes the option of a multiple-layer substrate. Fast, accurate results can be obtained using either method. This code has been used to reduce several sets of aerodynamic heating data, of which samples are included in this report.

Age-Related and Intelligence-Related Differences in Implicit Memory: Effects of Generation on a Word-Fragment Completion Test.

ERIC Educational Resources Information Center

Komatsu, Shin-Ichi; And Others

1996-01-01

Investigated developmental differences in implicit memory performance. Subjects ranged in age from second grade to college level. Results suggested that there are two different components in implicit memory, one that shows no developmental difference and relies heavily on perceptual processing and one that shows an age-related or…

Preconditioning for the Navier-Stokes equations with finite-rate chemistry

NASA Technical Reports Server (NTRS)

Godfrey, Andrew G.; Walters, Robert W.; Van Leer, Bram

1993-01-01

The preconditioning procedure for generalized finite-rate chemistry and the proper preconditioning for the one-dimensional Navier-Stokes equations are presented. Eigenvalue stiffness is resolved and convergence-rate acceleration is demonstrated over the entire Mach-number range from the incompressible to the hypersonic. Specific benefits are realized at low and transonic flow speeds. The extended preconditioning matrix accounts for thermal and chemical non-equilibrium and its implementation is explained for both explicit and implicit time marching. The effect of higher-order spatial accuracy and various flux splittings is investigated. Numerical analysis reveals the possible theoretical improvements from using proconditioning at all Mach numbers. Numerical results confirm the expectations from the numerical analysis. Representative test cases include flows with previously troublesome embedded high-condition-number regions.

Self-consistent field theory simulations of polymers on arbitrary domains

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

Ouaknin, Gaddiel, E-mail: gaddielouaknin@umail.ucsb.edu; Laachi, Nabil; Delaney, Kris

2016-12-15

We introduce a framework for simulating the mesoscale self-assembly of block copolymers in arbitrary confined geometries subject to Neumann boundary conditions. We employ a hybrid finite difference/volume approach to discretize the mean-field equations on an irregular domain represented implicitly by a level-set function. The numerical treatment of the Neumann boundary conditions is sharp, i.e. it avoids an artificial smearing in the irregular domain boundary. This strategy enables the study of self-assembly in confined domains and enables the computation of physically meaningful quantities at the domain interface. In addition, we employ adaptive grids encoded with Quad-/Oc-trees in parallel to automatically refinemore » the grid where the statistical fields vary rapidly as well as at the boundary of the confined domain. This approach results in a significant reduction in the number of degrees of freedom and makes the simulations in arbitrary domains using effective boundary conditions computationally efficient in terms of both speed and memory requirement. Finally, in the case of regular periodic domains, where pseudo-spectral approaches are superior to finite differences in terms of CPU time and accuracy, we use the adaptive strategy to store chain propagators, reducing the memory footprint without loss of accuracy in computed physical observables.« less

Numerical simulation of double‐diffusive finger convection

USGS Publications Warehouse

Hughes, Joseph D.; Sanford, Ward E.; Vacher, H. Leonard

2005-01-01

A hybrid finite element, integrated finite difference numerical model is developed for the simulation of double‐diffusive and multicomponent flow in two and three dimensions. The model is based on a multidimensional, density‐dependent, saturated‐unsaturated transport model (SUTRA), which uses one governing equation for fluid flow and another for solute transport. The solute‐transport equation is applied sequentially to each simulated species. Density coupling of the flow and solute‐transport equations is accounted for and handled using a sequential implicit Picard iterative scheme. High‐resolution data from a double‐diffusive Hele‐Shaw experiment, initially in a density‐stable configuration, is used to verify the numerical model. The temporal and spatial evolution of simulated double‐diffusive convection is in good agreement with experimental results. Numerical results are very sensitive to discretization and correspond closest to experimental results when element sizes adequately define the spatial resolution of observed fingering. Numerical results also indicate that differences in the molecular diffusivity of sodium chloride and the dye used to visualize experimental sodium chloride concentrations are significant and cause inaccurate mapping of sodium chloride concentrations by the dye, especially at late times. As a result of reduced diffusion, simulated dye fingers are better defined than simulated sodium chloride fingers and exhibit more vertical mass transfer.

An efficient finite differences method for the computation of compressible, subsonic, unsteady flows past airfoils and panels

NASA Astrophysics Data System (ADS)

Colera, Manuel; Pérez-Saborid, Miguel

2017-09-01

A finite differences scheme is proposed in this work to compute in the time domain the compressible, subsonic, unsteady flow past an aerodynamic airfoil using the linearized potential theory. It improves and extends the original method proposed in this journal by Hariharan, Ping and Scott [1] by considering: (i) a non-uniform mesh, (ii) an implicit time integration algorithm, (iii) a vectorized implementation and (iv) the coupled airfoil dynamics and fluid dynamic loads. First, we have formulated the method for cases in which the airfoil motion is given. The scheme has been tested on well known problems in unsteady aerodynamics -such as the response to a sudden change of the angle of attack and to a harmonic motion of the airfoil- and has been proved to be more accurate and efficient than other finite differences and vortex-lattice methods found in the literature. Secondly, we have coupled our method to the equations governing the airfoil dynamics in order to numerically solve problems where the airfoil motion is unknown a priori as happens, for example, in the cases of the flutter and the divergence of a typical section of a wing or of a flexible panel. Apparently, this is the first self-consistent and easy-to-implement numerical analysis in the time domain of the compressible, linearized coupled dynamics of the (generally flexible) airfoil-fluid system carried out in the literature. The results for the particular case of a rigid airfoil show excellent agreement with those reported by other authors, whereas those obtained for the case of a cantilevered flexible airfoil in compressible flow seem to be original or, at least, not well-known.

Effects of Turbulence Model on Prediction of Hot-Gas Lateral Jet Interaction in a Supersonic Crossflow

DTIC Science & Technology

2015-07-01

performance computing time from the US Department of Defense (DOD) High Performance Computing Modernization program at the US Army Research Laboratory...Approved OMB No. 0704-0188 Public reporting burden for this collection of information is estimated to average 1 hour per response, including the time ...dimensional, compressible, Reynolds-averaged Navier-Stokes (RANS) equations are solved using a finite volume method. A point-implicit time - integration

Phase Field Fracture Mechanics.

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

Robertson, Brett Anthony

For this assignment, a newer technique of fracture mechanics using a phase field approach, will be examined and compared with experimental data for a bend test and a tension test. The software being used is Sierra Solid Mechanics, an implicit/explicit finite element code developed at Sandia National Labs in Albuquerque, New Mexico. The bend test experimental data was also obtained at Sandia Labs while the tension test data was found in a report online from Purdue University.

Application of Parallel Time-Implicit Discontinuous Galerkin Finite Element Methods to Hypersonic Nonequilibrium Flow Problems

DTIC Science & Technology

2014-05-01

heating prediction to grid alignment along the shock . . . . . . . . 36 1-12 Large variation in heating predictions for 3D hypersonic flow over cylinder...100 4-12 Taylor Vortex problem . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 102 4-13 Taylor Vortex problem: 3D ...149 6-16 3D contours for temperature, T for MIG and US3D for only O2 test case . . . . 150 6-17 Stagnation line plots for only

Accuracy of the domain method for the material derivative approach to shape design sensitivities

NASA Technical Reports Server (NTRS)

Yang, R. J.; Botkin, M. E.

1987-01-01

Numerical accuracy for the boundary and domain methods of the material derivative approach to shape design sensitivities is investigated through the use of mesh refinement. The results show that the domain method is generally more accurate than the boundary method, using the finite element technique. It is also shown that the domain method is equivalent, under certain assumptions, to the implicit differentiation approach not only theoretically but also numerically.

Development of a steady potential solver for use with linearized, unsteady aerodynamic analyses

NASA Technical Reports Server (NTRS)

Hoyniak, Daniel; Verdon, Joseph M.

1991-01-01

A full potential steady flow solver (SFLOW) developed explicitly for use with an inviscid unsteady aerodynamic analysis (LINFLO) is described. The steady solver uses the nonconservative form of the nonlinear potential flow equations together with an implicit, least squares, finite difference approximation to solve for the steady flow field. The difference equations were developed on a composite mesh which consists of a C grid embedded in a rectilinear (H grid) cascade mesh. The composite mesh is capable of resolving blade to blade and far field phenomena on the H grid, while accurately resolving local phenomena on the C grid. The resulting system of algebraic equations is arranged in matrix form using a sparse matrix package and solved by Newton's method. Steady and unsteady results are presented for two cascade configurations: a high speed compressor and a turbine with high exit Mach number.

Unsteady free convection flow past a semi-infinite vertical plate with constant heat flux in water based nanofluids

NASA Astrophysics Data System (ADS)

Narahari, Marneni

2018-04-01

The unsteady free convective flow of nanofluids past a semi-infinite vertical plate with uniform heat flux has been investigated numerically. An implicit finite difference technique of Crank-Nicolson scheme has been employed to solve the governing partial differential equations. Five different types of water based nanofluids containing Cu, Ag, Al2O3, CuO and TiO2 nanoparticles are considered to study the fluid flow characteristics with various time and solid volume fraction parameters. It is found that the local as well as the average Nusselt number for nanofluids is higher than the pure fluid (water). The local skin-friction is higher for pure fluid as compared to the nanofluids. The present numerical results obtained for local Nusselt number are validated with the previously published correlation results for a limiting case and it is found that the results are in good agreement.

Incompressible spectral-element method: Derivation of equations

NASA Technical Reports Server (NTRS)

Deanna, Russell G.

1993-01-01

A fractional-step splitting scheme breaks the full Navier-Stokes equations into explicit and implicit portions amenable to the calculus of variations. Beginning with the functional forms of the Poisson and Helmholtz equations, we substitute finite expansion series for the dependent variables and derive the matrix equations for the unknown expansion coefficients. This method employs a new splitting scheme which differs from conventional three-step (nonlinear, pressure, viscous) schemes. The nonlinear step appears in the conventional, explicit manner, the difference occurs in the pressure step. Instead of solving for the pressure gradient using the nonlinear velocity, we add the viscous portion of the Navier-Stokes equation from the previous time step to the velocity before solving for the pressure gradient. By combining this 'predicted' pressure gradient with the nonlinear velocity in an explicit term, and the Crank-Nicholson method for the viscous terms, we develop a Helmholtz equation for the final velocity.

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.

National differences in gender–science stereotypes predict national sex differences in science and math achievement

PubMed Central

Nosek, Brian A.; Smyth, Frederick L.; Sriram, N.; Lindner, Nicole M.; Devos, Thierry; Ayala, Alfonso; Bar-Anan, Yoav; Bergh, Robin; Cai, Huajian; Gonsalkorale, Karen; Kesebir, Selin; Maliszewski, Norbert; Neto, Félix; Olli, Eero; Park, Jaihyun; Schnabel, Konrad; Shiomura, Kimihiro; Tulbure, Bogdan Tudor; Wiers, Reinout W.; Somogyi, Mónika; Akrami, Nazar; Ekehammar, Bo; Vianello, Michelangelo; Banaji, Mahzarin R.; Greenwald, Anthony G.

2009-01-01

About 70% of more than half a million Implicit Association Tests completed by citizens of 34 countries revealed expected implicit stereotypes associating science with males more than with females. We discovered that nation-level implicit stereotypes predicted nation-level sex differences in 8th-grade science and mathematics achievement. Self-reported stereotypes did not provide additional predictive validity of the achievement gap. We suggest that implicit stereotypes and sex differences in science participation and performance are mutually reinforcing, contributing to the persistent gender gap in science engagement. PMID:19549876

Implicit Geometry Meshing for the simulation of Rotary Friction Welding

NASA Astrophysics Data System (ADS)

Schmicker, D.; Persson, P.-O.; Strackeljan, J.

2014-08-01

The simulation of Rotary Friction Welding (RFW) is a challenging task, since it states a coupled problem of phenomena like large plastic deformations, heat flux, contact and friction. In particular the mesh generation and its restoration when using a Lagrangian description of motion is of significant severity. In this regard Implicit Geometry Meshing (IGM) algorithms are promising alternatives to the more conventional explicit methods. Because of the implicit description of the geometry during remeshing, the IGM procedure turns out to be highly robust and generates spatial discretizations of high quality regardless of the complexity of the flash shape and its inclusions. A model for efficient RFW simulation is presented, which is based on a Carreau fluid law, an Augmented Lagrange approach in mapping the incompressible deformations, a penalty contact approach, a fully regularized Coulomb-/fluid friction law and a hybrid time integration strategy. The implementation of the IGM algorithm using 6-node triangular finite elements is described in detail. The techniques are demonstrated on a fairly complex friction welding problem, demonstrating the performance and the potentials of the proposed method. The techniques are general and straight-forward to implement, and offer the potential of successful adoption to a wide range of other engineering problems.

A Meta-Analysis Suggests Different Neural Correlates for Implicit and Explicit Learning.

PubMed

Loonis, Roman F; Brincat, Scott L; Antzoulatos, Evan G; Miller, Earl K

2017-10-11

A meta-analysis of non-human primates performing three different tasks (Object-Match, Category-Match, and Category-Saccade associations) revealed signatures of explicit and implicit learning. Performance improved equally following correct and error trials in the Match (explicit) tasks, but it improved more after correct trials in the Saccade (implicit) task, a signature of explicit versus implicit learning. Likewise, error-related negativity, a marker for error processing, was greater in the Match (explicit) tasks. All tasks showed an increase in alpha/beta (10-30 Hz) synchrony after correct choices. However, only the implicit task showed an increase in theta (3-7 Hz) synchrony after correct choices that decreased with learning. In contrast, in the explicit tasks, alpha/beta synchrony increased with learning and decreased thereafter. Our results suggest that explicit versus implicit learning engages different neural mechanisms that rely on different patterns of oscillatory synchrony. Copyright © 2017 Elsevier Inc. All rights reserved.

A Data Parallel Multizone Navier-Stokes Code

NASA Technical Reports Server (NTRS)

Jespersen, Dennis C.; Levit, Creon; Kwak, Dochan (Technical Monitor)

1995-01-01

We have developed a data parallel multizone compressible Navier-Stokes code on the Connection Machine CM-5. The code is set up for implicit time-stepping on single or multiple structured grids. For multiple grids and geometrically complex problems, we follow the "chimera" approach, where flow data on one zone is interpolated onto another in the region of overlap. We will describe our design philosophy and give some timing results for the current code. The design choices can be summarized as: 1. finite differences on structured grids; 2. implicit time-stepping with either distributed solves or data motion and local solves; 3. sequential stepping through multiple zones with interzone data transfer via a distributed data structure. We have implemented these ideas on the CM-5 using CMF (Connection Machine Fortran), a data parallel language which combines elements of Fortran 90 and certain extensions, and which bears a strong similarity to High Performance Fortran (HPF). One interesting feature is the issue of turbulence modeling, where the architecture of a parallel machine makes the use of an algebraic turbulence model awkward, whereas models based on transport equations are more natural. We will present some performance figures for the code on the CM-5, and consider the issues involved in transitioning the code to HPF for portability to other parallel platforms.

Efficient Coupling of Fluid-Plasma and Monte-Carlo-Neutrals Models for Edge Plasma Transport

NASA Astrophysics Data System (ADS)

Dimits, A. M.; Cohen, B. I.; Friedman, A.; Joseph, I.; Lodestro, L. L.; Rensink, M. E.; Rognlien, T. D.; Sjogreen, B.; Stotler, D. P.; Umansky, M. V.

2017-10-01

UEDGE has been valuable for modeling transport in the tokamak edge and scrape-off layer due in part to its efficient fully implicit solution of coupled fluid neutrals and plasma models. We are developing an implicit coupling of the kinetic Monte-Carlo (MC) code DEGAS-2, as the neutrals model component, to the UEDGE plasma component, based on an extension of the Jacobian-free Newton-Krylov (JFNK) method to MC residuals. The coupling components build on the methods and coding already present in UEDGE. For the linear Krylov iterations, a procedure has been developed to ``extract'' a good preconditioner from that of UEDGE. This preconditioner may also be used to greatly accelerate the convergence rate of a relaxed fixed-point iteration, which may provide a useful ``intermediate'' algorithm. The JFNK method also requires calculation of Jacobian-vector products, for which any finite-difference procedure is inaccurate when a MC component is present. A semi-analytical procedure that retains the standard MC accuracy and fully kinetic neutrals physics is therefore being developed. Prepared for US DOE by LLNL under Contract DE-AC52-07NA27344 and LDRD project 15-ERD-059, by PPPL under Contract DE-AC02-09CH11466, and supported in part by the U.S. DOE, OFES.

Modeling the curing process of thick-section autoclave cured composites

NASA Technical Reports Server (NTRS)

Loos, A. C.; Dara, P. H.

1985-01-01

Temperature gradients are significant during cure of large area, thick-section composites. Such temperature gradients result in nonuniformly cured parts with high void contents, poor ply compaction, and variations in the fiber/resin distribution. A model was developed to determine the temperature distribution in thick-section autoclave cured composites. Using the model, long with temperature measurements obtained from the thick-section composites, the effects of various processing parameters on the thermal response of the composites were examined. A one-dimensional heat transfer model was constructed for the composite-tool assembly. The governing differential equations and associated boundary conditions describing one-dimensional unsteady heat-conduction in the composite, tool plate, and pressure plate are given. Solution of the thermal model was obtained using an implicit finite difference technique.

Orientational Order on Surfaces: The Coupling of Topology, Geometry, and Dynamics

NASA Astrophysics Data System (ADS)

Nestler, M.; Nitschke, I.; Praetorius, S.; Voigt, A.

2018-02-01

We consider the numerical investigation of surface bound orientational order using unit tangential vector fields by means of a gradient flow equation of a weak surface Frank-Oseen energy. The energy is composed of intrinsic and extrinsic contributions, as well as a penalization term to enforce the unity of the vector field. Four different numerical discretizations, namely a discrete exterior calculus approach, a method based on vector spherical harmonics, a surface finite element method, and an approach utilizing an implicit surface description, the diffuse interface method, are described and compared with each other for surfaces with Euler characteristic 2. We demonstrate the influence of geometric properties on realizations of the Poincaré-Hopf theorem and show examples where the energy is decreased by introducing additional orientational defects.

A modified Dodge algorithm for the parabolized Navier-Stokes equations and compressible duct flows

NASA Technical Reports Server (NTRS)

Cooke, C. H.; Dwoyer, D. M.

1983-01-01

A revised version of Dodge's split-velocity method for numerical calculation of compressible duct flow was developed. The revision incorporates balancing of mass flow rates on each marching step in order to maintain front-to-back continuity during the calculation. The (checkerboard) zebra algorithm is applied to solution of the three dimensional continuity equation in conservative form. A second-order A-stable linear multistep method is employed in effecting a marching solution of the parabolized momentum equations. A checkerboard iteration is used to solve the resulting implicit nonlinear systems of finite-difference equations which govern stepwise transition. Qualitative agreement with analytical predictions and experimental results was obtained for some flows with well-known solutions. Previously announced in STAR as N82-16363

Shock/vortex interaction and vortex-breakdown modes

NASA Technical Reports Server (NTRS)

Kandil, Osama A.; Kandil, H. A.; Liu, C. H.

1992-01-01

Computational simulation and study of shock/vortex interaction and vortex-breakdown modes are considered for bound (internal) and unbound (external) flow domains. The problem is formulated using the unsteady, compressible, full Navier-Stokes (NS) equations which are solved using an implicit, flux-difference splitting, finite-volume scheme. For the bound flow domain, a supersonic swirling flow is considered in a configured circular duct and the problem is solved for quasi-axisymmetric and three-dimensional flows. For the unbound domain, a supersonic swirling flow issued from a nozzle into a uniform supersonic flow of lower Mach number is considered for quasi-axisymmetric and three-dimensional flows. The results show several modes of breakdown; e.g., no-breakdown, transient single-bubble breakdown, transient multi-bubble breakdown, periodic multi-bubble multi-frequency breakdown and helical breakdown.

Parametric Shape Optimization of Lens-Focused Piezoelectric Ultrasound Transducers.

PubMed

Thomas, Gilles P L; Chapelon, Jean-Yves; Bera, Jean-Christophe; Lafon, Cyril

2018-05-01

Focused transducers composed of flat piezoelectric ceramic coupled with an acoustic lens present an economical alternative to curved piezoelectric ceramics and are already in use in a variety of fields. Using a displacement/pressure (u/p) mixed finite element formulation combined with parametric level-set functions to implicitly define the boundaries between the materials and the fluid-structure interface, a method to optimize the shape of acoustic lens made of either one or multiple materials is presented. From that method, two 400 kHz focused transducers using acoustic lens were designed and built with different rapid prototyping methods, one of them made with a combination of two materials, and experimental measurements of the pressure field around the focal point are in good agreement with the presented model.

Generation of linear dynamic models from a digital nonlinear simulation

NASA Technical Reports Server (NTRS)

Daniele, C. J.; Krosel, S. M.

1979-01-01

The results and methodology used to derive linear models from a nonlinear simulation are presented. It is shown that averaged positive and negative perturbations in the state variables can reduce numerical errors in finite difference, partial derivative approximations and, in the control inputs, can better approximate the system response in both directions about the operating point. Both explicit and implicit formulations are addressed. Linear models are derived for the F 100 engine, and comparisons of transients are made with the nonlinear simulation. The problem of startup transients in the nonlinear simulation in making these comparisons is addressed. Also, reduction of the linear models is investigated using the modal and normal techniques. Reduced-order models of the F 100 are derived and compared with the full-state models.

A Nonlinear Programming Perspective on Sensitivity Calculations for Systems Governed by State Equations

NASA Technical Reports Server (NTRS)

Lewis, Robert Michael

1997-01-01

This paper discusses the calculation of sensitivities. or derivatives, for optimization problems involving systems governed by differential equations and other state relations. The subject is examined from the point of view of nonlinear programming, beginning with the analytical structure of the first and second derivatives associated with such problems and the relation of these derivatives to implicit differentiation and equality constrained optimization. We also outline an error analysis of the analytical formulae and compare the results with similar results for finite-difference estimates of derivatives. We then attend to an investigation of the nature of the adjoint method and the adjoint equations and their relation to directions of steepest descent. We illustrate the points discussed with an optimization problem in which the variables are the coefficients in a differential operator.

Investigation of chemically reacting and radiating supersonic internal flows

NASA Technical Reports Server (NTRS)

Mani, M.; Tiwari, S. N.

1986-01-01

The two-dimensional spatially elliptic Navier-Stokes equations are used to investigate the chemically reacting and radiating supersonic flow of the hydrogen-air system between two parallel plates and in a channel with a ten degree compression-expansion ramp at the lower boundary. The explicit unsplit finite-difference technique of MacCormack is used to advance the governing equations in time until convergence is achieved. The chemistry source term in the species equation is treated implicitly to alleviate the stiffness associated with fast reactions. The tangent slab approximation is employed in the radiative flux formation. Both pseudo-gray and nongray models are used to represent the absorption characteristics of the participating species. Results obtained for specific conditions indicate that the radiative interaction can have a significant influence on the flow field.

Unsteady mixed convection flow of Casson fluid past an inclined stretching sheet in the presence of nanoparticles

NASA Astrophysics Data System (ADS)

Rawi, N. A.; Ilias, M. R.; Lim, Y. J.; Isa, Z. M.; Shafie, S.

2017-09-01

The influence of nanoparticles on the unsteady mixed convection flow of Casson fluid past an inclined stretching sheet is investigated in this paper. The effect of gravity modulation on the flow is also considered. Carboxymethyl cellulose solution (CMC) is chosen as the base fluid and copper as nanoparticles. The basic governing nonlinear partial differential equations are transformed using appropriate similarity transformation and solved numerically using an implicit finite difference scheme by means of the Keller-box method. The effect of nanoparticles volume fraction together with the effect of inclination angle and Casson parameter on the enhancement of heat transfer of Casson nanofluid is discussed in details. The velocity and temperature profiles as well as the skin friction coefficient and the Nusselt number are presented and analyzed.

Reducing Children's Implicit Racial Bias Through Exposure to Positive Out-Group Exemplars.

PubMed

Gonzalez, Antonya M; Steele, Jennifer R; Baron, Andrew S

2017-01-01

Studies with adults suggest that implicit preferences favoring White versus Black individuals can be reduced through exposure to positive Black exemplars. However, it remains unclear whether developmental differences exist in the capacity for these biases to be changed. This study included 369 children and examined whether their implicit racial bias would be reduced following exposure to positive Black exemplars. Results showed that children's implicit pro-White bias was reduced following exposure to positive Black exemplars, but only for older children (M age  = ~10 years). Younger children's (M age  = ~7 years) implicit bias was not affected by this intervention. These results suggest developmental differences in the malleability of implicit racial biases and point to possible age differences in intervention effectiveness. © 2016 The Authors. Child Development © 2016 Society for Research in Child Development, Inc.

Discrimination of Native-like States of Membrane Proteins with Implicit Membrane-based Scoring Functions.

PubMed

Dutagaci, Bercem; Wittayanarakul, Kitiyaporn; Mori, Takaharu; Feig, Michael

2017-06-13

A scoring protocol based on implicit membrane-based scoring functions and a new protocol for optimizing the positioning of proteins inside the membrane was evaluated for its capacity to discriminate native-like states from misfolded decoys. A decoy set previously established by the Baker lab (Proteins: Struct., Funct., Genet. 2006, 62, 1010-1025) was used along with a second set that was generated to cover higher resolution models. The Implicit Membrane Model 1 (IMM1), IMM1 model with CHARMM 36 parameters (IMM1-p36), generalized Born with simple switching (GBSW), and heterogeneous dielectric generalized Born versions 2 (HDGBv2) and 3 (HDGBv3) were tested along with the new HDGB van der Waals (HDGBvdW) model that adds implicit van der Waals contributions to the solvation free energy. For comparison, scores were also calculated with the distance-scaled finite ideal-gas reference (DFIRE) scoring function. Z-scores for native state discrimination, energy vs root-mean-square deviation (RMSD) correlations, and the ability to select the most native-like structures as top-scoring decoys were evaluated to assess the performance of the scoring functions. Ranking of the decoys in the Baker set that were relatively far from the native state was challenging and dominated largely by packing interactions that were captured best by DFIRE with less benefit of the implicit membrane-based models. Accounting for the membrane environment was much more important in the second decoy set where especially the HDGB-based scoring functions performed very well in ranking decoys and providing significant correlations between scores and RMSD, which shows promise for improving membrane protein structure prediction and refinement applications. The new membrane structure scoring protocol was implemented in the MEMScore web server ( http://feiglab.org/memscore ).

Theoretical restrictions on longest implicit time scales in Markov state models of biomolecular dynamics

NASA Astrophysics Data System (ADS)

Sinitskiy, Anton V.; Pande, Vijay S.

2018-01-01

Markov state models (MSMs) have been widely used to analyze computer simulations of various biomolecular systems. They can capture conformational transitions much slower than an average or maximal length of a single molecular dynamics (MD) trajectory from the set of trajectories used to build the MSM. A rule of thumb claiming that the slowest implicit time scale captured by an MSM should be comparable by the order of magnitude to the aggregate duration of all MD trajectories used to build this MSM has been known in the field. However, this rule has never been formally proved. In this work, we present analytical results for the slowest time scale in several types of MSMs, supporting the above rule. We conclude that the slowest implicit time scale equals the product of the aggregate sampling and four factors that quantify: (1) how much statistics on the conformational transitions corresponding to the longest implicit time scale is available, (2) how good the sampling of the destination Markov state is, (3) the gain in statistics from using a sliding window for counting transitions between Markov states, and (4) a bias in the estimate of the implicit time scale arising from finite sampling of the conformational transitions. We demonstrate that in many practically important cases all these four factors are on the order of unity, and we analyze possible scenarios that could lead to their significant deviation from unity. Overall, we provide for the first time analytical results on the slowest time scales captured by MSMs. These results can guide further practical applications of MSMs to biomolecular dynamics and allow for higher computational efficiency of simulations.

A transient FETI methodology for large-scale parallel implicit computations in structural mechanics

NASA Technical Reports Server (NTRS)

Farhat, Charbel; Crivelli, Luis; Roux, Francois-Xavier

1992-01-01

Explicit codes are often used to simulate the nonlinear dynamics of large-scale structural systems, even for low frequency response, because the storage and CPU requirements entailed by the repeated factorizations traditionally found in implicit codes rapidly overwhelm the available computing resources. With the advent of parallel processing, this trend is accelerating because explicit schemes are also easier to parallelize than implicit ones. However, the time step restriction imposed by the Courant stability condition on all explicit schemes cannot yet -- and perhaps will never -- be offset by the speed of parallel hardware. Therefore, it is essential to develop efficient and robust alternatives to direct methods that are also amenable to massively parallel processing because implicit codes using unconditionally stable time-integration algorithms are computationally more efficient when simulating low-frequency dynamics. Here we present a domain decomposition method for implicit schemes that requires significantly less storage than factorization algorithms, that is several times faster than other popular direct and iterative methods, that can be easily implemented on both shared and local memory parallel processors, and that is both computationally and communication-wise efficient. The proposed transient domain decomposition method is an extension of the method of Finite Element Tearing and Interconnecting (FETI) developed by Farhat and Roux for the solution of static problems. Serial and parallel performance results on the CRAY Y-MP/8 and the iPSC-860/128 systems are reported and analyzed for realistic structural dynamics problems. These results establish the superiority of the FETI method over both the serial/parallel conjugate gradient algorithm with diagonal scaling and the serial/parallel direct method, and contrast the computational power of the iPSC-860/128 parallel processor with that of the CRAY Y-MP/8 system.

Are implicit self-esteem measures valid for assessing individual and cultural differences?

PubMed

Falk, Carl F; Heine, Steven J; Takemura, Kosuke; Zhang, Cathy X J; Hsu, Chih-Wei

2015-02-01

Our research utilized two popular theoretical conceptualizations of implicit self-esteem: 1) implicit self-esteem as a global automatic reaction to the self; and 2) implicit self-esteem as a context/domain specific construct. Under this framework, we present an extensive search for implicit self-esteem measure validity among different cultural groups (Study 1) and under several experimental manipulations (Study 2). In Study 1, Euro-Canadians (N = 107), Asian-Canadians (N = 187), and Japanese (N = 112) completed a battery of implicit self-esteem, explicit self-esteem, and criterion measures. Included implicit self-esteem measures were either popular or provided methodological improvements upon older methods. Criterion measures were sampled from previous research on implicit self-esteem and included self-report and independent ratings. In Study 2, Americans (N = 582) completed a shorter battery of these same types of measures under either a control condition, an explicit prime meant to activate the self-concept in a particular context, or prime meant to activate self-competence related implicit attitudes. Across both studies, explicit self-esteem measures far outperformed implicit self-esteem measures in all cultural groups and under all experimental manipulations. Implicit self-esteem measures are not valid for individual or cross-cultural comparisons. We speculate that individuals may not form implicit associations with the self as an attitudinal object. © 2013 Wiley Periodicals, Inc.

Implicit visual learning and the expression of learning.

PubMed

Haider, Hilde; Eberhardt, Katharina; Kunde, Alexander; Rose, Michael

2013-03-01

Although the existence of implicit motor learning is now widely accepted, the findings concerning perceptual implicit learning are ambiguous. Some researchers have observed perceptual learning whereas other authors have not. The review of the literature provides different reasons to explain this ambiguous picture, such as differences in the underlying learning processes, selective attention, or differences in the difficulty to express this knowledge. In three experiments, we investigated implicit visual learning within the original serial reaction time task. We used different response devices (keyboard vs. mouse) in order to manipulate selective attention towards response dimensions. Results showed that visual and motor sequence learning differed in terms of RT-benefits, but not in terms of the amount of knowledge assessed after training. Furthermore, visual sequence learning was modulated by selective attention. However, the findings of all three experiments suggest that selective attention did not alter implicit but rather explicit learning processes. Copyright © 2012 Elsevier Inc. All rights reserved.

Age Differences in Explicit and Implicit Age Attitudes Across the Life Span.

PubMed

Chopik, William J; Giasson, Hannah L

2017-08-01

Biased judgments about others can operate both within and outside of our conscious awareness. However, little attention has been paid to how implicit and explicit attitudes differ across the life span, particularly with respect to age bias. In the current study, we examined age differences in implicit and explicit attitudes towards older individuals. Participants (N = 704,151) ranging from age 15 to 94 completed the Implicit Association Test and explicit self-report measures of bias against older adults. The associations between age bias and several demographic characteristics (e.g., gender, education) were also examined. A preference for younger people was found among participants of all ages; however, implicit and explicit attitudes showed divergent associations with age. Implicit preference for younger people was highest among older adults; explicit preference for younger people was lowest among older adults. Examining age differences in implicit and explicit attitudes sheds light into the development and complexities of aging perceptions in different age groups. The current study's findings are discussed in the context of applications to and implications of reducing prejudice toward older adults. © The Author 2017. Published by Oxford University Press on behalf of The Gerontological Society of America. All rights reserved. For permissions, please e-mail: journals.permissions@oup.com.

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

NASA Astrophysics Data System (ADS)

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

2016-12-01

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

Implicit Learning as an Ability

ERIC Educational Resources Information Center

Kaufman, Scott Barry; DeYoung, Caroline G.; Gray, Jeremy R.; Jimenez, Luis; Brown, Jamie; Mackintosh, Nicholas

2010-01-01

The ability to automatically and implicitly detect complex and noisy regularities in the environment is a fundamental aspect of human cognition. Despite considerable interest in implicit processes, few researchers have conceptualized implicit learning as an ability with meaningful individual differences. Instead, various researchers (e.g., Reber,…

Finite element analysis of residual stress field induced by laser shock peening

NASA Astrophysics Data System (ADS)

Nam, Taeksun

The finite element method is applied to analyze the laser shock peening process (LSP) for thick parts (considered as a semi-infinite half space) and thin parts (finite thickness domain). The technology of LSP is used to enhance mechanical properties such as fatigue life, fretting fatigue life, resistance to stress corrosion cracking and surface hardness. These enhanced material properties are directly related to the magnitude and distribution of the plastic strain and associated residual stresses due to shockwaves induced by LSP. To reduce the process development cost and time, the prediction of residual stress field is very useful to provide a base design guideline for selecting appropriate LSP conditions for evaluation. An axisymmetric Finite Element Analysis (FEA) code, named SHOCKWAVE, is developed in order to complement shortcomings of applying commercial FEA codes at extremely high strain rates (as high as 104 -106/sec). The rate dependent plasticity theory is applied along with the small strain assumption. The solution process consists of an explicit dynamic loading analysis for shock loading stage and a static unloading analysis (implicit) to determine the equilibrium state for the residual stress and plastic strain fields. Some of the highlights explored in this investigation entail: (i) overstress power law models for the rate dependence, (ii) various hardening models, (iii) a second-order accurate implicit algorithm for the plastic consistency condition, (iv) an adaptively expanding domain scheme to trace the stress-free boundary condition in a simple way, (v) a special uniform meshing scheme to avoid the usual assembly process and repeated calculations for the stiffness matrix, (vi) mesh sensitivity study, (vii) comparisons with measured data provided and supported by the LSP Technologies, Inc. The dynamic behavior of Ti-6Al-4V at high strain rates can be investigated by using the split torsional Hopkinson bar experiment and by a longitudinal shock loading simulation in uniaxial strain to obtain material parameters representing rate dependent plasticity. In case of the double-sided laser peening for a thin part, reversal in loading plays a significant role. The stress waves repeatedly recompose the pre-accumulated plastic strains because of the interaction of the primary and reflected stress waves. In an attempt to better represent the material behavior under repeated reversals and collapses in loading, a sequence of bend-reverse bend tests is performed to identify the material parameters of TI-6Al-4V needed for a nonlinear kinematic hardening model (Chaboche model). For a thick part (a semi-infinite domain), single shot as well as multiple shots (at the same location) cases are simulated and compared with measured data for two different loading magnitudes and three different hardening models. Some of the simulation results agree well with the measured data, depending on the choice of hardening model and the treatment of rate dependent material behavior at high strain rates. Only a single shot (on both sides) case is investigated for a thin part (a finite thickness domain) in terms of residual stress distribution. The disagreement between the computed results and the measured data is more pronounced in this case, needing further investigations on both sides of the fields.

Implementation of a kappa-epsilon turbulence model to RPLUS3D code

NASA Technical Reports Server (NTRS)

Chitsomboon, Tawit

1992-01-01

The RPLUS3D code has been developed at the NASA Lewis Research Center to support the National Aerospace Plane (NASP) project. The code has the ability to solve three dimensional flowfields with finite rate combustion of hydrogen and air. The combustion process of the hydrogen-air system are simulated by an 18 reaction path, 8 species chemical kinetic mechanism. The code uses a Lower-Upper (LU) decomposition numerical algorithm as its basis, making it a very efficient and robust code. Except for the Jacobian matrix for the implicit chemistry source terms, there is no inversion of a matrix even though a fully implicit numerical algorithm is used. A k-epsilon turbulence model has recently been incorporated into the code. Initial validations have been conducted for a flow over a flat plate. Results of the validation studies are shown. Some difficulties in implementing the k-epsilon equations to the code are also discussed.

Implementation of a kappa-epsilon turbulence model to RPLUS3D code

NASA Astrophysics Data System (ADS)

Chitsomboon, Tawit

1992-02-01

The RPLUS3D code has been developed at the NASA Lewis Research Center to support the National Aerospace Plane (NASP) project. The code has the ability to solve three dimensional flowfields with finite rate combustion of hydrogen and air. The combustion process of the hydrogen-air system are simulated by an 18 reaction path, 8 species chemical kinetic mechanism. The code uses a Lower-Upper (LU) decomposition numerical algorithm as its basis, making it a very efficient and robust code. Except for the Jacobian matrix for the implicit chemistry source terms, there is no inversion of a matrix even though a fully implicit numerical algorithm is used. A k-epsilon turbulence model has recently been incorporated into the code. Initial validations have been conducted for a flow over a flat plate. Results of the validation studies are shown. Some difficulties in implementing the k-epsilon equations to the code are also discussed.

Fully Implict Magneto-hydrodynamics Simulations of Coaxial Plasma Accelerators

DOE PAGES

Subramaniam, Vivek; Raja, Laxminarayan L.

2017-01-05

The resistive Magneto-Hydrodynamic (MHD) model describes the behavior of a strongly ionized plasma in the presence of external electric and magnetic fields. We developed a fully implicit MHD simulation tool to solve the resistive MHD governing equations in the context of a cell-centered finite-volume scheme. The primary objective of this study is to use the fully-implicit algorithm to obtain insights into the plasma acceleration and jet formation processes in Coaxial Plasma accelerators; electromagnetic acceleration devices that utilize self-induced magnetic fields to accelerate thermal plasmas to large velocities. We also carry out plasma-surface simulations in order to study the impact interactionsmore » when these high velocity plasma jets impinge on target material surfaces. Scaling studies are carried out to establish some basic functional relationships between the target-stagnation conditions and the current discharged between the coaxial electrodes.« less

Toward high-speed 3D nonlinear soft tissue deformation simulations using Abaqus software.

PubMed

Idkaidek, Ashraf; Jasiuk, Iwona

2015-12-01

We aim to achieve a fast and accurate three-dimensional (3D) simulation of a porcine liver deformation under a surgical tool pressure using the commercial finite element software Abaqus. The liver geometry is obtained using magnetic resonance imaging, and a nonlinear constitutive law is employed to capture large deformations of the tissue. Effects of implicit versus explicit analysis schemes, element type, and mesh density on computation time are studied. We find that Abaqus explicit and implicit solvers are capable of simulating nonlinear soft tissue deformations accurately using first-order tetrahedral elements in a relatively short time by optimizing the element size. This study provides new insights and guidance on accurate and relatively fast nonlinear soft tissue simulations. Such simulations can provide force feedback during robotic surgery and allow visualization of tissue deformations for surgery planning and training of surgical residents.

Finite element techniques for the Navier-Stokes equations in the primitive variable formulation and the vorticity stream-function formulation

NASA Technical Reports Server (NTRS)

Glaisner, F.; Tezduyar, T. E.

1987-01-01

Finite element procedures for the Navier-Stokes equations in the primitive variable formulation and the vorticity stream-function formulation have been implemented. For both formulations, streamline-upwind/Petrov-Galerkin techniques are used for the discretization of the transport equations. The main problem associated with the vorticity stream-function formulation is the lack of boundary conditions for vorticity at solid surfaces. Here an implicit treatment of the vorticity at no-slip boundaries is incorporated in a predictor-multicorrector time integration scheme. For the primitive variable formulation, mixed finite-element approximations are used. A nine-node element and a four-node + bubble element have been implemented. The latter is shown to exhibit a checkerboard pressure mode and a numerical treatment for this spurious pressure mode is proposed. The two methods are compared from the points of view of simulating internal and external flows and the possibilities of extensions to three dimensions.

Static Buckling Model Tests and Elasto-plastic Finite Element Analysis of a Pile in Layers with Various Thicknesses

NASA Astrophysics Data System (ADS)

Okajima, Kenji; Imai, Junichi; Tanaka, Tadatsugu; Iida, Toshiaki

Damage to piles in the liquefied ground is frequently reported. Buckling by the excess vertical load could be one of the causes of the pile damage, as well as the lateral flow of the ground and the lateral load at the pile head. The buckling mechanism is described as a complicated interaction between the pile deformation by the vertical load and the earth pressure change cased by the pile deformation. In this study, series of static buckling model tests of a pile were carried out in dried sand ground with various thickness of the layer. Finite element analysis was applied to the test results to verify the effectiveness of the elasto-plastic finite element analysis combining the implicit-explicit mixed type dynamic relaxation method with the return mapping method to the pile buckling problems. The test results and the analysis indicated the possibility that the buckling load of a pile decreases greatly where the thickness of the layer increases.

Real-time adaptive finite element solution of time-dependent Kohn-Sham equation

NASA Astrophysics Data System (ADS)

Bao, Gang; Hu, Guanghui; Liu, Di

2015-01-01

In our previous paper (Bao et al., 2012 [1]), a general framework of using adaptive finite element methods to solve the Kohn-Sham equation has been presented. This work is concerned with solving the time-dependent Kohn-Sham equations. The numerical methods are studied in the time domain, which can be employed to explain both the linear and the nonlinear effects. A Crank-Nicolson scheme and linear finite element space are employed for the temporal and spatial discretizations, respectively. To resolve the trouble regions in the time-dependent simulations, a heuristic error indicator is introduced for the mesh adaptive methods. An algebraic multigrid solver is developed to efficiently solve the complex-valued system derived from the semi-implicit scheme. A mask function is employed to remove or reduce the boundary reflection of the wavefunction. The effectiveness of our method is verified by numerical simulations for both linear and nonlinear phenomena, in which the effectiveness of the mesh adaptive methods is clearly demonstrated.

Development of an upwind, finite-volume code with finite-rate chemistry

NASA Technical Reports Server (NTRS)

Molvik, Gregory A.

1994-01-01

Under this grant, two numerical algorithms were developed to predict the flow of viscous, hypersonic, chemically reacting gases over three-dimensional bodies. Both algorithms take advantage of the benefits of upwind differencing, total variation diminishing techniques, and a finite-volume framework, but obtain their solution in two separate manners. The first algorithm is a zonal, time-marching scheme, and is generally used to obtain solutions in the subsonic portions of the flow field. The second algorithm is a much less expensive, space-marching scheme and can be used for the computation of the larger, supersonic portion of the flow field. Both codes compute their interface fluxes with a temporal Riemann solver and the resulting schemes are made fully implicit including the chemical source terms and boundary conditions. Strong coupling is used between the fluid dynamic, chemical, and turbulence equations. These codes have been validated on numerous hypersonic test cases and have provided excellent comparison with existing data.

One-Dimensional Ablation with Pyrolysis Gas Flow Using a Full Newton's Method and Finite Control Volume Procedure

NASA Technical Reports Server (NTRS)

Amar, Adam J.; Blackwell, Ben F.; Edwards, Jack R.

2007-01-01

The development and verification of a one-dimensional material thermal response code with ablation is presented. The implicit time integrator, control volume finite element spatial discretization, and Newton's method for nonlinear iteration on the entire system of residual equations have been implemented and verified for the thermochemical ablation of internally decomposing materials. This study is a continuation of the work presented in "One-Dimensional Ablation with Pyrolysis Gas Flow Using a Full Newton's Method and Finite Control Volume Procedure" (AIAA-2006-2910), which described the derivation, implementation, and verification of the constant density solid energy equation terms and boundary conditions. The present study extends the model to decomposing materials including decomposition kinetics, pyrolysis gas flow through the porous char layer, and a mixture (solid and gas) energy equation. Verification results are presented for the thermochemical ablation of a carbon-phenolic ablator which involves the solution of the entire system of governing equations.

Split Space-Marching Finite-Volume Method for Chemically Reacting Supersonic Flow

NASA Technical Reports Server (NTRS)

Rizzi, Arthur W.; Bailey, Harry E.

1976-01-01

A space-marching finite-volume method employing a nonorthogonal coordinate system and using a split differencing scheme for calculating steady supersonic flow over aerodynamic shapes is presented. It is a second-order-accurate mixed explicit-implicit procedure that solves the inviscid adiabatic and nondiffusive equations for chemically reacting flow in integral conservation-law form. The relationship between the finite-volume and differential forms of the equations is examined and the relative merits of each discussed. The method admits initial Cauchy data situated on any arbitrary surface and integrates them forward along a general curvilinear coordinate, distorting and deforming the surface as it advances. The chemical kinetics term is split from the convective terms which are themselves dimensionally split, thereby freeing the fluid operators from the restricted step size imposed by the chemical reactions and increasing the computational efficiency. The accuracy of this splitting technique is analyzed, a sufficient stability criterion is established, a representative flow computation is discussed, and some comparisons are made with another method.

A high order accurate finite element algorithm for high Reynolds number flow prediction

NASA Technical Reports Server (NTRS)

Baker, A. J.

1978-01-01

A Galerkin-weighted residuals formulation is employed to establish an implicit finite element solution algorithm for generally nonlinear initial-boundary value problems. Solution accuracy, and convergence rate with discretization refinement, are quantized in several error norms, by a systematic study of numerical solutions to several nonlinear parabolic and a hyperbolic partial differential equation characteristic of the equations governing fluid flows. Solutions are generated using selective linear, quadratic and cubic basis functions. Richardson extrapolation is employed to generate a higher-order accurate solution to facilitate isolation of truncation error in all norms. Extension of the mathematical theory underlying accuracy and convergence concepts for linear elliptic equations is predicted for equations characteristic of laminar and turbulent fluid flows at nonmodest Reynolds number. The nondiagonal initial-value matrix structure introduced by the finite element theory is determined intrinsic to improved solution accuracy and convergence. A factored Jacobian iteration algorithm is derived and evaluated to yield a consequential reduction in both computer storage and execution CPU requirements while retaining solution accuracy.

Implicit memory. Retention without remembering.

PubMed

Roediger, H L

1990-09-01

Explicit measures of human memory, such as recall or recognition, reflect conscious recollection of the past. Implicit tests of retention measure transfer (or priming) from past experience on tasks that do not require conscious recollection of recent experiences for their performance. The article reviews research on the relation between explicit and implicit memory. The evidence points to substantial differences between standard explicit and implicit tests, because many variables create dissociations between these tests. For example, although pictures are remembered better than words on explicit tests, words produce more priming than do pictures on several implicit tests. These dissociations may implicate different memory systems that subserve distinct memorial functions, but the present argument is that many dissociations can be understood by appealing to general principles that apply to both explicit and implicit tests. Phenomena studied under the rubric of implicit memory may have important implications in many other fields, including social cognition, problem solving, and cognitive development.

Combined effect of cortical cytoskeleton and transmembrane proteins on domain formation in biomembranes

PubMed Central

Sikder, Md. Kabir Uddin; Stone, Kyle A.; Kumar, P. B. Sunil; Laradji, Mohamed

2014-01-01

We investigate the combined effects of transmembrane proteins and the subjacent cytoskeleton on the dynamics of phase separation in multicomponent lipid bilayers using computer simulations of a particle-based implicit solvent model for lipid membranes with soft-core interactions. We find that microphase separation can be achieved by the protein confinement by the cytoskeleton. Our results have relevance to the finite size of lipid rafts in the plasma membrane of mammalian cells. PMID:25106608

An h-p Taylor-Galerkin finite element method for compressible Euler equations

NASA Technical Reports Server (NTRS)

Demkowicz, L.; Oden, J. T.; Rachowicz, W.; Hardy, O.

1991-01-01

An extension of the familiar Taylor-Galerkin method to arbitrary h-p spatial approximations is proposed. Boundary conditions are analyzed, and a linear stability result for arbitrary meshes is given, showing the unconditional stability for the parameter of implicitness alpha not less than 0.5. The wedge and blunt body problems are solved with both linear, quadratic, and cubic elements and h-adaptivity, showing the feasibility of higher orders of approximation for problems with shocks.

Three-Dimensional Viscous Alternating Direction Implicit Algorithm and Strategies for Shape Optimization

NASA Technical Reports Server (NTRS)

Pandya, Mohagna J.; Baysal, Oktay

1997-01-01

A gradient-based shape optimization based on quasi-analytical sensitivities has been extended for practical three-dimensional aerodynamic applications. The flow analysis has been rendered by a fully implicit, finite-volume formulation of the Euler and Thin-Layer Navier-Stokes (TLNS) equations. Initially, the viscous laminar flow analysis for a wing has been compared with an independent computational fluid dynamics (CFD) code which has been extensively validated. The new procedure has been demonstrated in the design of a cranked arrow wing at Mach 2.4 with coarse- and fine-grid based computations performed with Euler and TLNS equations. The influence of the initial constraints on the geometry and aerodynamics of the optimized shape has been explored. Various final shapes generated for an identical initial problem formulation but with different optimization path options (coarse or fine grid, Euler or TLNS), have been aerodynamically evaluated via a common fine-grid TLNS-based analysis. The initial constraint conditions show significant bearing on the optimization results. Also, the results demonstrate that to produce an aerodynamically efficient design, it is imperative to include the viscous physics in the optimization procedure with the proper resolution. Based upon the present results, to better utilize the scarce computational resources, it is recommended that, a number of viscous coarse grid cases using either a preconditioned bi-conjugate gradient (PbCG) or an alternating-direction-implicit (ADI) method, should initially be employed to improve the optimization problem definition, the design space and initial shape. Optimized shapes should subsequently be analyzed using a high fidelity (viscous with fine-grid resolution) flow analysis to evaluate their true performance potential. Finally, a viscous fine-grid-based shape optimization should be conducted, using an ADI method, to accurately obtain the final optimized shape.

Heating 7.2 user`s manual

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

Childs, K.W.

1993-02-01

HEATING is a general-purpose conduction heat transfer program written in Fortran 77. HEATING can solve steady-state and/or transient heat conduction problems in one-, two-, or three-dimensional Cartesian, cylindrical, or spherical coordinates. A model may include multiple materials, and the thermal conductivity, density, and specific heat of each material may be both time- and temperature-dependent. The thermal conductivity may also be anisotropic. Materials may undergo change of phase. Thermal properties of materials may be input or may be extracted from a material properties library. Heat-generation rates may be dependent on time, temperature, and position, and boundary temperatures may be time- andmore » position-dependent. The boundary conditions, which may be surface-to-environment or surface-to-surface, may be specified temperatures or any combination of prescribed heat flux, forced convection, natural convection, and radiation. The boundary condition parameters may be time- and/or temperature-dependent. General gray-body radiation problems may be modeled with user-defined factors for radiant exchange. The mesh spacing may be variable along each axis. HEATING uses a runtime memory allocation scheme to avoid having to recompile to match memory requirements for each specific problem. HEATING utilizes free-form input. Three steady-state solution techniques are available: point-successive-overrelaxation iterative method with extrapolation, direct-solution, and conjugate gradient. Transient problems may be solved using any one of several finite-difference schemes: Crank-Nicolson implicit, Classical Implicit Procedure (CIP), Classical Explicit Procedure (CEP), or Levy explicit method. The solution of the system of equations arising from the implicit techniques is accomplished by point-successive-overrelaxation iteration and includes procedures to estimate the optimum acceleration parameter.« less

Heating 7. 2 user's manual

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

Childs, K.W.

1993-02-01

HEATING is a general-purpose conduction heat transfer program written in Fortran 77. HEATING can solve steady-state and/or transient heat conduction problems in one-, two-, or three-dimensional Cartesian, cylindrical, or spherical coordinates. A model may include multiple materials, and the thermal conductivity, density, and specific heat of each material may be both time- and temperature-dependent. The thermal conductivity may also be anisotropic. Materials may undergo change of phase. Thermal properties of materials may be input or may be extracted from a material properties library. Heat-generation rates may be dependent on time, temperature, and position, and boundary temperatures may be time- andmore » position-dependent. The boundary conditions, which may be surface-to-environment or surface-to-surface, may be specified temperatures or any combination of prescribed heat flux, forced convection, natural convection, and radiation. The boundary condition parameters may be time- and/or temperature-dependent. General gray-body radiation problems may be modeled with user-defined factors for radiant exchange. The mesh spacing may be variable along each axis. HEATING uses a runtime memory allocation scheme to avoid having to recompile to match memory requirements for each specific problem. HEATING utilizes free-form input. Three steady-state solution techniques are available: point-successive-overrelaxation iterative method with extrapolation, direct-solution, and conjugate gradient. Transient problems may be solved using any one of several finite-difference schemes: Crank-Nicolson implicit, Classical Implicit Procedure (CIP), Classical Explicit Procedure (CEP), or Levy explicit method. The solution of the system of equations arising from the implicit techniques is accomplished by point-successive-overrelaxation iteration and includes procedures to estimate the optimum acceleration parameter.« less

Efficient and robust compositional two-phase reservoir simulation in fractured media

NASA Astrophysics Data System (ADS)

Zidane, A.; Firoozabadi, A.

2015-12-01

Compositional and compressible two-phase flow in fractured media has wide applications including CO2 injection. Accurate simulations are currently based on the discrete fracture approach using the cross-flow equilibrium model. In this approach the fractures and a small part of the matrix blocks are combined to form a grid cell. The major drawback is low computational efficiency. In this work we use the discrete-fracture approach to model the fractures where the fracture entities are described explicitly in the computational domain. We use the concept of cross-flow equilibrium in the fractures (FCFE). This allows using large matrix elements in the neighborhood of the fractures. We solve the fracture transport equations implicitly to overcome the Courant-Freidricks-Levy (CFL) condition in the small fracture elements. Our implicit approach is based on calculation of the derivative of the molar concentration of component i in phase (cαi ) with respect to the total molar concentration (ci ) at constant volume V and temperature T. This contributes to significant speed up of the code. The hybrid mixed finite element method (MFE) is used to solve for the velocity in both the matrix and the fractures coupled with the discontinuous Galerkin (DG) method to solve the species transport equations in the matrix, and a finite volume (FV) discretization in the fractures. In large scale problems the proposed approach is orders of magnitude faster than the existing models.

Computational manipulation of a radiative MHD flow with Hall current and chemical reaction in the presence of rotating fluid

NASA Astrophysics Data System (ADS)

Alias Suba, Subbu; Muthucumaraswamy, R.

2018-04-01

A numerical analysis of transient radiative MHD(MagnetoHydroDynamic) natural convective flow of a viscous, incompressible, electrically conducting and rotating fluid along a semi-infinite isothermal vertical plate is carried out taking into consideration Hall current, rotation and first order chemical reaction.The coupled non-linear partial differential equations are expressed in difference form using implicit finite difference scheme. The difference equations are then reduced to a system of linear algebraic equations with a tri-diagonal structure which is solved by Thomas Algorithm. The primary and secondary velocity profiles, temperature profile, concentration profile, skin friction, Nusselt number and Sherwood Number are depicted graphically for a range of values of rotation parameter, Hall parameter,magnetic parameter, chemical reaction parameter, radiation parameter, Prandtl number and Schmidt number.It is recognized that rate of heat transfer and rate of mass transfer decrease with increase in time but they increase with increasing values of radiation parameter and Schmidt number respectively.

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.

Weak imposition of frictionless contact constraints on automatically recovered high-order, embedded interfaces using the finite cell method

NASA Astrophysics Data System (ADS)

Bog, Tino; Zander, Nils; Kollmannsberger, Stefan; Rank, Ernst

2018-04-01

The finite cell method (FCM) is a fictitious domain approach that greatly simplifies simulations involving complex structures. Recently, the FCM has been applied to contact problems. The current study continues in this field by extending the concept of weakly enforced boundary conditions to inequality constraints for frictionless contact. Furthermore, it formalizes an approach that automatically recovers high-order contact surfaces of (implicitly defined) embedded geometries by means of an extended Marching Cubes algorithm. To further improve the accuracy of the discretization, irregularities at the boundary of contact zones are treated with multi-level hp-refinements. Numerical results and a systematic study of h-, p- and hp-refinements show that the FCM can efficiently provide accurate results for problems involving contact.

Finite element implementation of state variable-based viscoplasticity models

NASA Technical Reports Server (NTRS)

Iskovitz, I.; Chang, T. Y. P.; Saleeb, A. F.

1991-01-01

The implementation of state variable-based viscoplasticity models is made in a general purpose finite element code for structural applications of metals deformed at elevated temperatures. Two constitutive models, Walker's and Robinson's models, are studied in conjunction with two implicit integration methods: the trapezoidal rule with Newton-Raphson iterations and an asymptotic integration algorithm. A comparison is made between the two integration methods, and the latter method appears to be computationally more appealing in terms of numerical accuracy and CPU time. However, in order to make the asymptotic algorithm robust, it is necessary to include a self adaptive scheme with subincremental step control and error checking of the Jacobian matrix at the integration points. Three examples are given to illustrate the numerical aspects of the integration methods tested.

Efficient Computation of Atmospheric Flows with Tempest: Development of Next-Generation Climate and Weather Prediction Algorithms at Non-Hydrostatic Scales

NASA Astrophysics Data System (ADS)

Guerra, J. E.; Ullrich, P. A.

2015-12-01

Tempest is a next-generation global climate and weather simulation platform designed to allow experimentation with numerical methods at very high spatial resolutions. The atmospheric fluid equations are discretized by continuous / discontinuous finite elements in the horizontal and by a staggered nodal finite element method (SNFEM) in the vertical, coupled with implicit/explicit time integration. At global horizontal resolutions below 10km, many important questions remain on optimal techniques for solving the fluid equations. We present results from a suite of meso-scale test cases to validate the performance of the SNFEM applied in the vertical. Internal gravity wave, mountain wave, convective, and Cartesian baroclinic instability tests will be shown at various vertical orders of accuracy and compared with known results.

The single category implicit association test as a measure of implicit social cognition.

PubMed

Karpinski, Andrew; Steinman, Ross B

2006-07-01

The Single Category Implicit Association Test (SC-IAT) is a modification of the Implicit Association Test that measures the strength of evaluative associations with a single attitude object. Across 3 different attitude domains--soda brand preferences, self-esteem, and racial attitudes--the authors found evidence that the SC-IAT is internally consistent and makes unique contributions in the ability to understand implicit social cognition. In a 4th study, the authors investigated the susceptibility of the SC-IAT to faking or self-presentational concerns. Once participants with high error rates were removed, no significant self-presentation effect was observed. These results provide initial evidence for the reliability and validity of the SC-IAT as an individual difference measure of implicit social cognition. Copyright 2006 APA, all rights reserved.

Using implicit association tests for the assessment of implicit personality self-concepts of extraversion and neuroticism in schizophrenia.

PubMed

Suslow, Thomas; Lindner, Christian; Kugel, Harald; Egloff, Boris; Schmukle, Stefan C

2014-08-30

There is evidence from research based on self-report personality measures that schizophrenia patients tend to be lower in extraversion and higher in neuroticism than healthy individuals. Self-report personality measures assess aspects of the explicit self-concept. The Implicit Association Test (IAT) has been developed to assess aspects of implicit cognition such as implicit attitudes and implicit personality traits. The present study was conducted to investigate the applicability and reliability of the IAT in schizophrenia patients and test whether they differ from healthy individuals on implicitly measured extraversion and neuroticism. The IAT and the NEO-FFI were administered as implicit and explicit measures of extraversion and neuroticism to 34 schizophrenia patients and 45 healthy subjects. For all IAT scores satisfactory to good reliabilities were observed in the patient sample. In both study groups, IAT scores were not related to NEO-FFI scores. Schizophrenia patients were lower in implicit and explicit extraversion and higher in implicit and explicit neuroticism than healthy individuals. Our data show that the IAT can be reliably applied to schizophrenia patients and suggest that they differ from healthy individuals not only in their conscious representation but also in their implicit representation of the self with regard to neuroticism and extraversion-related characteristics. Copyright © 2014 Elsevier Ireland Ltd. All rights reserved.

Implicit and Explicit Attitudes of Educators toward the Emotional Disturbance Label

ERIC Educational Resources Information Center

Jones, James Patrick

2009-01-01

This study examined implicit and explicit attitudes of teachers toward the Emotional Disturbance (ED) label, the strength of association between implicit and explicit ratings, and the variance in attitudes between different types of teachers or among teachers in different settings. Ninety-eight teachers (52 regular education and 46 special…

Numerical investigation of nonlinear fluid-structure interaction dynamic behaviors under a general Immersed Boundary-Lattice Boltzmann-Finite Element method

NASA Astrophysics Data System (ADS)

Gong, Chun-Lin; Fang, Zhe; Chen, Gang

A numerical approach based on the immersed boundary (IB), lattice Boltzmann and nonlinear finite element method (FEM) is proposed to simulate hydrodynamic interactions of very flexible objects. In the present simulation framework, the motion of fluid is obtained by solving the discrete lattice Boltzmann equations on Eulerian grid, the behaviors of flexible objects are calculated through nonlinear dynamic finite element method, and the interactive forces between them are implicitly obtained using velocity correction IB method which satisfies the no-slip conditions well at the boundary points. The efficiency and accuracy of the proposed Immersed Boundary-Lattice Boltzmann-Finite Element method is first validated by a fluid-structure interaction (F-SI) benchmark case, in which a flexible filament flaps behind a cylinder in channel flow, then the nonlinear vibration mechanism of the cylinder-filament system is investigated by altering the Reynolds number of flow and the material properties of filament. The interactions between two tandem and side-by-side identical objects in a uniform flow are also investigated, and the in-phase and out-of-phase flapping behaviors are captured by the proposed method.

On the nature of implicit soul beliefs: when the past weighs more than the present.

PubMed

Anglin, Stephanie M

2015-06-01

Intuitive childhood beliefs in dualism may lay the foundation for implicit soul and afterlife beliefs, which may diverge from explicit beliefs formed later in adulthood. Brief Implicit Association Tests were developed to investigate the relation of implicit soul and afterlife beliefs to childhood and current beliefs. Early but not current beliefs covaried with implicit beliefs. Results demonstrated greater discrepancies in current than in childhood soul and afterlife beliefs among religious groups, and no differences in implicit beliefs. These findings suggest that implicit soul and afterlife beliefs diverge from current self-reported beliefs, stemming instead from childhood beliefs. © 2014 The British Psychological Society.

A Finite Element Solution of Lateral Periodic Poisson–Boltzmann Model for Membrane Channel Proteins

PubMed Central

Xu, Jingjie; Lu, Benzhuo

2018-01-01

Membrane channel proteins control the diffusion of ions across biological membranes. They are closely related to the processes of various organizational mechanisms, such as: cardiac impulse, muscle contraction and hormone secretion. Introducing a membrane region into implicit solvation models extends the ability of the Poisson–Boltzmann (PB) equation to handle membrane proteins. The use of lateral periodic boundary conditions can properly simulate the discrete distribution of membrane proteins on the membrane plane and avoid boundary effects, which are caused by the finite box size in the traditional PB calculations. In this work, we: (1) develop a first finite element solver (FEPB) to solve the PB equation with a two-dimensional periodicity for membrane channel proteins, with different numerical treatments of the singular charges distributions in the channel protein; (2) add the membrane as a dielectric slab in the PB model, and use an improved mesh construction method to automatically identify the membrane channel/pore region even with a tilt angle relative to the z-axis; and (3) add a non-polar solvation energy term to complete the estimation of the total solvation energy of a membrane protein. A mesh resolution of about 0.25 Å (cubic grid space)/0.36 Å (tetrahedron edge length) is found to be most accurate in linear finite element calculation of the PB solvation energy. Computational studies are performed on a few exemplary molecules. The results indicate that all factors, the membrane thickness, the length of periodic box, membrane dielectric constant, pore region dielectric constant, and ionic strength, have individually considerable influence on the solvation energy of a channel protein. This demonstrates the necessity to treat all of those effects in the PB model for membrane protein simulations. PMID:29495644

A Finite Element Solution of Lateral Periodic Poisson-Boltzmann Model for Membrane Channel Proteins.

PubMed

Ji, Nan; Liu, Tiantian; Xu, Jingjie; Shen, Longzhu Q; Lu, Benzhuo

2018-02-28

Membrane channel proteins control the diffusion of ions across biological membranes. They are closely related to the processes of various organizational mechanisms, such as: cardiac impulse, muscle contraction and hormone secretion. Introducing a membrane region into implicit solvation models extends the ability of the Poisson-Boltzmann (PB) equation to handle membrane proteins. The use of lateral periodic boundary conditions can properly simulate the discrete distribution of membrane proteins on the membrane plane and avoid boundary effects, which are caused by the finite box size in the traditional PB calculations. In this work, we: (1) develop a first finite element solver (FEPB) to solve the PB equation with a two-dimensional periodicity for membrane channel proteins, with different numerical treatments of the singular charges distributions in the channel protein; (2) add the membrane as a dielectric slab in the PB model, and use an improved mesh construction method to automatically identify the membrane channel/pore region even with a tilt angle relative to the z -axis; and (3) add a non-polar solvation energy term to complete the estimation of the total solvation energy of a membrane protein. A mesh resolution of about 0.25 Å (cubic grid space)/0.36 Å (tetrahedron edge length) is found to be most accurate in linear finite element calculation of the PB solvation energy. Computational studies are performed on a few exemplary molecules. The results indicate that all factors, the membrane thickness, the length of periodic box, membrane dielectric constant, pore region dielectric constant, and ionic strength, have individually considerable influence on the solvation energy of a channel protein. This demonstrates the necessity to treat all of those effects in the PB model for membrane protein simulations.

Corruption of accuracy and efficiency of Markov chain Monte Carlo simulation by inaccurate numerical implementation of conceptual hydrologic models

NASA Astrophysics Data System (ADS)

Schoups, G.; Vrugt, J. A.; Fenicia, F.; van de Giesen, N. C.

2010-10-01

Conceptual rainfall-runoff models have traditionally been applied without paying much attention to numerical errors induced by temporal integration of water balance dynamics. Reliance on first-order, explicit, fixed-step integration methods leads to computationally cheap simulation models that are easy to implement. Computational speed is especially desirable for estimating parameter and predictive uncertainty using Markov chain Monte Carlo (MCMC) methods. Confirming earlier work of Kavetski et al. (2003), we show here that the computational speed of first-order, explicit, fixed-step integration methods comes at a cost: for a case study with a spatially lumped conceptual rainfall-runoff model, it introduces artificial bimodality in the marginal posterior parameter distributions, which is not present in numerically accurate implementations of the same model. The resulting effects on MCMC simulation include (1) inconsistent estimates of posterior parameter and predictive distributions, (2) poor performance and slow convergence of the MCMC algorithm, and (3) unreliable convergence diagnosis using the Gelman-Rubin statistic. We studied several alternative numerical implementations to remedy these problems, including various adaptive-step finite difference schemes and an operator splitting method. Our results show that adaptive-step, second-order methods, based on either explicit finite differencing or operator splitting with analytical integration, provide the best alternative for accurate and efficient MCMC simulation. Fixed-step or adaptive-step implicit methods may also be used for increased accuracy, but they cannot match the efficiency of adaptive-step explicit finite differencing or operator splitting. Of the latter two, explicit finite differencing is more generally applicable and is preferred if the individual hydrologic flux laws cannot be integrated analytically, as the splitting method then loses its advantage.

Numerical solution of the two-dimensional time-dependent incompressible Euler equations

NASA Technical Reports Server (NTRS)

Whitfield, David L.; Taylor, Lafayette K.

1994-01-01

A numerical method is presented for solving the artificial compressibility form of the 2D time-dependent incompressible Euler equations. The approach is based on using an approximate Riemann solver for the cell face numerical flux of a finite volume discretization. Characteristic variable boundary conditions are developed and presented for all boundaries and in-flow out-flow situations. The system of algebraic equations is solved using the discretized Newton-relaxation (DNR) implicit method. Numerical results are presented for both steady and unsteady flow.

International Conference on Numerical Ship Hydrodynamics (6th), Held in Iowa City, Iowa on 2-5 August 1993,

DTIC Science & Technology

1994-01-01

length scales mensional hydrofoil and tip vortex flow around a F circulation three dimensional hydrofoil. The simulated mean v molecular viscosity flow...Unstructured Grid for Free Surface Flow Simulations , by T. Hino, L. Martinelli, and A. Jameson 173 "A Semi-Implicit Semi-Lagrangian Finite Element Model...Haussling Solid-Fluid Juncture Boundary Layer and Wake with Waves, by J.E. Choi and F. Stern 215 Direct Numerical and Large-Eddy Simulations of Turbulent

Multi-scale and multi-physics simulations using the multi-fluid plasma model

DTIC Science & Technology

2017-04-25

small The simulation uses 512 second-order elements Bz = 1.0, Te = Ti = 0.01, ui = ue = 0 ne = ni = 1.0 + e−10(x−6) 2 Baboolal, Math . and Comp. Sim. 55...DISTRIBUTION Clearance No. 17211 23 / 31 SUMMARY The blended finite element method (BFEM) is presented DG spatial discretization with explicit Runge...Kutta (i+, n) CG spatial discretization with implicit Crank-Nicolson (e−, fileds) DG captures shocks and discontinuities CG is efficient and robust for

Method of Lines Transpose an Implicit Vlasov Maxwell Solver for Plasmas

DTIC Science & Technology

2015-04-17

boundary crossings should be rare. Numerical results for the Bennett pinch are given in Figure 9. In order to resolve large gradients near the center of the...contributing to the large error at the center of the beam due to large gradients there) and with the finite beam cut-off radius and the outflow boundary...usable time step size can be limited by the numerical accuracy of the method when there are large gradients (high-frequency content) in the solution. We

Characteristic-based algorithms for flows in thermo-chemical nonequilibrium

NASA Technical Reports Server (NTRS)

Walters, Robert W.; Cinnella, Pasquale; Slack, David C.; Halt, David

1990-01-01

A generalized finite-rate chemistry algorithm with Steger-Warming, Van Leer, and Roe characteristic-based flux splittings is presented in three-dimensional generalized coordinates for the Navier-Stokes equations. Attention is placed on convergence to steady-state solutions with fully coupled chemistry. Time integration schemes including explicit m-stage Runge-Kutta, implicit approximate-factorization, relaxation and LU decomposition are investigated and compared in terms of residual reduction per unit of CPU time. Practical issues such as code vectorization and memory usage on modern supercomputers are discussed.

Gender Differences in Implicit Moral Orientation Associations: The Justice and Care Debate Revisited

ERIC Educational Resources Information Center

Agerstrom, Jens; Bjorklund, Fredrik; Carlsson, Rickard

2011-01-01

Employing new measures (Implicit Association Test) to study the classic issue of moral orientations, we predicted and found gender differences in implicit associations to the concepts of justice and care. Specifically, we found that men more strongly associate justice vs. care with importance and with themselves than women. However, participants'…

An efficient finite element method for simulation of droplet spreading on a topologically rough surface

NASA Astrophysics Data System (ADS)

Luo, Li; Wang, Xiao-Ping; Cai, Xiao-Chuan

2017-11-01

We study numerically the dynamics of a three-dimensional droplet spreading on a rough solid surface using a phase-field model consisting of the coupled Cahn-Hilliard and Navier-Stokes equations with a generalized Navier boundary condition (GNBC). An efficient finite element method on unstructured meshes is introduced to cope with the complex geometry of the solid surfaces. We extend the GNBC to surfaces with complex geometry by including its weak form along different normal and tangential directions in the finite element formulation. The semi-implicit time discretization scheme results in a decoupled system for the phase function, the velocity, and the pressure. In addition, a mass compensation algorithm is introduced to preserve the mass of the droplet. To efficiently solve the decoupled systems, we present a highly parallel solution strategy based on domain decomposition techniques. We validate the newly developed solution method through extensive numerical experiments, particularly for those phenomena that can not be achieved by two-dimensional simulations. On a surface with circular posts, we study how wettability of the rough surface depends on the geometry of the posts. The contact line motion for a droplet spreading over some periodic rough surfaces are also efficiently computed. Moreover, we study the spreading process of an impacting droplet on a microstructured surface, a qualitative agreement is achieved between the numerical and experimental results. The parallel performance suggests that the proposed solution algorithm is scalable with over 4,000 processors cores with tens of millions of unknowns.

Corrective Feedback and Second Language Acquisition: Differential Contributions of Implicit and Explicit Knowledge

ERIC Educational Resources Information Center

Ebadi, Mandana Rohollahzadeh; Saad, Mohd Rashid Mohd; Abedalaziz, Nabil

2014-01-01

The issue of error correction remains controversial in recent years due to the different positions of interface toward implicit and explicit knowledge of ESL learners. This study looks at the impacts of implicit corrective feedback in the form of recast on implicit and explicit knowledge of adult ESL learners. In an experimental study,…

Finite-size corrections in simulation of dipolar fluids

NASA Astrophysics Data System (ADS)

Belloni, Luc; Puibasset, Joël

2017-12-01

Monte Carlo simulations of dipolar fluids are performed at different numbers of particles N = 100-4000. For each size of the cubic cell, the non-spherically symmetric pair distribution function g(r,Ω) is accumulated in terms of projections gmnl(r) onto rotational invariants. The observed N dependence is in very good agreement with the theoretical predictions for the finite-size corrections of different origins: the explicit corrections due to the absence of fluctuations in the number of particles within the canonical simulation and the implicit corrections due to the coupling between the environment around a given particle and that around its images in the neighboring cells. The latter dominates in fluids of strong dipolar coupling characterized by low compressibility and high dielectric constant. The ability to clean with great precision the simulation data from these corrections combined with the use of very powerful anisotropic integral equation techniques means that exact correlation functions both in real and Fourier spaces, Kirkwood-Buff integrals, and bridge functions can be derived from box sizes as small as N ≈ 100, even with existing long-range tails. In the presence of dielectric discontinuity with the external medium surrounding the central box and its replica within the Ewald treatment of the Coulombic interactions, the 1/N dependence of the gmnl(r) is shown to disagree with the, yet well-accepted, prediction of the literature.

Recent applications of the transonic wing analysis computer code, TWING

NASA Technical Reports Server (NTRS)

Subramanian, N. R.; Holst, T. L.; Thomas, S. D.

1982-01-01

An evaluation of the transonic-wing-analysis computer code TWING is given. TWING utilizes a fully implicit approximate factorization iteration scheme to solve the full potential equation in conservative form. A numerical elliptic-solver grid-generation scheme is used to generate the required finite-difference mesh. Several wing configurations were analyzed, and the limits of applicability of this code was evaluated. Comparisons of computed results were made with available experimental data. Results indicate that the code is robust, accurate (when significant viscous effects are not present), and efficient. TWING generally produces solutions an order of magnitude faster than other conservative full potential codes using successive-line overrelaxation. The present method is applicable to a wide range of isolated wing configurations including high-aspect-ratio transport wings and low-aspect-ratio, high-sweep, fighter configurations.

Dynamics and optimal control of a non-linear epidemic model with relapse and cure

NASA Astrophysics Data System (ADS)

Lahrouz, A.; El Mahjour, H.; Settati, A.; Bernoussi, A.

2018-04-01

In this work, we introduce the basic reproduction number R0 for a general epidemic model with graded cure, relapse and nonlinear incidence rate in a non-constant population size. We established that the disease free-equilibrium state Ef is globally asymptotically exponentially stable if R0 < 1 and globally asymptotically stable if R0 = 1. If R0 > 1, we proved that the system model has at least one endemic state Ee. Then, by means of an appropriate Lyapunov function, we showed that Ee is unique and globally asymptotically stable under some acceptable biological conditions. On the other hand, we use two types of control to reduce the number of infectious individuals. The optimality system is formulated and solved numerically using a Gauss-Seidel-like implicit finite-difference method.

A Novel Approach with Time-Splitting Spectral Technique for the Coupled Schrödinger-Boussinesq Equations Involving Riesz Fractional Derivative

NASA Astrophysics Data System (ADS)

Saha Ray, S.

2017-09-01

In the present paper the Riesz fractional coupled Schrödinger-Boussinesq (S-B) equations have been solved by the time-splitting Fourier spectral (TSFS) method. This proposed technique is utilized for discretizing the Schrödinger like equation and further, a pseudospectral discretization has been employed for the Boussinesq-like equation. Apart from that an implicit finite difference approach has also been proposed to compare the results with the solutions obtained from the time-splitting technique. Furthermore, the time-splitting method is proved to be unconditionally stable. The error norms along with the graphical solutions have also been presented here. Supported by NBHM, Mumbai, under Department of Atomic Energy, Government of India vide Grant No. 2/48(7)/2015/NBHM (R.P.)/R&D II/11403

On the relation between phase-field crack approximation and gradient damage modelling

NASA Astrophysics Data System (ADS)

Steinke, Christian; Zreid, Imadeddin; Kaliske, Michael

2017-05-01

The finite element implementation of a gradient enhanced microplane damage model is compared to a phase-field model for brittle fracture. Phase-field models and implicit gradient damage models share many similarities despite being conceived from very different standpoints. In both approaches, an additional differential equation and a length scale are introduced. However, while the phase-field method is formulated starting from the description of a crack in fracture mechanics, the gradient method starts from a continuum mechanics point of view. At first, the scope of application for both models is discussed to point out intersections. Then, the analysis of the employed mathematical methods and their rigorous comparison are presented. Finally, numerical examples are introduced to illustrate the findings of the comparison which are summarized in a conclusion at the end of the paper.

A computer program for two-dimensional and axisymmetric nonreacting perfect gas and equilibrium chemically reacting laminar, transitional and-or turbulent boundary layer flows

NASA Technical Reports Server (NTRS)

Miner, E. W.; Anderson, E. C.; Lewis, C. H.

1971-01-01

A computer program is described in detail for laminar, transitional, and/or turbulent boundary-layer flows of non-reacting (perfect gas) and reacting gas mixtures in chemical equilibrium. An implicit finite difference scheme was developed for both two dimensional and axisymmetric flows over bodies, and in rocket nozzles and hypervelocity wind tunnel nozzles. The program, program subroutines, variables, and input and output data are described. Also included is the output from a sample calculation of fully developed turbulent, perfect gas flow over a flat plate. Input data coding forms and a FORTRAN source listing of the program are included. A method is discussed for obtaining thermodynamic and transport property data which are required to perform boundary-layer calculations for reacting gases in chemical equilibrium.

Biconvection flow of Carreau fluid over an upper paraboloid surface: A computational study

NASA Astrophysics Data System (ADS)

Khan, Mair; Hussain, Arif; Malik, M. Y.; Salahuddin, T.

Present article explored the physical characteristics of biconvection effects on the MHD flow of Carreau nanofluid over upper horizontal surface of paraboloid revolution along with chemical reaction. The concept of the Carreau nanofluid was introduced the new parameterization achieve the momentum governing equation. Using similarity transformed, the governing partial differential equations are converted into the ordinary differential equations. The obtained governing equations are solved computationally by using implicit finite difference method known as the Keller box technique. The numerical solutions are obtained for the velocity, temperature, concentration, friction factor, local heat and mass transfer coefficients by varying controlling parameters i.e. Biconvection parameter, fluid parameter, Weissenberg number, Hartmann number, Prandtl number, Brownian motion parameter, thermophoresis parameter, Lewis number and chemical reaction parameter. The obtained results are discussed via graphs and tables.

Prediction and control of slender-wing rock

NASA Technical Reports Server (NTRS)

Kandil, Osama A.; Salman, Ahmed A.

1992-01-01

The unsteady Euler equations and the Euler equations of rigid-body dynamics, both written in the moving frame of reference, are sequentially solved to simulate the limit-cycle rock motion of slender delta wings. The governing equations of the fluid flow and the dynamics of the present multidisciplinary problem are solved using an implicit, approximately-factored, central-difference-like, finite-volume scheme and a four-stage Runge-Kutta scheme, respectively. For the control of wing-rock motion, leading-edge flaps are forced to oscillate anti-symmetrically at prescribed frequency and amplitude, which are tuned in order to suppress the rock motion. Since the computational grid deforms due to the leading-edge flaps motion, the grid is dynamically deformed using the Navier-displacement equations. Computational applications cover locally-conical and three-dimensional solutions for the wing-rock simulation and its control.

A shifted Jacobi collocation algorithm for wave type equations with non-local conservation conditions

NASA Astrophysics Data System (ADS)

Doha, Eid H.; Bhrawy, Ali H.; Abdelkawy, Mohammed A.

2014-09-01

In this paper, we propose an efficient spectral collocation algorithm to solve numerically wave type equations subject to initial, boundary and non-local conservation conditions. The shifted Jacobi pseudospectral approximation is investigated for the discretization of the spatial variable of such equations. It possesses spectral accuracy in the spatial variable. The shifted Jacobi-Gauss-Lobatto (SJ-GL) quadrature rule is established for treating the non-local conservation conditions, and then the problem with its initial and non-local boundary conditions are reduced to a system of second-order ordinary differential equations in temporal variable. This system is solved by two-stage forth-order A-stable implicit RK scheme. Five numerical examples with comparisons are given. The computational results demonstrate that the proposed algorithm is more accurate than finite difference method, method of lines and spline collocation approach

Coupling between fluid dynamics and energy addition in arcjet and microwave thrusters

NASA Technical Reports Server (NTRS)

Micci, M. M.

1986-01-01

A new approach to numerically solving the problem of the constricted electric arcjet is presented. An Euler Implicit finite difference scheme is used to solve the full compressible Navier Stokes equations in two dimensions. The boundary and initial conditions represent the constrictor section of the arcjet, and hydrogen is used as a propellant. The arc is modeled as a Gaussian distribution across the centerline of the constrictor. Temperature, pressure and velocity profiles for steady state converged solutions show both axial and radial changes in distributions resulting from their interaction with the arc energy source for specific input conditions. The temperature rise is largest at the centerline where there is a the greatest concentration arc energy. The solution does not converge for all initial inputs and the limitations in the range of obtainable solutions are discussed.

Age differences in implicit memory: conceptual, perceptual, or methodological?

PubMed

Mitchell, David B; Bruss, Peter J

2003-12-01

The authors examined age differences in conceptual and perceptual implicit memory via word-fragment completion, word-stem completion, category exemplar generation, picture-fragment identification, and picture naming. Young, middle-aged, and older participants (N = 60) named pictures and words at study. Limited test exposure minimized explicit memory contamination, yielding no reliable age differences and equivalent cross-format effects. In contrast, explicit memory and neuropsychological measures produced significant age differences. In a follow-up experiment, 24 young adults were informed a priori about implicit testing. Their priming was equivalent to the main experiment, showing that test trial time restrictions limit explicit memory strategies. The authors concluded that most implicit memory processes remain stable across adulthood and suggest that explicit contamination be rigorously monitored in aging studies.

Implicit Weight Bias in Children Age 9 to 11 Years.

PubMed

Skinner, Asheley Cockrell; Payne, Keith; Perrin, Andrew J; Panter, Abigail T; Howard, Janna B; Bardone-Cone, Anna; Bulik, Cynthia M; Steiner, Michael J; Perrin, Eliana M

2017-07-01

Assess implicit weight bias in children 9 to 11 years old. Implicit weight bias was measured in children ages 9 to 11 ( N = 114) by using the Affect Misattribution Procedure. Participants were shown a test image of a child for 350 milliseconds followed by a meaningless fractal (200 milliseconds), and then they were asked to rate the fractal image as "good" or "bad." We used 9 image pairs matched on age, race, sex, and activity but differing by weight of the child. Implicit bias was the difference between positive ratings for fractals preceded by an image of a healthy-weight child and positive ratings for fractals preceded by an image of an overweight child. On average, 64% of abstract fractals shown after pictures of healthy-weight children were rated as "good," compared with 59% of those shown after pictures of overweight children, reflecting an overall implicit bias rate of 5.4% against overweight children ( P < .001). Healthy-weight participants showed greater implicit bias than over- and underweight participants (7.9%, 1.4%, and 0.3% respectively; P = .049). Implicit bias toward overweight individuals is evident in children aged 9 to 11 years with a magnitude of implicit bias (5.4%) similar to that in studies of implicit racial bias among adults. Copyright © 2017 by the American Academy of Pediatrics.

Solvent Reaction Field Potential inside an Uncharged Globular Protein: A Bridge between Implicit and Explicit Solvent Models?

PubMed Central

Baker, Nathan A.; McCammon, J. Andrew

2008-01-01

The solvent reaction field potential of an uncharged protein immersed in Simple Point Charge/Extended (SPC/E) explicit solvent was computed over a series of molecular dynamics trajectories, intotal 1560 ns of simulation time. A finite, positive potential of 13 to 24 kbTec−1 (where T = 300K), dependent on the geometry of the solvent-accessible surface, was observed inside the biomolecule. The primary contribution to this potential arose from a layer of positive charge density 1.0 Å from the solute surface, on average 0.008 ec/Å3, which we found to be the product of a highly ordered first solvation shell. Significant second solvation shell effects, including additional layers of charge density and a slight decrease in the short-range solvent-solvent interaction strength, were also observed. The impact of these findings on implicit solvent models was assessed by running similar explicit-solvent simulations on the fully charged protein system. When the energy due to the solvent reaction field in the uncharged system is accounted for, correlation between per-atom electrostatic energies for the explicit solvent model and a simple implicit (Poisson) calculation is 0.97, and correlation between per-atom energies for the explicit solvent model and a previously published, optimized Poisson model is 0.99. PMID:17949217

Solvent reaction field potential inside an uncharged globular protein: A bridge between implicit and explicit solvent models?

NASA Astrophysics Data System (ADS)

Cerutti, David S.; Baker, Nathan A.; McCammon, J. Andrew

2007-10-01

The solvent reaction field potential of an uncharged protein immersed in simple point charge/extended explicit solvent was computed over a series of molecular dynamics trajectories, in total 1560ns of simulation time. A finite, positive potential of 13-24 kbTec-1 (where T =300K), dependent on the geometry of the solvent-accessible surface, was observed inside the biomolecule. The primary contribution to this potential arose from a layer of positive charge density 1.0Å from the solute surface, on average 0.008ec/Å3, which we found to be the product of a highly ordered first solvation shell. Significant second solvation shell effects, including additional layers of charge density and a slight decrease in the short-range solvent-solvent interaction strength, were also observed. The impact of these findings on implicit solvent models was assessed by running similar explicit solvent simulations on the fully charged protein system. When the energy due to the solvent reaction field in the uncharged system is accounted for, correlation between per-atom electrostatic energies for the explicit solvent model and a simple implicit (Poisson) calculation is 0.97, and correlation between per-atom energies for the explicit solvent model and a previously published, optimized Poisson model is 0.99.

TECHNICAL NOTE: Direct finite-element analysis of the frequency response of a Y-Z lithium niobate SAW filter

NASA Astrophysics Data System (ADS)

Xu, Guanshui

2000-12-01

A direct finite-element model is developed for the full-scale analysis of the electromechanical phenomena involved in surface acoustic wave (SAW) devices. The equations of wave propagation in piezoelectric materials are discretized using the Galerkin method, in which an implicit algorithm of the Newmark family with unconditional stability is implemented. The Rayleigh damping coefficients are included in the elements near the boundary to reduce the influence of the reflection of waves. The performance of the model is demonstrated by the analysis of the frequency response of a Y-Z lithium niobate filter with two uniform ports, with emphasis on the influence of the number of electrodes. The frequency response of the filter is obtained through the Fourier transform of the impulse response, which is solved directly from the finite-element simulation. It shows that the finite-element results are in good agreement with the characteristic frequency response of the filter predicted by the simple phase-matching argument. The ability of the method to evaluate the influence of the bulk waves at the high-frequency end of the filter passband and the influence of the number of electrodes on insertion loss is noteworthy. We conclude that the direct finite-element analysis of SAW devices can be used as an effective tool for the design of high-performance SAW devices. Some practical computational challenges of finite-element modeling of SAW devices are discussed.

An unstructured-mesh finite-volume MPDATA for compressible atmospheric dynamics

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

Kühnlein, Christian, E-mail: christian.kuehnlein@ecmwf.int; Smolarkiewicz, Piotr K., E-mail: piotr.smolarkiewicz@ecmwf.int

An advancement of the unstructured-mesh finite-volume MPDATA (Multidimensional Positive Definite Advection Transport Algorithm) is presented that formulates the error-compensative pseudo-velocity of the scheme to rely only on face-normal advective fluxes to the dual cells, in contrast to the full vector employed in previous implementations. This is essentially achieved by expressing the temporal truncation error underlying the pseudo-velocity in a form consistent with the flux-divergence of the governing conservation law. The development is especially important for integrating fluid dynamics equations on non-rectilinear meshes whenever face-normal advective mass fluxes are employed for transport compatible with mass continuity—the latter being essential for flux-formmore » schemes. In particular, the proposed formulation enables large-time-step semi-implicit finite-volume integration of the compressible Euler equations using MPDATA on arbitrary hybrid computational meshes. Furthermore, it facilitates multiple error-compensative iterations of the finite-volume MPDATA and improved overall accuracy. The advancement combines straightforwardly with earlier developments, such as the nonoscillatory option, the infinite-gauge variant, and moving curvilinear meshes. A comprehensive description of the scheme is provided for a hybrid horizontally-unstructured vertically-structured computational mesh for efficient global atmospheric flow modelling. The proposed finite-volume MPDATA is verified using selected 3D global atmospheric benchmark simulations, representative of hydrostatic and non-hydrostatic flow regimes. Besides the added capabilities, the scheme retains fully the efficacy of established finite-volume MPDATA formulations.« less

An improved semi-implicit method for structural dynamics analysis

NASA Technical Reports Server (NTRS)

Park, K. C.

1982-01-01

A semi-implicit algorithm is presented for direct time integration of the structural dynamics equations. The algorithm avoids the factoring of the implicit difference solution matrix and mitigates the unacceptable accuracy losses which plagued previous semi-implicit algorithms. This substantial accuracy improvement is achieved by augmenting the solution matrix with two simple diagonal matrices of the order of the integration truncation error.

Age and Social Support Seeking: Understanding the Role of Perceived Social Costs to Others.

PubMed

Jiang, Li; Drolet, Aimee; Kim, Heejung S

2018-07-01

We examined age differences in the use of different types of social support and the reasons for these differences. We found that older adults (age 60+) seek explicit social support less compared with young adults (age 18-25), but there is no difference in implicit social support seeking. Concerns about the potential social costs of seeking explicit support mediate the age differences in explicit social support seeking. Whereas young adults view this strategy as conferring more benefits than costs, older adults have a more balanced view of the costs and benefits of explicit social support seeking. Older and young adults do not differ in perceptions of the relative costs versus benefits of implicit social support seeking. Finally, we found older adults benefit more from implicit (vs. explicit) social support emotionally than young adults, which further explains why age groups differ in their use of explicit versus implicit social support.

Implicit but not explicit self-esteem predicts future depressive symptomatology.

PubMed

Franck, Erik; De Raedt, Rudi; De Houwer, Jan

2007-10-01

To date, research on the predictive validity of implicit self-esteem for depressive relapse is very sparse. In the present study, we assessed implicit self-esteem using the Name Letter Preference Task and explicit self-esteem using the Rosenberg self-esteem scale in a group of currently depressed patients, formerly depressed individuals, and never depressed controls. In addition, we examined the predictive validity of explicit, implicit, and the interaction of explicit and implicit self-esteem in predicting future symptoms of depression in formerly depressed individuals and never depressed controls. The results showed that currently depressed individuals reported a lower explicit self-esteem as compared to formerly depressed individuals and never depressed controls. In line with previous research, all groups showed a positive implicit self-esteem not different from each other. Furthermore, after controlling for initial depressive symptomatology, implicit but not explicit self-esteem significantly predicted depressive symptoms at six months follow-up. Although implicit self-esteem assessed with the Name Letter Preference Test was not different between formerly depressed individuals and never depressed controls, the findings suggest it is an interesting variable in the study of vulnerability for depression relapse.

Engine dynamic analysis with general nonlinear finite element codes. II - Bearing element implementation, overall numerical characteristics and benchmarking

NASA Technical Reports Server (NTRS)

Padovan, J.; Adams, M.; Lam, P.; Fertis, D.; Zeid, I.

1982-01-01

Second-year efforts within a three-year study to develop and extend finite element (FE) methodology to efficiently handle the transient/steady state response of rotor-bearing-stator structure associated with gas turbine engines are outlined. The two main areas aim at (1) implanting the squeeze film damper element into a general purpose FE code for testing and evaluation; and (2) determining the numerical characteristics of the FE-generated rotor-bearing-stator simulation scheme. The governing FE field equations are set out and the solution methodology is presented. The choice of ADINA as the general-purpose FE code is explained, and the numerical operational characteristics of the direct integration approach of FE-generated rotor-bearing-stator simulations is determined, including benchmarking, comparison of explicit vs. implicit methodologies of direct integration, and demonstration problems.

Efficient Computation of Atmospheric Flows with Tempest: Validation of Next-Generation Climate and Weather Prediction Algorithms at Non-Hydrostatic Scales

NASA Astrophysics Data System (ADS)

Guerra, Jorge; Ullrich, Paul

2016-04-01

Tempest is a next-generation global climate and weather simulation platform designed to allow experimentation with numerical methods for a wide range of spatial resolutions. The atmospheric fluid equations are discretized by continuous / discontinuous finite elements in the horizontal and by a staggered nodal finite element method (SNFEM) in the vertical, coupled with implicit/explicit time integration. At horizontal resolutions below 10km, many important questions remain on optimal techniques for solving the fluid equations. We present results from a suite of idealized test cases to validate the performance of the SNFEM applied in the vertical with an emphasis on flow features and dynamic behavior. Internal gravity wave, mountain wave, convective bubble, and Cartesian baroclinic instability tests will be shown at various vertical orders of accuracy and compared with known results.

Copper Tube Compression in Z-Current Geometry, Numerical Simulations and Comparison with Cyclope Experiments

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

Lefrancois, A.; L'Eplattenier, P.; Burger, M.

2006-02-13

Metallic tubes compressions in Z-current geometry were performed at the Cyclope facility from Gramat Research Center in order to study the behavior of metals under large strain at high strain rate. 3D configurations of cylinder compressions have been calculated here to benchmark the new beta version of the electromagnetism package coupled with the dynamics in Ls-Dyna and compared with the Cyclope experiments. The electromagnetism module is being developed in the general-purpose explicit and implicit finite element program LS-DYNA{reg_sign} in order to perform coupled mechanical/thermal/electromagnetism simulations. The Maxwell equations are solved using a Finite Element Method (FEM) for the solid conductorsmore » coupled with a Boundary Element Method (BEM) for the surrounding air (or vacuum). More details can be read in the references.« less

The contributions of Lewis Fry Richardson to drainage theory, soil physics, and the soil-plant-atmosphere continuum

NASA Astrophysics Data System (ADS)

Knight, John; Raats, Peter

2016-04-01

The EGU Division on Nonlinear Processes in Geophysics awards the Lewis Fry Richardson Medal. Richardson's significance is highlighted in http://www.egu.eu/awards-medals/portrait-lewis-fry-richardson/, but his contributions to soil physics and to numerical solutions of heat and diffusion equations are not mentioned. We would like to draw attention to those little known contributions. Lewis Fry Richardson (1881-1953) made important contributions to many fields including numerical weather prediction, finite difference solutions of partial differential equations, turbulent flow and diffusion, fractals, quantitative psychology and studies of conflict. He invented numerical weather prediction during World War I, although his methods were not successfully applied until 1950, after the invention of fast digital computers. In 1922 he published the book `Numerical weather prediction', of which few copies were sold and even fewer were read until the 1950s. To model heat and mass transfer in the atmosphere, he did much original work on turbulent flow and defined what is now known as the Richardson number. His technique for improving the convergence of a finite difference calculation is known as Richardson extrapolation, and was used by John Philip in his 1957 semi-analytical solution of the Richards equation for water movement in unsaturated soil. Richardson's first papers in 1908 concerned the numerical solution of the free surface problem of unconfined flow of water in saturated soil, arising in the design of drain spacing in peat. Later, for the lower boundary of his atmospheric model he needed to understand the movement of heat, liquid water and water vapor in what is now called the vadose zone and the soil plant atmosphere system, and to model coupled transfer of heat and flow of water in unsaturated soil. Finding little previous work, he formulated partial differential equations for transient, vertical flow of liquid water and for transfer of heat and water vapor. He paid considerable attention to the balances of water and energy at the soil-atmosphere and plant-atmosphere interfaces, making use of the concept of transfer resistance introduced by Brown and Escombe (1900) for leaf-atmosphere interfaces. He incorporated finite difference versions of all equations into his numerical weather forecasting model. From 1916, Richardson drove an ambulance in France in World War I, did weather computations in his spare time, and wrote a draft of his book. Later researchers such as L.A. Richards, D.A. de Vries and J.R. Philip from the 1930s to the 1950s were unaware that Richardson had anticipated many of their ideas on soil liquid water, heat, water vapor, and the soil-plant-atmosphere system. The Richards (1931) equation could rightly be called the Richardson (1922) equation! Richardson (1910) developed what we now call the Crank Nicolson implicit method for the heat or diffusion equation. To save effort, he used an explicit three level method after the first time step. Crank and Nicolson (1947) pointed out the instability in the explicit method, and used his implicit method for all time steps. Hanks and Bowers (1962) adapted the Crank Nicolson method to solve the Richards equation. So we could say that Hanks and Bowers used the Richardson finite difference method to solve the Richardson equation for soil water flow!

Prediction of asymmetric vortical flows around slender bodies using Navier-Stokes equations

NASA Technical Reports Server (NTRS)

Liu, C. H.; Wong, Tin-Chee; Kandil, Osama A.

1992-01-01

Steady and unsteady asymmetric vortical flows around slender bodies at high angles of attack are solved using the unsteady, compressible, thin-layer Navier-Stokes equations. An implicit, upwind-biased, flux-difference splitting, finite-volume scheme is used for the numerical computations. For supersonic flows past point cones, the locally conical flow assumption have been used for efficient computational studies of this phenomenon. Asymmetric flows past a 5-deg semiapex-angle circular cone at different angles of attack, free-stream Mach numbers, and Reynolds numbers have been studied in responses to different sources of disturbances. The effects of grid fineness and computational domain size have also been investigated. Next, the responses of three-dimensional supersonic asymmetric flow around a 5-deg circular cone at different angles of attack and Reynolds numbers to short-duration sideslip disturbances are presented. The results show that flow asymmetry becomes stronger as the Reynolds number and angles of attack are increased. One of the cases of flow over a cone-cylinder configuration is validated fairly well by experimental data.

A comparison of physician implicit racial bias towards adults versus children

PubMed Central

Johnson, Tiffani J.; Winger, Daniel G.; Hickey, Robert W.; Switzer, Galen E.; Miller, Elizabeth; Nguyen, Margaret B.; Saladino, Richard A.; Hausmann, Leslie R. M.

2016-01-01

Background and Objectives The general population and most physicians have implicit racial bias against black adults. Pediatricians also have implicit bias against black adults, albeit less than other specialties. There is no published research on the implicit racial attitudes of pediatricians or other physicians towards children. Our objectives were to compare implicit racial bias towards adults versus children among resident physicians working in a pediatric emergency department (ED), and to assess whether bias varied by specialty (pediatrics, emergency medicine, or other), gender, race, age, and year of training. Methods We measured implicit racial bias of residents before a pediatric ED shift using the Adult and Child Race Implicit Association Tests (IATs). Generalized linear models compared Adult and Child IAT scores and determined the association of participant demographics with Adult and Child IAT scores. Results Among 91 residents, we found moderate pro-white/anti-black bias on both the Adult (M=0.49, SD=0.34) and Child Race IAT (M=0.55, SD=0.37). There was no significant difference between Adult and Child Race IAT scores (difference=0.06, p=0.15). Implicit bias was not associated with resident demographic characteristics, including specialty. Conclusions This is the first study demonstrating that resident physicians have implicit racial bias against black children, similar to levels of bias against black adults. Bias in our study did not vary by resident demographic characteristics, including specialty, suggesting that pediatric residents are as susceptible as other physicians to implicit bias. Future studies are needed to explore how physicians’ implicit attitudes towards parents and children may impact inequities in pediatric healthcare. PMID:27620844

Numerical investigation of MHD flow of blood and heat transfer in a stenosed arterial segment

NASA Astrophysics Data System (ADS)

Majee, Sreeparna; Shit, G. C.

2017-02-01

A numerical investigation of unsteady flow of blood and heat transfer has been performed with an aim to provide better understanding of blood flow through arteries under stenotic condition. The blood is treated as Newtonian fluid and the arterial wall is considered to be rigid having deposition of plaque in its lumen. The heat transfer characteristic has been analyzed by taking into consideration of the dissipation of energy due to applied magnetic field and the viscosity of blood. The vorticity-stream function formulation has been adopted to solve the problem using implicit finite difference method by developing well known Peaceman-Rachford Alternating Direction Implicit (ADI) scheme. The quantitative profile analysis of velocity, temperature and wall shear stress as well as Nusselt number is carried out over the entire arterial segment. The streamline and temperature contours have been plotted to understand the flow pattern in the diseased artery, which alters significantly in the downstream of the stenosis in the presence of magnetic field. Both the wall shear stress and Nusselt number increases with increasing magnetic field strength. However, wall shear stress decreases and Nusselt number enhances with Reynolds number. The results show that with an increase in the magnetic field strength upto 8 T, does not causes any damage to the arterial wall, but the study is significant for assessing temperature rise during hyperthermic treatment.

Parametric analysis of the biomechanical response of head subjected to the primary blast loading--a data mining approach.

PubMed

Zhu, Feng; Kalra, Anil; Saif, Tal; Yang, Zaihan; Yang, King H; King, Albert I

2016-01-01

Traumatic brain injury due to primary blast loading has become a signature injury in recent military conflicts and terrorist activities. Extensive experimental and computational investigations have been conducted to study the interrelationships between intracranial pressure response and intrinsic or 'input' parameters such as the head geometry and loading conditions. However, these relationships are very complicated and are usually implicit and 'hidden' in a large amount of simulation/test data. In this study, a data mining method is proposed to explore such underlying information from the numerical simulation results. The heads of different species are described as a highly simplified two-part (skull and brain) finite element model with varying geometric parameters. The parameters considered include peak incident pressure, skull thickness, brain radius and snout length. Their interrelationship and coupling effect are discovered by developing a decision tree based on the large simulation data-set. The results show that the proposed data-driven method is superior to the conventional linear regression method and is comparable to the nonlinear regression method. Considering its capability of exploring implicit information and the relatively simple relationships between response and input variables, the data mining method is considered to be a good tool for an in-depth understanding of the mechanisms of blast-induced brain injury. As a general method, this approach can also be applied to other nonlinear complex biomechanical systems.

Aerothermodynamic Design Sensitivities for a Reacting Gas Flow Solver on an Unstructured Mesh Using a Discrete Adjoint Formulation

NASA Astrophysics Data System (ADS)

Thompson, Kyle Bonner

An algorithm is described to efficiently compute aerothermodynamic design sensitivities using a decoupled variable set. In a conventional approach to computing design sensitivities for reacting flows, the species continuity equations are fully coupled to the conservation laws for momentum and energy. In this algorithm, the species continuity equations are solved separately from the mixture continuity, momentum, and total energy equations. This decoupling simplifies the implicit system, so that the flow solver can be made significantly more efficient, with very little penalty on overall scheme robustness. Most importantly, the computational cost of the point implicit relaxation is shown to scale linearly with the number of species for the decoupled system, whereas the fully coupled approach scales quadratically. Also, the decoupled method significantly reduces the cost in wall time and memory in comparison to the fully coupled approach. This decoupled approach for computing design sensitivities with the adjoint system is demonstrated for inviscid flow in chemical non-equilibrium around a re-entry vehicle with a retro-firing annular nozzle. The sensitivities of the surface temperature and mass flow rate through the nozzle plenum are computed with respect to plenum conditions and verified against sensitivities computed using a complex-variable finite-difference approach. The decoupled scheme significantly reduces the computational time and memory required to complete the optimization, making this an attractive method for high-fidelity design of hypersonic vehicles.

Coupled Thermo-Hydro-Mechanical Numerical Framework for Simulating Unconventional Formations

NASA Astrophysics Data System (ADS)

Garipov, T. T.; White, J. A.; Lapene, A.; Tchelepi, H.

2016-12-01

Unconventional deposits are found in all world oil provinces. Modeling these systems is challenging, however, due to complex thermo-hydro-mechanical processes that govern their behavior. As a motivating example, we consider in situ thermal processing of oil shale deposits. When oil shale is heated to sufficient temperatures, kerogen can be converted to oil and gas products over a relatively short timespan. This phase change dramatically impact both the mechanical and hydrologic properties of the rock, leading to strongly coupled THMC interactions. Here, we present a numerical framework for simulating tightly-coupled chemistry, geomechanics, and multiphase flow within a reservoir simulator (the AD-GPRS General Purpose Research Simulator). We model changes in constitutive behavior of the rock using a thermoplasticity model that accounts for microstructural evolution. The multi-component, multiphase flow and transport processes of both mass and heat are modeled at the macroscopic (e.g., Darcy) scale. The phase compositions and properties are described by a cubic equation of state; Arrhenius-type chemical reactions are used to represent kerogen conversion. The system of partial differential equations is discretized using a combination of finite-volumes and finite-elements, respectively, for the flow and mechanics problems. Fully implicit and sequentially implicit method are used to solve resulting nonlinear problem. The proposed framework is verified against available analytical and numerical benchmark cases. We demonstrate the efficiency, performance, and capabilities of the proposed simulation framework by analyzing near well deformation in an oil shale formation.

Implicit cognitive processes in psychopathology: an introduction.

PubMed

Wiers, Reinout W; Teachman, Bethany A; De Houwer, Jan

2007-06-01

Implicit or automatic processes are important in understanding the etiology and maintenance of psychopathological problems. In order to study implicit processes in psychopathology, measures are needed that are valid and reliable when applied to clinical problems. One of the main topics in this special issue concerns the development and validation of new or modified implicit tests in different domains of psychopathology. The other main topic concerns the prediction of clinical outcomes and new ways to directly influence implicit processes in psychopathology. We summarize the contributions to this special issue and discuss how they further our knowledge of implicit processes in psychopathology and how to measure them.

Dynamical Approach Study of Spurious Steady-State Numerical Solutions of Nonlinear Differential Equations. Part 2; Global Asymptotic Behavior of Time Discretizations

NASA Technical Reports Server (NTRS)

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

1995-01-01

The global asymptotic nonlinear behavior of 11 explicit and implicit time discretizations for four 2 x 2 systems of first-order autonomous nonlinear ordinary differential equations (ODEs) is analyzed. The objectives are to gain a basic understanding of the difference in the dynamics of numerics between the scalars and systems of nonlinear autonomous ODEs and to set a baseline global asymptotic solution behavior of these schemes for practical computations in computational fluid dynamics. We show how 'numerical' basins of attraction can complement the bifurcation diagrams in gaining more detailed global asymptotic behavior of time discretizations for nonlinear differential equations (DEs). We show how in the presence of spurious asymptotes the basins of the true stable steady states can be segmented by the basins of the spurious stable and unstable asymptotes. One major consequence of this phenomenon which is not commonly known is that this spurious behavior can result in a dramatic distortion and, in most cases, a dramatic shrinkage and segmentation of the basin of attraction of the true solution for finite time steps. Such distortion, shrinkage and segmentation of the numerical basins of attraction will occur regardless of the stability of the spurious asymptotes, and will occur for unconditionally stable implicit linear multistep methods. In other words, for the same (common) steady-state solution the associated basin of attraction of the DE might be very different from the discretized counterparts and the numerical basin of attraction can be very different from numerical method to numerical method. The results can be used as an explanation for possible causes of error, and slow convergence and nonconvergence of steady-state numerical solutions when using the time-dependent approach for nonlinear hyperbolic or parabolic PDEs.

Dynamical Approach Study of Spurious Steady-State Numerical Solutions of Nonlinear Differential Equations. 2; Global Asymptotic Behavior of Time Discretizations; 2. Global Asymptotic Behavior of time Discretizations

NASA Technical Reports Server (NTRS)

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

1995-01-01

The global asymptotic nonlinear behavior of 1 1 explicit and implicit time discretizations for four 2 x 2 systems of first-order autonomous nonlinear ordinary differential equations (ODES) is analyzed. The objectives are to gain a basic understanding of the difference in the dynamics of numerics between the scalars and systems of nonlinear autonomous ODEs and to set a baseline global asymptotic solution behavior of these schemes for practical computations in computational fluid dynamics. We show how 'numerical' basins of attraction can complement the bifurcation diagrams in gaining more detailed global asymptotic behavior of time discretizations for nonlinear differential equations (DEs). We show how in the presence of spurious asymptotes the basins of the true stable steady states can be segmented by the basins of the spurious stable and unstable asymptotes. One major consequence of this phenomenon which is not commonly known is that this spurious behavior can result in a dramatic distortion and, in most cases, a dramatic shrinkage and segmentation of the basin of attraction of the true solution for finite time steps. Such distortion, shrinkage and segmentation of the numerical basins of attraction will occur regardless of the stability of the spurious asymptotes, and will occur for unconditionally stable implicit linear multistep methods. In other words, for the same (common) steady-state solution the associated basin of attraction of the DE might be very different from the discretized counterparts and the numerical basin of attraction can be very different from numerical method to numerical method. The results can be used as an explanation for possible causes of error, and slow convergence and nonconvergence of steady-state numerical solutions when using the time-dependent approach for nonlinear hyperbolic or parabolic PDES.

The neural basis of implicit learning and memory: a review of neuropsychological and neuroimaging research.

PubMed

Reber, Paul J

2013-08-01

Memory systems research has typically described the different types of long-term memory in the brain as either declarative versus non-declarative or implicit versus explicit. These descriptions reflect the difference between declarative, conscious, and explicit memory that is dependent on the medial temporal lobe (MTL) memory system, and all other expressions of learning and memory. The other type of memory is generally defined by an absence: either the lack of dependence on the MTL memory system (nondeclarative) or the lack of conscious awareness of the information acquired (implicit). However, definition by absence is inherently underspecified and leaves open questions of how this type of memory operates, its neural basis, and how it differs from explicit, declarative memory. Drawing on a variety of studies of implicit learning that have attempted to identify the neural correlates of implicit learning using functional neuroimaging and neuropsychology, a theory of implicit memory is presented that describes it as a form of general plasticity within processing networks that adaptively improve function via experience. Under this model, implicit memory will not appear as a single, coherent, alternative memory system but will instead be manifested as a principle of improvement from experience based on widespread mechanisms of cortical plasticity. The implications of this characterization for understanding the role of implicit learning in complex cognitive processes and the effects of interactions between types of memory will be discussed for examples within and outside the psychology laboratory. Copyright © 2013 Elsevier Ltd. All rights reserved.

Development and applications of algorithms for calculating the transonic flow about harmonically oscillating wings

NASA Technical Reports Server (NTRS)

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

1984-01-01

A finite difference method to solve the unsteady transonic flow about harmonically oscillating wings was investigated. The procedure is based on separating the velocity potential into steady and unsteady parts and linearizing the resulting unsteady differential equation for small disturbances. The differential equation for the unsteady velocity potential is linear with spatially varying coefficients and with the time variable eliminated by assuming harmonic motion. An alternating direction implicit procedure was investigated, and a pilot program was developed for both two and three dimensional wings. This program provides a relatively efficient relaxation solution without previously encountered solution instability problems. Pressure distributions for two rectangular wings are calculated. Conjugate gradient techniques were developed for the asymmetric, indefinite problem. The conjugate gradient procedure is evaluated for applications to the unsteady transonic problem. Different equations for the alternating direction procedure are derived using a coordinate transformation for swept and tapered wing planforms. Pressure distributions for swept, untaped wings of vanishing thickness are correlated with linear results for sweep angles up to 45 degrees.

On solving the compressible Navier-Stokes equations for unsteady flows at very low Mach numbers

NASA Technical Reports Server (NTRS)

Pletcher, R. H.; Chen, K.-H.

1993-01-01

The properties of a preconditioned, coupled, strongly implicit finite difference scheme for solving the compressible Navier-Stokes equations in primitive variables are investigated for two unsteady flows at low speeds, namely the impulsively started driven cavity and the startup of pipe flow. For the shear-driven cavity flow, the computational effort was observed to be nearly independent of Mach number, especially at the low end of the range considered. This Mach number independence was also observed for steady pipe flow calculations; however, rather different conclusions were drawn for the unsteady calculations. In the pressure-driven pipe startup problem, the compressibility of the fluid began to significantly influence the physics of the flow development at quite low Mach numbers. The present scheme was observed to produce the expected characteristics of completely incompressible flow when the Mach number was set at very low values. Good agreement with incompressible results available in the literature was observed.

A three dimensional immersed smoothed finite element method (3D IS-FEM) for fluid-structure interaction problems

NASA Astrophysics Data System (ADS)

Zhang, Zhi-Qian; Liu, G. R.; Khoo, Boo Cheong

2013-02-01

A three-dimensional immersed smoothed finite element method (3D IS-FEM) using four-node tetrahedral element is proposed to solve 3D fluid-structure interaction (FSI) problems. The 3D IS-FEM is able to determine accurately the physical deformation of the nonlinear solids placed within the incompressible viscous fluid governed by Navier-Stokes equations. The method employs the semi-implicit characteristic-based split scheme to solve the fluid flows and smoothed finite element methods to calculate the transient dynamics responses of the nonlinear solids based on explicit time integration. To impose the FSI conditions, a novel, effective and sufficiently general technique via simple linear interpolation is presented based on Lagrangian fictitious fluid meshes coinciding with the moving and deforming solid meshes. In the comparisons to the referenced works including experiments, it is clear that the proposed 3D IS-FEM ensures stability of the scheme with the second order spatial convergence property; and the IS-FEM is fairly independent of a wide range of mesh size ratio.

Development of an upwind, finite-volume code with finite-rate chemistry

NASA Technical Reports Server (NTRS)

Molvik, Gregory A.

1995-01-01

Under this grant, two numerical algorithms were developed to predict the flow of viscous, hypersonic, chemically reacting gases over three-dimensional bodies. Both algorithms take advantage of the benefits of upwind differencing, total variation diminishing techniques and of a finite-volume framework, but obtain their solution in two separate manners. The first algorithm is a zonal, time-marching scheme, and is generally used to obtain solutions in the subsonic portions of the flow field. The second algorithm is a much less expensive, space-marching scheme and can be used for the computation of the larger, supersonic portion of the flow field. Both codes compute their interface fluxes with a temporal Riemann solver and the resulting schemes are made fully implicit including the chemical source terms and boundary conditions. Strong coupling is used between the fluid dynamic, chemical and turbulence equations. These codes have been validated on numerous hypersonic test cases and have provided excellent comparison with existing data. This report summarizes the research that took place from August 1,1994 to January 1, 1995.