Numerical solution on flow problems on a parallel computer

Povitsky, Alex; Wolfshtein, M.

doi:10.2514/6.1995-1698

Cited by 2 publications

(2 citation statements)

References 5 publications

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“…Figure 5a depicts the stability region for large S, while Figure 5b enlarges the small-S region. It may be seen that the scheme is stable (G 3 0 for large n) for cell Reynolds numbers jRej 2 and Re 0 regardless of the stability ratio S and the damping coef®cient R. This is con®rmed by previous computations of G 1,2 Still the stability region is broader than in the explicit case for all values of S (compare Figures 2 and 5). Fortunately, for R 0 the semi-implicit scheme is stable for all jRej 4 2 regardless of S. The same results are obtained by computations of G 1,2 for jRej 1 and S 10 (see Figures 4a and 4d).…”

Section: Semi-implicit Schemesupporting

confidence: 74%

Multidomain implicit numerical scheme

Povitsky

Wolfshtein

1997

Int. J. Numer. Meth. Fluids

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A multidomain method for the solution of elliptic CFD problems with an ADI scheme is described. Two methods of treatment of internal boundary conditions for ADI functions are discussed, namely an explicit and a semi‒implicit method. Stability conditions for the proposed methods are derived theoretically. The semi‒implicit scheme is more stable than the explicit scheme, leading to improved numerical efficiency for multidomain computations. Numerical computations for a linear convection‐diffusion equation, for buoyancy‒driven recirculating flow in a square cavity and for turbulent flow in a square duct confirmed the theoretical results. Computer runs of the multidomain code in a distributed memory multiprocessor system were successful and efficient and produced reliable results. © 1997 John Wiley & Sons, Ltd.

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Section: Semi-implicit Schemesupporting

confidence: 74%

Multidomain implicit numerical scheme

Povitsky

Wolfshtein

1997

Int. J. Numer. Meth. Fluids

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“…There has been somewhat less work involving parallel implicit schemes, most of it in the context of structured grids (Chyczewski et al 1993;Tysinger & Caughey 1993;Stagg et al 1993;Ajmani, Liou & Dyson 1994;Candler, Wright & McDonald 1994;Drikakis, Schreck & Durst 1994;Hixon & Sankar 1994;Ajmani & Liou 1995;Povitsky & Wolfstein 1995), but some work has been done with implicit unstructured flow solvers (Venkatakrishnan 1994;Venkatakrishnan 1995;Lanteri & Loriot 1996;Silva & Almeida 1996). Lanteri and Loriot (1996) describe the performance of a production flow solver using Euler implicit time integration with a fixed number of Jacobi iterations for the inner problem.…”

Section: Introductionmentioning

confidence: 99%

Parallelization of the Euler equations on unstructured grids

Bruner¹,

Walters

1997

13th Computational Fluid Dynamics Conference

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Aerospace Engineering (ABSTRACT)Several different time-integration algorithms for the Euler equations are investigated on two distributed-memory parallel computers using an explicit message-passing paradigm: these are classic Euler Explicit, four-stage Jameson-style Runge-Kutta, Block Jacobi, Block Gauss-Seidel, and Block Symmetric Gauss-Seidel. A finite-volume formulation is used for the spatial discretization of the physical domain. Both two-and three-dimensional test cases are evaluated against five reference solutions to demonstrate accuracy of the fundamental sequential algorithms. Different schemes for communicating or approximating data that are not available on the local compute node are discussed and it is shown that complete sharing of the evolving solution to the inner matrix problem at every iteration is faster than the other schemes considered. Speedup and efficiency issues pertaining to the various time-integration algorithms are then addressed for each system. Of the algorithms considered, Symmetric Block Gauss-Seidel has the overall best performance. It is also demonstrated that using parallel efficiency as the sole means of evaluating performance of an algorithm often leads to erroneous conclusions; the clock time needed to solve a problem is a much better indicator of algorithm performance. A general method for extending one-dimensional limiter formulations to the unstructured case is also discussed and applied to Van Albada's limiter as well as Roe's Superbee limiter. Solutions and convergence histories for a two-dimensional supersonic ramp problem using these limiters are presented along with computations using the limiters of Barth & Jesperson and Venkatakrishnan -the Van Albada limiter has performance similar to Venkatakrishnan's. IntroductionAlthough sequential computer performance has historically increased exponentially, this trend cannot continue indefinitely. Due to the finite speed of light and other physical limitations, there is an absolute speed limit for sequential computers, and we are rapidly approaching that limit. Bergman and Vos (1991) estimate that computer performance on the order of 10 12 -10 18 floating-point operations per second is necessary to model an entire airplane (including the aerodynamics, structure, and propulsion and control systems) and obtain turnaround times short enough to impact a design. This kind of performance can only be achieved using parallel computers (Simon, et al. 1992, 28). Gropp, Lusk, and Skjellum Gauss-Seidel, and Block Symmetric Gauss-Seidel iterative schemes are also implemented to solve the matrix problem that arises with Euler implicit time integration (Stoer & Bulirsch 1980, 560-562; Golub & Van Loan 1989, 513-514).Several authors have investigated parallel explicit time integration schemes on structured grids (Deshpande et al. 1993;Otto 1993;Underwood et al. 1993;Scherr 1995;Drikakis 1996;Peric & Schreck 1996;Stamatis & Papailiou 1996). Others have used parIntroduction 2 allel explicit time integration schemes on unstructured...

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Numerical solution on flow problems on a parallel computer

Cited by 2 publications

References 5 publications

Multidomain implicit numerical scheme

Multidomain implicit numerical scheme

Parallelization of the Euler equations on unstructured grids

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