×

Acceleration of a Navier–Stokes equation solver for unstructured grids using agglomeration multigrid and parallel processing. (English) Zbl 1106.76405

Summary: This paper focuses on the parallelization of the agglomeration multigrid technique for the numerical solution of the 2D and 3D Favre-averaged Navier–Stokes equations on unstructured grids. The agglomeration algorithm conforms with the finite-volume discretization scheme and operates independently of the algorithm used to define the concurrently treated subdomains. The computational platform is a cluster of interconnected processors, each of which is associated with one subdomain and requires repetitive communication with the other processors, carried out through the PVM library. Emphasis is laid on (a) the agglomeration strategy, by comparing isotropic and directional agglomeration techniques depending on grid stretching, (b) the discretization schemes for the inviscid fluxes, based on identical edge-wise computations at any multigrid level along with flux limiting techniques, (c) the discretization schemes for the viscous fluxes, for which the triangle- or tetrahedron-based scheme on the fine mesh switches to a computationally less demanding edge-wise scheme on the coarser grids and (d) the modification to the multigrid operators for the one- and two-equation turbulence models. Isolated airfoil, wing and turbomachinery cascade flow problems are used to demonstrate the efficiency of multigrid.

MSC:

76M12 Finite volume methods applied to problems in fluid mechanics
76N15 Gas dynamics (general theory)
65Y05 Parallel numerical computation
65M55 Multigrid methods; domain decomposition for initial value and initial-boundary value problems involving PDEs
PDFBibTeX XMLCite
Full Text: DOI

References:

[1] T. Arts, M.L. de Rouvroit, Aero-thermal investigation of a highly-loaded transonic linear turbine guide vane cascade. A test case for inviscid and viscous flow computations, VKI-Technical Note 174, September 1990; T. Arts, M.L. de Rouvroit, Aero-thermal investigation of a highly-loaded transonic linear turbine guide vane cascade. A test case for inviscid and viscous flow computations, VKI-Technical Note 174, September 1990
[2] T.J. Barth, D. Jespersen, The design and application of upwind schemes on unstructured meshes, AIAA Paper 89-0366, 1989; T.J. Barth, D. Jespersen, The design and application of upwind schemes on unstructured meshes, AIAA Paper 89-0366, 1989
[3] T.J. Barth, Numerical aspects of computing viscous high Reynolds numbers flows on unstructured meshes, AIAA Paper 91-0721, 1991; T.J. Barth, Numerical aspects of computing viscous high Reynolds numbers flows on unstructured meshes, AIAA Paper 91-0721, 1991
[4] A. Brandt, Multigrid Techniques: 1984 Guide with Applications to Fluid Dynamics, Department of Applied Mathematics, The Weizmann Institute of Science, Rehovot 76100, Israel, 1984; A. Brandt, Multigrid Techniques: 1984 Guide with Applications to Fluid Dynamics, Department of Applied Mathematics, The Weizmann Institute of Science, Rehovot 76100, Israel, 1984
[5] Carre, G.; Fournier, L.; Lanteri, S., Parallel linear multigrid algorithm for the acceleration of compressible flow calculations, Comput. Methods Appl. Mech. Eng., 184, 427-448 (2000) · Zbl 0978.76055
[6] Connell, S. D.; Holmes, D. G., Three-dimensional unstructured adaptive multigrid scheme for the Euler equations, AIAA J., 32, 1626-1632 (1994) · Zbl 0815.76053
[7] P. Eliasson, S. Wallin, A positive multigrid scheme for computations with two-equation turbulence models, in: Proc. ECCOMAS 2000, European Congress on Computational Methods in Applied Sciences and Engineering, Barcelona, September 2000; P. Eliasson, S. Wallin, A positive multigrid scheme for computations with two-equation turbulence models, in: Proc. ECCOMAS 2000, European Congress on Computational Methods in Applied Sciences and Engineering, Barcelona, September 2000
[8] L. Fezoui, S. Lanteri, B. Larrouturou, C. Olivier, Resolution numerique des equations de Navier-Stokes pour un fluide compressible en maillage triangulaire, INRIA Report, No. 1033, Programme 7, 1989; L. Fezoui, S. Lanteri, B. Larrouturou, C. Olivier, Resolution numerique des equations de Navier-Stokes pour un fluide compressible en maillage triangulaire, INRIA Report, No. 1033, Programme 7, 1989
[9] Geist, A.; Beguelin, A.; Dongarra, J.; Jiang, W.; Manchek, R.; Sunderam, V., PVM: Parallel Virtual Machine. A User’s Guide and Tutorial for Networked Parallel Computing (1994), The MIT Press · Zbl 0849.68032
[10] Giotis, A. P.; Giannakoglou, K. C.; Mantel, B.; Periaux, J., Efficient Partitioning Methods for 3-D Unstructured Grids Using Genetic Algorithms, Evolutionary Algorithms in Engineering and Computer Science (1999), John Wiley and Sons, pp. 425-434
[11] D.G. Koubogiannis, K.C. Giannakoglou, Implementation and assessment of low-Reynolds turbulence models for airfoil flows on unstructured grids, in: Proc. ECCOMAS 2000, European Congress on Computational Methods in Applied Sciences and Engineering, Barcelona, September 2000; D.G. Koubogiannis, K.C. Giannakoglou, Implementation and assessment of low-Reynolds turbulence models for airfoil flows on unstructured grids, in: Proc. ECCOMAS 2000, European Congress on Computational Methods in Applied Sciences and Engineering, Barcelona, September 2000
[12] Koubogiannis, D. G.; Athanasiadis, A. N.; Giannakoglou, K. C., One- and two-equation turbulence models for the prediction of complex cascade flows using unstructured grids, Comp. Fluids, 32, 403-430 (2003) · Zbl 1159.76339
[13] Lallemand, M.-H.; Herve, S.; Dervieux, A., Unstructured multigridding by volume agglomeration: current status, Comp. Fluids, 21, 397-433 (1992) · Zbl 0753.76136
[14] Launder, B. E.; Spalding, D. B., The numerical computation of turbulent flows, Comput. Methods Appl. Mech. Eng., 103, 456-460 (1974) · Zbl 0277.76049
[15] Mavriplis, D. J., Directional agglomeration multigrid techniques for high-Reynolds-number viscous flows, AIAA J., 37, 1222-1230 (1999)
[16] Merci, B.; Steelant, J.; Vierendeels, J.; Riemslagh, K.; Dick, E., Computational treatment of source terms in two-equation turbulence models, AIAA J., 38, 2085-2093 (2000)
[17] J.G. Moore, J. Moore, Realizability in turbulence modelling for turbomachinery CFD, ASME Paper 99-GT-24, 1999; J.G. Moore, J. Moore, Realizability in turbulence modelling for turbomachinery CFD, ASME Paper 99-GT-24, 1999
[18] Ollivier-Gooch, C. F., Multigrid acceleration of an upwind Euler solver on unstructured meshes, AIAA J., 33, 1822-1827 (1995) · Zbl 0856.76064
[19] Roe, P., Approximate Riemann solvers, parameter vectors and difference schemes, J. Comp. Phys., 43, 357-372 (1981) · Zbl 0474.65066
[20] V. Schmitt, F. Charpin, Pressure distributions on the ONERA-M6-Wing at transonic Mach Numbers. Experimental Data Base for Computer Program Assessment, AGARD AR 138, May 1979; V. Schmitt, F. Charpin, Pressure distributions on the ONERA-M6-Wing at transonic Mach Numbers. Experimental Data Base for Computer Program Assessment, AGARD AR 138, May 1979
[21] P. Spalart, S. Allmaras, A one-equation turbulence model for aerodynamic flows, AIAA Paper 92-0439, 1992; P. Spalart, S. Allmaras, A one-equation turbulence model for aerodynamic flows, AIAA Paper 92-0439, 1992
[22] W. Steinert, B. Eisenberg, H. Starken, Design and testing of a controlled diffusion airfoil cascade for industrial axial flow compressor applications, ASME Paper 90-GT-140, 1990; W. Steinert, B. Eisenberg, H. Starken, Design and testing of a controlled diffusion airfoil cascade for industrial axial flow compressor applications, ASME Paper 90-GT-140, 1990
[23] Tsourakis, G. I.; Koubogiannis, D. G.; Giannakoglou, K. C., Transition and heat transfer predictions in a turbine cascade at various free-stream turbulence intensities through a one-equation turbulence model, Int. J. Numer. Meth. Fluids, 38, 1091-1110 (2002) · Zbl 1094.76520
[24] van Leer, B., Towards the ultimate conservative difference scheme: I. The quest of monotonicity, Lect. Notes Phys., 18, 163 (1972)
[25] Venkatakrishnan, V., Convergence to steady state solutions of the Euler equations on unstructured grids with limiters, J. Comp. Phys., 118, 120-130 (1995) · Zbl 0858.76058
[26] Venkatakrishnan, V.; Mavriplis, D. J., Agglomeration multigrid for the three-dimensional Euler equations, AIAA J., 33, 445-453 (1995) · Zbl 0925.76477
[27] Weiss, J. M.; Maruszewski, J. P.; Smith, W. A., Implicit solution of preconditioned Navier-Stokes equations using algebraic multigrid, AIAA J., 37, 29-36 (1991)
[28] White, F. M., Viscous Fluid Flow (1974), McGraw-Hill · Zbl 0356.76003
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.