Adaptive parallel multigrid solution of 2D incompressible Navier-Stokes equations

International Journal for Numerical Methods in Fluids

Volumn 24, Issue 9, 1997, Pages 875-892

  Wu, Jian ^a,b   Ritzdorf, Hubert ^a   Oosterlee, Kees ^a   Steckel, Barbara ^a   Schüller, Anton ^a  

^a FRAUNHOFER INSTITUTE FOR APPLIED INFORMATION TECHNOLOGY FIT   (Germany)

^b Ger Res Ctr for Info Technology   (Germany)

Author keywords

Adaptive parallel multigrid method; Hole pressure problem; Incompressible Navier Stokes equations; Local refinement criteria

Indexed keywords

APPROXIMATION THEORY; CHANNEL FLOW; COMPUTATIONAL METHODS; ERROR DETECTION; FINITE ELEMENT METHOD; PARALLEL ALGORITHMS; PARALLEL PROCESSING SYSTEMS;

ADAPTIVE PARALLEL MULTIGRID METHOD; HOLE PRESSURE PROBLEM; MULTILEVEL ADAPTIVE TECHNIQUE (MLAT); POISEUILLE CHANNEL FLOW;

NAVIER STOKES EQUATIONS;

CHANNELS; NAVIER-STOKES EQUATIONS; POISEUILLE FLOW;

EID: 0031147878     PISSN: 02712091     EISSN: None     Source Type: Journal    
DOI: 10.1002/(sici)1097-0363(19970515)24:9<875::aid-fld517>3.0.co;2-n     Document Type: Article

References (18)

1. H. Ritzdorf, A., Schüller, B. Steckel and K. Stüben, 'LiSS - an environment for the parallel differential equations on general 2D domains', Parallel Comput., 20, 1559-1570 (1994).
2. B. Eisfeld, H. Ritsdorf, H.-M. Bleeke and N. Kroll, 'POPINDA Ein BMFT-Verbundprojekt mit DASA, Deutsche Airbus, DLR, Dornier, GMD und IBM zur protablen Parallelisierung industrieller Anwendungen', Proc. 3rd Workshop on Scientific Computing, 30-43, Braunschweig, 4-6.10. 1994.
3. A. Brandt, 'Multi-level adaptive solutions to boundary-value problems', Math. Comput., 31, 333-390 (1977).
4. A. Brandt, 'Multigrid techniques: 1984 guide, with applications to fluid dynamics', GMD-Studie 85, GMD, St. Augustin, 1984.
5. Th. Sonar, 'Strong and weak norm refinement indicators based on the finite element residual for compressible flow', in Impact of Computing in Science and Engineering, 5, 111-127 (1993).
6. H. Ritzdorf and K. Stüben, 'Adaptive multigrid on distributed memory computers', in P. W. Hemker and P. Wesseling (eds), Multigrid Methods IV, Birkhäuser, 77-95, 1993.
7. E. Dick and J. Linden, 'A multigrid method for steady incompressible Navier-Stokes equations based on flux difference splitting', j. numer. methods fluids, 14, 1311-1323 (1992).
8. W. Hackbusch, Multi-grid Methods and Applications, Springer, Berlin, 1985, p. 288.
9. B. van Leer, 'Flux-vector splitting for Euler equations', Lecture Notes Phys., 170, 507-512 (1982).
10. L. Linden, B. Steckel and K. Stüben, 'Parallel multigrid solution of the Navier-Stokes equations', Parallel Comput., 7, 461-475 (1988).
11. R. Calkin, R. Hempel, H. C. Hoppe and P. Wypior, 'Portable programming with the PARMACS message-passing library', Parallel Comput., 20, 615-632 (1994).
12. D. S. Malkus, 'Calculation of hole error by finite element methods', in C. Klason and J. Kubat (eds), Prov. VIIth Int. Congr. on Rheology, 1976, p. 618.
13. G. D. Richards and P. Townsend, 'A finite element computer model of the hole pressure problem', Rheol. Acta, 20, 261 (1981).
14. N. R. Jackson and B. R. Finlayson, 'Calculation of hole pressure: I. Newtonian fluids', J. Non-Newtonian Fluid Mech., 10, 55-69 (1982).
15. M. J. Crochet, S. Dupont and J. M. Marchal, 'Numerical calculation of the Newtonian liquid circular hole pressure', J. Rheol., 30, 91 (1986).
16. A. S. Lodge, W. G. Pritchard and L. R. Scott, 'The hole-pressure problem', IMA J. Appl. Math., 46, 39-66 (1991).
17. P. Laasonen, 'On the truncation error of discrete approximations to the solutions of Dirichlet problems in a domain with corners', J. Assoc. Comput. Mech., 5, 32-38 (1958).
18. W. Kaspar and R. Remke, 'Die numerische Behandlung der Poisson-Gleichung auf einem Gebiet mit einspringenden Ecken', Computing, 22, 141-151 (1979).