On the efficiency and quality of numerical solutions in CFD problems using the interface strip preconditioner for domain decomposition methods

International Journal for Numerical Methods in Fluids

Volumn 52, Issue 1, 2006, Pages 89-118

  Paz, Rodrigo R ^a   Nigro, Norberto M ^a   Storti, Mario A ^a  

^a UNIVERSIDAD NACIONAL DEL LITORAL   (Argentina)

Author keywords

Computational fluid dynamics; Domain decomposition methods; Iterative solutions; Parallel computing

Indexed keywords

COMPRESSIBLE FLOW; FINITE ELEMENT METHOD; INCOMPRESSIBLE FLOW; ITERATIVE METHODS; PARALLEL PROCESSING SYSTEMS; VISCOUS FLOW;

DOMAIN DECOMPOSITION METHODS; INTERFACE STRIP PRECONDITIONER;

COMPUTATIONAL FLUID DYNAMICS;

COMPRESSIBLE FLOW; COMPUTATIONAL FLUID DYNAMICS; FINITE ELEMENT METHOD; INCOMPRESSIBLE FLOW; ITERATIVE METHODS; PARALLEL PROCESSING SYSTEMS; VISCOUS FLOW;

EID: 33747585879     PISSN: 02712091     EISSN: 10970363     Source Type: Journal    
DOI: 10.1002/fld.1176     Document Type: Article

References (36)

1. Bramble JH, Pasciak JE, Schatz AH. The construction of preconditioners for elliptic problems by substructuring, I. Mathematics of Computation 1986; 47(175):103-134.
2. Bramble JH, Pasciak JE, Schatz AH. The construction of preconditioners for elliptic problems by substructuring, IV. Mathematics of Computation 1989; 53(187):1-24.
3. Farhat C, Roux FX. A method of finite element tearing and interconnecting and its parallel solution algorithm. International Journal for Numerical Methods in Engineering 1991; 32:1205-1227.
4. Mandel J. Balancing domain decomposition. Communications in Applied Numerical Methods 1993; 9:233-241.
5. Smith B, Bjørstad P, Gropp W. Domain Decomposition: Parallel Multilevel Methods for Elliptic Partial Differential Equations. Cambridge University Press: Cambridge, MA, 1996.
6. Le Tallec P, Vidrascu M. Solving large scale structural problems on parallel computers using domain decomposition techniques. In Parallel Solution Methods in Computational Mechanics, Chapter 2, Papadrakakis M (ed.). Wiley: New York, NY, 1997; 49-85.
7. Meurant G. Computer Solution of Large Linear Systems. Studies in Mathematics and its Applications, vol. 28. North-Holland: Amsterdam, 1999.
8. Saad Y. Iterative Methods for Sparse Linear Systems. PWS Publishing Co.: MA, 2000. http://www-users.cs.umn.edu/saad/books.html
9. Rachowicz W. An anisotropic h-adaptive finite element method for compressible Navier-Stokes equations. Computer Methods in Applied Mechanics and Engineering 1997; 146:231-252.
10. Storti MA, Dalcin L, Paz RR, Yommi A, Sonzogni V, Nigro N. An interface strip preconditioner for domain decomposition methods. Journal of Computational Methods in Science and Engineering, 2003, in press.
11. Paz RR, Storti MA. An interface strip preconditioner for domain decomposition methods: application to hydrology. International Journal for Numerical Methods in Engineering 2005; 62(13):1873-1894.
12. Brooks AN, Hughes TJR. Streamline upwind/Petrov-Galerkin formulations for convection dominated flows with particular emphasis on the incompressible Navier-Stokes equations. Computer Methods in Applied Mechanics and Engineering 1982; 32:199-259.
13. Tezduyar T, Mittal S, Ray S, Shih R. Incompressible flow computations with stabilized bilinear and linear equal order interpolation velocity pressure elements. Computer Methods in Applied Mechanics and Engineering 1992; 95(95):221-242.
14. Smagorinsky J. General circulation experiments with the primitive equations. Monthly Weather Review 1963; 91(3):99-165.
15. Codina R. Pressure stability in fractional step finite element methods for incompressible flows. Journal of Computational Physics 2001; 170:112-140.
16. Aliabadi SK. Parallel finite element computations in aerospace applications. Ph.D. Thesis, Department of Aerospace Engineering and Mechanics, University of Minnesota, 1994.
17. Tezduyar T, Senga M. Determination of the shock-capturing parameters in supg formulation of compressible flows. In Computational Mechanics WCCM IV, Springler (ed.). Tsinghua University Press: Beijing, China, 2004.
18. De Roeck YH, Le Tallec P. Analysis and test of a local domain decomposition preconditioner. In Fourth International Symposium on Domain Decomposition Methods for Partial Differential Equations, Glowinski, Kuznetsov, Meurant, Pèriaux, Widlund (eds). SIAM: Philadelphia, PA, 1991.
19. Storti MA, Nigro NM, Paz RR. PETSc-FEM: a general purpose, parallel, multi-physics FEM program. http://www.cimec.org.ar/petscfem
20. Carter JE. Numerical solutions of the Navier-Stokes equations for the supersonic laminar flow over two-dimensional compression corner. Technical Report R-385, National Aeronautics and Space Administration (NASA), 1972.
21. Grasso F, Leone G, Delery J. Validation procedure for the analysis of shock-wave/boundary-layer interaction problems. AIAA Journal 1994; 32(9):1820-1827.
22. Gropp W, Lusk E, Skjellum A. Using MPI: Portable Parallel Programming with the Message-Passing Interface (2nd edn). MIT Press: London, England, 1994.
23. Balay S, Gropp WD, Curfman McInnes L, Smith BE. PETSc 2.2.0 User's Manual. Argonne National Laboratory, 2004. http://www-unix.mcs.anl.gov/ petsc
24. George K. METIS: family of multilevel partitioning algorithms (1996-2005), http://www-users.cs.umn.edu/karypis/metis
25. Koo J, Kleinstreuer C. Liquid flow in micro-channels: experimental observations and computational analysis of microfluidics effects. Journal of Micromechanics and Microengineering 2003; 13:568-579.
26. Stay MS, Barocas VH. Coupled lubrication and Stokes flow finite elements. International Journal for Numerical Methods in Fluids 2003; 42(2):129-146.
27. Braza M, Chassaing P, Ha Minh H. Numerical study and physical analysis of the pressure and velocity fields in the near wake of a circular cylinder. Journal of Fluid Mechanics 1986; 164:79-130.
28. Chorin AJ. Numerical study of slightly viscous flow. Journal of Fluid Mechanics 1973; 57:785-796.
29. Shih R, Tezduyar TE. Numerical experiments with the location of the downstream boundary for flow past a cylinder. Research Report UMSI 90/ 38, University of Minnesota Supercomputer Institute, 1990.
30. Behr M, Liou J, Shih R, Tezduyar TE. Vorticity-stream function formulation of unsteady incompressible flow past a cylinder: sensitivity of the computed flow field to the location of the downstream boundary. Research Report UMSI 90/87, University of Minnesota Supercomputer Institute, 1990.
31. Roshko A. On the drag and shedding frequency of two dimensional bluff bodies. Technical Note 3169, National Advisory Committee for Aeronautics (NACA), 1954.
32. Williamson CHK. Evolution of a single wake behind a pair of bluff bodies. Journal of Fluid Mechanics 1985; 159:1-18.
33. Norberg C. Flow around a circular cylinder: aspects of fluctuating lift. Journal of Fluids and Structures 2001; 15:459-469.
34. Ghia U, Ghia KN, Shin CT. High-Re solutions for incompressible flow using the Navier Stokes equations and a multigrid method. Journal of Computational Physics 1982; 48:387-411.
35. Krajnovié S, Davidson L. Numerical study of the flow around the bus-shaped body. Journal of Fluids Engineering (ASME) 2003; 125:500-509.
36. Ahmed SR, Ramm G, Faltin G. Some salient features of the times-averaged ground vehicle wake. SAE Society of Automotive Engineering Inc 1984; 1(840300):1-31.