Resolution of the Navier-Stokes equations on block-structured meshes

International Journal for Numerical Methods in Fluids

Volumn 54, Issue 10, 2007, Pages 1239-1268

  Rome C ^a   Glockner, S ^a   Caltagirone, J P ^a  

^a CNRS   (France)

Author keywords

Block structured meshes; Interpolation; Navier Stokes; Non conforming; Non matching; Overlapping

Indexed keywords

BLOCK-STRUCTURED MESHES; CURVILINEAR MESHES; SPATIAL CONVERGENCE ORDER; TWO DIMENSIONAL LAMINAR FLOWS;

COMPUTER SIMULATION; CONVERGENCE OF NUMERICAL METHODS; INTERPOLATION; NAVIER STOKES EQUATIONS; TWO DIMENSIONAL;

LAMINAR FLOW;

COMPUTER SIMULATION; CONVERGENCE OF NUMERICAL METHODS; INTERPOLATION; LAMINAR FLOW; NAVIER STOKES EQUATIONS; TWO DIMENSIONAL;

EID: 34447581214     PISSN: 02712091     EISSN: 10970363     Source Type: Journal    
DOI: 10.1002/fld.1439     Document Type: Article

References (57)

1. Romé C, Glockner S. An implicit multiblock coupling for the incompressible Navier-Stokes equations. International Journal for Numerical Methods in Fluids 2005; 47:1261-1267.
2. Khadra K, Parneix S, Angot P, Caltagirone J-P. Fictitious domain approach for numerical modelling of Navier-Stokes equations. International Journal for Numerical Methods in Fluids 2000; 34:651-684.
3. Peyret R, Taylor TD. Computational Methods for Fluid Flow. Springer: New York, 1983.
4. Girault V, Raviart P-A. Finite Element Methods for Navier-Stokes Equations. Springer Series in Computational Mathematics. Springer: New York, 1986.
5. Fortin M, Glowinski R. Méthodes de Lagrangien Augmenté, Application à la résolution numérique de problèmes aux limites. Collection Méthodes Mathématiques de l'Informatique, Dunod, 1982.
6. Vincent S, Caltagirone J-P, Lubin P, Randrianarivelo TN. An adaptative augmented Lagrangian method for three-dimensional multimaterial flows. Computers and Fluids 2004; 33:1273-1289.
7. Breil J, Caltagirone JP. Three dimensional computer simulation of mould filling with N fluids by VOF PLIC and projection methods. ICCFD, Kyoto, 10-14 July 2000.
8. Le Bot C, Vincent S, Arquis E. Impact and solidification of indium droplets on a dry substrate. International Journal of Thermal Sciences 2005; 44:219-233.
9. Lubin P, Vincent S, Caltagirone JP, Abadie S. Fully three-dimensional direct numerical simulation of a plunging breaker. Comptes Rendus - Mecanique 2003; 331(7):495-501.
10. Chorin AJ. A numerical method for solving incompressible viscous flow problems. Journal of Computational Physics 1967; 2:12-26.
11. Chorin AJ. Numerical simulation of the Navier-Stokes equations. Mathematics of Computation 1968; 22:745-762.
12. Gresho PM, Chan ST. On the theory of semi-implicit projection methods for viscous incompressible flow and its implementation via a finite element method that also introduces a nearly consistent mass matrix. Part I: Theory. Part II: Implementation. International Journal for Numerical Methods in Fluids 1990; 11:587-620, 621-659.
13. Hugues S, Randriamampianina A. An improved projection scheme applied to pseudospectral methods for the incompressible Navier-Stokes equations. International Journal for Numerical Methods in Fluids 1998; 28:501-521.
14. Goda K. A multistep technique with implicit difference schemes for calculating two- or three-dimensional cavity flows. Journal of Computational Physics 1978; 30:76-95.
15. Timmermans LJP, Minev PD, Van de Vosse FN. An approximate projection scheme for incompressible flow using spectral elements. International Journal for Numerical Methods in Fluids 1996; 22:673-688.
16. Patankar SV, Spalding D. A calculation procedure for heat mass and momentum transfer in three dimensional parabolic flows. International Journal of Heat and Mass Transfer 1972; 15:1787-1806.
17. Patankar SV. Numerical Heat Transfer and Fluidflow. Hemisphere Publishing Corporation: New York, 1980.
18. Caltagirone JP, Breil J. Sur une méthode de projection vectorielle pour la résolution des équations de Navier-Stokes. Comptes Rendus de l' Academie des Sciences, Paris, Serie IIb 1999; 327:1179-1184.
19. Harlow FH, Welsh JE. Numerical calculation of time dependent viscous incompressible flows. The Physics of Fluids 1965; 8:2182-2189.
20. Amestoy PR, Duff IS, L'Excellent J-Y. Multifrontal parallel distributed symmetric and unsymmetric solvers. Computer Methods in Applied Mechanics and Engineering 2000; 184:501-520.
21. Quarteroni A, Valli A. Domain Decomposition Methods for Partial Differential Equations. Numerical Mathematics and Scientific Computation. Oxford Science Publications: Oxford, 1999.
22. Lions PL. On the Schwarz alternating method III: a variant for nonoverlapping subdomains. Third International Symposium on Domain Decomposition Methods for Partial Differential Equations, Philadelphia, 1990.
23. Bernardi C, Maday Y, Patera AT. Domain decomposition by the mortar element method. In Asymptotic and Numerical Methods for Partial Differential Equations with Critical Parameters. Kaper HG, Garbey M (eds). NATO ASI Series C, vol. 384. Kluwer Academic Publishers: Dordrecht, 1993; 269-286.
24. Cai XC, Dryja M, Sarkis M. Overlapping nonmatching grid Mortar element methods for elliptic problems. SIAM Journal on Numerical Analysis 1999; 36:581-606.
25. Achdou Y, Maday Y, Widlund OB. Iterative substructuring preconditioners for mortar element methods in two dimensions. SIAM Journal on Numerical Analysis 1999; 36(2):551-580.
26. Achdou Y, Japhet C, Maday Y, Nataf F. A new cement to glue non-conforming grids with Robin interface conditions: the finite volume case. Numerische Mathematik 2002; 92(4):593-620.
27. Arbogast T, Yotov I. A non-mortar mixed finite element method for elliptic problems on non-matching multiblock grids. Computer Methods in Applied Mechanics and Engineering 1997; 149(1-4):255-265.
28. Benek JA, Buning PG, Steger JL. A 3-D Chimera grid embedding technique. AIAA 85-1523CP, 1985.
29. Steger JL, Benek JA. On the use of composite grid schemes in computational aerodynamics. Computer Methods in Applied Mechanics and Engineering 1987; 64:301-320.
30. Houzeaux G, Codina R. A Chimera method based on a Dirichlet/Neumann (Robin) coupling for the Navier-Stokes equations. Computer Methods in Applied Mechanics and Engineering 2003; 192:3343-3377.
31. Brezzi F, Lions JL, Pironneau O. Analysis of a Chimera method. Comptes Rendus de l' Academic des Sciences, Paris, Série I 2001; 332(I):655-660.
32. Cadafalch J, Oliva A, Pérez-Segarra CD, Costa M, Salom J. Comparative study of conservative and nonconservative interpolation schemes for the domain decomposition method on laminar incompressible flow. Numerical Heat Transfer, Part B 1999; 35:65-84.
33. Henshaw WD, Watson TJ. A fourth-order accurate method for the incompressible Navier-Stokes equations on overlapping grids. Journal of Computational Physics 1994; 113(1):13-25.
34. Meakin RL. On the spatial and temporal accuracy of overset grid methods for moving body problems. AIAA Applied Aerodynamics Conference, 12th, Colorado Springs, CO, 20-22 June 1994, Technical Papers, Pt. 2 (A94-30939 10-02), American Institute of Aeronautics and Astronautics, Washington, DC, 1994; 858-871.
35. Burggraf OR. Analytical and numerical studies of the structure of the steady separated flow. Journal of Fluid Mechanics 1966; 24:113-151.
36. Botella O, Peyret R. Benchmark spectral results on the lid-driven cavity flow. Computers and Fluids 1998; 4:421-433.
37. Ghia U, Ghia KN, Shin CT. High-resolutions for incompressible flow using the Navier-Stokes equations and a multi-grid method. Journal of Computational Physics 1982; 48:387-411.
38. Schreiber R, Keller HB. Driven cavity flow by efficient numerical techniques. Journal of Computational Physics 1983; 49:310-333.
39. Bruneau CH, Jouron C. An efficient scheme for solving steady incompressible Navier-Stokes equations. Journal of Computational Physics 1990; 89:389-413.
40. Barragy E, Carey GE Stream function-vorticity driven cavity solution using p finite elements. Computers and Fluids 1997; 26:453-468.
41. Armaly PH, Durst F, Pereira JCF, Schonung F. Experimental and theoretical investigation of backward-facing step flow. Journal of Fluid Mechanics 1983; 127:473-496.
42. Lee T, Matescu D. Experimental and numerical investigation of 2-D backward-facing step flow. Journal of Fluids and Structures 1988; 12:703-717.
43. Kim J, Moin P. Application of a fractional-step method to incompressible Navier-Stokes equations. Journal of Computational Physics 1985; 59:308-323.
44. Barton IE. A numerical study of flow over a confined backward-facing step. International Journal for Numerical Methods in Fluids 1995; 21:653-665.
45. Williams PT, Baker AJ. Numerical simulations of laminar flow over a 3D backward-facing step. International Journal for Numerical Methods in Fluids 1997; 24:1159-1183.
46. Gartling DK. A test problem for outflow boundary conditions - flow over a backward-facing step. International Journal for Numerical Methods in Fluids 1990; 11:953-967.
47. Sohn J. Evaluation of FIDAP on some classical laminar and turbulent benchmarks. International Journal for Numerical Methods in Fluids 1988; 8:1469-1490.
48. Taneda S. Experimental investigation of the wakes behind cylinder at low Reynolds numbers. Journal of the Physical Society of Japan 1956; 11:302-306.
49. Tritton DJ. Experiments on the flow past a circular cylinder at low Reynolds numbers. Journal of Fluid Mechanics 1959; 6:547-567.
50. Acrivos A, Leal LG, Snowden DD, Pan F. Further experiments on steady separated flows past bluff objects. Journal of Fluid Mechanics 1968; 34:25-48.
51. Coutanceau M, Bouard R. Experimental determination of the main features of the viscous flow in the wake of a circular cylinder in uniform translation. Part 1. Steady flow. Journal of Fluid Mechanics 1977; 79:231-256.
52. Dennis SCR, Chang GZ. Numerical solutions for steady viscous flow past a circular cylinder. Journal of Fluid Mechanics 1970; 42:471-489.
53. Nieuwstadt F, Keller HB. Viscous flow past circular cylinders. Computer and Fluids 1973; 1:59.
54. Fornberg B. A numerical study of steady viscous flow past a circular cylinder. Journal of Fluid Mechanics 1980; 98:819-855.
55. He X, Doolen G. Lattice Boltzman method on curvilinear coordinates system: flow around a circular cylinder. Journal of Computational Physics 1997; 134:306-315.
56. Williamson CHK, Brown GL. A series in 1/√Re to represent the Strouhal-Reynolds number relationship of the cylinder wake. Journal of Fluids and Structures 1998; 12:1073-1085.
57. Prabhakar V, Reddy JN. Spectral/hp penalty least-squares finite element formulation for the steady incompressible Navier-Stokes equations. Journal of Computational Physics 2006; 215(1):274-297.