A transient higher order compact scheme for incompressible viscous flows on geometries beyond rectangular

Journal of Computational Physics

Volumn 225, Issue 1, 2007, Pages 1100-1124

  Pandit, Swapan K ^a   Kalita, Jiten C ^a   Dalal, D C ^a  

^a INDIAN INSTITUTE OF TECHNOLOGY GUWAHATI   (India)

Author keywords

Constricted channel; HOC schemes; N S equations; Non uniform grid; Reynolds number; Transient

Indexed keywords

BOUNDARY CONDITIONS; FINITE DIFFERENCE METHOD; REYNOLDS NUMBER; SHEAR FLOW; VISCOUS FLOW;

CONSTRICTED CHANNELS; HIGH-ORDER COMPACT FINITE DIFFERENCE SCHEMES; HIGH-ORDER COMPACT SCHEME; INCOMPRESSIBLE VISCOUS FLOWS; IRREGULAR GEOMETRIES; NAVIER-STOKES EQUATION; NON-UNIFORM GRIDS; ORTHOGONAL GRID; REYNOLD NUMBER; TWO-DIMENSIONAL;

NAVIER STOKES EQUATIONS;

EID: 34447269218     PISSN: 00219991     EISSN: 10902716     Source Type: Journal    
DOI: 10.1016/j.jcp.2007.01.016     Document Type: Article

References (44)

1. Ferziger J.H., and Peric M. Computational Methods for Fluid Dynamics (2002), Springer
2. Visbal M.R., Gaitonde D.V., and Rizzetta D.P. High-order schemes for DNS/LES and CAA on curvilinear dynamic meshes. DNS/LES Progress and Challenges (2001), Greyden Press. 1-57074-488-2 August
3. Auteri F., Quartapelle L., and Vigevano L. Accurate ψ-ζ spectral solution of the singular driven cavity problem. J. Comput. Phys. 180 (2002) 597-615
4. Barragy E., and Carey G.F. Stream function-vorticity driven cavity solution using p finite elements. Comput. Fluids 26 5 (1997) 453-468
5. Botella O., and Peyret R. Benchmark spectral results on the lid-driven cavity flow. Comput. Fluids 27 (1998) 421-433
6. Brüger A., Gustafsson B., Lötstedt P., and Nilsson J. High order accurate solution of the incompressible Navier Stokes equations. J. Comput. Phys. 203 (2005) 49-51
7. Bruneau C.H., and Saad M. The 2D lid-driven cavity problem revisited. Comput. Fluids 35 (2005) 326-348
8. J.E. Castillo, S. Steinberg, The sensitivity and accuracy of fourth order finite-difference schemes on nonuniform grids in one dimension, DE-AC04-76DP00789, 1995.
9. Chen Y.N., Yang S.C., and Yang J.Y. Implicit weighted essentially non-oscillatory schemes for the incompressible Navier-Stokes equations. Int. J. Numer. Methods Fluids 31 (1999) 747-765
10. Chorin A.J. Numerical solution of the Navier-Stokes equation. Math. Comput. 22 (1968) 747-762
11. Chudanov V.V., Popkov A.G., Churbanov A.G., Vabishchevich P.N., and Makarov M.M. Operator-splitting schemes for the streamfunction-vorticity formulation. Comput. Fluids 24 7 (1995) 771-786
12. L. Ge, J. Zhang, Accuracy iterative solution of convection diffusion equation with boundary layers on nonuniform grids, Technical Report, University of Kentucky, Lexington, KY, No. 288-99, 1999.
13. Ghia U., Ghia K.N., and Shin C.T. High-Re solutions for incompressible Navier-Stokes equation and a multigrid method. J. Comput. Phys. 48 (1982) 387-411
14. Goodrich J.W., Gustafson K., and Halasi K. Hopf bifurcation in the driven cavity. J. Comput. Phys. 90 (1990) 219-261
15. Gupta M.M., Manohar R.M., and Stephenson J.H. A single cell high order scheme for the convection-diffusion equation with variable coefficients. Int. J. Numer. Methods Fluids 4 (1984) 641-651
16. Gupta M.M. High accuracy solutions of incompressible Navier-Stokes equations. J. Comput. Phys. 93 (1991) 343-357
17. Hou S., Zou Q., Chen S., Doolen G., and Cogley A. Simulation of cavity flows by the lattice Boltzmann method. J. Comput. Phys. 118 (1995) 329-347
18. Hoffman J.D. Relationship between the truncation errors of centered finite-difference approximations on uniform and nonuniform meshes. J. Comput. Phys. 46 (1982) 469-474
19. Kalita J.C., Dalal D.C., and Dass A.K. A class of higher order compact schemes for the unsteady two-dimensional convection-diffusion equation with variable convection coefficients. Int. J. Numer. Methods Fluids 38 (2002) 1111-1131
20. Kalita J.C., Dass A.K., and Dalal D.C. A transformation-free HOC for steady convection-diffusion on nonuniform grids. Int. J. Numer. Methods Fluids 44 (2004) 33-53
21. Kalita J.C., Dalal D.C., and Dass A.K. Fully compact higher order computation of steady-state natural convection in a square cavity. Phys. Rev. E 64 6 (2001) 066703 (1-13)
22. Kawamura T., Takami H., and Kuwahara K. A new high order upwind scheme for incompressible Navier-Stokes equations. Lect Notes Phys. 218 (1985)
23. Kennedy C.A., and Carpenter M.H. Several new numerical methods for compressible shear-layer simulations. Appl. Numer. Math. 14 2 (1994) 397-433
24. Kim J., and Moin P. Application of fractional step method to incompressible Navier-Stokes equation. J. Comput. Phys. 59 (1985) 308-323
25. Koseff J.R., and Street R.L. The lid-driven cavity flow: A synthesis of qualitative and quantitative observations. ASME J. Fluids Eng. 106 (1984) 390-398
26. Kupferman R.A. A central-difference scheme for a pure stream function formulation of incompressible viscous flows. SIAM J. Sci. Comput. 23 1 (2001) 1-18
27. Lele S.K. Compact finite difference schemes with spectral like resolution. J. Comput. Phys. 103 (1992) 16-42
28. Leonard B.P. The ULTIMATE conservative difference scheme applied to unsteady one-dimensional advection. Comput. Methods Appl. Mech. Eng. 88 1 (1991) 17-74
29. Li M., Tang T., and Fornberg B. A compact fourth order finite difference scheme for the steady incompressible Navier-Stokes equations. Int. J. Numer. Methods Fluids 20 (1995) 1137-1151
30. Li M., and Tang T. A compact fourth order finite difference scheme for unsteady viscous incompressible flows. SIAM J. Sci. Comput. 16 1 (2001) 29-45
31. Luchini P. Higher-order difference approximations of the Navier-Stokes equations. Int. J. Numer. Methods Fluids 12 (1991) 491-506
32. Mackinnon R.J., and Johnson R.W. Differential equation based representation of truncation errors for accurate numerical solution. Int. J. Numer. Methods Fluids 13 (1991) 739-757
33. Mancera P.F.A., and Hunt R. Fourth order method for solving the Navier Stokes equations in a constricted channel. Int. J. Numer. Methods Fluids 25 (1997) 1119-1135
34. Mancera P.F.A. A study of numerical solution of the steady two dimensional Navier-Stokes equations in a constricted channel problem by a compact fourth order method. Appl. Math. Comput. 146 (2003) 771-790
35. Moffat M.K. Viscous and resistive eddies near a sharp corner. J. Fluid Mech. 18 (1964) 1-18
36. Sanyasiraju Y.V.S.S., and Manjula V. Higher order semi compact scheme to solve transient incompressible Navier-Stokes equations. Comput. Mech. 35 (2005) 441-448
37. Schreiber R., and Keller H.B. Driven cavity flows by efficient numerical techniques. J. Comput. Phys. 49 (1983) 310-333
38. Shankar P.N., and Deshpande M.D. Fluid mechanics in the driven cavity. Annu. Rev. Fluid Mech. 32 (2000) 93-136
39. Spotz W.F., and Carey G.F. Formulation and experiments with high-order compact schemes for nonuniform grids. Int. J. Numer. Methods Heat Fluid Flow 8 3 (1998) 288-303
40. Spotz W.F., and Carey G.F. High-order compact scheme for the steady stream-function vorticity equations. Int. J. Numer. Methods Eng. 38 (1995) 3497-3512
41. Strikwerda J.C. High-order accurate schemes for incompressible viscous flow. Int. J. Numer. Methods Fluids 24 (1997) 715-734
42. Van Der Vorst H. BiCGSTAB : a fast and smoothly converging variant of BiCG for the solution of nonsymmetric linear systems. SIAM J. Sci. Comput. 13 (1992) 631-644
43. Vanka S.P. Block-implicit multigrid solution of Navier-Stokes equations in primitive variables. J. Comput. Phys. 65 (1986) 138-158
44. Yanwen M., Dexun F., Kobayashi T., and Taniguchi N. Numerical solution of the incompressible Navier-Stokes equations with an upwind compact difference scheme. Int. J. Numer. Methods Fluids 30 (1999) 509-521