A Fourth-Order-Accurate Finite Volume Compact Method for the Incompressible Navier-Stokes Solutions

Journal of Computational Physics

Volumn 167, Issue 1, 2001, Pages 217-243

  Pereira, J M C ^a   Kobayashi, M H ^a   Pereira, J C F ^a  

^a UNIVERSITY OF LISBON   (Portugal)

Author keywords

Compact schemes; Finite volume; High order schemes; Navier stokes equations

Indexed keywords

FINITE VOLUME METHOD; NUMERICAL METHODS; RUNGE KUTTA METHODS; UNSTEADY FLOW; VISCOUS FLOW;

COMPACT SCHEMES; DISCRETIZATIONS; FINITE-VOLUME; FOURTH ORDER ACCURATE COMPACT SCHEME; FOURTH-ORDER; HIGH-ORDER SCHEME; INCOMPRESSIBLE NAVIER-STOKES; MATRIX-FREE METHODS; NAVIER STOKES SOLUTION; NAVIER-STOKES EQUATION;

NAVIER STOKES EQUATIONS;

EID: 0141935064     PISSN: 00219991     EISSN: None     Source Type: Journal    
DOI: 10.1006/jcph.2000.6673     Document Type: Article

References (21)

1. S. K. Lele, Compact finite difference schemes with spectral-like resolution, J. Comput. Phys. 103, 16 (1992).
2. K. Mahesh, A family of high order finite difference schemes with good spectral resolution, J. Comput. Phys. 145, 332 (1998).
3. A. I. Tolstykh and M. V. Lipavskii, On performance of methods with third- and fifth-order compact upwind differencing, J. Comput. Phys. 140, 205 (1998).
4. N. A. Adams and K. Shariff, A high-resolution hybrid compact-ENO scheme for shock-turbulence interaction problems, J. Comput. Phys. 127, 27 (1996).
5. H. C. Yee, Explicit and implicit multidimensional compact high-resolution shock-capturing methods: Formulation, J. Comput. Phys. 131, 216 (1997).
6. M. M. Gupta, High accuracy solutions of incompressible Navier-Stokes equations, J. Comput. Phys. 93, 343 (1991).
7. M. Li, T. Tang, and B. Fornberg, A compact fourth-order finite difference scheme for the steady incompressible Navier-Stokes equations, Int. J. Numer. Methods Fluids 20, 1137 (1995).
8. W. F. Spotz and G. F. Carey, High-order compact scheme for the steady stream-function vorticity equations, Int. J. Numer. Methods Eng. 38, 3497 (1995).
9. R. V. Wilson and A. O. Demuren, Numerical simulation of turbulent jets With rectangular cross-section, J. Fluids Eng. 120, 285, ICASE, NASA Langley Research Center, Hampton, VA (1998).
10. R. V. Wilson, A. O. Demuren, and M. Carpenter, Higher-Order Compact Schemes for Numerical Simulation of Incompressible Flows, ICASE Technical Report 98-13 (1998).
11. D. Gaitonde and J. S. Shang, Optimized compact-difference-based finite-volume schemes for linear wave phenomena, J. Comput. Phys. 138, 617 (1997).
12. M. H. Kobayashi, On a class of Padé finite volume methods, J. Comput. Phys. 156, 137 (1999).
13. N. P. Marques and J. C. Pereira, Comparison of Matrix-Free Acceleration Techniques in Compressible Navier-Stokes Calculations, in Proceedings of 1999 International Conference on Preconditioning Techniques for Large Sparse Matrix Problems in Industrial Applications, Minneapolis, Minnesota, June 10-12, 1999.
14. A. Harten, B. Engquist, S. Osher, and S. R. Chakravarthy, Uniformly high order accuracy essentially non-oscillatory schemes III, J. Comput. Phys. 71, 231 (1987).
15. M. H. Carpenter, D. Gottlieb, and S. Abarbanel, The stability of numerical boundary treatments for compact high-order finite-difference schemes, J. Comput. Phys. 108, 272 (1993).
16. P. N. Brown and Y. Saad, Hybrid Krylov methods for nonlinear systems of equations, SIAM J. Sci. Stat. Comput. 11, 450 (1990).
17. V. Girault and P. Raviart, Finite Element Methods for Navier-Stokes Equations (Springer-Verlag, Berlin, 1986).
18. T. M. Shih, C. H. Tan, and B. C. Hwang, Effects of grid staggering on numerical schemes, Int. J. Numer. Methods Fluids 9, 193 (1989).
19. U. Ghia, K. N. Ghia, and C. T. Shin, High-Re solutions for incompressible flow using the Navier-Stokes equations and a multigrid method, J. Comput. Phys. 48, 387 (1982).
20. O. Botella and R. Peyret, Benchmark spectral results on the lid-driven cavity flow, Comput. Fluids 27, 421 (1998).
21. B. P. Leonard, A stable and accurate convective modeling procedure based on quadratic upstream interpolation, Comput. Meth. Appl. Mech. Eng. 19, 59 (1979).