A stable and conservative high order multi-block method for the compressible Navier-Stokes equations

Journal of Computational Physics

Volumn 228, Issue 24, 2009, Pages 9020-9035

  Nordström, Jan ^a,b,c   Gong, Jing ^c   van der Weide, Edwin ^d   Svärd, Magnus ^e  

^a UNIVERSITY OF THE WITWATERSRAND   (South Africa)

^b SWEDISH DEFENCE RESEARCH AGENCY   (Sweden)

^c UPPSALA UNIVERSITY   (Sweden)

^d UNIVERSITY OF TWENTE   (Netherlands)

^e UNIVERSITY OF OSLO   (Norway)

Author keywords

Conservation; Finite difference; High order; Navier Stokes; Stability

Indexed keywords

FINITE DIFFERENCE METHOD; VISCOUS FLOW;

A-STABLE; BLOCK METHODS; COMPRESSIBLE NAVIER-STOKES EQUATIONS; FINITE DIFFERENCE; HIGH-ORDER; HIGHER-ORDER; MULTIBLOCKS; NAVIER STOKES; SUMMATION-BY-PARTS OPERATORS; TIME DEPENDENT;

NAVIER STOKES EQUATIONS;

EID: 70350018301     PISSN: 00219991     EISSN: 10902716     Source Type: Journal    
DOI: 10.1016/j.jcp.2009.09.005     Document Type: Article

References (29)

1. Abarbanel S., and Gottlieb D. Optimal time splitting for two- and three-dimensional Navier-Stokes equations with mixed derivatives. Journal of Computational Physics 41 (1981) 1-43
2. Berger M.J. Stability of interfaces with mesh refinement. Mathematics of Computation 45 (1985) 551-574
3. Carpenter M.H., Nordström J., and Gottlieb D. A stable and conservative interface treatment of arbitrary spatial accuracy. Journal of Computational Physics 148 (1999) 341-365
4. Darbandi M., and Naderi A. Multiblock hybrid grid finite volume method to solve flow in irregular geometries. Computer Methods in Applied Mechanics and Engineering 196 (2006) 321-336
5. de Nicola C., Pinto G., and Tognaccini R. A normal mode stability analysis of multiblock algorithms for the solution of fluid-dynamics equations. Applied Numerical Mathematics 19 (1996) 419-431
6. Ferm L., and Lötstedt P. Accurate and stable grid interfaces for finite volume methods. Applied Numerical Mathematics 49 (2004) 207-224
7. Gong J., and Nordström J. A stable and efficient hybrid method for viscous problems in complex geometries. Journal of Computational Physics 226 2 (2007) 1291-1309
8. Gustafsson B. The convergence rate for difference approximation to mixed initial boundary value problems. Mathematics of Computation 29 (1975)
9. Gustafsson B. The convergence rate for difference approximation to general mixed initial boundary value problems. SIAM Journal on Numerical Analysis 18 2 (1981) 179-190
10. Gustafsson B., Kreiss H.-O., and Oliger J. Time Dependent Problems and Difference Methods (1995), John Wiley & Sons Inc.
11. Horn R.A., and Johnson C.R. Topics in Matrix Analysis (1991), Cambridge University Press
12. Kreiss H.-O., and Scherer G. Finite element and finite difference methods for hyperbolic partial differential equations. In: De Boor C. (Ed). Mathematical Aspects of Finite Elements in Partial Differential Equation (1974), Academic Press, New York
13. Le H., and Moin P. An improvement of fractional step methods for the incompressible Navier-Stokes equations. Journal of Computational Physics 92 (1991) 369-379
14. Lerat A., and Wu Z.N. Stable conservative multidomain treatments for implicit solvers. Journal of Computational Physics 123 (1995) 45-64
15. Nordström J., and Carpenter M.H. Boundary and interface conditions for high order finite difference methods applied to the Euler and Navier-Stokes equations. Journal of Computational Physics 148 (1999) 621-645
16. Nordström J., and Carpenter M.H. High-order finite difference methods, multidimensional linear problems and curvilinear coordinates. Journal of Computational Physics 173 (2001) 149-174
17. Nordström J., and Gong J. A stable hybrid method for hyperbolic problems. Journal of Computational Physics 212 (2006) 436-453
18. Nordström J., and Gustafsson R. High order finite difference approximations of electromagnetic wave propagation close to material discontinuities. Journal of Scientific Computing 18 2 (2003) 215-234
19. Nordström J., Ham F., Shoeybi M., van der Weide E., Svärd M., Mattsson K., Iaccarino G., and Gong J. A hybrid method for unsteady fluid flow. Computers and Fluids 38 (2009) 875-882
20. Nordström J., and Svärd M. Well-posed boundary conditions for the Navier-Stokes equations. SIAM Journal on Numerical Analysis 43 3 (2005) 1231-1255
21. Olsson F., and Petersson N.A. Stability of interpolation on overlapping grids. Computers and Fluids 25 (1996) 583-605
22. Pärt-Enander E., and Sjögren B. Conservative and non-conservative interpolation between overlapping grids for finite volume solutions of hyperbolic problems. Computers and Fluids 23 (1994) 551-574
23. Rizzi A., Eliasson P., Lindblad I., Hirsch C., Lacour C., and Hauser J. The engineering of multiblock multi-grid software for Navier-Stokes flows on structured meshes. Computers and Fluids 22 (1993) 341-367
24. Strand B. Summation by parts for finite difference approximation for d / dx. Journal of Computational Physics 110 1 (1994) 47-67
25. Strickwerda J.C. Initial boundary value problems for incompletely parabolic systems. Communications on Pure and Applied Mathematics 9 3 (1977) 797-822
26. Svärd M., Carpenter M.H., and Nordström J. A stable high-order finite difference scheme for the compressible Navier-Stokes equations: far-field boundary conditions. Journal of Computational Physics 225 1 (2007) 1020-1038
27. Svärd M., and Nordström J. On the order of accuracy for difference approximations of initial-boundary value problems. Journal of Computational Physics 218 1 (2006) 333-352
28. Svärd M., and Nordström J. A stable high-order finite difference scheme for the compressible Navier-Stokes equations: no-slip wall boundary conditions. Journal of Computational Physics 227 10 (2008) 4805-4824
29. E. van der Weide, G. Kalitzin, J. Schluter, J.J. Alonso, Unsteady turbomachinery computations using massively parallel platforms, AIAA Paper 2006-421, 2006.