Accurate and stable grid interfaces for finite volume methods

Applied Numerical Mathematics

Volumn 49, Issue 2, 2004, Pages 207-224

  Ferm, Lars ^a   Lötstedt, Per ^a  

^a UPPSALA UNIVERSITY   (Sweden)

Author keywords

Finite volume method; Grid refinement; Second order accuracy; Stability

Indexed keywords

APPROXIMATION THEORY; COMPUTATIONAL METHODS; CONVERGENCE OF NUMERICAL METHODS; DIFFUSION; HEAT CONVECTION; INTERPOLATION; ITERATIVE METHODS; MATHEMATICAL MODELS; MAXWELL EQUATIONS; NAVIER STOKES EQUATIONS;

GRID REFINEMENT; SECOND ORDER ACCURACY;

FINITE VOLUME METHOD;

EID: 1642587674     PISSN: 01689274     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.apnum.2003.07.004     Document Type: Article

References (27)

1. Almgren A.S., Bell J.B., Colella P., Howell L.H., Welcome M.L. A conservative adaptive projection method for the variable density incompressible Navier-Stokes equations. J. Comput. Phys. 142:1998;1-46.
2. Berger M. Stability at interfaces with mesh refinement. Math. Comp. 45:1985;301-318.
3. Berger M. On conservation at grid interfaces. SIAM J. Numer. Anal. 24:1987;967-984.
4. Berger M., Colella P. Local adaptive mesh refinement for shock hydrodynamics. J. Comput. Phys. 82:1989;64-84.
5. Cathers B., Bates S. Spurious numerical refraction. Internat. J. Numer. Meth. Fluids. 21:1995;1049-1066.
6. Cathers B., Bates S., O'Connor B.A. Internal wave reflections and transmissions arising from a non-uniform mesh. Part I: An analysis for the Crank-Nicholson linear finite element scheme. Internat. J. Numer. Meth. Fluids. 9:1989;783-810.
7. Colella P., Dorr M.R., Wake D.D. Numerical solution of plasma fluid equations using locally refined grids. J. Comput. Phys. 152:1999;550-583.
8. Collino F., Fouquet T., Joly P. A conservative space-time mesh refinement method for the 1-D wave equation, Part I: Construction. Numer. Math. 95:2003;197-221.
9. Collino F., Fouquet T., Joly P. A conservative space-time mesh refinement method for the 1-D wave equation. Part II: Analysis. Numer. Math. 95:2003;223-251.
10. Ferm L., Lötstedt P. Blockwise adaptive grids with multigrid acceleration for compressible flow. AIAA J. 37:1999;121-123.
11. Ferm L., Lötstedt P. Adaptive error control for steady state solutions of inviscid flow. SIAM J. Sci. Comput. 23:2002;1777-1798.
12. Ferm L., Lötstedt P. Anisotropic grid adaptation for Navier-Stokes' equations. J. Comput. Phys. 190:2003;22-41.
13. Gustafsson B., Kreiss H.-O., Oliger J. Time Dependent Problems and Difference Methods. 1995;Wiley, New York.
14. Hornung R.D., Trangenstein J.A. Adaptive mesh refinement and multilevel iteration for flow in porous media. J. Comput. Phys. 136:1997;522-545.
15. Kim I.S., Hoefer W.J.R. A local mesh refinement algorithm for the time-domain finite-difference method using Maxwell's curl equations. IEEE Trans. Microwave Theory Techn. 38:1990;812-815.
16. LeVeque R.J. Finite Volume Methods for Hyperbolic Problems. 2002;Cambridge University Press, Cambridge.
17. Lötstedt P., Söderberg S., Ramage A., Hemmingsson-Frändén L. Implicit solution of hyperbolic equations with space-time adaptivity. BIT. 42:2002;134-158.
18. A. Jameson, W. Schmidt, E. Turkel, Numerical solutions of the Euler equations by finite volume methods using Runge-Kutta time-stepping schemes, AIAA-Paper 81-1259, 1981.
19. Martin D.F., Colella P. A cell-centered adaptive projection method for the incompressible Euler equations. J. Comput. Phys. 163:2000;271-312.
20. Okoniewski M., Okoniewski E., Stuchly M.A. Three-dimensional subgridding algorithm for FDTD. IEEE Trans. Antennas Propagation. 45:1997;422-429.
21. Otto K. Analysis of preconditioners for hyperbolic partial differential equations. SIAM J. Numer. Anal. 33:1996;2131-2165.
22. Pärt-Enander E., Sjögreen B. Conservative and non-conservative interpolation between overlapping grids for finite volume solutions of hyperbolic problems. Comput. Fluids. 23:1994;551-574.
23. Prescott D.T., Shuley N.V. A method for incorporating different sized cells into the finite-difference time-domain analysis technique. IEEE Microwave Guided Wave Lett. 2:1992;434-436.
24. Powell K.G., Roe P.L., Linde T.J., Gombosi T.I., De Zeeuw D.L. A solution adaptive upwind scheme for ideal magnetohydrodynamics. J. Comput. Phys. 154:1999;284-309.
25. Schlichting H. Boundary-Layer Theory. seventh ed. 1979;McGraw-Hill, New York.
26. Wesseling P. Principles of Computational Fluid Dynamics. 2001;Springer, Berlin.
27. Zivanovic S.S., Yee K.S., Mei K.K. A subgridding method for the time-domain finite-difference method to solve Maxwell's equations. IEEE Trans. Microwave Theory Techn. 39:1991;471-479.