Construction of second-order accurate monotone and stable residual distribution schemes for steady problems

Journal of Computational Physics

Volumn 195, Issue 2, 2004, Pages 474-507

  Abgrall, Rémi ^a,b   Mezine, Mohamed ^a  

^a UNIVERSITÉ BORDEAUX 1   (France)

^b INSTITUT UNIVERSITAIRE DE FRANCE   (France)

Author keywords

Compressible flow solvers; Multidimensional up winding; Residual schemes; Unstructured meshes

Indexed keywords

COMPUTATIONAL METHODS;

BASIC CONCEPTS; COMPRESSIBLE FLOW SOLVER; DISTRIBUTION SCHEME; FLOW SOLVER; MULTIDIMENSIONAL UP-WINDING; RESIDUAL DISTRIBUTION SCHEMES; RESIDUAL SCHEME; SECOND ORDERS; SIMPLE WAVE; UNSTRUCTURED MESHES;

LINEAR SYSTEMS;

EID: 1842733453     PISSN: 00219991     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.jcp.2003.09.022     Document Type: Article

References (27)

1. R. Abgrall, On essentially non-oscillatory schemes on unstructured meshes: analysis and implementation, J. Comput. Phys. 114 (1994) 45-54.
2. R. Abgrall, Toward the ultimate conservative scheme: following the quest, J. Comput. Phys. 167 (2001) 277-315.
3. R. Abgrall, T. Barth, Weighted residual distribution schemes for conservation laws via adaptive quadrature, SIAM J. Sci. Comput. 24 (2002) 732-769.
4. R. Abgrall, S. Lantéri, T. Sonar, Eno schemes for compressible fluid dynamics, ZAMM 79 (1999) 3-28.
5. R. Abgrall, K. Mer, B. Nkonga, A Lax-Wendroff type theorem for residual schemes, in: M. Hafez, J. Chattot (Eds.), Innovative methods for numerical solutions of partial differential equations, World Scientific, Singapore, 2002, pp. 243-266.
6. R. Abgrall, M. Mezine, Construction of second-order accurate monotone and stable residual distribution schemes for unsteady flow problems, J. Comput. Phys. 188 (2003) 16-55.
7. p, Math. Scand. 19 (1966) 23-27.
8. p.α, Ark. Mat. 11 (1973) 75-101.
9. H. Deconinck, P. Roe, R. Struijs, A multidimensional generalisation of Roe's difference splitter for the Enter equations, Comput. Fluids 22 (1993) 215-222.
10. H. Deconinck, K. Sermeus, R. Abgrall, Status of multidimensional upwind residual distribution schemes and applications in aeronautics, AIAA paper 2000-2328, June 2000, AIAA CFD Conference, Denver, USA.
11. H. Deconinck, R. Struijs, G. Bourgeois, P. Roe, Compact advection schemes on unstructured meshes, VKI Lecture Series 1993-04, Comput. Fluid Dynamics, 1993.
12. L. Fezoui, B. Stoufflet, A class of implicit upwind schemes for Euler simulations with unstructured meshes, J. Comput. Phys. 84 (1989) 174-206.
13. O. Friedrich, Weighted essentially non-oscillatory schemes for the interpolation of mean values on unstructured grids., J. Comput. Phys. 144 (1998) 194-212.
14. E. Godlewski, P. Raviart, Hyperbolic systems of conservations laws, I, Ellipse, 1991.
15. E. Godlewski, P. Raviart, Hyperbolic systems of conservations laws, Applied Mathematical Sciences, Springer, Berlin, 1995.
16. A. Harten, S. Chakravarthy, Multidimensional ENO schemes for general geometries, Tech. Rep. 91-33, ICASE, 1991.
17. C. Hu, C. Shu, Weighted essentially non-oscillatory schemes on triangular meshes, J. Comput. Phys. 150 (1999) 97-127.
18. T.J.R. Hughes, M. Mallet, A new finite element formulation for computational fluid dynamics. IV. A discontinuity-capturing operator for multidimensional advective-diffusive systems, Comput. Methods Appl. Mech. Eng. 58 (1986) 329-336.
19. M. Hussaini, B. van Leer, J. van Rosendal (Eds.), Upwind and high resolution schemes, Springer, Berlin, 1997.
20. C. Johnson, U. Nävert, J. Pitkäranta, Finite element methods for linear hyperbolic problems, Comput. Methods Appl. Mech. Eng. 45 (1984) 285-312.
21. H. Paillère, Multidimensional upwind residual discretisation schemes for the Euler and Navier-Stokes equations on unstructured meshes, Ph.D. Thesis, Université Libre de Bruxelles, 1995.
22. P. Roe, D. Sidilkover, Optimum positive linear schemes for advection in two and three dimensions, SIAM J. Numer. Anal. 29 (1992) 1542-1588.
23. R. Struijs, H. Deconinck, P.L. Roe, Fluctuation splitting schemes for the 2D Euler equations, VKI LS 1991-01, Comput. Fluid Dynamics, 1991.
24. E. van der Weide, Compressible flow simulation on unstructured grids using multi-dimensional upwind schemes, Ph.D. Thesis, Delft University of Technology, Netherlands, 1998.
25. E. van der Weide, H. Deconinck, Positive matrix distribution schemes for hyperbolic systems, in: Désidéri, C. Hirch, P.Le Tallec, M. Pandolfi, J. Périaux (Eds.), Computational fluid dynamics '96, Wiley, New York, 1996, pp. 747-753.
26. B. van Leer, Progress in multidimensional upwinding, Tech. Rep. 92-43, ICASE, 1992.
27. P. Vankeirsbilk, H. Deconinck, Solution of the compressible euler equations with high order eno-schemes on general unstructured meshes, in: C. Hirsch, P.Le Périaux, W. Kordulla (Eds.), Computational fluid dynamics '92, Elsevier, Amsterdam, 1992, pp. 843-850.