New lax-Friedrichs-type finite volume schemes on 2 and 3D Cartesian staggered grids

14th Computational Fluid Dynamics Conference

Volumn , Issue , 1999, Pages 938-945

  Arminjon, P ^a,b   Madrane, A ^a,c   St Cyr, A ^a,d  

^a UNIVERSITÉ DE MONTRÉAL   (Canada)

^b Department of Mathematics and Statistics ^*  (Canada)

^c Centre de Recherches   (Canada)

^d Dhp de mathématiques et de statistique   (Canada)

Author keywords

[No Author keywords available]

Indexed keywords

COMPUTATIONAL FLUID DYNAMICS; NUMERICAL METHODS; PARTIAL DIFFERENTIAL EQUATIONS;

CENTRAL DIFFERENCE SCHEME; FINITE VOLUME SCHEMES; FINITE-VOLUME FORMULATION; HYPERBOLIC EQUATIONS; INITIAL CONDITIONS; NUMERICAL RESULTS; PROJECTION METHOD; SPATIAL RESOLUTION;

PIECEWISE LINEAR TECHNIQUES;

EID: 84983135010     PISSN: None     EISSN: None     Source Type: Conference Proceeding    
DOI: 10.2514/6.1999-3362     Document Type: Conference Paper

References (17)

1. P. Arminjon, D. Stanescu and M. C. Viallon, (1995), A two-dimensional finite volume extension of the Lax-Friedrichs and Nessyahu- Tadmor schemes for compressible flows, Proc.of the 6th. Int. Symp. on Comp. Fluid Dynamics, Lake Tahoe (Nevada) September 4-8, 1995, M.Hafez and K. Oshima, editors, Vol. IV, pp. 7-14.
2. P. Arminjon and M. C. Viallon, (1995), Generalisation du schema de Nessayahu-Tadmor pour une equation hyperbolique a deux dimensions d'espace, C.R. Acad. Sei. Paris, t.320, serie I (1995), pp. 85-88.
3. P. Arminjon and M. C. Viallon, (1999), Convergence of a finite volume extension of the Nessyahu- Tadmor scheme on unstructured grids for a two-dimensional linear hyperbolic equation, SIAM J. Num. Anal., Vol. 36, No.3, pp. 738-771.
4. P. Arminjon, M.C. Viallon and A. Madrane, (1994), A Finite Volume Extension of the Lax-Friedrichs and Nessyahu-Tadmor Schemes for Conservation Laws on Unstructured Grids, revised version with numerical applications, Int. J. of Comp. Fluid Dynamics (1997), Vol. 9, No. 1, 1-22.
5. P.D. Lax, (1954), Weak solutions of nonlinear hyperbolic equation and their numerical computation, Comm. Pure and Applied Math.7, pp. 159-193.
6. A.C. Hindmarsh, P.M. Gresho and D.F. Griffiths, (1984), The stability of explicit Euler time integration for certain finite difference approximations of the multidimensional advection diffusion equation, Int. J. for Numerical Methods in Fluids, 4, 853-97.
7. G. Jiang and E. Tadmor, (1998), Non-oscillatory Central Schemes for Multidimensional Hyperbolic Conservation Laws, SIAM J. Seien. Comp., Vol. 19,No. 6, pp. 1892-1917.
8. H. Nessyahu and E. Tadmor, (1990), Non-oscillatory central differencing for hyperbolic conservation laws, J. Comp. Phys., 87, No. 2, pp. 408-463.
9. B. van Leer, (1977), Towards the ultimate conservative difference scheme IV. A new approch to numerical convection, J.Comp.Physics, 23, pp. 276-299.
10. B. van Leer, (1979), Towards the ultimate conservative difference scheme V. A Second-Order Sequel to Godunov's Method, J. Comp. Physics, 32, pp. 101-136.
11. G.D. van Albada, B. van Leer, W.W. Roberts, (1982), A comparative study of computational methods in cosmic gas dynamics, Astron. astrophys. 108, pp 76-84.
12. V. Venkatakrishnan, (1995), Convergence to Steady State Solutions of the Euler Equations on Unstructured Grids with Limiters, J. Comp. Phys. 118, pp. 120-130.
13. P. Woodward and P. Colella, (1984), The Numerical Simulation of Two-Dimensional Fluid Flow with strong Shocks, J. Comp. Phys. 54, pp. 115-173.
14. C. Hirsch, Numerical Computation of Internal and External Flows, Vol.1,1988, Vol.II,1990, John Wiley, New York.
15. E. Godlewski and P.A. Raviart (1996), Numerical Approximation of Hyperbolic Systems of Conservation Laws, Springer-Verlag, New York.
16. A. Jameson (1997),Essential Elements of Computational Algorithms for Aerodynamic Analysis and Design, ICASE Report No. 97-68.
17. P. Arminjon, A. Madrane, A. St-Cyr, JVew 2 and 3-dimensional non oscillatory central finite volume methods for staggered cartesian grids, to appear.