ADER: Arbitrary high order godunov approach

Journal of Scientific Computing

Volumn 17, Issue 1-4, 2002, Pages 609-618

  Titarev, V A ^a   Toro, E F ^a  

^a MANCHESTER METROPOLITAN UNIVERSITY   (United Kingdom)

Author keywords

ADER; Essentialy non oscillatory; Generalised Riemann problem; Godunov

Indexed keywords

COMPUTATIONAL METHODS; GALERKIN METHODS; MATHEMATICAL MODELS; NONLINEAR SYSTEMS; RUNGE KUTTA METHODS;

ADVECTION DIFFUSION REACTION (ADER) APPROACH; GENERALISED RIEMANN PROBLEM; GODUNOV;

PROBLEM SOLVING;

EID: 0008392886     PISSN: 08857474     EISSN: None     Source Type: Journal    
DOI: 10.1023/A:1015126814947     Document Type: Article

References (14)

1. Balsara, D. S., and Shu, C. W. (2000). Monotonicity preserving weighted essentially non-oscillatory schemes with increasingly high order of accuracy. J. Comp. Phys. v160, 405-452.
2. Ben-Artzi, M., and Falcovitz, J. (1984). A second-order Godunov-type scheme for compressible fluid dynamics. J. Comp. Phys. 55, 1-32.
3. Canuto, C., and Quarteroni, A. (1990). Spectral and Higher Order Methods for Partial Differencial Equations, North-Holland.
4. Cockburn, B., and Shu, C. W. (1998). The Runge-Kutta discontinuous Galerkin method for conservation laws V: Multidimensional systems. J. of Comput. Phys. v141, 199-224.
5. Godunov, S. K. (1959). A finite difference method for the computation of discontinuous solutions of the equation of fluid dynamics. Mat. Sb. 47, 357-393.
6. Jiang, G. S., and Shu, C. W. (1996). Efficient implementation of weighed ENO schemes. J. Comput. Phys. v126, 202-212.
7. Harten, A., and Engquist, B., and Osher, S., and Chakravarthy, S. R. (1987). Uniformly high order accurate essentially non-oscillatory schemes. III. J. Comput. Phys. v71, 231-303.
8. Lax, D., and Wendroff, B. (1960). Systems of conservation laws. Communications in Pure and Applied Mathematics v13, 217-237.
9. Schwartzkopff, T., Munz, C. D., Toro, C. D., and Millington, C. D. (2001). ADER-2D: A high-order approach for linear hyperbolic systems in 2D. In European Congress on Computational Methods in Applied Sciences and Engineering ECCOMAS Computational Fluid Dynamics Conference 2001, Swansea, Wales, United Kingdom, 4-7 September.
10. Toro, E. F., Millington, R. C., and Nejad, L. A. M. (2001). Towards very high order to schemes. In Toro, E. F. (ed.), Godunov Methods: Theory and Applications, Kluwer Academic/Plenum Publishers, New York, pp. 907-940.
11. Titarev, V. A. (2001). Very High Order ADER Schemes for Nonlinear Conservation Laws, Department of Computing and Mathematics, Manchester Metropolitan University, United Kingdom, MSc. Thesis.
12. Tolstykh, A. I. (1994). High Accuracy Non-Centered Compact Difference Schemes for Fluid Dynamics Applications, World Scientific Publishing.
13. Toro, E. F., and Titarev, V. A. (2001). Solution of the generalised Riemann problem for advection-reaction equations. Proc. Roy. Soc. London 458 (2018), 271-281.
14. Toro, E. F. (1998). Primitive, conservative and adaptive schemes for hyperbolic conservation laws. In Toro, E. F., and Clarke, J. F. (eds.) Numerical Methods for Wave Propagation, Kluwer Academic Publishers.