Free Access
Issue
ESAIM: M2AN
Volume 38, Number 6, November-December 2004
Page(s) 989 - 1009
DOI https://doi.org/10.1051/m2an:2004047
Published online 15 December 2004
  1. F. Bouchut, Construction of BGK models with a family of kinetic entropies for a given system of conservation laws. J. Statist. Phys. 95 (1999) 113–170. [CrossRef] [MathSciNet] [Google Scholar]
  2. Y. Brenier, Average multivalued solutions for scalar conservation laws. SIAM J. Numer. Anal. 21 (1984) 1013–1037. [CrossRef] [MathSciNet] [Google Scholar]
  3. D.S. Butler, The numerical solution of hyperbolic systems of partial differential equations in three independent variables, in Proc. Roy. Soc. 255A (1960) 232–252. [Google Scholar]
  4. C. Cercignani, The Boltzmann equation and its applications. Springer-Verlag, New York (1988). [Google Scholar]
  5. R. Courant and D. Hilbert, Methods of Mathematical Physics II. Interscience Publishers, New York (1962). [Google Scholar]
  6. S.M. Deshpande, A second-order accurate kinetic-theory-based method for inviscid compressible flows. NASA Technical Paper 2613 (1986). [Google Scholar]
  7. H. Deconinck, P.L. Roe and R. Struijs, A multidimensional generalization of Roe's flux difference splitter for the Euler equations. Comput. Fluids 22 (1993) 215–222. [CrossRef] [MathSciNet] [Google Scholar]
  8. M. Fey, Ein echt mehrdimensionales Verfahren zur Lösung der Eulergleichungen. Dissertation, ETH Zürich, Switzerland (1993). [Google Scholar]
  9. M. Fey, Multidimensional upwinding. I. The method of transport for solving the Euler equations. J. Comput. Phys. 143 (1998) 159–180. [CrossRef] [MathSciNet] [Google Scholar]
  10. M. Fey, Multidimensional upwinding. II. Decomposition of the Euler equations into advection equations. J. Comput. Phys. 143 (1998) 181–199. [CrossRef] [MathSciNet] [Google Scholar]
  11. M. Fey, S. Noelle and C.v. Törne, The MoT-ICE: a new multi-dimensional wave-propagation-algorithm based on Fey's method of transport. With application to the Euler- and MHD-equations. Int. Ser. Numer. Math. 140, 141 (2001) 373–380. [Google Scholar]
  12. E. Godlewski and P.A. Raviart, Numerical approximation of hyperbolic systems of conservation laws. Springer-Verlag, New York (1996). [Google Scholar]
  13. A. Jeffrey and T. Taniuti, Non-linear wave propagation. Academic Press, New York (1964). [Google Scholar]
  14. M. Junk, A kinetic approach to hyperbolic systems and the role of higher order entropies. Int. Ser. Numer. Math. 140, 141 (2001) 583–592. [Google Scholar]
  15. M. Junk and J. Struckmeier, Consistency analysis of mesh-free methods for conservation laws, Mitt. Ges. Angew. Math. Mech. 24, No. 2, 99 (2001). [Google Scholar]
  16. T. Kröger, Multidimensional systems of hyperbolic conservation laws, numerical schemes, and characteristic theory. Dissertation, RWTH Aachen, Germany (2004). [Google Scholar]
  17. T. Kröger and S. Noelle, Numerical comparison of the method of transport to a standard scheme. Comp. Fluids (2004) (doi: 10.1016/j.compfluid.2003.12.002) (in print). [Google Scholar]
  18. D. Kröner, Numerical schemes for conservation laws. Wiley Teubner, Stuttgart (1997). [Google Scholar]
  19. R.J. LeVeque, Numerical methods for conservation laws. Birkhäuser, Basel (1990). [Google Scholar]
  20. P. Lin, K.W. Morton and E. Süli, Characteristic Galerkin schemes for scalar conservation laws in two and three space dimensions. SIAM J. Numer. Anal. 34 (1997) 779–796. [CrossRef] [MathSciNet] [Google Scholar]
  21. M. Lukáčová-Medviďová, K.W. Morton and G. Warnecke, Evolution Galerkin methods for hyperbolic systems in two space dimensions. Math. Comp. 69 (2000) 1355–1384. [CrossRef] [MathSciNet] [Google Scholar]
  22. M. Lukáčová-Medviďová, K.W. Morton and G. Warnecke, Finite volume evolution Galerkin (FVEG) methods hyperbolic systems. SIAM J. Sci. Comp. 26 (2004) 1–30. [CrossRef] [Google Scholar]
  23. M. Lukáčová-Medviďová, J. Saibertová and G. Warnecke, Finite volume evolution Galerkin methods for nonlinear hyperbolic systems. J. Comp. Phys. 183 (2002) 533–562. [CrossRef] [Google Scholar]
  24. S. Noelle, The MoT-ICE: a new high-resolution wave-propagation algorithm for multidimensional systems of conservation laws based on Fey's Method of Transport. J. Comput. Phys. 164 (2000) 283–334. [CrossRef] [MathSciNet] [Google Scholar]
  25. S. Ostkamp, Multidimensional Characteristic Galerkin Schemes and Evolution Operators for Hyperbolic Systems. Dissertation, Hannover University, Germany (1995). [Google Scholar]
  26. S. Ostkamp, Multidimensional characteristic Galerkin methods for hyperbolic systems. Math. Meth. Appl. Sci. 20 (1997) 1111–1125. [CrossRef] [Google Scholar]
  27. B. Perthame, Boltzmann type schemes for gas dynamics and the entropy property. SIAM J. Numer. Anal. 27 (1990) 1405–1421. [CrossRef] [MathSciNet] [Google Scholar]
  28. B. Perthame, Second-order Boltzmann schemes for compressible Euler equations in one and two space dimensions. SIAM J. Numer. Anal. 29 (1992) 1–19. [CrossRef] [MathSciNet] [Google Scholar]
  29. P. Prasad, Nonlinear hyperbolic waves in multi-dimensions. Chapman & Hall/CRC, New York (2001). [Google Scholar]
  30. J. Quirk, A contribution to the great Riemann solver debate. Int. J. Numer. Meth. Fluids 18 (1994) 555–574. [NASA ADS] [CrossRef] [Google Scholar]
  31. P. Roe, Discrete models for the numerical analysis of time-dependent multidimensional gas dynamics. J. Comput. Phys. 63 (1986) 458–476. [NASA ADS] [CrossRef] [MathSciNet] [Google Scholar]
  32. J.L. Steger and R.F. Warming, Flux vector splitting of the inviscid gasdynamic equations with application to finite-difference methods. J. Comput. Phys. 40 (1981) 263–293. [CrossRef] [MathSciNet] [Google Scholar]
  33. C.v. Törne, MOTICE – Adaptive, Parallel Numerical Solution of Hyperbolic Conservation Laws. Dissertation, Bonn University, Germany. Bonner Mathematische Schriften, No. 334 (2000). [Google Scholar]
  34. E. Toro, Riemann solvers and numerical methods for fluid dynamics. Second edition, Springer, Berlin (1999). [Google Scholar]
  35. K. Xu, Gas-kinetic schemes for unsteady compressible flow simulations. Lect. Ser. Comp. Fluid Dynamics, VKI report 1998-03 (1998). [Google Scholar]
  36. S. Zimmermann, The method of transport for the Euler equations written as a kinetic scheme. Int. Ser. Numer. Math. 141 (2001) 999–1008. [Google Scholar]
  37. S. Zimmermann, Properties of the Method of Transport for the Euler Equations. Dissertation, ETH Zürich, Switzerland (2001). [Google Scholar]

Current usage metrics show cumulative count of Article Views (full-text article views including HTML views, PDF and ePub downloads, according to the available data) and Abstracts Views on Vision4Press platform.

Data correspond to usage on the plateform after 2015. The current usage metrics is available 48-96 hours after online publication and is updated daily on week days.

Initial download of the metrics may take a while.

Recommended for you