论文信息 - Polynomial upwind schemes for hyperbolic systems

Polynomial upwind schemes for hyperbolic systems

Abstract In this paper, we present an upwinding methodology for systems of conservation laws. Our aim is to construct upwind schemes which do not require the extraction of the eigensystem of the Jacobian matrix (but just the knowledge of the eigenvalues) and rely on the introduction of an appropriate polynomial approximation.

[1] Gérard Gallice,et al. Roe Matrices for Ideal MHD and Systematic Construction of Roe Matrices for Systems of Conservation Laws , 1997 .

[2] M. Brio,et al. An upwind differencing scheme for the equations of ideal magnetohydrodynamics , 1988 .

[3] Thierry Gallouët,et al. Un schéma de Godunov approché , 1996 .

[4] B. V. Leer,et al. Towards the ultimate conservative difference scheme. II. Monotonicity and conservation combined in a second-order scheme , 1974 .

[5] P. Lax,et al. On Upstream Differencing and Godunov-Type Schemes for Hyperbolic Conservation Laws , 1983 .

[6] Stanley Osher,et al. Convex ENO High Order Multi-dimensional Schemes without Field by Field Decomposition or Staggered Grids , 1998 .

[7] P. Roe,et al. On Godunov-type methods near low densities , 1991 .