Space-time Generalized Riemann Problem Solvers of Order k for Linear Advection with Unrestricted Time Step

作者：Berthon Christophe; Sarazin Celine; Turpault Rodolphe^*

来源：Journal of Scientific Computing, 2013, 55(2): 268-308.

DOI：10.1007/s10915-012-9632-5

• GRP solvers
• Linear systems of conservation laws
• Arbitrary high-order scheme
• Large time steps

This work concerns high-order approximations of the linear advection equation in very long time. A GRP-type scheme of arbitrary high-order in space and time with no restriction on the time step is developed. In the usual GRP solvers, we consider a polynomial approximation of the solution in space in each cell at the initial time. Here, we add a second polynomial approximation of the solution in time in each interface. Thanks to this double approximation, the resulting scheme is compact. It is proved to be of order k+1 in space and time, where k is the degree of the polynomials. Thanks to the compactness of the scheme, a two-dimensional extension is detailed on unstructured meshes made of triangles. Several numerical test-cases and comparison with existing methods illustrate the excellent behaviour of the scheme.

• 出版日期2013-6