The aim of this work is to solve hyperbolic conservation laws by means of a finite volume method for both spatial and time discretization. We extend the ideas developed in [X.-D. Liu and S. Osher, SIAM J. Numer. Anal., 33 (1996), pp. 760–779; X.-D. Liu and E. Tadmor, Numer. Math., 79 (1998), pp. 397–425] to fourth-order upwind and central schemes. In order to do this, once we know the cell-aver...

Article history: Received 30 April 2008 Received in revised form 17 February 2009 Accepted 27 July 2009 Available online 30 July 2009 MSC: 65M70 76M12 76U05

The Residual Distribution (RD) schemes are an alternative to standard high order accurate finite volume schemes. They have several advantages: a better accuracy, a much more compact stencil, easy parallelization. However, they face several problems, at least for steady problems which are the only cases considered here. The solution is obtained via an iterative method. The iterative convergence ...

We discuss a new fifth-order, semi-discrete, central-upwind scheme for solving one-dimensional systems of conservation laws. This scheme combines a fifthorder WENO reconstruction, a semi-discrete central-upwind numerical flux, and a strong stability preserving Runge–Kutta method. We test our method with various examples, and give particular attention to the evolution of the total variation of t...

A relaxation system for the incompressible and compressible Euler and Navier-Stokes equations is considered. A numerical scheme working uniformly in the above limits is constructed using higher-order nonoscillatory upwind discretiaations and higher-order implicit-explicit t ime discretization. Numerical results are presented for several test cases. @ 2003 Elsevier Ltd. All rights reserved. Keyw...

A commodity-type graphics card (GPU) is used to simulate nonlinear water waves described by a system of balance laws called the shallow-water system. To solve this hyperbolic system we use explicit high-resolution central-upwind schemes, which are particularly well suited for exploiting the parallel processing power of the GPU. In fact, simulations on the GPU are found to run 15–30 times faster...