Riemann solvers on extended domains for higher order schemes

Abstract

A new method for solving hyperbolic conservation laws is proposed by defining an approximate Riemann solver over a finite space across the interface instead of solving only at the cell boundary. The approximations for the Riemann solver are obtained by using the information across the interface and by applying the physical wave propagation characteristics inside the element. The resulting scheme is accurate and compact, depending only on the immediate neighbours. The accuracy of the scheme is tested for a linear advection of Gaussian pulse and a non-linear Burger's equation. Convergence of up to 7 th order accuracy are obtained in both cases. The performance of the scheme in the presence of shocks is demonstrated for Burger's equation. Copyright © 2009 by the American Institute of Aeronautics and Astronautics, Inc.