Riemann solvers with evolved initial conditions
The scope of this paper is three fold. We first formulate upwind and symmetric schemes for hyperbolic equations with non-conservative terms. Then we propose upwind numerical schemes for conservative and non-conservative systems, based on a Riemann solver, the initial conditions of which are evolved non-linearly in time, prior to a simple linearization that leads to closed-form solutions. The Riemann solver is easily applied to complicated hyperbolic systems. Finally, as an example, we formulate conservative schemes for the three-dimensional Euler equations for general compressible materials and give numerical results for a variety of test problems for ideal gases in one and two space dimensions. Copyright (c) 2006 John Wiley & Sons, Ltd.
non-conservative terms hyperbolic systems euler equations numerical results riemann problem evolution of data linearized riemann solver general equation of state