an:05123769
Zbl 1108.65091
Toro, E. F.
Riemann solvers with evolved initial conditions
EN
Int. J. Numer. Methods Fluids 52, No. 4, 433-453 (2006).
00186796
2006
j
65M06 35L65 76M20 76N15
hyperbolic systems; non-conservative terms; Riemann problem; evolution of data; linearized Riemann solver; Euler equations; general equation of state; numerical results; gas dynamics
Summary: 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 nonlinearly 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.