A General, NonIterative Riemann Solver for Godunov's Method
Abstract
Godunov's method is characterized by the use of a Riemann problem solution to resolve discontinuities at the interface between cells. The major drawback of this method is the difficulty and the high cost of solving the (nonlinear) Riemann problem exactly, especially for materials with complex equations of state. This paper describes a simplified and noniterative approximate Riemann solver which is characterized by only two materialdependent parameters. For a given material, these parameters are the local speed of sound and a parameter which is directly related to the shock density ratio in the limit of strong shocks. These parameters are conveniently obtained from a linear fit to the experimental data for the shock Hugoniot in various materials. The approximate Riemann solver retains the essential quadratic nonlinearity which enables it to deal with the whole range of cases from weak sound waves to strong shocks.
 Publication:

Journal of Computational Physics
 Pub Date:
 October 1985
 DOI:
 10.1016/00219991(85)900646
 Bibcode:
 1985JCoPh..61..119D
 Keywords:

 Cauchy Problem;
 Problem Solving;
 Shock Discontinuity;
 Shock Wave Propagation;
 Viscosity;
 Acoustic Velocity;
 Approximation;
 Conservation Equations;
 Parameter Identification;
 Fluid Mechanics and Heat Transfer