Increasing the approximation order of the Godunov scheme based on a solution to the generalized Riemann problem
Abstract
The generalized Riemann problem is considered in the small neighborhood of a discontinuity point on a plane (x, t). The problem is solved analytically to a first approximation, and analytical formulas are obtained for discontinuity paths on the plane (x, t). The solution is then used to construct the Godunov finite difference scheme. It is shown that, over smooth solutions, the scheme has a second order of approximation with respect to both space and time.
 Publication:

Zhurnal Vychislitelnoi Matematiki i Matematicheskoi Fiziki
 Pub Date:
 September 1990
 Bibcode:
 1990ZVMMF..30.1357M
 Keywords:

 Cauchy Problem;
 Finite Difference Theory;
 Gas Dynamics;
 SpaceTime Functions;
 Two Dimensional Flow;
 Approximation;
 Computational Fluid Dynamics;
 Fluid Flow;
 Hydrodynamic Equations;
 Riemann Manifold;
 Fluid Mechanics and Heat Transfer