A numerical method for systems of hyperbolic conservation laws with single stencil reconstructions

摘要

A numerical method for systems of hyperbolic conservation laws is presented. It uses a single stencil for all components of a system of hyperbolic conservation law for reconstructions. The solution to a generalized Riemann problem is approximated by a solution to a Riemann problem plus Lagrangian interpolations. The method requires only one evaluation of a Riemann problem per grid point, per time step which is comparable to the first-order Godunov method, while produces solutions with significantly better resolution than results of the Godunov method. Numerical tests are calculated for the system of equations for gas dynamics.