Godunov-format Linear Riemann Solver Sub,

In order to use the Godunov Method to approximate solutions of hyperbolic conservation laws, the classical Riemann Solver requires iterative procedure ,which is the most computationally expensive task. Therefore, Roe, Osher, Harten, Lax and van Leer have ever simplified the process, and achieved the approximate Riemann Solvers. However, most of these solvers need entropy fix.In this paper, a linear Riemann Solver is proposed and studied, using some features of the characteristic lines and Riemann invariants in order to linearize eigenvalues and eigenvectors, and obtain approximate numerical fluxes in the Godunov scheme. Comparing with the Roe method, the proposed Riemann Solver has the advantage of being easily constructed and avoiding entropy fix. The linear Riemann Solver for isentropic Euler equations both in Lagrangian coordinates and Eulerian coordinates are constructed.In Lagrangian coordinates, the proposed linear Riemann Solver is tested. We compare our solutions with exact solutions and those by the Roe method, and the result is quite satisfactory.In Eulerian coordinates, the condition of the linear Riemann Solver is more complicated. For some cases, the proposed numerical solution is better than that by the Roe method without entropy fix. While for others, the vaccum prevents the implemetation of the current apporach.