Homotopy method based on WENO schemes for solving steady state problems of hyperbolic conservation laws.

摘要

Homotopy continuation is an efficient tool for solving polynomial systems. Its efficiency relies on utilizing adaptive stepsize and adaptive precision path tracking, and endgames. In this article, we apply homotopy continuation to solve steady state problems of hyperbolic conservation laws. The algorithm is based on discretization of the hyperbolic PDEs by a third order finite difference weighted essentially non-oscillatory (WENO) scheme with Lax-Friedrichs flux splitting. This new approach is free of CFL condition constraint. Extensive numerical examples in both scalar and system test problems in one and two dimensions demonstrate the efficiency and robustness of the new method.