Unconditionally stable methods for Hamilton-Jacobi equations

JOURNAL OF COMPUTATIONAL PHYSICS

卷:180

Article

Karlsen, KH ; Risebro, NH

关键词: Hamilton-Jacobi equation;    conservation law;    discontinuous coefficient;    numerical method;    front tracking;    operator splitting;    numerical example;   

DOI  :  10.1006/jcph.2002.7113

来源: Elsevier

【 摘 要 】

We present new numerical methods for constructing approximate solutions to the Cauchy problem for Hamilton-Jacobi equations of the form u(t) + H(D(x)u) = 0. The methods are based on dimensional splitting and front tracking for solving the associated (non-strictly hyperbolic) system of conservation laws p(t) + DxH (p) = 0, where p = D(x)u. In particular, our methods depend heavily on a front tracking method for one-dimensional scalar conservation laws with discontinuous coefficients. The proposed methods are unconditionally stable in the sense that the time step is not limited by the space discretization and they can be viewed as large-time-step Godunov-type (or front tracking) methods. We present several numerical examples illustrating the main features of the proposed methods. We also compare our methods with several methods from the literature. (C) 2002 Elsevier Science (USA).

【 授权许可】

Free