A modified higher order Godunov's scheme for stiff source conservative hydrodynamics

JOURNAL OF COMPUTATIONAL PHYSICS

卷:224

Article

Miniati, Francesco ; Colella, Phillip

关键词: hydrodynamics;    numerical methods;    Godunov methods;    Stiff equations;   

DOI  :  10.1016/j.jcp.2006.10.008

来源: Elsevier

【 摘 要 】

We present an efficient second-order accurate scheme to treat stiff source terms within the framework of higher order Godunov's methods. We employ Duhamel's formula to devise a modified predictor step which accounts for the effects of stiff source terms on the conservative fluxes and recovers the correct isothermal behavior in the limit of an infinite cooling/ reaction rate. Source term effects on the conservative quantities are fully accounted for by means of a one-step, second-order accurate semi-implicit corrector scheme based on the deferred correction method of Dutt et al. We demonstrate the accurate, stable and convergent results of the proposed method through a set of benchmark problems for a variety of stiffness conditions and source types. (c) 2006 Elsevier Inc. All rights reserved.

【 授权许可】

Free