## Capturing Shock Reflections: An improved flux formula (1996)

Venue: | J. Comput. Phys |

Citations: | 18 - 5 self |

### BibTeX

@ARTICLE{Donat96capturingshock,

author = {Rosa Donat and Antonio Marquina},

title = {Capturing Shock Reflections: An improved flux formula},

journal = {J. Comput. Phys},

year = {1996},

volume = {125},

pages = {42--58}

}

### OpenURL

### Abstract

Godunov type schemes, based on exact or approximate solutions to the Riemann problem, have proven to be an excellent tool to compute approximate solutions to hyperbolic systems of conservation laws. However, there are many instances in which a particular scheme produces inappropriate results. In this paper we consider several situations in which Roe's scheme gives incorrect results (or blows up all together) and propose an alternative flux formula that produces numerical approximations in which the pathological behavior is either eliminated or reduced to computationally acceptable levels. Key Words. Nonlinear Systems of Conservation Laws, Shock Capturing schemes, Shock Reflections. AMS-MOS Classification: Primary 65M05, Secondary 65M10 1 Introduction Shock capturing techniques for the computation of discontinuous solutions to hyperbolic conservation laws are based on an old (by now) theorem of Lax and Wendroff establishing that the limit solutions of a consistent scheme in conservat...