High-order finite difference methods with subcell resolution for hyperbolic conservation laws with stiff reaction terms: preliminary results

Authors

W. Wang, Florida International University
C.-W. Shu, Brown University
Helen Yee, NASA Ames Research CenterFollow
Bjorn Sjögreen, Lawrence Livermore National LaboratoryFollow

Date of this Version

2010

Citation

Center for Turbulence Research Annual Research Briefs 2010

Comments

U.S. government work

Abstract

The motivation for this research stems from the high-speed chemical reacting flows which have stiff reaction terms, where the chemical time scales are often much smaller than the fluid dynamics time scales. It is usually too expensive to resolve all the spatial/ temporal scales if we are only interested in the main flow. On the other hand, insufficient spatial/temporal resolution will cause the speed of propagation of discontinuities to be incorrectly predicted for many numerical methods. This numerical phenomenon was first observed by Colella et al. (1986). Then LeVeque & Yee (1990) showed that a similar spurious propagation phenomenon can be observed even with scalar equations.

Our objective in this study is to develop a high-order finite difference method which can capture the correct detonation speed in an under-resolved mesh and will maintain highorder accuracy in the smooth part of the flow.