Physical Sciences and Mathematics Commons^™

High Order Finite Difference Methods With Subcell Resolution For Advection Equations With Stiff Source Terms, Wei Wang, Chi-Wang Shu, H.C. Yee, Björn Sjögreen

United States National Aeronautics and Space Administration: Publications

A new high order finite-difference method utilizing the idea of Harten ENO subcell resolution method is proposed for chemical reactive flows and combustion. In reaction problems, when the reaction time scale is very small, e.g., orders of magnitude smaller than the fluid dynamics time scales, the governing equations will become very stiff. Wrong propagation speed of discontinuity may occur due to the underresolved numerical solution in both space and time. The present proposed method is a modified fractional step method which solves the convection step and reaction step separately. In the convection step, any high order shock-capturing method can be …