High Order Finite Difference Methods with Subcell Resolution for Stiff Multispecies Discontinuity Capturing (Communications in Computational Physics, 2020)
In this paper, we extend the high order finite-difference method with subcellresolution (SR) in [34] for two-species stiff one-reaction models to multispecies andmultireaction inviscid chemical reactive flows, which are significantly more difficultbecause of the multiple scales generated by different reactions. For reaction problems,when the reaction time scale is very small, the reaction zone scale is also small andthe governing equations become very stiff. Wrong propagation speed of discontinuitymay occur due to the underresolved numerical solution in both space and time.The present SR method for reactive Euler system is a fractional step method. In theconvection step, any high order shock-capturing method can be used. In the reactionstep, an ODE solver is applied but with certain computed flow variables in the shockregion modified by the Harten subcell resolution idea. Several numerical examplesof multispecies and multireaction reactive flows are performed in both one and twodimensions. Studies demonstrate that the SR method can capture the correct propagationspeed of discontinuities in very coarse meshes.