Comparisons of numerical methods for the analysis of unsteady shock-induced combustion

Abstract

Numerical experiments were performed to investigate the characteristics of the various numerical approaches in the analysis of periodically unstable shock-induced combustion around a blunt body. Inviscid Euler equations and species conservation equations are used as the governing equations with a detailed chemistry mechanism of hydrogen-air combustion. The base-line numerical method is composed of the third order accurate spatial discretization scheme based on Roe’s FDS method and the second order time accurate LU-SGS scheme with exact flux Jacobian splitting and Newton sub-iteration. As a first step of the numerical experiments, simulations of experimental results were conducted to confirm the reliability of base-line method. Secondly, some numerical experiments were conducted for a selected experimental case to compare time integration strategies. The effects of the order of time integration, the number of sub-iterations and the use of approximate flux Jacobian splitting were examined. The point-implicit method and Crank-Nicolson type fully implicit method were compared with base-line time integration method through time step refinement studies. In view point of spatial discretization method, the use of various limiter functions and the use of AUSM based flux splitting methods were examined. Grid refinement study was also performed in addition.