Computational fluid dynamics algorithms for unsteady shock-induced combustion, part 1: Validation

A computational study is carried out to develop a fully implicit and time-accurate computational fluid dynamics code for the analysis of reactive flow systems. Periodically oscillating shock-induced combustion around a blunt body in a stoichiometric hydrogen-air mixture is used as a validation problem of examining various numerical considerations. Euler equations and species conservation equations are used as the governing equations for the chemically reacting flow. Spatial discretization of the governing equation is based on Roe's approximate Riemann solver with a MUSCL-type total variation diminishing scheme for higher-order spatial resolution. The second-order-accurate time integration method is based on a lower-upper symmetric Gauss-Seidel scheme, using a Newton subiteration method and Steger-Warming flux Jacobian splitting. As a first step of the validation procedure, simulations of experimental results were carried out to confirm the reliability of the baseline method. In the next step, the general aspects of the baseline method were examined, including order of time integration, number of subiterations, and use of approximate Bur Jacobian splitting. Appropriateness of the grid system is also examined by using a grid refinement study.