Resolving the shock-induced combustion by an adaptive mesh redistribution method

An adaptive mesh method is presented for numerical simulation of shock-induced combustion. The method is composed of two independent ingredients: a flow solver and a mesh redistribution algorithm. The flow solver is a finite-volume based second-order upwind TVD scheme, together with a lower-upper symmetric Gauss-Seidel relaxation scheme for solving the multispecies Navier-Stokes equations with finite rate chemistry. The adaptive mesh is determined by a grid generation method based on solving Poisson equations, with the monitor function carefully designed to resolve both sharp fronts and the induction zone between them. Numerically it is found that the resolution of the induction zone is particularly critical to the combustion problems, and an under-resolved numerical method may cause excessive energy release and spurious runaway reactions. The monitor function proposed in this paper, which is based on the relative rate of change of mass fraction, covered this issue satisfactorily. Numerical simulations of supersonic flows past an axisymmetric projectile in a premixed hydrogen/oxygen (or air) mixture are carried out. The results show that the spurious runaway chemical reactions appearing on coarse grids can be eliminated by using adaptive meshes without invoking any ad hoc treatment for reaction rates. The adaptive mesh approach is more effective than the fixed mesh one in obtaining grid-independent results. Finally, discrepancies between the numerical and benchmark experimental results and difficulties in simulating the detonation waves are delineated which appeal for further investigation.