A parallel adaptive mesh refinement scheme for hypersonic flows with an equilibrium high-temperature equation of state

An explicit parallel adaptive mesh refinement (AMR) scheme is proposed and developed for the solution of the partial differential equations governing two-dimensional hypersonic turbulent flows in conjunction with a high temperature equilibrium equation of state and the k-o turbulence model. A finite-volume spatial discretization procedure is applied to the conservative form of the five governing equations: continuity, momentum and energy with two equations for the turbulence model, on structured body-fitted quadrilateral meshes. Limited piecewise-linear solution reconstruction with various approximate Riemann solvers modified to account for the high temperature equation of state is used in the numerical evaluation of the inviscid fluxes. The gradients for evaluating the viscous fluxes are calculated using centrally-weighted diamond path reconstruction. A block-based AMR scheme is used that allows for local anisotropic refinement of the grid and efficient parallel implementation via domain decomposition. The system of non-linear ordinary differential equations resulting from the finite volume discretization of steady-state boundary value problems is solved using explicit time marching methods with multigrid acceleration. Numerical results are presented and discussed for flows having Mach numbers in the range M<8. The results demonstrate the validity of the equilibrium high-temperature equation of state and the computational efficiency of the parallel explicit AMR schemes.