Development of a solution adaptive Cartesian-grid solver for two-dimensional thermochemical nonequilibrium flows

A solution adaptive Cartesian grid solver is developed for 2-D, inviscid, perfect gas, equilibrium, and nonequilibrium flows. The grid points are represented by a binary-tree data structure. The cut-cell approach is used to treat the cells intersecting with the body. The HLLC approximate Riemann solver together with a linear reconstruction method is adopted to compute the fluxes at the edges of cells and two solution adaptation strategies are investigated. The solver is first tested for frozen perfect gas flows. The solver is modified for equilibrium flows by incorporating the curve fits for the ratio of specific heats and pressure of equilibrium air. The solver is further modified for nonequilibrium flows. A 5-species air chemistry model is incorporated into the solver. The one-temperature model and two-temperature model correspond to chemical nonequilibrium and thermochemical nonequilibrium cases, respectively. Use of the solution adapted Cartesian grid approach is found to yield improved solution resolution with similar or fewer number of grid points relative to structured and overlapping grids. Improved efficiency of Cartesian grid methods lend themselves well to equilibrium and thermochemical nonequilibrium simulations. The point implicit approach is found to be an efficient solution strategy for nonequilibrium simulations with a Cartesian grid based code.