Unstructured Cartesian Grid Methodology for Inviscid Nonequilibrium Hypersonic Flows

In this work, a solution-adaptive unstructured Cartesian grid solver for thermochemical nonequilibrium hypersonic flows with a two-temperature model is developed. The Cartesian grid methodology offers the convenience of automatic grid generation over three-dimensional complex geometries with minimum user intervention. At the same time, an accurate higher-order flux calculation over unstructured-grid topologies is provided. To avoid convergence problems in the explicit flow solver, a point-implicit method is adopted to discretize the source terms. The AUSMPW+ numerical scheme with MUSCL data reconstruction is used, preventing nonphysical oscillations and carbuncle phenomena. The accuracy of the present methodology was verified against DPLR (NASA Ames Research Center's structured-grid nonequilibrium flow solver), showing a good agreement between the two codes. As expected, the AUSMPW+ scheme effectively resolved the large gradients of the flow properties at the shock waves. In parallel, the point-implicit technique used for the source terms allows the original Courant-Friedrichs-Lewy constraints of the explicit solver to be maintained.