Hybrid Navier–Stokes–Direct Simulation Monte Carlo Automatic Mesh Optimization for Hypersonics

This paper describes the development of an unstructured hybrid finite element Navier–Stokes (NS)–direct simulation Monte Carlo (DSMC) framework for hypersonic flows. State-based coupling is employed and simulations of varying thermochemical complexity demonstrate the accuracy, robustness, and computational efficiency of the hybrid all-Mach algorithm. An automatic mesh optimization process using a posteriori error estimates based on the Hessian of the solution goes much further than traditional mesh adaptation processes by equidistributing the error estimator and producing a “single optimal hybrid mesh” with no increase in mesh size and with much higher accuracy. The DSMC region cells of the resulting optimal mesh are smaller than in NS regions and are sized to the local mean free path. Mesh optimization is also shown to greatly improve the quality of the hybrid interfaces from those of the initial mesh. Unstructured meshes are found to represent the hybrid interfaces smoothly, while structured meshes showcase a castellated pattern in the interfaces. The optimal hybrid meshes are found to be statistically similar to optimal full DSMC meshes, thus highlighting the solver independence of the optimizer. Such a coupled hybrid mesh optimization strategy can therefore tackle hypersonic flows with multiscale flow features at any degree of rarefaction.