Analysis of Compressible Viscous Flow Solvers with Adaptive Cartesian Mesh

Abstract

This paper reports an analysis of compressible Navier-Stokes (NS) solvers with adaptive Cartesian mesh. A particular focus is on performance and grid requirements for these solvers for problems of viscous flows past blunt bodies under different conditions. We find that the immersed boundary method (IBM) for the treatment of embedded solid surfaces offers great improvements for calculation of skin friction and heat fluxes for external flows in comparison with the cut-cell methods. To improve the performance of the implemented NS solvers, we propose special methods of automatic meshing around the solid objects. The methods include building layered meshes around the surfaces and employing meshes whose solid refinement levels increase during a simulation. We find that to obtain grid converged results similar grid resolution is required for the implemented NS solvers and those using body-conforming meshes and that this resolution can be determined in terms of cell Reynolds number. We compare the traditional NS schemes, gas-kinetic and hybrid traditional-kinetic schemes for different flow regimes. Comparison with analytical solutions, experimental data and results obtained NS solvers with body-conforming meshes show that compressible viscous flow solvers with adaptive Cartesian mesh offer viable alternative to the conventional CFD methods.