Progress towards a cartesian cut-cell method for viscous compressible flow

We present preliminary development of an approach for simulating steady viscous compressible flow in two space dimensions using a Cartesian cut-cell finite volume method. We consider laminar and turbulent flow with both low and high cell Reynolds numbers near the wall. The approach solves the full Navier-Stokes equations in all cells and uses a wall model to both address the resolution requirements near boundaries and to mitigate mesh irregularities in cut cells. We present a quadratic wall model for low cell Reynolds numbers. At high cell Reynolds numbers, the quadratic is replaced with a newly developed analytic wall model stemming from solution of a limiting form of the Spalart-Allmaras turbulence model which features an explicit evaluation for flow velocity, and exactly matches characteristics of the SA turbulence model in the field. We develop multigrid operators which attain convergence rates similar to inviscid multigrid. Investigations focus on preliminary verification and validation of the method. Flows over flat plates and compressible airfoils show good agreement with both theoretical results and experimental data. Mesh convergence studies on sub- and transonic airfoil flows show convergence of surface pressures with wall spacings as large as ∼0.1% chord. With the current analytic wall model, mesh converged skin friction requires near-wall cells two to four times smaller.