Multigrid solution of compressible turbulent flow on unstructured meshes using a two‐equation model

The steady state solution of the system of equations consisting of the full Navier‐Stokes equations and two turbulence equations has been obtained using a multigrid strategy on unstructured meshes. The flow equations and turbulence equations are solved in a loosely coupled manner. The flow equations are advanced in time using a multistage Runge‐Kutta time‐stepping scheme with a stability‐bound local time step, while the turbulence equations are advanced in a point‐implicit scheme with a time step which guarantees stability and positivity. Low‐Reynolds‐number modifications to the original two‐equation model are incorporated in a manner which results in well‐behaved equations for arbitrarily small wall distances. A variety of aerodynamic flows are solved, initializing all quantities with uniform freestream values. Rapid and uniform convergence rates for the flow and turbulence equations are observed.