Implicit computation of three-dimensional compressible Navier-Stokes equations using k-epsilon closure

Abstract

A computational method for the numerical integration of the Favre-Reynolds-averaged three-dimensional compressible Navier-Stokes equations using the Launder-Sharma near-wall k-e turbulence closure is developed. The mean flow and turbulence transport equations are discretized using a finite volume method based on MUSCL Van Leer flux-vector splitting with Van Albada limiters. The mean flow and turbulence equations are integrated in time using a fully coupled approximately factored implicit backward Euler method. The resulting scheme is robust and was found stable for local-time steps with Courant-Friedrichs-Lewy number equal to 50. Higher time steps are possible but not optimal for convergence. Results are presented for the three Delery transonic channel test-cases. Although these test-cases are nominally two dimensional, three-dimensional computations presented quantify the important three-dimensional effects induced by the sidewall boundary layers. Finally computational results are compared with the experiment for a geometrically three-dimensional transonic nozzle.