Compressible Fluid Flow and Heat Transfer Navier-Stokes Predictions on Unstructured Grids

Abstract

A second-order accurate finite volume method for solving compressible 2D flows on hybrid structured-unstructured grids is presented. Separate reconstruction and evolution steps are taken to discretize the convective terms. For the reconstruction step, a data-dependent Least-Squares procedure is used, while for the evolution step two recent flux functions are included: the HLLC approximate Riemann solver and the AUSM+ flux vector splitting. Steady-state solutions are obtained with an implicit backward Euler scheme. The assembled system is solved by iterative means (BiCGSTAB, GMRES) with ILU pre-conditioning. Two internal, steady, 2D flow test cases are presented to validate the code: a supersonic 10° ramp inside a channel and a laminar flow through a double-throated nozzle. The code proved accurate with the use of both flux functions when comparing the computed results with both an analytical (ramp) and a reference solution (nozzle). The GMRES solver generally required less CPU time until convergence for the inviscid test-case while the BiCGSTAB solver got the edge for the viscous calculations.