Compressible viscous flow solver

Abstract

Nowadays, in spite of disadvantages of turbulence closure models for RANS (Reynolds Averaged Navier-Stokes equations), they are at present the only tools available for the computation of complex turbulent flows of practical relevance. Their popularity comes from high efficiency in terms of accuracy and computational cost, which makes them widely used in commercial codes and related multidisciplinary applications. Hence, for modelling compressible flow, as a framework of complex inverse design optimisation tool, Navier-Stokes solver is implemented by using k-ω turbulence model in C++ environment. The governing equations in conservative form are deduced by using Favre averaging to filter local fluctuations. The code is based on structured, density based cell centred finite volume method. The convective terms are discretized by Roe approximated Riemann method. Central discretization is applied for diffusive terms. MUSCL approach is implemented for higher order spatial reconstruction with Mulder limiter for monotonicity preserving. Wilcox k-ω two equations turbulence model is implemented for turbulence modelling. The explicit system of the equations is solved by the 4^th order Runge-Kutta method. The numerical boundary conditions are based on the method of characteristics. The interest is mostly in high speed aeronautical applications with the possibility of extension for surface optimisation. Hence, the applied validational test cases are in transonic and supersonic flow regime: circular bump in the transonic channel and compression corner.