Numerical algorithm for the computation of compressible turbulent flows at arbitrary Mach number regimes

Mach-uniform algorithms are unified numerical algorithms for the computation of fluid flows at arbitrary Mach number regimes. These methods are important for practical engineering applications that involve both compressible and incompressible fluid flows together, such as shock wave/boundary layer interactions and cavitating fluid flows. In the present study, a pressure-based Mach-uniform algorithm is formulated to solve viscous fluid flows at arbitrary Mach number regimes encompassing subsonic, transonic, supersonic and hypersonic, in an accurate, robust and flexible manner. The core concept is based upon a hybrid integration of pressure-based algorithm and Simple Low-dissipation Advection Upstream Splitting Method II (SLAU2). In the present thesis, a novel numerical algorithm is developed for computation of compressible fluid flows. A pressure equation is postulated and a momentum interpolation method is developed within the framework. Furthermore, the numerical algorithm is extended to solve compressible turbulent flows using Favre-averaged Navier-Stokes turbulence model and Partially-averaged Navier-Stokes turbulence model. The performance of the two turbulence models are investigated and compared. Systematic and comparative computations are conducted to investigate the capability of the numerical algorithm for various types of complex flow topologies at a wide spectrum of Mach number regimes. All comparisons show extremely good performance and have proven that the algorithm is capable of dealing with flows that involve both incompressible and compressible regimes. The proposed algorithm achieve both the superiority of the SLAU2 numerical scheme in the computation of high-Mach number regime with shock capturing properties and the high-fidelity of the pressure-based algorithm in the computation of low-Mach number viscous flow field. These properties render the present algorithm capable of computing complex flow topologies at arbitrary Mach number regimes