On the behavior of upwind schemes applied to three-dimensional supersonic and hypersonic cold gas flow simulations of aerospace configurations. - Farney Coutinho Moreira (2007)
The present work describes the efforts towards the implementation of upwind schemes to simulate supersonic and hypersonic cold gás flows. The class of flux vector splitting schemes has been chosen, and the particular methods implemented are the van Leer and Liou schemes. Results for different freestream Mach numbers and mesh topologies are discussed in order to assess the comparative performance of the various spatial discretization schemes. The flow is modeled by 3-D Euler equations through the use of a cell centered, face-based data structure finite voluma method applied in an unstructured grid context. Time integration of the system of equations is performed using an explicit, 5-stage, Runge-Kutta scheme. Mesh refinement routines are available in the original code and they are able to handle tetrahedra, hexahedra, triangular-base prisms and square-base pyramids. The full multigrid procedure is also available in the base code to accelerate the convergence to steady state. In the present work, the author has studied possible forms of integrating the multigrid and the mesh refinement procedures, which were both originally available in the base code. The results obtained provide evaluation and comparison of the present methods with regard to oblique shock wave capturing, as well as the behavior of property values such as pressure, density and Mach number contours. Finally, the work presents a discussion on the relative characteristics of each method.