High Order Methods for the Numerical Simulations of Reactive High Speed Flows

摘要

The goal of this research was to study the computational issues involved in constructing an accurate, efficient and flexible computational framework for the modeling of supersonics reactive flows, and to apply the methods thus developed to problems originated from the Air-Force labs. The main components of this framework are: High order accuracy numerical methods are applied in order to resolve the important detailed features of the flow. Spectral multi-domain methods. Weighted Essentially Non Oscillatory (WENO) methods. High Order compact finite difference schemes. Domain decomposition techniques are used, the methods are based on penalty impositions of interface boundary conditions in a proven timetable way. The discontinuous Galerkin methodology is implemented in the finite differences component of the research. Structured as well as unstructured grid multi-domain spectral methods are being developed. In the structured grid methods the building blocks are cubes (in 3D) or rectangles (in 2D). The grid is predefined by a tensor product of Gaussian points to assure spectral accuracy. The standard building blocks in the unstructured grid methods are the tetrahedral elements (in 3D) or triangles (in 2D) with a newly developed unstructured nodal basis within each element.