Computational Fluid Dynamics Based on the Method of Space-Time Conservation Element and Solution Element

摘要

The space-time Conservation Element and Solution Element (CE/SE) method has been further developed and applied to solve more general flow problems during the present third year of NASA support. Not only the flow problems originally proposed but also some related problems have been solved using this method. The following is a brief description of the major works that have been performed under the present support of this grant: (1) Numerical Simulation of an Unsteady Implosion/Explosion Process of a Polygonal Shock Wave in a Box. This problem that has been studied using a traditional TVD scheme is now solved by using a 2-D CE/SE Euler solver based on the dual-mesh pattern. In addition to the early stage of the implosion/explosion process, the later wave development which was not dealt with is also simulated in this work. The work has successfully demonstrated that (a) the robustness of the present Euler scheme in handling the reflecting boundary condition for both horizontal and vertical solid walls, and (b) the feasibility of introducing the dual-mesh pattern in the CE/SE numerical scheme, which provides a strong support for the future construction of the CE/SE Navier-Stokes solver. (2) Numerical Simulation of Shock Reflection over a Dust Layer Model, Different patterns of shock wave reflection over a wedge with a smooth surface have been computed previously using the CE/SE Euler solver, in which the corresponding experimental pictures were shown to demonstrate their close agreements. (3) Numerical Simulation of Shock Wave Interaction with Canister. The interaction of shock wave with a complex geometry canister suspended above an elevated rigid surface has been studied using a finite-element flux-corrected transport scheme based on unstructured grids with adaptive refinement. (4) A Two-Dimensional Euler Solver Based on Varied CEs and SEs. A 2-D Euler solver has been constructed based on nonuniform grids for handling flow problem involving curved surface/bodies, in which the reflecting boundary condition imposed on solid surface was implemented.