The Application of an Adaptive Unstructured Grid Method to the Solution of Hypersonic Flows Past Double Ellipse and Double Ellipsoid Configurations
In this contribution, we use an adaptive finite element algorithm for the solution of inviscid and laminar compressible viscous flows past double ellipse and double ellipsoid configurations. The spatial discretisation is achieved with linear triangular elements in two dimensions and linear tetrahedral elements in three dimensions, while the time discretisation is accomplished in either a fully explicit or in an implicit/explicit fashion. In the analysis of a given problem, the elements in the computational grid may be partitioned into an explicit group and an implicit group and the appropriate form of the algorithm used directly within each group. The implicit formulation uses one of a family of finite difference methods devised originally by Lerat and co-workers [1,2], while the complete algorithm has the desirable feature that, in its explicit form, it reduces to a solution scheme that we have previously employed [3,4]. The explicit form of the algorithm is applied in the solution of inviscid flows while viscous flows are solved using the explicit/implicit version. In two dimensional simulations, several authors [5,6], while nominally employing an unstructured grid method to simulate viscous flows, have used a structured grid in the vicinity of solid surfaces. In the present context, such an approach leads to a natural partitioning in which the elements which are treated implicitly lie in the vicinity of solid walls so that the grid structure, in both the normal and tangential directions, can be utilised in a line relaxation procedure for the solution of the resulting equation system. However, in the simulation of three dimensional flows, the physical boundaries will be represented by an unstructured assembly of triangular elements. Now a grid which is structured only in the normal direction is employed near the solid surfaces and the implicit equation system is solved by appealing to a newly developed line relaxation process for unstructured grids .
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