Kenneth Morgan

The computation of three-dimensional flows using unstructured grids

Abstract A general method is described for automatically discretising, into unstructured assemblies of tetrahedra, the three-dimensional solution domains of complex shape which are of interest in practical computational aerodynamics. An algorithm for the solution of the compressible Euler equations which can be implemented on such general unstructured tetrahedral grids is described. This is an explicit cell-vertex scheme which follows a general Taylor-Galerkin philosophy. The approach is employed to compute a transonic inviscid flow over a standard wing and the results are shown to compare favourably with experimental observations. As a more practical demonstration, the method is then applied to the analysis of inviscid flow over a complete modern fighter configuration. The effect of using mesh adaptivity is illustrated when the method is applied to the solution of high speed flow in an engine inlet.

A three-dimensional upwind finite element point implicit unstructured grid Euler solver

A three dimensional upwind finite element technique that uses cell centered quantities and implicit andfor explicit time marching has been developed for computing hypersonic inviscid flows using adaptive unstructured grids. The overall strategy of flow solution and adaptive remeshing previously developed for 2D has been extended to 3D and applied to realistic problems of current interest in order to assess the problems encountered in applying the approach to 3D problems. This technique has been used to predict shock interference on a swept cylinder, with a view to determine the flowfield and, in particular, the pressure augmentation caused by an impinging shock on the swept leading edge of a cowl lip of an engine inlet. Flow solutions on a sequence of adaptively generated grids of tetrahedral elements is demonstrated in order to assess coupling an existing mesh generator with the flow solver. The overall trends of wall pressure compare well qualitatively with experimental data, but are underpredicted because the remeshing has not been carried out to convergence. Three dimensional corner flow, typically encountered in engine inlets due to compression of the flow by ramps in the walls, is also modelled. This procedure is the first step in developing a threedimensional viscous finite element supersonic flow solver for an integrated fluid, thermal. structural analysis capability for hypersonic flight vehicles like the National Aero-SDace Plane.

The Application of an Adaptive Upwind Unstructured Grid Solution Algorithm to the Simulation of Compressible Laminar Viscous Flows Over Compression Corners

In this contribution, we use an adaptive unstructured grid algorithm for the solution of steady laminar compressible viscous flows over compression corners. The spatial discretisation is achieved by means of general assemblies of triangular or quadrilateral cells, while the temporal discretisation is accomplished in a fully implicit fashion. The unknowns are associated with the cell vertices [1,2] and a first order upwind algorithm results from the use of the flux difference splitting method of Roe [3]. A higher order extension is achieved by using the MUSCL concepts of van Leer [4]. This requires a monotonic linear reconstruction of the solution on a general unstructured grid and this is accomplished by the use of variational recovery [5] with the incorporation of the slope limiting [6]. The solution of the implicit equation system is obtained by a point implicit relaxation process.

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 [7].