J. Peraire

Adaptive remeshing for three-dimensional compressible flow computations

An adaptive mesh procedure for computing steady state solutions of the compressible Euler equations in three dimensions is presented. The method is an extension of previous work in two dimensions. The approach requires the coupling of a surface triangulator, an automatic tetrahedral mesh generator, a finite element flow solver and an error estimation procedure. An example involving flow at high Mach number is included to demonstrate the numerical performance of the proposed approach. The example shows that the use of this form of adaptivity in three dimensions offers the potential of even greater computational savings than those attained in the corresponding two-dimensional implementation.

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.

Finite element multigrid solution of Euler flows past installed aero-engines

A finite element based procedure for the solution of the compressible Euler equations on unstructured tetrahedral grids is described. The spatial discretisation is accomplished by means of an approximate variational formulatin, with the explicit addition of a matrix form of artificial viscosity. The solution is advanced in time by means of an explicit multi-stage time stepping procedure. The method is implemented in terms of an edge based representation for the tetrahedral grid. The solution procedure is accelerated by use of a fully unstructured multigrid algorithm. The approach is applied to the simulation of the flow past an installed aero-engine nacelle, at three different free stream conditions. Comparison is made between the numerical predictions and experimental pressure observations.

Partitioning and scheduling algorithms and their implementation in FELISA - An unstructured grid euler solver

Publisher Summary The numerical solution of partial differential equations with finite element algorithms on distributed memory parallel computers demands that the global mesh be divided into subdomains, the number of which corresponds to the number of processors. The decomposition should be such that the number of elements per subdomain is roughly the same—to ensure global load balancing—and the number of shared faces between the two subdomains are minimized—to reduce the communication costs. This chapter compares a number of established grid partitioning algorithms. A new hybrid algorithm that is found to be highly competitive on small to medium size meshes is proposed in the chapter. Once a partitioning has been established for an irregular grid, a communication scheme needs to be devised to organize the communication among processors. A message passing scheme using blocked pairwise exchange in a number of stages is described in the chapter. The chapter develops algorithms to deal with non-uniform message lengths. The algorithms attempt to minimize the communication time by scheduling messages of similar lengths in the same stage of the message passing scheme. It is found that the load balancing of communication can reduce the communication costs by up to 30%. The partitioning and scheduling algorithms are used as a preprocessor in a parallel version of the unstructured grid finite element 3D explicit Euler equation solver FELISA. The results for a parallel implementation of FELISA code using the most efficient grid decomposition and message scheduling algorithms are presented in the chapter.

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].