Jaime Peraire

Simulation of a store separation using the finite element method

A 2D finite-element-based flow simulator for store separation problems is presented. The method accounts for continuous grid deformation and utilizes an automatic remeshing procedure that periodically regenerates the mesh in order to avoid excessive element distortion. The algorithm adopted for the solution of the Euler equations is analogous, in the absence of grid motion, to a two-step Taylor-Galerkin procedure. Results are presented for the application of this technique to two separate simulations.

An implicit/explicit scheme for compressible viscous high speed flows

Abstract An implicit/explicit finite element based algorithm for the solution of 2D steady compressible viscous high speed flows is presented. A structured grid is employed in the vicinity of solid walls and the implicit form of the algorithm is implemented in this region. The explicit form of the algorithm is used in the remainder of the flow domain, which is discretised with an unstructured assembly of triangles. The quality of the computed solution is improved by the application of solution adaptive remeshing. The computed results for two examples are compared with experimental observations to illustrate the performance of the proposed scheme.

The characteristic-Galerkin method for advection-dominated problems—an assessment

Abstract In this note we present results of an accuracy analysis of a recent characteristic-based Galerkin method suited for advection-dominated problems. The analysis shows that the numerical propagation characteristics of the explicit time-stepping scheme which uses linear basis functions for spatial discretization are superior to those of the related classical Lax-Wendroff method and the implicit Crank-Nicolson scheme. The model is subjected to three analytical test problems which embrace many essential realistic features of environmental and coastal hydrodynamic applications: pure advection of a steep Gaussian profile, dispersion of a continuous source in an oscillating flow, and long-wave propagation with bottom frictional dissipation in a rectangular channel. The numerical results demonstrate that the accuracy achieved with the present scheme is excellent and comparable to that of a characteristic-based finite difference scheme which uses Hermitian cubic interpolating polynomials. The results reported herein suggest strongly further use and testing of this robust model in engineering practice.

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.