Bruno Stoufflet

A class of implicit upwind schemes for Euler simulations with unstructured meshes

Abstract A class of implicit finite element upwind schemes for solving Euler equations is presented. Steady flows with extreme conditions such as high Mach numbers or/and large angles of attack on unstructured meshes can be simulated. Upwind methods are used for the spatial approximation. Higher rates of convergence are obtained by using an implicit scheme relying on a linearization of fluxes and a partial resolution of the systems by a Gauss-Seidel algorithm. The scheme that we get is more efficient and robust than explicit time integration.

TVD Schemes to Compute Compressible Viscous Flows on Unstructured Meshes

Finite volume TVD schemes derived for the Euler equations are extended to the Navier-Stokes system. The numerical diffusion introduced in the approximation of the convective part is chosen through a total variation analysis taking in account the physical diffusion. Two dimensional numerical simulations are presented, using an algorithm to solve cheaply the steady equations.

Non-Oscillatory Schemes for Multidimensional Euler Calculations with Unstructured Grids

The purpose of this paper is to present a synthesis of our recent studies related to the design of multi-dimensional non-oscillatory schemes, applying to non-structured finite-element simplicial meshes (triangles, tetrahedra). While the direct utilization of 1-D concepts may produce robust and accurate schemes when applied to non-distorted structured meshes, it cannot when non-structured triangulations are to be used. The subject of the paper is to study the adaptation of the so-called TVD methods to that context. TVD methods have been derived for the design of hybrid first-order/second-order accurate schemes which present in simplified cases monotonicity properties (see, for example, the review [2]). A various collection of first-order accurate schemes can be used, they are derived from an artificial viscosity model or from an approximate Riemann solver. However, the main feature in the design is the choice of the second-order accurate scheme; this choice can rely either on central differencing or on upwind differencing.

Recent improvements in Galerkin and upwind Euler solvers and application to 3-D transonic flow in aircraft design

Abstract In this paper, recent studies in the implementation of Euler solvers relying on the Galerkin approximation or the upwind one are presented. The control of non-linear instabilities is achieved in the context of strongly non-regular 3-D tetrahedrizations. For this stabilization, monotone first-order accurate schemes are introduced for both approaches.

EUROPT — A European Initiative on Optimum Design Methods in Aerodynamics

This volume contains a set of methodologies and solutions for a number of selected optimum design problems in aerospace engineering. The methodologies for the solution of these problems cover optimization and inverse problems, external and internal flows, subsonic and transsonic regimes, different flow solvers and different discretizations schemes. These were presented at the EUROPT BRITE/EURAM project. This book should be of interest to engineers and scientists working in computing, optimization and control theory.

Synthesis of the Workshop Test Cases

This section contains the synthesis of the different contributions presented for the resolution of the workshop test cases. This synthesis contains, for each test case, the reasons that make the test case interesting for the workshop, the special difficulties for the resolution, its possible interest for a future workshop in the context of the ECARP Brite/Euram project and a comparison of the results presented by different contributors.

Conclusions and Further Comments

The most significant outcomes of the workshop on “Optimum Design in Aerodynamics” concern the progress accomplished in the following methodologies: Design with Euler solvers. Fast one pass inverse methods for rotational flows. Hierarchical multi level methods for control variables. automatic adaptive remeshing.

Unstructured-Grid Algorithms for High-Speed CFD Analysis

In the field of compressible high Mach number flow, the availability of robust and versatile solvers capable of handling both severe flow conditions and general geometries, and including local mesh refinement, is of crucial importance in Aerospace Engineering studies.

Implicit Euler Calculations Using a Galerkin Finite Element Approximation on Adapted Non-Structured Meshes

In this paper, we present a finite element method based on an implicit second order accurate scheme for solving the steady Euler equations on non structureel adapted meshes. The basic idea is to use a conservative Galerkin variational formulation including an artificial viscosity model discretized with Lagrangian continuous piecewise linear elements [1]. A pseudo unsteady approach is considered in which the time stepping is a two-step Richtmyer implicit scheme: a continuous approximation for variables is evaluated explicitly during a first step, and then computed implicitly via a block relaxation procedure [2] allowing large CFL numbers during the corrector step.