Michel Mallet

A relationship between stabilized finite element methods and the Galerkin method with bubble functions

Abstract A relation between stabilized finite element methods and the Galerkin method employing interpolations with bubble functions is established for the advective-diffusive model and for the linearized compressible Navier-Stokes equations. The bubble functions are shown to help in stabilizing the advective operator without recourse to upwinding or any other numerical strategy. In particular, for the advective-diffusive model, the Galerkin method employing piecewise linears with bubble functions is shown to be equivalent to the streamline-upwind/Petrov-Galerkin (SUPG) method in the diffusive limit.

LES and DES Simulations for Aircraft Design

The paper first describes developments performed to achieve an accurate and efficient simulation capacity using turbulence models based on the LES and DES approaches. The development is performed within the industrial code used at Dassault for the aerodynamics design of both military aircraft and business jets. The issues of subgrid scale implementation and wall treatment approaches are addressed. The paper then presents industrial applications performed at Dassault related to aerodynamic design. Examples demonstrate the impact of LES and DES on key design issues where complex flow features are present.

A Multi-platform Shared- or Distributed-Memory Navier-Stokes Code

Computational Fluid Dynamics (CFD) has always been an avid consumer of computing resources, and thus developed concurrently with the progresses in computer hardware. Born with the good old mainframes, CFD came to maturity with the vector architectures of the eighties (Cray, Convex, IBM, NEC). In 1992, VIRGINIE, the Navier–Stokes code in use at Dassault Aviation, was successfully ported onto the Intel IPSC 860 at ONERA. The first in-house massively parallel architecture dedicated to CFD was an IBM SPl, soon upgraded to an SP2. The high level of vectorization of Dassault–Aviations Navier–stokes code enabled performances in the 500 MFLOPS range. The implementations of VIRGINIE are described in this chapter on both the IBM SP2 and the NEC SX-4. The idea behind the SX-4 port was to keep the alterations to VIRGIN IE at their minimum and to use a code as close as possible to the SP2 version. Parallel computations are performed on a daily basis in the Aerodynamic Modelization Department at Dassault Aviation. A few civil and military applications are presented. The chapter also presents two parallel ports of the same vectorized finite-element Navier–stokes code onto two different parallel architectures, the IBM SP2 and the NEC SX-4. The SP2 is conceptually simpler since it implements a paradigm close to the idea of a finite element method. The unique drawback is that more effort must be deployed in order to split every new mesh into blocks.

Status and Future Challenges of CFD in a Coupled Simulation Environment for Aircraft Design

The state of the art of Computational Fluid Dynamics and the axis of improvements are described. The issue of flutter prediction is addressed first: the use of linearized Euler solvers for transonic flutter is explained. Recent advances in optimum aerodynamic shape design are presented next, the results demonstrate the applicability of optimization based on the Euler equations and open the way to multidisciplinary optimum design. Finally, the use of Large Eddy Simulation for accurate turbulent flow simulation is illustrated.

SOLVING LINEAR SYSTEMS WITH MULTIPLE RIGHT-HAND SIDES WITH GMRES : AN APPLICATION TO AIRCRAFT DESIGN

To create efficient new aerodynamic designs or predict the onset of flutter, the linearised Navier-Stokes equations might be used. In some cases, many right-hand sides must be solved keeping the same matrix. In this paper, techniques which enable to solve several righthand sides at the same time, such as Block GMRes, or reuse pieces of information computed in the previous solves, such as Krylov space recycling, are investigated. They will be tested on both simple and industrial test cases.

Contribution to Problem 6 using an upwind Euler solver with unstructured meshes

The goal of this paper is to discuss the application on critical problems encountered during reentry of space vehicles of an Euler flow solver developped in the past using unstructured meshes to handle equilibrium and/or nonequilibrium reactive flow simulations. Results in two dimensions for three test cases selected among those proposed around a double ellipse geometry at high Mach number and high angle of attack are presented.

Contribution to Problem 3 using a Galerkin Least Square Finite Element Method

A Navier Stokes solver based on a Galerkin - Least Square formulation is used; entropy variables are introduced to ensure dimensional consistency and satisfy the stability inequality as the second law of Thermodynamics. Convergence to the steady state solution is obtained with an implicit technique using a preconditioned GMRES linear solver. This method has been developped in close cooperation with F. Chalot, T.J.R Hughes, Z. Johan and F. Shakib at Stanford University.