Finite Volume/Element Discretization on Unstructured Meshes of the Multiscale Formulation of the Large Eddy Simulation Method and Application to Vortex Shedding

A finite volume/element discretization on tetrahedral meshes of the variation- al multiscale formulation of large eddy simulations is proposed for turbulent compressible flows. This discretization features an economical procedure based on agglomeration for separating a priori the scales, a corresponding projector for eliminating the small scales from the system of equations, and an effective control of the numerical dissipation induced by upwinding. The resulting LES method is validated with the three-dimensional numerical simulation of a low-speed flow past a square cylinder at M_¥ = 0.1 and Re = 22,000, and various comparisons with experimental data

Finite Volume/Element Discretization on Unstructured Meshes of the Multiscale Formulation of the Large Eddy Simulation Method and Application to Vortex Shedding

A finite volume/element discretization on tetrahedral meshes of the variation- al multiscale formulation of large eddy simulations is proposed for turbulent compressible flows. This discretization features an economical procedure based on agglomeration for separating a priori the scales, a corresponding projector for eliminating the small scales from the system of equations, and an effective control of the numerical dissipation induced by upwinding. The resulting LES method is validated with the three-dimensional numerical simulation of a low-speed flow past a square cylinder at M_¥ = 0.1 and Re = 22,000, and various comparisons with experimental data

Spatial discretization issues for the energy conservation in compressible flow problems on moving grids

The prediction of interaction phenomena between a compressible flow in a moving domain and other models like structural ones requires that some conservation properties need to be satisfied by the numerical schemes. In this paper we investigate the important problem of the work-energy conservation within the fluid for the discrete formulation on moving grids. In the case of a compressible flow, the work performed on the fluid by the moving interface has to be properly translated in a variation of the total fluid energy. We present a numerical model that satisfies this energy conservation property without loosing some other conservation properties such as the Geometric Conservation Law

Aerodynamical and sonic boom optimization of a supersonic aircraft

Sonic Boom Reduction will be an issue of utmost importance in future supersonic carriers, due to strong regulations on acoustic nuisance. The present work introduces a technique for optimizing the aerodynamical performan- ce and the sonic boom production, through optimal shape design. Based in a so-called CAD-free parametrization method, which relies on the discretized shape by working in a parameter space determined by the skin nodes physical location, this methodology introduces several distinctive features. First, an additive multilevel optimization preconditioner is designed, which both smoothes the iterated shape and speeds up the optimization convergence. Second, the sonic boom is reduced indirectly by reducing what we call the sonic boom emission. Third, an ad-hoc simple cost functional is constructe- d which considers both aerodynamical parameters and sonic boom emission

Dynamic and hybrid variational multiscale models for the simulation of bluff-body flows on unstructured grids

The computation of massively separated flows is a challenging problem of particular in- terest in industrial applications. For the purpose of properly simulating these complex flows on not too heavy unstructured meshes as usually employed in industry, appropriate numerical and turbulent models must be used. In the present work, the computation of the flow past a circular cylinder at different Reynolds numbers is chosen as benchmark. The spatial discretization is based on a mixed finite element/finite volume formulation on unstructured grids. The numerical dissipation of the upwind scheme is made of sixth-order space derivatives in order to limit as far as possible the interactions between numerical and subgrid scale (SGS) dissipation, which could deteriorate the accuracy of the results [4]. A variational multi-scale large-eddy simulation (VMS-LES) with dynamic SGS models and a RANS/VMS-LES model are evaluated on the proposed benchmark for subcritical and supercritical flow regimes respectively (see Fig. 1 and Tab. 1). In the VMS-LES used in this work, the separation between the large and the small resolved scales is obtained through a variational projection operator based on spatial average on agglomerated cells [1]. The dynamic procedure allows the adaptation of the constant of the SGS model to the spatial and temporal variation of the flow characteristics, while the VMS formulation restricts the SGS model effects to the smallest resolved scales. The dynamic versions of the Smagorinsky and of the WALE SGS models are considered herein. The non-dynamic counterparts of these SGS models are also used in order to evaluate the impact of dy- namic SGS modeling in the considered VMS-LES approach for the simulation of massively separated flows. However, the Reynolds number range useful for LES-like simulation is limited as LES grid needs to be sufficiently fine to resolve a significant part of the turbulence scales. With the aim of simulating high Reynolds number flows, it is considered in the present work a hybridization strategy using a blending parameter, such that a VMS- LES simulation is obtained where the grid resolution is fine enough to resolve a significant part of the turbulence fluctuations [2], while a RANS model is acting in the regions of coarse grid resolution, as, for instance, near the body surface

Spatial discretization issues for the energy conservation in compressible flow problems on moving grids

The prediction of interaction phenomena between a compressible flow in a moving domain and other models like structural ones requires that some conservation properties need to be satisfied by the numerical schemes. In this paper we investigate the important problem of the work-energy conservation within the fluid for the discrete formulation on moving grids. In the case of a compressible flow, the work performed on the fluid by the moving interface has to be properly translated in a variation of the total fluid energy. We present a numerical model that satisfies this energy conservation property without loosing some other conservation properties such as the Geometric Conservation Law

Reverse Automatic Differentiation for Optimum Design: from Adjoint State Assembly to Gradient Computation

The utilization of reverse mode Automatic Differentiation to the adjoint method for solving an Optimal Design problem is described. Using the reverse mode, we obtain the adjoint system residual in a rather efficient way. But memory requirements may be very large. The family of programs to differentiate involves many independant calculations, typically in parallel loops. Then we propose to apply a reverse differentiation «by iteration». This demands much less memory storage. This methods is used for the computing of the adjoint state and gradient related to the Optimal Design problem

Optimization loops for shape and error control: extended lecture notes

The power and versatility of the so-called adjoint methods used in optimization problems is addressed by presenting a combined methodology: shape and error control. In a first part we describe novel technologies for solving shape design problems: constrained optimum formulation with adjoint, one-shot optimization algorithms and multi-level optimization preconditioning. The application to a shape design problem related to sonic boom minimization is reported. In a second part, after some remarks on mesh adaptation, we examine the problem of formulating mesh adaptation in terms of an optimization problem, presenting some applications to interpolation and to Partial Differential Equations. The implications of the proposed method become clear: by combining together both ideas cost effective methods can be developed where the optimization loops involve both shape optimization, to improve an aerodynamic design, and mesh adaptivity, to cope with the difficulties of the CFD problem involved. Ce document présente la version détaillée des notes de cours au ``PROMUVAL Short Course on Multidisciplinary Modelling Simulation and Validation in Aeronautics'', qui s'est tenu à Barcelone (E), les 28-29 juin 2004

Three-dimensional CFD simulations with large displacement of the geometries using a connectivity-change moving mesh approach

This paper deals with three-dimensional (3D) numerical simulations involving 3D moving geometries with large displacements on unstructured meshes. Such simulations are of great value to industry, but remain very time-consuming. A robust moving mesh algorithm coupling an elasticity-like mesh deformation solution and mesh optimizations was proposed in previous works, which removes the need for global remeshing when performing large displacements. The optimizations, and in particular generalized edge/face swapping, preserve the initial quality of the mesh throughout the simulation. We propose to integrate an Arbitrary Lagrangian Eulerian compressible flow solver into this process to demonstrate its capabilities in a full CFD computation context. This solver relies on a local enforcement of the discrete geometric conservation law to preserve the order of accuracy of the time integration. The displacement of the geometries is either imposed, or driven by fluid–structure interaction (FSI). In the latter case, the six degrees of freedom approach for rigid bodies is considered. Finally, several 3D imposed-motion and FSI examples are given to validate the proposed approach, both in academic and industrial configurations