Charles-Henri Bruneau

A penalization method to take into account obstacles in incompressible viscous flows

Abstract. From the Navier-Stokes/Brinkman model, a penalization method has been derived by several authors to compute incompressible Navier-Stokes equations around obstacles. In this paper, convergence theorems and error estimates are derived for two kinds of penalization. The first one corresponds to

Low-order modelling of laminar flow regimes past a confined square cylinder

L^2

Enablers for robust POD models

penalization inducing a Darcy equation in the solid body, the second one corresponds to a

An efficient scheme for solving steady incompressible Navier-Stokes equations

H^1

An elasto-visco-plastic model for immortal foams or emulsions

penalization and induces a Brinkman equation in the body. Numerical tests are performed to confirm the efficiency and accuracy of the method.

Level-set, penalization and cartesian meshes: A paradigm for inverse problems and optimal design

A proper orthogonal decomposition based model is considered for two-dimensional vortex shedding past a confined square cylinder. The aim is to study the validity of such a model for Reynolds numbers and blockage ratios that are different from those for which the model was derived. Using a calibration procedure it is shown that reliable results can be obtained in terms of short-term (one period) dynamics. Long-term dynamics are accurately captured with a variation of the Reynolds number, whereas the error becomes large when the blockage ratio changes. The controllability and observability of vortex shedding at a slightly supercritical Reynolds number is investigated relying on the accurate low-order models obtained

NUMERICAL STUDY OF ELLIPTIC-HYPERBOLIC DAVEY–STEWARTSON SYSTEM: DROMIONS SIMULATION AND BLOW-UP

This paper focuses on improving the stability as well as the approximation properties of Reduced Order Models (ROM) based on Proper Orthogonal Decomposition (POD). The ROM is obtained by seeking a solution belonging to the POD subspace and that at the same time minimizes the Navier-Stokes residuals. We propose a modified ROM that directly incorporates the pressure term in the model. The ROM is then stabilized making use of a method based on the fine scale equations. An improvement of the POD solution subspace is performed thanks to an hybrid method that couples direct numerical simulations and reduced order model simulations. The methods proposed are tested on the two-dimensional confined square cylinder wake flow in laminar regime.

Numerical resolution of some nonlinear Schrödinger‐like equations in plasmas

Abstract The steady incompressible Navier-Stokes equations in a 2D driven cavity are solved in primitive variables by means of the multigrid method. The pressure and the components of the velocity are discretized on staggered grids, a block-implicit relaxation technique is used to achieve a good convergence and a simplified FMG-FAS algorithm is proposed. Special focus on the finite differences scheme used to approach the convection terms is made and a large discussion with other schemes is given. Results in a square driven cavity are obtained for Reynolds numbers as high as 15,000 on fine uniform meshes and the solution is in good agreement with other studies. For Re = 5000 the secondary vortices are very well represented showing the robustness of the method. For Reynolds numbers higher than 5000 the loss of stability for the steady solution is discussed. Moreover, some computations on a rectangular cavity of aspect ratio equal to two are presented. In addition the method is very efficient as far as CPU time is concerned; for instance, the solution for Re = 1000 on a 128 × 128 grid is obtained within 24 s on a SIEMENS VP 200.

Passive Control Around the Two-Dimensional Square Back Ahmed Body Using Porous Devices

Abstract.A variety of complex fluids consists in soft, round objects (foams, emulsions, assemblies of copolymer micelles or of multilamellar vesicles--also known as onions). Their dense packing induces a slight deviation from their prefered circular or spherical shape. As a frustrated assembly of interacting bodies, such a material evolves from one conformation to another through a succession of discrete, topological events driven by finite external forces. As a result, the material exhibits a finite yield threshold. The individual objects usually evolve spontaneously (colloidal diffusion, object coalescence, molecular diffusion), and the material properties under low or vanishing stress may alter with time, a phenomenon known as aging. We neglect such effects to address the simpler behaviour of (uncommon) immortal fluids: we construct a minimal, fully tensorial, rheological model, equivalent to the (scalar) Bingham model. Importantly, the model consistently describes the ability of such soft materials to deform substantially in the elastic regime (be it compressible or not) before they undergo (incompressible) plastic creep--or viscous flow under even higher stresses.

Intensity of vortices: from soap bubbles to hurricanes

The aim of this work is to combine penalization and level-set methods to solve inverse or shape optimization problems on uniform cartesian meshes. Penalization is a method to impose boundary conditions avoiding the use of body-fitted grids, whereas level-sets allow a natural non-parametric description of the geometries to be optimized. In this way, the optimization problem is set in a larger design space compared to classical parametric representation of the geometries, and, moreover, there is no need of remeshing at each optimization step. Special care is devoted to the solution of the governing equations in the vicinity of the penalized regions and a method is introduced to increase the accuracy of the discretization. Another essential feature of the optimization technique proposed is the shape gradient preconditioning. This aspect turns out to be crucial since the problem is infinite dimensional in the limit of grid resolution. Examples pertaining to model inverse problems and to shape design for Stokes flows are discussed, demonstrating the effectiveness of this approach.