Georges-Henri Cottet

A LEVEL SET METHOD FOR FLUID-STRUCTURE INTERACTIONS WITH IMMERSED SURFACES

This paper is devoted to the derivation and the validation of a level set method for fluid-structure interaction problems with immersed surfaces. The test case of a pressurized membrane is used to compare our method to Peskins Immersed Boundary methods in the two-dimensional case and to demonstrate its capabilities for three-dimensional flows. The method in particular exhibits appealing mass and energy conservation properties.

Multilevel Adaptive Particle Methods for Convection-Diffusion Equations

We present novel multilevel particle methods with extended adaptivity in areas where increased resolution is required. We present two complementary approaches as inspired by r-adaptivity and adaptive mesh refinement (AMR) concepts introduced in finite difference and finite element schemes. For the r-adaptivity a new class of particle based mapping functions is introduced while the particle-AMR method uses particle remeshing in overlapping domains as a key element. The advantages and drawbacks of the proposed particle methods are illustrated based on results from the solution of one-dimensional convection-diffusion equations while the extension of the method to higher dimensions is demonstrated in simulations of the inviscid evolution of an elliptical vortex.

A multiresolution remeshed Vortex-In-Cell algorithm using patches

We present a novel multiresolution Vortex-In-Cell algorithm using patches of varying resolution. The Poisson equation relating the fluid vorticity and velocity is solved using Fast Fourier Transforms subject to free space boundary conditions. Solid boundaries are implemented using the semi-implicit formulation of Brinkman penalization and we show that the penalization can be carried out as a simple interpolation. We validate the implementation against the analytic solution to the Perlman test case and by free-space simulations of the onset flow around fixed and rotating circular cylinders and bluff body flows around bridge sections.

Convergence of the Grid-free point Vortex method for the three-dimensional Euler equations

Convergence of the grid-free point vortex method is proved for three-dimensional Euler equations with smooth solutions. Two new techniques are used to obtain consistency and stability of the method. The first one is Strang’s trick [Numer. Math., 6 (1964), pp. 37–46] which allows smooth approximate solutions to be constructed to the vortex method equations with arbitrarily small errors. This result is used to obtain consistency and nonlinear stability. The second tool is the use of a very special discrete negative norm in

Convergence Analysis of a Penalization Method for the Three-Dimensional Motion of a Rigid Body in an Incompressible Viscous Fluid

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Particle methods for direct numerical simulations of three-dimensional wakes

space for vorticity which gives rise to the linear stability result. Combining these two techniques proves uniform convergence of the method with second-order accuracy.

Particle Mesh Hydrodynamics for Astrophysics Simulations

We present and analyze a penalization method which extends the the method of [Ph. Angot, C.-H. Bruneau, and P. Fabrie, Numer. Math., 81 (1999), pp. 487-520] to the case of a rigid body moving freely in an incompressible fluid. The fluid-solid system is viewed as a single variable density flow. The interface is captured by a color function satisfying a transport equation. The solid velocity is computed by averaging at every time the flow velocity in the solid phase. This velocity is used to penalize the flow velocity at the fluid-solid interface and to move the interface. Numerical illustrations are provided to illustrate our convergence result. A discussion of our result in the light of existing existence results is also given.

A particle model for fluid–structure interaction

In this paper we describe recent advances in the development of particle methods for the direct numerical simulations of three-dimensional wakes. Both body-fitted and immersed boundary techniques are considered. The accuracy and numerical cost of the proposed numerical methods are discussed on the benchmark cases of a flow past a cylinder and of a vortex ring impinging on a cylinder. This article was chosen from Selected Proceedings of the 4th International Workshop on Vortex Flows and Related Numerical Methods (UC Santa-Barbara, 17-20 March 2002) ed E Meiburg, G H Cottet, A Ghoniem and P Koumoutsakos. Present address: MIP, Complexe Scientifique de Rangueil, 31077 Toulouse Cedex 4, France.

Multi-physics and particle methods

We present a particle method for the simulation of three dimensional compressible hydrodynamics based on a hybrid Particle-Mesh discretization of the governing equations. The method is rooted on the regularization of particle locations as in remeshed Smoothed Particle Hydrodynamics (rSPH). The rSPH method was recently introduced to remedy problems associated with the distortion of computational elements in SPH, by periodically re-initializing the particle positions and by using high order interpolation kernels. In the PMH formulation, the particles solely handle the convective part of the compressible Euler equations. The particle quantities are then interpolated onto a mesh, where the pressure terms are computed. PMH, like SPH, is free of the convection CFL condition while at the same time it is more efficient as derivatives are computed on a mesh rather than particle-particle interactions. PMH does not detract from the adaptive character of SPH and allows for control of its accuracy. We present simulations of a benchmark astrophysics problem demonstrating the capabilities of this approach.

Advances in direct numerical simulations of 3D wall-bounded flows by Vortex-in-Cell methods

We propose a particle method to handle fluid–structure interactions on a 1D model problem. Interactions between fluid and solid particles implicitly enforce the continuity of stresses on the interface. Comparisons with results obtained by ALE methods allow one to evaluate the robustness and accuracy of the method. To cite this article: G.-H. Cottet, C. R. Acad. Sci. Paris, Ser. I 335 (2002) 833–838.