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In this work, we develop and analyze a Hybrid High-Order (HHO) method for steady non-linear Leray-Lions problems. The proposed method has several assets, including the support for arbitrary approximation orders and general polytopal meshes.…
A stable numerical solution of the steady Stokes problem requires compatibility between the choice of velocity and pressure approximation that has traditionally proven problematic for meshless methods. In this work, we present a…
This paper deals with a new solid-fluid coupling algorithm between a rigid body and an unsteady compressible fluid flow, using an Embedded Boundary method. The coupling with a rigid body is a first step towards the coupling with a Discrete…
While intersection cohomology is stable under small resolutions, both ordinary and intersection cohomology are unstable under smooth deformation of singularities. For complex projective algebraic hypersurfaces with an isolated singularity,…
In this paper we introduce a constructive approach to study well-posedness of solutions to stochastic fluid-structure interaction with stochastic noise. We focus on a benchmark problem in stochastic fluid-structure interaction, and prove…
We study a nonlinear, unsteady, moving boundary, fluid-structure (FSI) problem in which the structure is composed of two layers: a thin layer which is in contact with the fluid, and a thick layer which sits on top of the thin structural…
The main result of this work is a homogenization theorem via variational convergence for elastic materials with stiff checkerboard-type heterogeneities under the assumptions of physical growth and non-self-interpenetration. While the…
We compute the first order correction of the effective viscosity for a suspension containing solid particles with arbitrary shapes. We rewrite the computation as an homogenization problem for the Stokes equations in a perforated domain.…
Finite elasticity problems commonly include material and geometric nonlinearities and are solved using various numerical methods. However, for highly nonlinear problems, achieving convergence is relatively difficult and requires small load…
A stable partitioned algorithm is developed for fluid-structure interaction (FSI) problems involving viscous incompressible flow and rigid bodies. This {\em added-mass partitioned} (AMP) algorithm remains stable, without sub-iterations, for…
A stable added-mass partitioned (AMP) algorithm is developed for fluid-structure interaction (FSI) problems involving viscous incompressible flow and compressible elastic solids. Deforming composite grids are used to effectively handle the…
In this article, we present a new unified finite element method (UFEM) for simulation of general Fluid-Structure interaction (FSI) which has the same generality and robustness as monolithic methods but is significantly more computationally…
A stable partitioned algorithm for coupling incompressible flows with compressible elastic solids is described. This added-mass partitioned (AMP) scheme requires no sub-iterations, can be made fully second- or higher-order accurate, and…
The adjoint method allows efficient calculation of the gradient with respect to the design variables of a topology optimization problem. This method is almost exclusively used in combination with traditional Finite-Element-Analysis, whereas…
Arnold pointed out that the Euler equation of incompressible ideal hydrodynamics describes geodesics on the group of volume-preserving diffeomorphisms. A simple analogue is the Euler equation for a rigid body, which is the geodesic equation…
Robust, broadly applicable fluid-structure interaction (FSI) algorithms remain a challenge for computational mechanics. In previous work, we introduced an immersed interface method (IIM) for discrete surfaces and an extension based on an…
This paper describes a novel partitioned algorithm for fluid-structure interaction (FSI) problems that couples the motion of rigid bodies and incompressible flow. This is the first partitioned algorithm that remains stable and second-order…
We develop an immersed boundary (IB) method for modeling flows around fixed or moving rigid bodies that is suitable for a broad range of Reynolds numbers, including steady Stokes flow. The spatio-temporal discretization of the fluid…
In this work we study the coupled system of partial and ordinary differential equations describing the interaction between a compressible isentropic viscous fluid and a rigid body moving freely inside the fluid. In particular the position…
This paper deals with the numerical modelling of the interaction between a fluid and an incompressible solid (Neo Hookean) in small perturbations with the lattice Boltzmann method (LBM). In order to use a monolithic formulation and to solve…