Related papers: A function space approach to the shape optimizatio…
This paper sets up an approach for shape optimization problems constrained by variational inequalities (VI) in an appropriate shape space. In contrast to classical VI, where no explicit dependence on the domain is given, VI constrained…
This paper addresses the stability and large-time behavior problem on the perturbations near the hydrostatic balance of the two dimensional Boussinesq system, taking into account vertical dissipation and horizontal thermal diffusion. The…
We show the existence and optimal regularity of the optimal temperature configuration in a problem in heat conduction with minimal temperature constraint, interior heating and exterior insulation. Regularity of the two free boundaries is…
A model for the development of turbulent shear flows, created by non-uniform parallel flows in a confining channel, is used to identify the diffuser shape that maximises pressure recovery when the inflow is non-uniform. Wide diffuser angles…
We consider the evolution of contact lines for thermal convection of viscous fluids in a 2D open-top vessel. The domain is bounded above by a free moving boundary and otherwise by the solid wall of a vessel. The dynamics of the fluid are…
The optimal insulation of a heat conducting body by a thin film of variable thickness can be formulated as a nondifferentiable, nonlocal eigenvalue problem. The discretization and iterative solution for the reliable computation of…
In this work, we investigate a particular class of shape optimization problems under uncertainties on the input parameters. More precisely, we are interested in the minimization of the expectation of a quadratic objective in a situation…
The evolution of three-dimensional, cellular convective flows in a plane horizontal layer of a Boussinesq fluid heated from below is well studied. Here we review results from the investigation of this system as well as a number of related…
The optimal control of thermally convective flows is usually modeled by an optimization problem with constraints of Boussinesq equations that consist of the Navier-Stokes equation and an advection-diffusion equation. This optimal control…
The present contribution investigates shape optimisation problems for a class of semilinear elliptic variational inequalities with Neumann boundary conditions. Sensitivity estimates and material derivatives are firstly derived in an…
This paper explores the reconstruction of a space-dependent parameter in inverse diffusion problems, proposing a shape-optimization-based approach. We consider a Robin boundary condition, physically motivated in diffuse optical tomography…
Computational design optimization in fluid dynamics usually requires to solve non-linear partial differential equations numerically. In this work, we explore a Bayesian optimization approach to minimize an object's drag coefficient in…
Shape optimization models with one or more shapes are considered in this chapter. Of particular interest for applications are problems in which where a so-called shape functional is constrained by a partial differential equation (PDE)…
In this paper, we will consider an optimal shape problem of heat insulation introduced by Bucur-Buttazzo-Nitsch. We will establish the existence of optimal shapes in the class of $M$-uniform domains. We will also show that balls are stable…
We study an initial and boundary value problem modelling the motion of a rigid body in a heat conducting gas. The solid is supposed to be a perfect thermal insulator. The gas is described by the compressible Navier-Stokes-Fourier equations,…
In this research, we investigate a general shape optimization problem in which the state equation is expressed using a nonlocal and nonlinear operator. We prove the existence of a minimum point for a functional $F$ defined on the family of…
We study temperature and velocity output tracking problem for a two-dimensional room model with the fluid dynamics governed by the linearized translated Boussinesq equations. Additionally, the room model includes finite-dimensional models…
In this paper we study the validity of the so-called Oberbeck-Boussinesq approximation for compressible viscous perfect gases in the whole three-dimensional space. Both the cases of uids with positive heat conductivity and zero conductivity…
In this paper, we consider the global well-posedness of the initial-boundary value problem to a nonlinear Boussinesq-fluid-structure interaction system, which describes the motion of an incompressible Boussinesq-fluid surrounded by an…
The aim of this work is to analyse a shape optimization problem in a mechanical friction context. Precisely we perform a shape sensitivity analysis of a Tresca friction problem, that is, a boundary value problem involving the usual linear…