Fluid-structure interaction modeling of artery aneurysms with steady-state configurations

This paper addresses numerical simulations of fluid-structure interaction (FSI) problems involving artery aneurysms, focusing on steady-state configurations. Both the fluid flow and the hyperelastic material are incompressible. A monolithic formulation for the FSI problem is considered, where the deformation of the fluid domain is taken into account according to an Arbitrary Lagrangian Eulerian (ALE) scheme. The numerical algorithm is a Newton-Krylov method combined with geometric multigrid preconditioner and smoothing based on domain decomposition. The system is modeled using a specific equation shuffling that aims at improving the row pivoting. Due to the complexity of the operators, the exact Jacobian matrix is evaluated using automatic differentiation tools. We describe benchmark settings which shall help to test and compare different numerical methods and code implementations for the FSI problem in hemodynamics. The configurations consist of realistic artery aneurysms. A case of endovascular stent implantation on a cerebral aneurysm is also presented. Hybrid meshes are employed in such configurations. We show numerical results for the described aneurysm geometries for steady-state boundary conditions. Parallel implementation is also addressed

FEMuS-Platform: a numerical platform for multiscale and multiphysics code coupling

Nowadays, many open-source numerical codes are available to solve physical problems in structural mechanics, fluid flow, heat transfer, and neutron diffusion. However, even if these codes are often highly specialized in the numerical simulation of a particular type of physics, none of them allows simulating complex systems involving all the physical problems mentioned above. In this work we present a numerical framework, based on the SALOME platform, developed to perform multiscale and multiphysics simulations involving all the mentioned physical problems. In particular, the developed numerical platform includes the multigrid finite element in-house code FEMuS for heat transfer, fluid flow, turbulence and fluid-structure modeling; the open-source finite volume CFD software OpenFOAM; the multiscale neutronic code DONJON-DRAGON; and a system-scale code used for thermal-hydraulic simulations. Efficient data exchange among these codes is performed within computer memory by using the MED libraries, provided by the SALOME platform

Analysis of optimal control problems for the incompressible MHD equations and implementation in a finite element multiphysics code

This thesis deals with the study of optimal control problems for the incompressible Magnetohydrodynamics (MHD) equations. Particular attention to these problems arises from several applications in science and engineering, such as fission nuclear reactors with liquid metal coolant and aluminum casting in metallurgy. In such applications it is of great interest to achieve the control on the fluid state variables through the action of the magnetic Lorentz force. In this thesis we investigate a class of boundary optimal control problems, in which the flow is controlled through the boundary conditions of the magnetic field. Due to their complexity, these problems present various challenges in the definition of an adequate solution approach, both from a theoretical and from a computational point of view. In this thesis we propose a new boundary control approach, based on lifting functions of the boundary conditions, which yields both theoretical and numerical advantages. With the introduction of lifting functions, boundary control problems can be formulated as extended distributed problems. We consider a systematic mathematical formulation of these problems in terms of the minimization of a cost functional constrained by the MHD equations. The existence of a solution to the flow equations and to the optimal control problem are shown. The Lagrange multiplier technique is used to derive an optimality system from which candidate solutions for the control problem can be obtained. In order to achieve the numerical solution of this system, a finite element approximation is considered for the discretization together with an appropriate gradient-type algorithm. A finite element object-oriented library has been developed to obtain a parallel and multigrid computational implementation of the optimality system based on a multiphysics approach. Numerical results of two- and three-dimensional computations show that a possible minimum for the control problem can be computed in a robust and accurate manner

Fluid-structure interaction modeling of artery aneurysms with steady-state configurations

This paper addresses numerical simulations of fluid-structure interaction (FSI) problems involving artery aneurysms, focusing on steady-state configurations. Both the fluid flow and the hyperelastic material are incompressible. A monolithic formulation for the FSI problem is considered, where the deformation of the fluid domain is taken into account according to an Arbitrary Lagrangian Eulerian (ALE) scheme. The numerical algorithm is a Newton-Krylov method combined with geometric multigrid preconditioner and smoothing based on domain decomposition. The system is modeled using a specific equation shuffling that aims at improving the row pivoting. Due to the complexity of the operators, the exact Jacobian matrix is evaluated using automatic differentiation tools. We describe benchmark settings which shall help to test and compare different numerical methods and code implementations for the FSI problem in hemodynamics. The configurations consist of realistic artery aneurysms. A case of endovascular stent implantation on a cerebral aneurysm is also presented. Hybrid meshes are employed in such configurations. We show numerical results for the described aneurysm geometries for steady-state boundary conditions. Parallel implementation is also addressed

Boundary Control Problems in Convective Heat Transfer with Lifting Function Approach and Multigrid Vanka-Type Solvers

This paper deals with boundary optimal control problems for the heat and Navier-Stokes equations and addresses the issue of defining controls in function spaces which are naturally associated to the volume variables by trace restriction. For this reason we reformulate the boundary optimal control problem into a distributed problem through a lifting function approach. The stronger regularity requirements which are imposed by standard boundary control approaches can then be avoided. Furthermore, we propose a new numerical strategy that allows to solve the coupled optimality system in a robust way for a large number of unknowns. The optimality system resulting from a finite element discretization is solved by a local multigrid algorithm with domain decomposition Vanka-type smoothers. The purpose of these smoothers is to solve the optimality system implicitly over subdomains with a small number of degrees of freedom, in order to achieve robustness with respect to the regularization parameters in the cost functional. We present the results of some test cases where temperature is the observed quantity and the control quantity corresponds to the boundary values of the fluid temperature in a portion of the boundary. The control region for the observed quantity is a part of the domain where it is interesting to match a desired temperature value