We present a space-time finite element formulation of the Navier-Stokes equations which is stabilized via the Galerkin/least-squares approach. The variational equation is based on the time discontinuous Galerkin method and is written in terms of the physical entropy variables over the moving and deforming space-time slabs. The formulation thus becomes analogous to the classical arbitrary Lagran...

In this thesis, mixed primitive variable based finite element formulations are developed to solve linear and nonlinear fluid-structure interaction problems involving incompressible (or almost incompressible) fluid models. The mixed elements are used according to the inf-sup condition. It is pointed out that along the fluid-structure interfaces, different coupling conditions can be used accordin...

We present two methods for calculating resonant frequencies and mode shapes for fluid-structure vibration problems. We model the fluid-structure interaction problem using the #-V-P, finite element technique. This eigenproblem is more complicated than for ordinary structural analyses, as the formulation produces a quadratic eigenproblem (similar to those for gyroscopic systems). We derive proper...

Fluid–structure interaction problems arise in many application fields such as flows around elastic structures or blood flow problems in arteries. One method for solving such a problem is based on a reduction to an equation on the interface, involving the so-called Steklov–Poincaré operators. This interface equation is solved by a Newton iteration for which directional derivatives with respect t...

We consider the problem of numerical integration of a function over a discrete surface to high-order accuracy. Surface integration is a common operation in numerical computations for scientific and engineering problems. Integration over discrete surfaces (such as a surface triangulation) is typically limited to only first or second-order accuracy due to the piecewise linear approximations of th...

Fluid-structure interaction problems arise in many fields of application such as flows around elastic structures or blood flow in arteries. The method presented in this paper for solving such a problem is based on a reduction to an equation at the interface, involving the so-called Steklov-Poincaré operators. This interface equation is solved by a Newton iteration, for which directional derivat...

The Boundary Element Method is now well established as a valid numerical technique for the solution of field problems, equal to the Finite Element Method in generality and surpassing it in computational efficiency in some cases.’ In this paper is presented a ‘Regular Boundary Element Method’ as applied to inviscid laminar fluid flow problems. It involves the formation of a system of regular int...