Fluid-Structure Interaction in a Monolithic ALE Framework with Focus on Stationary Problems

Modelling and simulation of fluid-structure interaction problems (FSI) has many applications in engineering, biomechanics and medical sciences. For example, modelling elasto-plastic material deformations covered with lubricant or simulation of blood flow in veins and diseases of the cardiovascular system. The mathematical approach for investigating monolithic FSI problems via the 'arbitrary Lagrangian-Eulerian' method (ALE) will be presented. The resulting equations are nonlinear and have been solved by the Newton's method. After that, some results derived so far in my PhD project will be discussed. The focus is on stationary problems (e.g. an obstacle problem) and Benchmark configurations verifying the programming code.