UC Berkeley

The simulation of the dynamics of thin elastic surfaces is an essential component in applications ranging from cardiovascular medicine to flapping wing aerospace engineering. In this thesis we introduce a fully Eulerian method for accurately simulating elastic surfaces. Our approach can be applied to membranes and shells with nonlinear elastic properties, either moving under their own dynamics or immersed in a Fluid. By representing the surface with a level set function and a set of advected reference coordinates, we are able to evaluate the full elastic surface forces. Our approach is compatible with compatible with implicit interface representations, including level set techniques, and can make use of high-order finite difference stencils or more sophisticated techniques. We introduce our method and its implementation, including new solution techniques for several problems associated with immersed interface representations. We demonstrate second order accurate numerical results for a range of model problems in two and three dimensions.