Past Event: Oden Institute Seminar

An Immersed Boundary Energy-Based Method for Incompressible Viscoelasticity

Dharshi Devendran, Courant Institute of Mathematical Sciences

Abstract

Incompressible viscoelastic materials are prevalent in biological applications. We present a method for incompressible viscoelasticity which does not use stress tensors and in which Lagrangian (material) coordinates are used to describe elastic forces, and Eulerian (spatial) coordinates are used for the equations of motion and incompressibility condition. The elastic forces are computed directly from an energy functional and the immersed boundary method is used to communicate between Lagrangian and Eulerian variables. The method is first applied to a warm-up problem, in which a viscoelastic incompressible material fills a two-dimensional periodic domain. Incompressibility is well maintained, as indicated by area conservation in this 2D problem. Next, we apply the method to a three-dimensional fluid-structure interaction problem.