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Unconditionally Stable CutFEM for Dynamic Interfaces in a Fluid Structure Interaction Problem

Banff International Research Station for Mathematical Innovation and Discovery

Interface problems arise in several applications including heart models, cochlea models, aquatic animal locomotion, blood cell motion, front-tracking in porous media flows and material science, to name a few. One of the difficulties in these problems is that solutions are normally not smooth across interfaces, and therefore standard numerical methods will lose accuracy near the interface unless the meshes align to it. However, it is advantageous to have meshes that do not align with the interface, especially for time dependent problems where the interface moves with time. Remeshing at every time step can be prohibitively costly, can destroy the structure of the mesh, or can deteriorate the well-conditioning of the stiffness matrix, and affect the stability of the problem. For a simple moving interface fluid-membrane interaction, we present a formal second-order finite element discretization in space and first-order in time where the finite element triangulation does not fit the interface and it is unconditionally stable in time independently of mesh parameters and fluid viscosity and membrane stiffness. This is a joint work with Kyle Dunn and Roger Lui from WPI.

Mathematics; Numerical analysis; Partial differential equations

video/mp4

Author affiliation: Mathematical Sciences Department - Worcester Polytechnic Institute

2019-03-17

Attribution-NonCommercial-NoDerivatives 4.0 International

http://hdl.handle.net/2429/68831

Unreviewed

http://creativecommons.org/licenses/by-nc-nd/4.0/