Mathematical Sciences Department Numerical Methods Seminar - Thomas Fai, Brandeis University

Title: Lubricated Immersed Boundary Method with Application to Fiber Bundles

Abstract: Fluid-mediated near contact of elastic structures is a recurring theme in biofluids. The thin fluid layers that arise in applications such as the flow of red blood through blood vessels are difficult to resolve by standard computational fluid dynamics methods based on uniform fluid grids. A key assumption of the lubricated immersed boundary method, which incorporates a subgrid model to resolve thin fluid layers between immersed boundaries, is that the average velocity of nearby boundaries can be accurately computed from under-resolved simulations to bridge between different spatial scales. Here, we present a one-dimensional numerical analysis to assess this assumption and quantify the performance of the average velocity as a multiscale quantity. We explain how this analysis leads to more accurate formulations of the method and present examples from two-dimensional simulations, including applications to filament bundles.