On the Efficient Computation of Immersed Boundaries in Complex Fluids

The dynamics of flexible immersed boundaries in complex, viscoelastic fluids is of significant relevance in many important applications, including the locomotion of micro-organisms and the dynamics of drops and emulsions in a non-Newtonian matrix. The coupled Navier-Stokes and Fokker-Planck equations are used in the modeling of complex fluids with an immersed, elastic boundary.  This coupling leads to a high-dimensional system of nonlinear equations, which are prohibitively costly to solve using standard numerical techniques.  In this work we employ a novel approach that takes advantage of the localization of the viscoelastic stresses in the vicinity of the moving, immersed boundary.  To this effect we combined an efficient version of Peskin’s Immersed Boundary Method with a multiresolution analysis.  We examine the overall efficiency of the numerical method, identify potential areas for improvement, and compare it to existing methods.