CAREER: Regularization methods for fluid/filament interactions in three dimensions

Tulane University, New Orleans LA

Investigators

Abstract

Cortez 0094179 The investigator develops, analyzes, and applies computational techniques for the motion of elastic filaments embedded in an incompressible fluid. This general situation arises in many physical contexts, including the motion of microorganisms, swimming of aquatic animals, fluid flow around elastic bodies, bubble motion and more. The project encompasses the development of numerical methods for flows corresponding to a wide range of length scales. The methods are based on the use of a force field along filaments made of localized but smooth terms rather than delta distributions. Regular expressions for the fluid and filament velocities induced by the forces are then derived as the basis for the methods. Important properties of this approach are that it eliminates the singularities that would normally be present if the forces are assumed to be delta distributions, the volume of fluid within elastic boundaries is conserved extremely well, and high accuracy can be achieved. The work is aimed at extending well-known numerical techniques to three-dimensional flows driven by forces along filaments and to the full range of length scales. Analysis of the methods is carried out to establish and improve their stability, convergence and accuracy properties. The applications that are pursued include a wide variety of flagellar motions, the motion of flexible membranes around obstacles, and others. The motion of microorganisms in a liquid and the flow of blood in capillaries are two examples of phenomena that can be studied with computational methods. Computer techniques that can accurately simulate motions of this type are very valuable because they can be used to determine how arteries become obstructed or how flagellated organisms perform specific functions in the human body and the effects of defects in this mechanism. From a mathematical point of view, these computer simulations are not ready for scientists to use; there is a need to improve the accuracy with which the underlying equations are being solved and increase the reliability of the methods. This project is aimed at developing computational methods for fluid flows interacting with elastic structures. The goal is to develop high-accuracy methods, improve on their mathematical properties, and apply them to problems from biological sciences.