Numerical methods for non-Newtonian fluid structure interaction problems

点击翻译按钮获取中文摘要

This research project is focused on the stable and efficient numerical approximation of equations describing the flow of a non-Newtonian fluid interacting with an elastic structure. Such fluid flows are ubiquitous in our everyday lives, from the flow of blood in our bodies to flow in industrial processes such as pharmaceutical blending and microfluidics. This theoretical investigation will provide a solid foundation for the further development of numerical algorithms for such systems. The research project will also broaden the mathematical basis for the numerical simulation of non-Newtonian fluid flow in physically realistic settings. The goal of this research project is the development and analysis of stable and efficient numerical schemes for non-Newtonian fluid structure interactions. There has been significant mathematical research for Newtonian fluid flow problems, but to date few investigations of non-Newtonian flows. The systems studied in this project involve coupled domains representing multi-physics behavior. This increases the numerical complexity as both stress and velocity must be resolved in the domains, and the strong interaction between the governing equations requires solution algorithms that achieve optimal convergence rates for efficiency while splitting the operators. Because of the large number of unknowns required to compute an accurate approximation of non-Newtonian (in particular viscoelastic) fluids, there is a need to develop efficient solvers for these problems. This research will contribute to the development and rigorous analysis of stability and accuracy properties of numerical methods for non-Newtonian fluid structure interactions.