Modelling and simulation of complex flows with multiple scales and multi-physics

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Some of the most challenging problems facing computational scientists today arise from applications in fluid dynamics, and most notably problems where a fluid flow interacts with some other physical process. In this proposal we focus on two classes of such multi-physics phenomena: fluid-structure interaction problems in which a deformable, solid structure interacts with a fluid; and transport in porous media for which flow through a porous material introduces an additional drag force on the fluid. Examples include the flow of blood in the heart and arteries; suspensions of flexible wood pulp fibers in the paper making process; transport of reactants in a hydrogen fuel cell; and concrete degradation mediated by moisture transport. While these problems seem on the surface to be fundamentally different, all can be modelled using nonlinear systems of partial differential equations, and are characterised by complex, coupled physics that occur over widely-varying length and time scales. It is a major computational challenge to resolve these various scales in the solution while at the same time maintaining some degree of efficiency. In this research, my basic approach is two-fold: first, to derive analytical solutions or asymptotic approximations that afford some insight into solution behaviour; and second, to use the analytical results as a guide in designing more accurate and efficient numerical solution strategies. One major application of this work is the use of the "immersed boundary method" to simulate flexible fiber suspensions; swimming marine organisms, and dynamics of biological membranes. I am also investigating a variety of problems involving flow in porous media with industrial applications, such as concrete degradation, fuel cell catalyst layer design, and groundwater contamination and remediation.