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

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This proposal is concerned with problems in fluid dynamics where an underlying fluid flow interacts with some other physical, biological or chemical process. The flows of interest originate from a variety of industrial, engineering and biomedical applications that can be organized under two themes: ******Theme I: Fluid-structure interaction involving deformable, elastic structures immersed in an incompressible fluid. Applications include flow of wood pulp fiber suspensions; biomechanics of fluid-filled organs such as the heart or cochlea (or inner ear); and swimming behavior of organisms such as jellyfish, squid or marine worms.******Theme II: Multiphase flow in a porous medium, where the flow is coupled with heat transport, phase change, or reaction chemistry. Applications include sap flow in trees; water uptake in soil or concrete; and flow of condensing gases in hydrogen fuel cells.******My approach to solving all of these problems follows a common strategy: (1) develop a detailed mathematical model based on careful physical reasoning; (2) employ mathematical techniques such as asymptotics, linear stability analysis or periodic homogenization to simplify the governing equations and to obtain insight into solution behavior; and (3) develop an accurate and efficient numerical algorithm, which can be used to perform extensive simulations and validate the model against both analytical solutions and experimental data.***The problems listed under Themes I and II encompass a diverse range of physical phenomena and numerical solution techniques. Nevertheless, there are several common aspects that unify the modelling and computational issues arising in this work:***** systems of nonlinear partial differential equations with strong coupling between solution components; **** presence of interior or boundary layers and a wide range of spatial scales that can benefit from the use of multiscale analysis and/or adaptive numerical methods; and **** numerical stiffness arising from widely varying time scales that necessitates use of implicit time-stepping algorithms. ***A defining characteristic of this proposal is the tight interplay between mathematical analysis and algorithm development, wherein knowledge about the analytical solution is exploited to make informed decisions about the choice of numerical method and specific algorithmic improvements. This work should have significant impact in terms of developing novel solution algorithms as well as advancing knowledge of complex multi-physics flow phenomena. For example, detailed knowledge of cardiac flow instabilities could lead to improved understanding of heart arrhythmias, and new insights into sap flow in maple trees may be used to optimize sap harvesting practices. Many sub-projects involve collaborations with companies or other non-academic partners, which will help to ensure that results are actually put into practical use in industry.**