Mathematical modelling and numerical simulation of fluid-structure interaction for complex viscous fluids

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Materials encountered in industry and medicine often fall outside the classical models of Newtonian viscous fluids. The aim of the proposed project is deep understanding of complex behavior of shear-dependent non-Newtonian fluids in time-dependent moving domains. Thus, our aims are two-fold: theoretical analysis of the corresponding mathematical model and the development of a reliable numerical scheme for experimental simulations. Non-Newtonian fluids we have in mind belong to the class of shear-thinning/shear-thickening fluids, for which the viscous stress tensor is a nonlinear function of shear rate. They are extensively used in industry or biomedicine in order to simulate flow of technical oils, composites, polymers, biological fluids, etc. As an exemplatory application blood flow in compliant vessels will be considered in particular. To assure that the derived numerical schemes are robust and reliable for such complex models, an in-depth numerical analysis including convergence and error analysis will be necessary.