Fast numerical methods for large-scale multiphysics problems

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The first type of problems to be considered in this project are linear and nonlinear fluid-structure interaction problems. They appear in a whole range of applications starting from aircraft design, to simulation of flows in human arteries, heart, and the alveoli of the airways. The intention is to explore a new approach to such problems that, to our knowledge, has not been used so far. The key idea of this approach is to reformulate both, the fluid and the structure problems in terms of a new variable, the stress tensor. Further, by using a proper splitting approach, the 3D time-discrete system of equations can be reduced to a set of much simpler, lower-dimensional problems that can be resolved much easier. So, the resulting numerical algorithm will be significantly faster and easier to implement on parallel computers. Another very pleasant outcome of this new setting of fluid-structure interaction problems is that since in both domains it uses only the stress as a variable, it does not require explicit tracking of the shape of the structure domain that is usually quite problematic in the existing methods in primitive variables.