Model-Order-Reduction for Non-Linear Fluid-Structure-Concentration Interaction Problems
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In this presentation, we explore the use of proper orthogonal decomposition (POD) [1,2,3,4] and the discrete empirical interpolation method (DEIM) [5] to solve fluid-structure-concentration interaction (FSCI) [6]. Specifically, the system couples incompressible Navier-Stokes equations with elastodynamic momentum balance, which is coupled to growth-induced kinematics equations and advective-diffusive transport equations. To address the different coordinate systems, we employ the Arbitrary Lagrangian-Eulerian (ALE) framework [7,8]. A low-dimensional projection space is created using POD to reduce the system. DEIM is then used to reduce dependencies on the original system dynamics. In our numerical tests, we compare the preservation of a simplified linear system with that of the full nonlinear system. Additionally, we analyze the variation of material parameters with constant snapshot datasets in terms of data preservation. Furthermore, we undertake analyses of computational costs.
