Topology Optimization for Unsteady Flow with Applications in Biomedical Flows
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In this thesis, we will apply a topology optimization method to unsteady fluid flow, using a density model and level set method, in order to optimize the shape of a coronary artery bypass anastomosis. The fluid movement is described by the unsteady, incompressible Navier-Stokes equations combined with Darcy's equation. These equations are discretized using a finite element approach in space and a backward Euler method in time, and solved using an incremental pressure correction scheme (IPCS). We will consider different objective functionals for the optimization problems. The topological derivative will be calculated based on an adjoint formulation of the Navier-Stokes equations combined with Darcy's equation, and used as a search direction in a gradient-based algorithm, in order to find the optimal channel shape.