Lattice Boltzmann Simulation of Power-Law Fluids in a Fontan Geometry
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Abstract
Numerical Modeling can provide insight and improve processes in human health. Thismasters thesis is a Python implementation of the lattice Boltzmann method in twodimensions to model flows related to the Fontan cardiac procedure.To begin, solvers were created for pipe flow. Pressure boundaries were used for the inletand outlet. The solver was tested by matching the analytical solution for flow withNewtonian fluids. Non-Newtonian fluids were added to the solver using the power lawmodel. Similarly, this solver was tested by matching the flow to the non-Newtoniananalytical solution.Next more complex geometries were added to the solver. This was done using a maskingfunction in Python. Then the geometry for the veins in the Fontan procedure wereimplemented into the solver.Simulations were performed at various power-law indexes. It was found that an increasein the power-law index resulted in an increase in the Reynolds number, velocity and flowrate.