Efficient and accurate simulations of three-dimensional flows past obstacles with vorticity-based penalization methods
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- This Master's thesis focuses on the implementation of three-dimensional penalization techniques, used to accurately model flows past arbitrary shaped obstacles on structured grids. More specifically, this work is divided into two parts. Firstly, we present the methodology and the underlying equations, which are based on the vorticity-velocity formulation of the Navier-Stokes equations. We describe three different penalization methods, gradually increasing in terms of accuracy, each of which acts as a correction to the classical vorticity field. We consider an explicit approach, an implicit one based on the velocity-pressure Navier-Stokes formulation, and an iterative method that solves the problem with an over-relaxed Jacobi algorithm. Secondly, we perform different Direct Numerical Simulations (DNS) and analyze the results. The equations are implemented in a partial differential equations (PDE) solver called "Murphy," which is an exascale-ready framework jointly developed by UCLouvain and the Van Rees Lab at MIT. As a starting point, we consider the widely used benchmark of an impulsively started flow past a cylinder. We consider the cases of Re=550 and Re=9500, compare the different penalization techniques and perform different convergence analysis. Then, we perform short and long-term simulations on a flow past a sphere at Re=300. We compare quantities such as aerodynamic coefficients and shedding frequencies. Lastly, as more complex geometries, we analyze the case of flows past extruded airfoils at Re=1000 and Re=5000. We consider different airfoil shapes. As a conclusion of this work, we discuss the general outcomes of this study, as well as perspectives for possible further improvements.