Mimetic Spectral Element Method for 2D Potential Flow

The thesis aims to solve partial differential equations numerically using mimetic spectral element method. The method rewrites the PDEs with differential forms so the resulting equations are able to preserve geometrical characteristics in physics. The equation we focus is the Poisson equation, which can be utilized for potential flow problems. The physical domain to be tested is a typical flow around cylinder domain. Due to the curved surface, a curvilinear mesh is generated by transfinite interpolation so that the mesh can be perfectly fitted to the body. The implementation of the mimetic spectral element method involves a Python package called MimeticFEM developed by Group of Aerodynamics, Faculty of Aerospace Engineering. The package provides a series of handy functions and methods to build system equations efficiently. A manufactured solution is made for error analysis of the numerical results. In addition, both h-refinement and p-refinement are made to test the convergence rate.