Computational Fluid Dynamics (CFD) has become important in designing aerospace and transport products. It allows for predicting the key flow properties. The CFD techniques were developed in the late 20th century. Mimetic schemes are relatively new in the realm of CFD, although they have been applied to a wide range of Partial Differential equations (PDE) problems. Some attempts have been made to draw comparisons between Finite Volume Methods and Finite Element Methods along with other conventional CFD techniques but not much attention has been paid towards the comparison of the Mimetic Spectral Element Method (MSEM) with these most conventional techniques. Further analysis is required in order to make judgments regarding the effectiveness, stability and accuracy of MSEM against conventional methods.   

The purpose of this report is to present the findings and outcomes of 2D incompressible Navier-Stokes flow simulation techniques. Then, the comparison between the MSEM and conventional CFD will be made. The mass, energy, enstrophy and vorticity conserving (MEEVC) was chosen as a MSEM solver. MEEVC employs mixed finite element discretization which allows for the preservation of mass, energy, enstrophy and vorticity. The phyem package for Python created by Yi Zhang et al. is used to carry out MEEVC. Because a non-linear system needs to be solved, a Newton linearization is implemented. ANSYS Fluent represents the conventional CFD due to its built-in 2D solver. A coupled solver is selected as it solves for both pressure and velocity simultaneously compared to usually used segregated methods.

Four test cases were conducted using both software, and the results were compared with the literature for validation. They were selected in order to capture different flow conditions, including internal and external, steady and unsteady flows. The study validates both methods against the literature and analytical solutions. Then, a cross-case study is performed in order to answer the research questions.