Low Complexity, Time Accurate, Model Accurate Algorithms in Computational Fluid Dynamics

Computational fluid dynamics is an essential research area that is of crucial importance in comprehending of fluid flows in mechanical and hydrodynamic processes. Accurate, efficient and reliable simulation of flows occupies a central place in the development of computational science. In this work, we explore various numerical methods and utilize them to improve flow predication. Four research projects are conducted and show evidence in enhancement of accuracy, efficiency and reliability of prediction of fluid motion. We first propose a low computationally complex, stable and adaptive method for time accurate approximation of the evolutionary stokes Darcy system and Navier-Stokes equations. The improved method post-processes the solutions of the Backward Euler scheme by adding no more than three lines to an existing program. Time accuracy is increased from first to second order and the overdamping of the Backward Euler method is removed. The second project is to develop an efficient method to describe magnetohydrodynamic flows at low magnetic Reynolds numbers. The decoupled method is based on the artificial compression and partitioned schemes. Computational efficiency is greatly improved because we only need to solve linear problems at each time step with systems decouple by physical processes. Last but not least, we introduce a way to correct the Baldwin-Lomax model for non-equilibrium turbulence, which is often considered impossible to simulate due to backscatter. The corrected Baldwin-Lomax model not only shows that effects of fluctuations on means are dissipative on time average but also can have bursts for which energy flow reverses. For each project, we present comprehensive error and stability analysis and provide different numerical experiments to further support theoretical theories.