Large eddy simulation of turbulent transport processes by a Least squares finite element method.

摘要

The Least-squares finite element method (LSFEM) based on the formulation of first-order partial differential equations has been successfully used in the studies of three-dimensional low Reynolds number flows and transport processes. It is important to apply this method to turbulent flows and transport processes at high Reynolds number because they are common in nature and engineering.;In this dissertation, we first study different first-order formulations and alternative forms used in the LSFEM. Our numerical results show that formulations have significant effects on the convergence rate of the iteration solver of the resulting linear systems. It is found that the three-dimensional velocity-stress-pressure formulation leads to faster convergence rate although it is not commonly used in engineering applications. We have successfully applied this formulation to the LES of turbulent channel flows, the recirculating flows in a lid-driven cavity, and thermal turbulent flows. The numerical results are compared with those of direct numerical simulation and experiments. The comparison validates the approach of combining LSFEM and LES.;In addition, domain-decomposition with message-passing technique is used to develop parallel LSFEM algorithm. The results indicate that the algorithm is efficient and has potentials to simulate large scale fluid flows and transport processes.;Large eddy simulation (LES) is one of the three main numerical approaches for turbulent flows. The dynamical subgrid scale models make it possible to use the LES for more complex flows. For the first time, we develop and apply the LSFEM to carry out LES of turbulent flows and transport processes.