最小二乘有限元法的湍流大涡模拟及其并行计算

The Least-squares Finite Element Method (LSFEM) has a broad application prospect in fluid computation. Compared to the Finite Volume Method,it has been proved to be a good convergence,well universal and can easy to obtain high-order accuracy.Therefore,based on the theoretical frame of LSFEM and the method of Large Eddy Simulation (LES), programme of LSFEM is developed and improved to carry out all kinds of fluid problems which include laminar flow and turbulent flow. The Graphics Processing Unit (GPU) parallel method which has occurred for several years is applied to carry out the LES of turbulent flow using LSFEM on GPU so that the problem of long computational time generated by itself huge computational work in the turbulent simulation can be solved. Message Passing Interface (MPI) parallel techniques is applied and parallel calculation on different GPUs is done to solve all complex fluid problems quickly and accurately. A new direction is put forward to forcast the problems of unsteady flow and aerodynamic noise in the engineering application.

最小二乘有限元法（Least-squares Finite Element Method,LSFEM）在流体计算中具有广阔的应用前景。与有限体积法相比，它具有收敛性好、通用性强，且易于获得高阶精度等优点。为此，本项目基于LSFEM的理论框架和大涡模拟方法，开发和完善LSFEM程序，实现利用LSFEM求解层流和湍流等各种流体计算问题。应用近年来新出现的GPU并行加速方法，实现单GPU平台下的LSFEM的大涡模拟计算，解决湍流计算中，自身计算量大所导致的计算时间长的问题。利用信息传输界面（Message Passing Interface, MPI）技术，开展多GPU平台之间的并行计算，使之能够快速、准确求解各类复杂的流体问题。为精确、高效预测工程中各类非定常流动和气动噪声问题提供新的方向。

最小二乘有限元法具有较好的收敛性和鲁棒性，较强的通用性和较高的精度，在计算流体力学有着广泛的应用前景。本项目基于C++开发了基于最小二乘有限元法的层流流动计算程序，并使之能应用到各类网格中。发展了应力形式的最小二乘有限元解法，并采用后台阶流、圆柱绕流和方腔流进行了验证，获得了比现有FLUENT软件更为准确的结果。引入大涡模拟方法，对滤波后的控制方程和亚格子应力项进行了处理，得到可用于湍流计算的大涡模拟计算程序。方腔流计算结果和实验结果一致性表明大涡模拟程序的正确性。针对最小二乘有限元法计算量大，计算速度慢的特点，开发了单GPU和双GPU程序。单GPU获得约70倍的加速，双GPU获得近95倍的加速，有效提升最小二乘有限元法的计算效率。通过本项目研究可为最小二乘有限元法在湍流计算推广和应用提供依据。