多组分混合流体的大规模高效并行迭代算法研究

Multi-component flow is a common physical phenomenon that exists in nature, and numerical simulation techniques related to this are applied widely in the engineering industry and researches. However, with the increasing of complexity, conventional numerical simulation methods suffer from the low convergence speed, poor stability and robustness. Because of the nonlinearity of this problem, product-type iteration methods like GPBiCG and BiCGSTAB are required. These methods occupy so much memory and computational time that they are difficult to be applied to large scale simulations. In order to improve the computational speed and resolution, an improved characteristic curve method to approximate the path of flow particles is employed to handle the nonlinear convection term in Navier-Stokes equations. The stiffness matrix is symmetric; therefore high-efficiency preconditioned iteration methods can be used, and memory usage will be greatly reduced. . This research is based on the Hierarchical Domain Decomposition Method. The Balancing Domain Decomposition preconditioning technique is utilized to accelerate the convergence of interface problem, and the interior problem is solved directly by backward substitution. By present study, a high-efficiency parallel solver for large scale multi-component flows will be developed, and numerical simulations with up to 100 million degrees of freedom can be solved by normal PC clusters. In addition, more theoretical evidences can be provided for real world engineering applications.

多组分混合流动问题在自然界中广泛存在的一种物理现象，与之相关的数值模拟技术在工程中广泛应用。随着研究问题的复杂化，传统数值模拟技术的求解速度、收敛性和健壮性都受到了挑战。究其原因，是涉及的问题为非线性，采用GPBiCG或BiCGSTAB之类的迭代算法内存占用量高、稳定性差，很难被应用于大规模仿真计算。为了提高对其数值模拟的求解速度和分辨率，本研究中拟通过优化的特征曲线法追踪流体粒子的运动路径，来处理NS方程中的非线性项。该方法还可以保持刚度矩阵的对称性，从而可以使用高效的预条件迭代算法对其进行求解，内存消耗量也大幅消减。. 本研究基于分级区域分解法，采用平衡区域分解预条件技术加速求解表面自由度问题，内部自由度则通过代换法直接求出。通过本项目的研究，将实现大规模多组分混合流动问题的高速并行求解，预期可以在普通PC集群上进行上亿自由度规模的数值，为工程中的实际问题提供更详尽的理论依据。

本研究基于分级区域分解法，采用平衡区域分解预条件技术加速求解表面自由度问题，内部自由度则通过代换法直接求出。通过本项目的研究，实现了大规模多组分混合流动问题的高速并行求解，在普通PC集群上进行上亿自由度规模的数值，为工程中的实际问题提供更详尽的理论依据。