二维可压缩流体力学Lagrange有限点方法

Lagrangian Finite Point Method for Two-dimensional Compressible Flows

提出二维可压缩流体力学问题的拉格朗日有限点方法,将求解区域离散为适当的点集.在每个时间步,每个离散点与其周围适当的五个邻点组成一个基本计算单元.在每个计算单元上,利用有限点方法中的典型微分算子的五点近似公式直接离散流体力学方程中的微分算子,并在每个方程中加上一个人为拉普拉斯粘性项,达到稳定格式的目的.给出时间步长的自动选取算法.数值算例结果验证了算法的有效性,初步展示了其计算大变形流体问题的良好发展潜力.

A Lagrangian finite point method for two-dimensional compressible hydrodynamics problems is presented.The numerical scheme is based on scattered points inside a computational domain without need for a specific connectivity.A cloud of five neighbors is selected around each point at each time step,and this cloud is used to implement finite point schemes based on five-point approximation formulas to gather information about flow derivatives.For numerical stability concerns,four artificial Laplace operators are introduced and added to corresponding conservative equations,respectively.Furthermore,an adaptive strategy for time step is also provided.Numerical results show validity and potential interest on this approach.