一种包含运动边界的高精度流场数值计算方法

为了准确快速地模拟运动边界的流场，提出一种反馈力源形式的包含运动边界的非定常流场数值计算方法。该方法采用完全正交的网格，以反馈力源作用点的运动来模拟边界的运动。采用物理量及其各阶导数在边界两侧的突跃修正中心差分格式，使之达到二阶精度，以此离散求解二维不可压Navier-Stokes方程。并且提出了与运动边界相适应的反馈力源构造方法及对边界上速度进行插值的方法。基于此数值计算方法，对低雷诺数的圆柱绕流、静止流体中的振荡圆柱以及昆虫振翅运动的二维非定常流场进行了数值计算，计算结果与以往的数值及实验结果非常吻合，表明本文方法与Peskin的浸入式边界方法在处理运动边界问题时具有同样的高效率，且精度高于浸入式边界方法。

A Numerical Method for Simulating Flow Involving Moving Boundaries with High Order Accuracy

To simulate a flow involving moving boundaries accurately and efficiently, this paper presents a numerical method for the simulation of moving boundary problems with a feedback force which is used to represent the effects of rigid boundaries. The method uses the movements of feedback forces to represent moving boundaries on a cartesian grid. The central difference scheme is corrected by incorporating the jump conditions of velocities and pressure to achieve second-order accuracy and the incompressible Navier-Stokes equation is solved. In addition, suitable methods for the construction of feedback forces and velocity interpolation on the boundaries are presented. Using this method, the paper simulated a flow passing a stationary cylinder and the flows subjected to an oscillating cylinder and a flapping insect wing at low Reynolds numbers. The results are consistent with previous numerical and experimental work. They show that the method is as efficient as Peskin's immersed boundary method when dealing with moving boundaries, but it achieves a higher-order of accuracy.