三维非定常不可压N-S方程一个高精度求解格式

对三维、非定常、不可压Navier-Stokes方程提出了一种新的数值计算方法.在时间离散上应用3阶精度混合显-隐相结合的分裂格式,空间离散在x及y轴向采用非等间距网格的紧致有限差分格式与z向应用Fourier谱展开相杂交的数值方法逼近.经平板边界层流的验证表明,该算法具有计算精度高、稳定性好、收敛速度快等特点.同时也研究了三维、非定常流体运动下游边界问题,提出了无反射出流边界条件,以减少在有限计算区域内人工出流边界反射引起的数值误差,保证直接数值模拟的精度和准确性.该算法的提出对于求解边界层、射流及混合层等流动中的转捩与演化问题具有重要的理论意义.

A high accuracy scheme for 3-D unsteady incompressible N-S equations

A new method is worked out for numerical simulation of 3-D unsteady incompressible N-S equations.For time discretization,the third-order accuracy explicit-implicit mixed fraction scheme is employed.For spatial discretization,the compact finite difference schemes on non-uniform meshes in x and y direction are adopted with Fourier spectral expansion for numerical approximation in z direction,the spanwise direction.Numerical results of flat plate boundary laminar flow show that the present method is of high accuracy,stability and rate of convergency.Meanwhile,the downstream boundary problem for 3-D unsteady flow is studied,and a non-reflecting outflow boundary condition is put forward.The algorithm reduces the error induced by reflection from artificial outflow boundary in the limited computational region,and ensures the accuracy of direct numerical simulation.It also has important significance for numerical simulation of disturbance evolution and turbulence transition in boundary layers,jets,mixed layers,etc.