算子分裂法求解旋转坐标系下不可压黏性流动

提出了求解旋转坐标系下的不可压黏性流动问题的θ格式算子分裂算法．通过算子分裂，把不可压缩性、非线性和哥氏力占优三大耦合困难分割开来．采用亚网格尺度稳定化方法消除了Galerkin方法求解时由于不可压缩性和哥氏力占优所引发的数值振荡．结合最小二乘和共轭梯度法间接求解非线性子问题，排除了强对流作用所引发的数值振荡，避免了引入迎风格式离散对流项的必要性．同时该算法保证了迭代过程中有限元总刚度矩阵正定不变的特性，为求解线性方程组采用高效的求解器提供了可能．数值试验表明，该算法具有稳定性好、收敛速度快、计算精度高的特点．

Operator Splitting Methods for Solution of Incompressible Viscous Flows in a Rotating Frame

An operator splitting method was developed to solve the incompressible Navier-Stokes equations defined in a rotating frame of reference. Based on the operator splitting, this method provides an efficient way to decouple the three main difficulties of the problem, the incompressibility, the nonlinearity and the numerical oscillations due to the presence of the dominated Coriolis forces. The sub-grid scale stabilized method was used to eliminate the oscillations caused by incompressibility and dominated Coriolis forces when Galerkin method was employed. Leastsquares conjugate gradient algorithms were applied to solve for the nonlinear instability, which avoids the necessity of introducing the upwind scheme to discrete the convective term. Compared with other numerical methods, the present method ensures the resulting coefficient matrices to be positive definite and invariable, which can be efficiently stored and solved. Several numerical examples indicate that the method displays improved stability, fast convergence and high accuracy.