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. Least-squares 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.