Analysis of a Stabilized CNLF Method with Fast Slow Wave Splittings for Flow Problems

In this work we study Crank-Nicolson Leap-Frog (CNLF) methods with fast slow wave splittings for Navier-Stokes equation plus a Coriolis force term, which is a simplification of geophysical flows. We present a new stabilized CNLF method where the added stabilization completely removes the method’s CFL time step condition. We give a comprehensive stability and error analysis. We prove that for Oseen equation + rotation term, the unstable mode (for which un+1 +un−1 ≡ 0) of CNLF is asymptotically stable. Numerical results are provided to verify the stability and the convergence of the methods.