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

by Nan Jiang, Hoang A Tran
Publication Type
Journal
Journal Name
Computational Methods in Applied Mathematics
Publication Date
Page Numbers
307 to 330
Volume
15
Issue
3

In this work, we study Crank-Nicolson leap-frog (CNLF) methods with fast-slow wave splittings for Navier-Stokes equations (NSE) with a rotation/Coriolis force term, which is a simplification of geophysical flows. We propose a new stabilized CNLF method where the added stabilization completely removes the method's CFL time step condition. A comprehensive stability and error analysis is given. We also prove that for Oseen equations with the rotation term, the unstable mode (for which u(n+1) + u(n-1) equivalent to 0) of CNLF is asymptotically stable. Numerical results are provided to verify the stability and the convergence of the methods.