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Licensed Unlicensed Requires Authentication Published by De Gruyter April 2, 2015

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

  • Nan Jiang EMAIL logo and Hoang Tran

Abstract

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 un+1+un-10) of CNLF is asymptotically stable. Numerical results are provided to verify the stability and the convergence of the methods.

Funding source: NSF

Award Identifier / Grant number: DMS 1216465

Funding source: AFOSR

Award Identifier / Grant number: FA 9550-12-1-0191

We would like to thank Professor William J. Layton for suggesting the problem and for his continuous support and guidance.

Received: 2015-1-24
Revised: 2015-3-4
Accepted: 2015-3-16
Published Online: 2015-4-2
Published in Print: 2015-7-1

© 2015 by De Gruyter

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