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

Author

Nan Jiang, Missouri University of Science and TechnologyFollow
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 + u^n-1 ≡ 0) of CNLF is asymptotically stable. Numerical results are provided to verify the stability and the convergence of the methods.

Recommended Citation

N. Jiang and H. Tran, "Analysis of a Stabilized CNLF Method with Fast Slow Wave Splittings for Flow Problems," Computational Methods in Applied Mathematics, vol. 15, no. 3, pp. 307 - 330, Walter de Gruyter GmbH, Jul 2015.

The definitive version is available at https://doi.org/10.1515/cmam-2015-0010

Department(s)

Mathematics and Statistics

Keywords and Phrases

Convergence of numerical methods; Numerical methods; Stabilization; Asymptotically stable; CNLF; Crank-Nicolson; Geophysical flows; NSE; Numerical results; Slow wave; Unstable modes; Navier Stokes equations; Fast-Slow Wave Splitting

International Standard Serial Number (ISSN)

1609-4840; 1609-9389

Document Type

Article - Journal

Document Version

Citation

File Type

text

Language(s)

English

Rights

© 2015 Walter de Gruyter GmbH, All rights reserved.

Publication Date

01 Jul 2015