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

Journal Article · Wed Apr 01 00:00:00 EDT 2015 · Computational Methods in Applied Mathematics

DOI:https://doi.org/10.1515/cmam-2015-0010· OSTI ID:1335320

Jiang, Nan ^[1]; Tran, Hoang A. ^[2]

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1. Missouri Univ. of Science and Technology, Rolla, MO (United States)
2. Oak Ridge National Lab. (ORNL), Oak Ridge, TN (United States)

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.

• Research Organization: Oak Ridge National Lab. (ORNL), Oak Ridge, TN (United States)
• Sponsoring Organization: USDOE
• Grant/Contract Number: AC05-00OR22725
• OSTI ID: 1335320
• Journal Information: Computational Methods in Applied Mathematics, Vol. 15, Issue 3; ISSN 1609-4840
• Publisher: de Gruyter
• Country of Publication: United States
• Language: English

Related Subjects

97 MATHEMATICS AND COMPUTING
CNLF
NSE
Stabilization
Fast-Slow Wave Splitting
NAVIER-STOKES EQUATIONS
TIME DISCRETIZATION
EVOLUTION-EQUATIONS
NUMERICAL-ANALYSIS
APPROXIMATION
REGULARIZATION
IMPLICIT
EXPLICIT
FILTER