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

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 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.

Authors:
 [1];  [2]
  1. Missouri Univ. of Science and Technology, Rolla, MO (United States)
  2. Oak Ridge National Lab. (ORNL), Oak Ridge, TN (United States)
Publication Date:
Research Org.:
Oak Ridge National Lab. (ORNL), Oak Ridge, TN (United States)
Sponsoring Org.:
USDOE
OSTI Identifier:
1335320
Grant/Contract Number:  
AC05-00OR22725
Resource Type:
Journal Article: Accepted Manuscript
Journal Name:
Computational Methods in Applied Mathematics
Additional Journal Information:
Journal Volume: 15; Journal Issue: 3; Journal ID: ISSN 1609-4840
Publisher:
de Gruyter
Country of Publication:
United States
Language:
English
Subject:
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

Citation Formats

Jiang, Nan, and Tran, Hoang A. Analysis of a Stabilized CNLF Method with Fast Slow Wave Splittings for Flow Problems. United States: N. p., 2015. Web. doi:10.1515/cmam-2015-0010.
Jiang, Nan, & Tran, Hoang A. Analysis of a Stabilized CNLF Method with Fast Slow Wave Splittings for Flow Problems. United States. doi:10.1515/cmam-2015-0010.
Jiang, Nan, and Tran, Hoang A. Wed . "Analysis of a Stabilized CNLF Method with Fast Slow Wave Splittings for Flow Problems". United States. doi:10.1515/cmam-2015-0010. https://www.osti.gov/servlets/purl/1335320.
@article{osti_1335320,
title = {Analysis of a Stabilized CNLF Method with Fast Slow Wave Splittings for Flow Problems},
author = {Jiang, Nan and Tran, Hoang A.},
abstractNote = {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.},
doi = {10.1515/cmam-2015-0010},
journal = {Computational Methods in Applied Mathematics},
number = 3,
volume = 15,
place = {United States},
year = {Wed Apr 01 00:00:00 EDT 2015},
month = {Wed Apr 01 00:00:00 EDT 2015}
}

Journal Article:
Free Publicly Available Full Text
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