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Title: Exponential Time Differencing Gauge Method for Incompressible Viscous Flows

Abstract

Abstract In this paper, we study an exponential time differencing method for solving the gauge system of incompressible viscous flows governed by Stokes or Navier-Stokes equations. The momentum equation is decoupled from the kinematic equation at a discrete level and is then solved by exponential time stepping multistep schemes in our approach. We analyze the stability of the proposed method and rigorously prove that the first order exponential time differencing scheme is unconditionally stable for the Stokes problem. We also present a compact representation of the algorithm for problems on rectangular domains, which makes FFT-based solvers available for the resulting fully discretized system. Various numerical experiments in two and three dimensional spaces are carried out to demonstrate the accuracy and stability of the proposed method.

Authors:
;
Publication Date:
Research Org.:
Univ. of South Carolina, Columbia, SC (United States)
Sponsoring Org.:
USDOE Office of Science (SC)
OSTI Identifier:
1537204
DOE Contract Number:  
SC0008087; SC0016540
Resource Type:
Journal Article
Journal Name:
Communications in Computational Physics
Additional Journal Information:
Journal Volume: 22; Journal Issue: 2; Journal ID: ISSN 1815-2406
Publisher:
Global Science Press
Country of Publication:
United States
Language:
English
Subject:
Physics

Citation Formats

Ju, Lili, and Wang, Zhu. Exponential Time Differencing Gauge Method for Incompressible Viscous Flows. United States: N. p., 2017. Web. doi:10.4208/cicp.oa-2016-0234.
Ju, Lili, & Wang, Zhu. Exponential Time Differencing Gauge Method for Incompressible Viscous Flows. United States. doi:10.4208/cicp.oa-2016-0234.
Ju, Lili, and Wang, Zhu. Wed . "Exponential Time Differencing Gauge Method for Incompressible Viscous Flows". United States. doi:10.4208/cicp.oa-2016-0234.
@article{osti_1537204,
title = {Exponential Time Differencing Gauge Method for Incompressible Viscous Flows},
author = {Ju, Lili and Wang, Zhu},
abstractNote = {Abstract In this paper, we study an exponential time differencing method for solving the gauge system of incompressible viscous flows governed by Stokes or Navier-Stokes equations. The momentum equation is decoupled from the kinematic equation at a discrete level and is then solved by exponential time stepping multistep schemes in our approach. We analyze the stability of the proposed method and rigorously prove that the first order exponential time differencing scheme is unconditionally stable for the Stokes problem. We also present a compact representation of the algorithm for problems on rectangular domains, which makes FFT-based solvers available for the resulting fully discretized system. Various numerical experiments in two and three dimensional spaces are carried out to demonstrate the accuracy and stability of the proposed method.},
doi = {10.4208/cicp.oa-2016-0234},
journal = {Communications in Computational Physics},
issn = {1815-2406},
number = 2,
volume = 22,
place = {United States},
year = {2017},
month = {6}
}