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Exponential Time Differencing Gauge Method for Incompressible Viscous Flows

Part of: Computer aspects of numerical algorithms Partial differential equations, initial value and time-dependent initial-boundary value problems Incompressible viscous fluids

Published online by Cambridge University Press:  21 June 2017

Lili Ju  and
Zhu Wang
Lili Ju*
Affiliation:
Department of Mathematics, University of South Carolina, Columbia, SC 29208, USA
Zhu Wang*
Affiliation:
Department of Mathematics, University of South Carolina, Columbia, SC 29208, USA
*
*Corresponding author. Email addresses:ju@math.sc.edu (L. Ju), wangzhu@math.sc.edu (Z.Wang)
*Corresponding author. Email addresses:ju@math.sc.edu (L. Ju), wangzhu@math.sc.edu (Z.Wang)
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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.

Keywords

Incompressible flowsStokes equationsNavier-Stokes equationsgauge methodexponential time differencing

MSC classification

Secondary: 65M06: Finite difference methods 65M22: Solution of discretized equations 65Y20: Complexity and performance of numerical algorithms 76D05: Navier-Stokes equations 76D07: Stokes and related (Oseen, etc.) flows

Information

Type
Research Article
Information
Communications in Computational Physics , Volume 22 , Issue 2 , August 2017 , pp. 517 - 541
Copyright
Copyright © Global-Science Press 2017 

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