A reduced-order SMFVE extrapolation algorithm based on POD technique and CN method for the non-stationary Navier-Stokes equations

Zhendong Luo

doi:10.3934/dcdsb.2015.20.1189

Article Contents

2015, Volume 20, Issue 4: 1189-1212. Doi: 10.3934/dcdsb.2015.20.1189

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A reduced-order SMFVE extrapolation algorithm based on POD technique and CN method for the non-stationary Navier-Stokes equations

Zhendong Luo^1,

1.
School of Mathematics and Physics, North China Electric Power University, Beijing, 102206

Received: September 30, 2012

Revised: June 30, 2014

Published: May 2015

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Abstract

In this article, we employ proper orthogonal decomposition (POD) technique to establish a POD-based reduced-order stabilized mixed finite volume element (SMFVE) extrapolation algorithm based on two local Gaussian integrals, parameter-free, and Crank-Nicolson (CN) method with fewer degrees of freedom for the non-stationary Navier-Stokes equations. The error estimates between the POD-based reduced-order SMFVE solutions and the classical SMFVE solutions and the implementation for the POD-based reduced-order SMFVE extrapolation algorithm are provided. A numerical example is used to illustrate that the numerical results are consistent with theoretical conclusions. Moreover, it is shown that the POD-based reduced-order SMFVE extrapolation algorithm is feasible and efficient for finding numerical solutions for the non-stationary Navier-Stokes equations.

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Mathematics Subject Classification: Primary: 65M08, 65N08; Secondary: 65N30.

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