Open Access

ARTICLE

A Fully Discrete SCNFVE Formulation for the Non-stationary Navier-Stokes Equations

by Zhendong Luo¹, Fei Teng²

1 School of Mathematics and Physics, North China Electric Power University, Beijing 102206, China.
2 School of Mathematics Sciences, Kaili college, Kaili, 556011, China.

Computer Modeling in Engineering & Sciences 2014, 101(1), 33-58. https://doi.org/10.3970/cmes.2014.101.033

Abstract

A semi-discrete Crank-Nicolson (CN) formulation about time and a fully discrete stabilized CN finite volume element (SCNFVE) formulation based on two local Gauss integrals and parameter-free with the second-order time accuracy are established for the non-stationary Navier-Stokes equations. The error estimates of the semi-discrete and fully discrete SCNFVE solutions are derived. Some numerical experiments are presented to illustrate that the fully discrete SCNFVE formulation possesses more advantages than its stabilized finite volume element formulation with the first-order time accuracy, thus validating that the fully discrete SCNFVE formulation is feasible and efficient for finding the numerical solutions of the non-stationary Navier-Stokes equations.

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Keywords

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