A New Higher Order Fractional-Step Method for the Incompressible Navier-Stokes Equations

A New Higher Order Fractional-Step Method for the Incompressible Navier-Stokes Equations

Year:    2020

Author:    Rong An, Can Zhou, Jian Su

Advances in Applied Mathematics and Mechanics, Vol. 12 (2020), Iss. 2 : pp. 362–385

Abstract

In this paper, we present a rigorous error analysis of a new higher order fractional-step scheme for approximation of the time-dependent Navier-Stokes equations. The main feature of the proposed scheme is twofold. First, it is a two-step scheme in which the incompressibility and nonlinearities are split. Second, this scheme is a linear scheme and is simple to implement. It is shown that the proposed scheme possesses the convergence rate $\mathcal O((\Delta t)^{3/2})$ in the discrete $l^2$(H$_0^1)\cap$ $l^\infty$(L$^2$)-norm for the end-of-step velocity. Two different numerical experiments are presented to confirm the theoretical analysis and the efficiency of the proposed scheme.

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Journal Article Details

Publisher Name:    Global Science Press

Language:    English

DOI:    https://doi.org/10.4208/aamm.OA-2018-0258

Advances in Applied Mathematics and Mechanics, Vol. 12 (2020), Iss. 2 : pp. 362–385

Published online:    2020-01

AMS Subject Headings:    Global Science Press

Copyright:    COPYRIGHT: © Global Science Press

Pages:    24

Keywords:    Incompressible Navier-Stokes equations fractional-step method Crank-Nicolson scheme temporal errors estimates.

Author Details

Rong An

Can Zhou

Jian Su