Runge-Kutta Finite Element Method Based on the Characteristic for the Incompressible Navier-Stokes Equations
Year: 2019
Author: Shaokai Liao, Yan Zhang, Da Chen
Advances in Applied Mathematics and Mechanics, Vol. 11 (2019), Iss. 6 : pp. 1415–1435
Abstract
In this paper, a finite element method based on the characteristic for the incompressible Navier-Stokes equations is proposed by introducing Runge-Kutta method. At first, coordinate transformation operation is performed to obtain the alternative Navier-Stokes equations without convection term. Then, instead of the classical characteristic-based split (CBS) method, we use the third-order Runge-Kutta method along the characteristic to carry out time discretization in order to improve calculation accuracy, and segregate the calculation of the pressure from that of the velocity based on the momentum-pressure Poisson equation method. Finally, some classical benchmark problems are used to validate the effectiveness of the present method. Compared with the classical method, the present method has lower dissipation, larger permissible time step, and higher time accuracy. The code can be downloaded at DOI: 10.13140/RG.2.2.36336.56329.
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Journal Article Details
Publisher Name: Global Science Press
Language: English
DOI: https://doi.org/10.4208/aamm.OA-2018-0150
Advances in Applied Mathematics and Mechanics, Vol. 11 (2019), Iss. 6 : pp. 1415–1435
Published online: 2019-01
AMS Subject Headings: Global Science Press
Copyright: COPYRIGHT: © Global Science Press
Pages: 21
Keywords: Finite element method characteristic Navier-Stokes equations Runge-Kutta method accuracy.