Volume 11, Issue 6
Runge-Kutta Finite Element Method Based on the Characteristic for the Incompressible Navier-Stokes Equations

Adv. Appl. Math. Mech., 11 (2019), pp. 1415-1435.

Published online: 2019-09

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• 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.

65M12, 76D05

yan.zhang@hhu.edu.cn (Yan Zhang)

chenda@hhu.edu.cn (Da Chen)

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@Article{AAMM-11-1415, author = {Liao , ShaokaiZhang , Yan and Chen , Da}, title = {Runge-Kutta Finite Element Method Based on the Characteristic for the Incompressible Navier-Stokes Equations}, journal = {Advances in Applied Mathematics and Mechanics}, year = {2019}, volume = {11}, number = {6}, pages = {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.

}, issn = {2075-1354}, doi = {https://doi.org/10.4208/aamm.OA-2018-0150}, url = {http://global-sci.org/intro/article_detail/aamm/13310.html} }
TY - JOUR T1 - Runge-Kutta Finite Element Method Based on the Characteristic for the Incompressible Navier-Stokes Equations AU - Liao , Shaokai AU - Zhang , Yan AU - Chen , Da JO - Advances in Applied Mathematics and Mechanics VL - 6 SP - 1415 EP - 1435 PY - 2019 DA - 2019/09 SN - 11 DO - http://doi.org/10.4208/aamm.OA-2018-0150 UR - https://global-sci.org/intro/article_detail/aamm/13310.html KW - Finite element method, characteristic, Navier-Stokes equations, Runge-Kutta method, accuracy. AB -

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.

Shaokai Liao, Yan Zhang & Da Chen. (2019). Runge-Kutta Finite Element Method Based on the Characteristic for the Incompressible Navier-Stokes Equations. Advances in Applied Mathematics and Mechanics. 11 (6). 1415-1435. doi:10.4208/aamm.OA-2018-0150
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