TY - JOUR
T1 - A practical finite difference scheme for the Navier–Stokes equation on curved surfaces in R3
AU - Yang, Junxiang
AU - Li, Yibao
AU - Kim, Junseok
N1 - Funding Information:
J. Yang is supported by China Scholarship Council ( 201908260060 ). Y.B. Li is supported by National Natural Science Foundation of China (No. 11601416 , No. 11631012 ). The corresponding author (J.S. Kim) was supported by Basic Science Research Program through the National Research Foundation of Korea (NRF) funded by the Ministry of Education ( NRF-2019R1A2C1003053 ). The authors greatly appreciate the reviewers for their constructive comments and suggestions, which have improved the quality of this paper.
Publisher Copyright:
© 2020 Elsevier Inc.
PY - 2020/6/15
Y1 - 2020/6/15
N2 - We present a practical finite difference scheme for the incompressible Navier–Stokes equation on curved surfaces in three-dimensional space. In the proposed method, the curved surface is embedded in a narrow band domain and the governing equation is extended to the narrow band domain. We use the standard seven-point stencil for the Laplace operator instead of a discrete Laplacian–Beltrami operator by using the closet point method and pseudo-Neumann boundary condition. The well-known projection method is used to solve the incompressible Navier–Stokes equation in the narrow band domain. To make the velocity field be parallel to the surface, a velocity correction step is used. Various numerical experiments, such as the divergence-free test, the convergence rate, and the energy dissipation, are performed on curved surfaces, which demonstrated that our proposed method is robust and practical.
AB - We present a practical finite difference scheme for the incompressible Navier–Stokes equation on curved surfaces in three-dimensional space. In the proposed method, the curved surface is embedded in a narrow band domain and the governing equation is extended to the narrow band domain. We use the standard seven-point stencil for the Laplace operator instead of a discrete Laplacian–Beltrami operator by using the closet point method and pseudo-Neumann boundary condition. The well-known projection method is used to solve the incompressible Navier–Stokes equation in the narrow band domain. To make the velocity field be parallel to the surface, a velocity correction step is used. Various numerical experiments, such as the divergence-free test, the convergence rate, and the energy dissipation, are performed on curved surfaces, which demonstrated that our proposed method is robust and practical.
KW - Closest-point method
KW - Curved surfaces
KW - Incompressible Navier–Stokes equation
KW - Narrow band domain
KW - Projection method
UR - http://www.scopus.com/inward/record.url?scp=85081980450&partnerID=8YFLogxK
U2 - 10.1016/j.jcp.2020.109403
DO - 10.1016/j.jcp.2020.109403
M3 - Article
AN - SCOPUS:85081980450
VL - 411
JO - Journal of Computational Physics
JF - Journal of Computational Physics
SN - 0021-9991
M1 - 109403
ER -