TY - JOUR
T1 - Moving Mesh Finite Element Methods for the Incompressible Navier--Stokes Equations
AU - Di, Yana
AU - Li, Ruo
AU - Tang, Tao
AU - Zhang, Pingwen
N1 - Funding information:
School of Mathematical Sciences, Peking University, 100871, Beijing, People’s Republic of China ([email protected], [email protected], [email protected]). The research of the first and second authors was supported in part by the Joint Applied Mathematics Research Institute between Peking University and Hong Kong Baptist University. The research of the fourth author was supported in part by the special funds for Major State Research Projects and National Science Foundation of China for Distinguished Young Scholars.
Department of Mathematics, Hong Kong Baptist University, Kowloon Tong, Kowloon, Hong Kong ([email protected]). The research of this author was supported in part by the Hong Kong Research Grants Council and the International Research Team on Complex System of Chinese Academy of Sciences.
Publisher copyright:
Copyright © 2005 Society for Industrial and Applied Mathematics
PY - 2005/5
Y1 - 2005/5
N2 - This work presents the first effort in designing a moving mesh algorithm to solve the incompressible Navier--Stokes equations in the primitive variables formulation. The main difficulty in developing this moving mesh scheme is how to keep it divergence-free for the velocity field at each time level. The proposed numerical scheme extends a recent moving grid method based on harmonic mapping [R. Li, T. Tang, and P. W. Zhang, J. Comput. Phys., 170 (2001), pp. 562--588], which decouples the PDE solver and the mesh-moving algorithm. This approach requires interpolating the solution on the newly generated mesh. Designing a divergence-free-preserving interpolation algorithm is the first goal of this work. Selecting suitable monitor functions is important and is found challenging for the incompressible flow simulations, which is the second goal of this study. The performance of the moving mesh scheme is tested on the standard periodic double shear layer problem. No spurious vorticity patterns appear when even fairly coarse grids are used.
AB - This work presents the first effort in designing a moving mesh algorithm to solve the incompressible Navier--Stokes equations in the primitive variables formulation. The main difficulty in developing this moving mesh scheme is how to keep it divergence-free for the velocity field at each time level. The proposed numerical scheme extends a recent moving grid method based on harmonic mapping [R. Li, T. Tang, and P. W. Zhang, J. Comput. Phys., 170 (2001), pp. 562--588], which decouples the PDE solver and the mesh-moving algorithm. This approach requires interpolating the solution on the newly generated mesh. Designing a divergence-free-preserving interpolation algorithm is the first goal of this work. Selecting suitable monitor functions is important and is found challenging for the incompressible flow simulations, which is the second goal of this study. The performance of the moving mesh scheme is tested on the standard periodic double shear layer problem. No spurious vorticity patterns appear when even fairly coarse grids are used.
KW - Divergence-free-preserving interpolation
KW - Incompressible flow
KW - Moving mesh method
KW - Navier--Stokes equations
UR - http://www.scopus.com/inward/record.url?scp=19744364449&partnerID=8YFLogxK
U2 - 10.1137/030600643
DO - 10.1137/030600643
M3 - Journal article
AN - SCOPUS:19744364449
SN - 1064-8275
VL - 26
SP - 1036
EP - 1056
JO - SIAM Journal on Scientific Computing
JF - SIAM Journal on Scientific Computing
IS - 3
ER -