TY - JOUR T1 - An Adaptive Moving Mesh Method for Two-Dimensional Incompressible Viscous Flows AU - Zhijun Tan, K. M. Lim & B. C. Khoo JO - Communications in Computational Physics VL - 3 SP - 679 EP - 703 PY - 2008 DA - 2008/03 SN - 3 DO - http://doi.org/ UR - https://global-sci.org/intro/article_detail/cicp/7870.html KW - AB -

In this paper, we present an adaptive moving mesh technique for solving the incompressible viscous flows using the vorticity stream-function formulation. The moving mesh strategy is based on the approach proposed by Li et al. [J. Comput. Phys., 170 (2001), pp. 562–588] to separate the mesh-moving and evolving PDE at each time step. The Navier-Stokes equations are solved in the vorticity stream-function form by a finite-volume method in space, and the mesh-moving part is realized by solving the Euler-Lagrange equations to minimize a certain variation in conjunction with a more sophisticated monitor function. A conservative interpolation is used to redistribute the numerical solutions on the new meshes. This paper discusses the implementation of the periodic boundary conditions, where the physical domain is allowed to deform with time while the computational domain remains fixed and regular throughout. Numerical results demonstrate the accuracy and effectiveness of the proposed algorithm.