An Adaptive Moving Mesh Method for Two-Dimensional Incompressible Viscous Flows (Communications in Computational Physics, 2008)
In this paper, we present an adaptive moving mesh technique for solvingthe incompressible viscous flows using the vorticity stream-function formulation. Themoving 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 timestep. The Navier-Stokes equations are solved in the vorticity stream-function form bya finite-volume method in space, and the mesh-moving part is realized by solving theEuler-Lagrange equations to minimize a certain variation in conjunction with a moresophisticated monitor function. A conservative interpolation is used to redistributethe numerical solutions on the new meshes. This paper discusses the implementationof the periodic boundary conditions, where the physical domain is allowed to deformwith time while the computational domain remains fixed and regular throughout. Numerical results demonstrate the accuracy and effectiveness of the proposed algorithm.