Commun. Comput. Phys.,
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Volume 3.


An Adaptive Moving Mesh Method for Two-Dimensional Incompressible Viscous Flows

Zhijun Tan 1, K. M. Lim 2, B. C. Khoo 3*

1 Singapore-MIT Alliance, 4 Engineering Drive 3, National University of Singapore, Singapore 117576, Singapore.
2 Department of Mechanical Engineering, National University of Singapore, 10 Kent Ridge Crescent, Singapore 119260, Singapore.
3 Singapore-MIT Alliance, 4 Engineering Drive 3, National University of Singapore, Singapore 117576, Singapore; and Department of Mechanical Engineering, National University of Singapore, 10 Kent Ridge Crescent, Singapore 119260, Singapore.

Received 26 January 2007; Accepted (in revised version) 22 July 2007
Available online 30 October 2007

Abstract

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. [{\em 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.

AMS subject classifications: 65M06, 65M50, 76D05

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Key words: Moving mesh method, finite volume method, Navier-Stokes equations, vorticity stream-function, incompressible flow.

*Corresponding author.
Email: smatz@nus.edu.sg (Z. Tan), limkm@nus.edu.sg (K. M. Lim), mpekbc@nus.edu.sg (B. C. Khoo)
 

The Global Science Journal