Open Access

ARTICLE

An Adaptive Discretization of Incompressible Flow using Node-Based Local Meshes

Weiwei Zhang¹, Yufeng Nie¹, Li Cai¹, Nan Qi²

1 Department of Applied Mathematics, School of Science, Northwestern Polytechnical University, Xi’an 710129, PR China. E-mail: yfnie@nwpu.edu.cn
2 School of Mathematics and Statistics, University of Glasgow, Glasgow G12 8QW, UK.

Computer Modeling in Engineering & Sciences 2014, 102(1), 55-82. https://doi.org/10.3970/cmes.2014.102.055

Abstract

In this paper, we derive an adaptive mesh generation method for discretizing the incompressible flow using node-based local grids. The flow problem is described by the Stokes equations which are solved by a stabilized low-order P1-P1 (linear velocity, linear pressure) mixed finite element method. The proposed node-based adaptive mesh generation method consists of four components: mesh size modification, a node placement procedure, a node-based local mesh generation strategy and an error estimation technique, which are combined so as to guarantee obtaining a conforming refined/coarsened mesh. The nodes are considered as particles with interaction forces, which are generated by dynamic simulation according to Newton’s second law of motion. Then the successive meshes in adaptive procedure are obtained by using Bubble-type Local Mesh Generation (BLMG) method. At each refinement level, the refining and coarsening are archived simultaneously by appropriately modifying the mesh size function, such that the resulting meshes can be refined in regions where the errors are relatively large and coarsened in regions where the errors are relatively small. Numerical results show that the nodebased adaptive strategy is applicable and efficient to approximate the true solution and detect local singularities in the flow problems.

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Keywords

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