Commun. Comput. Phys., 9 (2011), pp. 68-88.

Quadrilateral Cell-Based Anisotropic Adaptive Solution for the Euler Equations

H. W. Zheng 1, N. Qin 1*, F. C. G. A. Nicolleau 1, C. Shu 2

1 Department of Mechanical Engineering, University of Sheffield, Mappin Street, Sheffield S1 3JD, UK.
2 Department of Mechanical Engineering, National University of Singapore, 10 Kent Ridge Crescent, Singapore 119260.

Received 10 October 2009; Accepted (in revised version) 12 February 2010
Available online 5 August 2010


An anisotropic solution adaptive method based on unstructured quadrilateral meshes for inviscid compressible flows is proposed. The data structure, the directional refinement and coarsening, including the method for initializing the refined new cells, for the anisotropic adaptive method are described. It provides efficient high resolution of flow features, which are aligned with the original quadrilateral mesh structures. Five different cases are provided to show that it could be used to resolve the anisotropic flow features and be applied to model the complex geometry as well as to keep a relative high order of accuracy on an efficient anisotropic mesh.

AMS subject classifications: 51E12, 65M08, 68U05, 68U20

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Key words: Anisotropic adaptive mesh refinement, quadrilateral mesh, finite volume, face-based algorithm, HLLC, Euler equation.

*Corresponding author.
Email: (H. W. Zheng), (N. Qin), (F. C. G. A. Nicolleau), (C. Shu)

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