An isotropic unstructured mesh generation method based on a fluid relaxation analogy

In this paper, we propose an unstructured mesh generation method based on Lagrangian-particle fluid relaxation, imposing a global optimization strategy. With the presumption that the geometry can be described as a zero level set, an adaptive isotropic mesh is generated by three steps. First, three c...

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Bibliographic Details
Published in:Computer methods in applied mechanics and engineering 2019-06, Vol.350, p.396-431
Main Authors: Fu, Lin, Han, Luhui, Hu, Xiangyu Y., Adams, Nikolaus A.
Format: Article
Language:English
Subjects:
Boundary conditions
Computational fluid dynamics
Delaunay triangulation
Finite element method
Fluid flow
Global optimization
Isotropy
Level-set
Mathematical models
Mesh generation
Particle density (concentration)
Smooth particle hydrodynamics
Smoothing
Smoothness
SPH
Unstructured mesh
Voronoi diagram
Voronoi graphs
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Summary:In this paper, we propose an unstructured mesh generation method based on Lagrangian-particle fluid relaxation, imposing a global optimization strategy. With the presumption that the geometry can be described as a zero level set, an adaptive isotropic mesh is generated by three steps. First, three characteristic fields based on three modeling equations are computed to define the target mesh-vertex distribution, i.e. target feature-size function and density function. The modeling solutions are computed on a multi-resolution Cartesian background mesh. Second, with a target particle density and a local smoothing-length interpolated from the target field on the background mesh, a set of physically-motivated model equations is developed and solved by an adaptive-smoothing-length Smoothed Particle Hydrodynamics (SPH) method. The relaxed particle distribution conforms well with the target functions while maintaining isotropy and smoothness inherently. Third, a parallel fast Delaunay triangulation method is developed based on the observation that a set of neighboring particles generates a locally valid Voronoi diagram at the interior of the domain. The incompleteness of near domain boundaries is handled by enforcing a symmetry boundary condition. A set of two-dimensional test cases shows the feasibility of the method. Numerical results demonstrate that the proposed method produces high-quality globally optimized adaptive isotropic meshes even for high geometric complexity.
ISSN:0045-7825
1879-2138
DOI:10.1016/j.cma.2018.10.052