Multigrid Acceleration in a 3D Navier-Stokes Solver Using Unstructured Hexahedral Meshes with Adaptation

Leonard, Benoit; Patel, Alpesh; Hirsch, Charles

doi:10.1007/978-3-642-58312-4_20

Cited by 2 publications

(1 citation statement)

References 4 publications

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“…A hexmesh H resulting from a non-degenerate volume parameterization is suitable for partial differencial equation (PDE) solving, tensorproduct/trivariate spline fitting Li and Qin 2012;Martin et al 2008], Isogeometric Analysis (IGA) [Hughes et al 2005;Bazilevs et al 2006], and multi-grid and adaptive computations [Leonard et al 2000;Wada et al 2006]. …”

Section: Introductionmentioning

confidence: 99%

Hexahedral mesh re-parameterization from aligned base-complex

2015

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Figure 1: (a) An input hex-mesh : The image on the left shows its base-complex that partitions the hexahedral mesh into different large components, illustrated with different colors on the right. Due to the misalignments between singularities, many (typically small) components arise. For instance, a strip of small components near the sharp feature is highlighted. (b) Our alignment algorithm reduces the complexity of the base-complex but leads to a hex-mesh with a large distortion. (c) Both the singularity placement and the element quality of the resulting hex-mesh are improved by our structure-aware optimization algorithm. AbstractRecently, generating a high quality all-hex mesh of a given volume has gained much attention. However, little, if any, effort has been put into the optimization of the hex-mesh structure, which is equally important to the local element quality of a hex-mesh that may influence the performance and accuracy of subsequent computations. In this paper, we present a first and complete pipeline to optimize the global structure of a hex-mesh. Specifically, we first extract the base-complex of a hex-mesh and study the misalignments among its singularities by adapting the previously introduced hexahedral sheets to the base-complex. Second, we identify the valid removal base-complex sheets from the base-complex that contain misaligned singularities. We then propose an effective algorithm to remove these valid removal sheets in order. Finally, we present a structure-aware optimization strategy to improve the geometric quality of the resulting hex-mesh after fixing the misalignments. Our experimental results demonstrate that our pipeline can significantly reduce the number of components of a variety of hex-meshes generated by state-of-the-art methods, while maintaining high geometric quality.

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Section: Introductionmentioning

confidence: 99%

Hexahedral mesh re-parameterization from aligned base-complex

2015

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Robust structure simplification for hex re-meshing

et al. 2017

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We introduce a robust and automatic algorithm to simplify the structure and reduce the singularities of a hexahedral mesh. Our algorithm interleaves simplification operations to collapse sheets and chords of the base complex of the input mesh with a geometric optimization, which improves the elements quality. All our operations are guaranteed not to introduce elements with negative Jacobians, ensuring that our algorithm always produces valid hex-meshes, and not to increase the Hausdorff distance from the original shape more than a user-defined threshold, ensuring a faithful approximation of the input geometry. Our algorithm can improve meshes produced with any existing hexahedral meshing algorithm --- we demonstrate its effectiveness by processing a dataset of 194 hex-meshes created with octree-based, polycube-based, and field-aligned methods.

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Multigrid Acceleration in a 3D Navier-Stokes Solver Using Unstructured Hexahedral Meshes with Adaptation

Cited by 2 publications

References 4 publications

Hexahedral mesh re-parameterization from aligned base-complex

Hexahedral mesh re-parameterization from aligned base-complex

Robust structure simplification for hex re-meshing

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