Anisotropic sources for surface and volume boundary layer mesh generation

Abstract A new approach to model and compute the metric tensor corresponding to a-priori prescribed surface and volume boundary layers is presented. This is achieved by the use of sources that model the combined anisotropic metric. Algorithms are presented to both evaluate the resulting metric value at any point in space and the efficient approximation of the minimum and maximum metric over an axis-aligned box which enables fast evaluation of the anisotropic metric independent of the approach used for mesh generation. The ability to model and evaluate the anisotropic sizing independently ensure that mesh generation algorithms that use it can produce meshes that correctly and predictably capture the sizing fields induced by the user prescribed boundary layer attributes. The method is unique in producing globally smooth representations of the final anisotropic metric including the influence of implicit anisotropy due to boundary curvature and any prescribed isotropic sizes. As a result, it addresses robustness and size smoothness issues in legacy approaches that decouple the surface and volume mesh generation stages. The value of the new method is demonstrated by several examples that include both surface and volume boundary layers prescribed on geometries with curved boundaries.

[1]  Jean-François Remacle,et al.  Anisotropic Mesh Gradation Control , 2004, IMR.

[2]  S. Pirzadeh.  Advanced Unstructured Grid Generation for Complex Aerodynamic Applications , 2013 .

[3]  Frédéric Alauzet,et al.  Alignment and orthogonality in anisotropic metric-based mesh adaptation , 2015 .

[4]  Micha Sharir.  Almost tight upper bounds for lower envelopes in higher dimensions , 1994, Discret. Comput. Geom..

[5]  Hans Hagen,et al.  Visualization and Processing of Tensor Fields , 2014 .

[6]  Saikat Dey,et al.  Boundary layer mesh generation on arbitrary geometries , 2017 .

[7]  Shahyar Pirzadeh,et al.  Advanced Unstructured Grid Generation for Complex Aerodynamics Applications , 2008 .

[8]  J. Peiro,et al.  Adaptive remeshing for three-dimensional compressible flow computations , 1992 .

[9]  Barbara Glut,et al.  Tree-based Control Space Structures for Discrete Metric Sources in 3D Meshing , 2019, Comput. Sci..

[10]  Saikat Dey,et al.  An Entropy Satisfying Boundary Layer Surface Mesh Generation , 2015, SIAM J. Sci. Comput..

[11]  Jianjun Chen,et al.  Automatic sizing functions for unstructured surface mesh generation , 2017 .

[12]  Rainald Löhner,et al.  Linear Sources for Mesh Generation , 2013, SIAM J. Sci. Comput..

[13]  Alex M. Andrew,et al.  Level Set Methods and Fast Marching Methods: Evolving Interfaces in Computational Geometry, Fluid Mechanics, Computer Vision, and Materials Science (2nd edition) , 2000 .

[14]  Houman Borouchaki,et al.  Metric tensor recovery for adaptive meshing , 2017, Math. Comput. Simul..

[15]  C. Jones,et al.  Entropy solution at concave corners and ridges, and volume boundary layer tangential adaptivity , 2019, J. Comput. Phys..

[16]  David L. Marcum,et al.  Generation of unstructured grids for viscous flow applications , 1995 .

[17]  S. Pirzadeh.  Structured background grids for generation of unstructured grids by advancing front method , 1991 .

[18]  N. Ayache,et al.  Log‐Euclidean metrics for fast and simple calculus on diffusion tensors , 2006, Magnetic resonance in medicine.

[19]  Eric L. Mestreau,et al.  Smooth anisotropic sources with application to three-dimensional surface mesh generation , 2015, Engineering with Computers.

[20]  Adrien Loseille,et al.  On 3D Anisotropic Local Remeshing for Surface, Volume and Boundary Layers , 2009, IMR.

[21]  Frédéric Alauzet,et al.  Aligned Metric-based Anisotropic Solution Adaptive Mesh Generation , 2014 .

[22]  Zhiwei Liu,et al.  Automatic Sizing Functions for 3D Unstructured Mesh Generation , 2017 .

[23]  Weiming Cao,et al.  An Interpolation Error Estimate on Anisotropic Meshes in Rn and Optimal Metrics for Mesh Refinement , 2007, SIAM J. Numer. Anal..

[24]  Frédéric Alauzet,et al.  Continuous Mesh Framework Part I: Well-Posed Continuous Interpolation Error , 2011, SIAM J. Numer. Anal..

[25]  Shahyar Pirzadeh,et al.  Viscous unstructured three-dimensional grids by the advancing-layers method , 1994 .

[26]  Frédéric Alauzet,et al.  Size gradation control of anisotropic meshes , 2010 .

[27]  Rainald Loehner,et al.  Matching semi-structured and unstructured grids for Navier-Stokes calculations , 1993 .

[28]  D. Marcum,et al.  On a robust boundary layer mesh generation process , 2017 .

[29]  Guillaume Houzeaux,et al.  A surface remeshing approach , 2010 .

[30]  Nigel P. Weatherill,et al.  Fully automatic and fast mesh size specification for unstructured mesh generation , 2004, Engineering with Computers.