Inserting a Curve into an Existing Two Dimensional Unstructured Mesh

In this work, a new method for inserting a curve as an internal boundary into an existing mesh is developed. The curve insertion is done with minimal adjustment to the original topology while maintaining the original sizing of the mesh. The curve is discretized by initially placing vertices, defining a length scale at every location on the curve based on the local underlying mesh, and equidistributing length scale along the curve between vertices. This results in the final discretization being spaced in a way that is consistent with the initial mesh. The new points are then inserted into the mesh and local refinement is performed, resulting in a final mesh containing a representation of the curve while preserving mesh quality. The advantage of this algorithm over generating a new mesh from scratch is in allowing for the majority of existing simulation data to be preserved, and not have to be interpolated onto the new mesh.

[1]  Mark S. Shephard,et al.  Accounting for curved domains in mesh adaptation , 2003 .

[2]  John M. Stockie,et al.  A Moving Mesh Method for One-dimensional Hyperbolic Conservation Laws , 2000, SIAM J. Sci. Comput..

[3]  Bharat K. Soni,et al.  Handbook of Grid Generation , 1998 .

[4]  Robert D. Russell,et al.  Anr-Adaptive Finite Element Method Based upon Moving Mesh PDEs , 1999 .

[5]  Weizhang Huang,et al.  Moving mesh partial differential equations (MMPDES) based on the equidistribution principle , 1994 .

[6]  Renato Paciorri,et al.  A shock-fitting technique for 2D unstructured grids , 2009 .

[7]  WEIZHANG HUANG,et al.  A Moving Mesh Method Based on the Geometric Conservation Law , 2002, SIAM J. Sci. Comput..

[8]  Serge Gosselin.  Delaunay refinement mesh generation of curve-bounded domains , 2009 .

[9]  Xiangmin Jiao,et al.  Proceedings of the 21st International Meshing Roundtable , 2014 .

[10]  Paul Andries Zegeling,et al.  Moving Grid Techniques , 1998 .

[11]  Douglas Pagnutti.  Anisotropic adaptation: metrics and meshes , 2008 .

[12]  Charles Boivin,et al.  Guaranteed‐quality triangular mesh generation for domains with curved boundaries , 2002 .

[13]  Robert Russell,et al.  An h-r Moving Mesh Method for One-Dimensional Time-Dependent PDEs , 2012, IMR.

[14]  Benjamin Crestel.  Moving meshes on general surfaces , 2011 .

[15]  Carl Ollivier-Gooch,et al.  Tetrahedral mesh improvement using swapping and smoothing , 1997 .

[16]  J. Shewchuk,et al.  Delaunay refinement mesh generation , 1997 .

[17]  Charles Boivin,et al.  Guaranteed-Quality Simplical Mesh Generation with Cell Size and Grading Control , 2001, Engineering with Computers.

[18]  Tamal K. Dey,et al.  Delaunay Mesh Generation , 2012, Chapman and Hall / CRC computer and information science series.

[19]  Jean-Yves Trépanier,et al.  A Conservative Shock Fitting Method on Unstructured Grids , 1996 .