Abstract
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.
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References
Weatherill, N.P., Thompson, J.F., Soni, B.K. (eds.): Handbook of Grid Generation. CRC Press (1999)
Cheng, S.W., Dey, T.K., Shewchuk, J.R.: Delaunay Mesh Generation. Chapman & Hall (2012)
Boivin, C., Ollivier-Gooch, C.F.: Guaranteed-quality triangular mesh generation for domains with curved boundaries 55(10), 1185–1213 (2002)
Li, X., Shephard, M., Beall, M.: Accounting for curved domains in mesh adaptation 58, 246–276 (2003)
Gosselin, S.: Delaunay Refinement Mesh Generation of Curve-bounded Domains. Ph. D. thesis (2009)
Trepanier, J.-Y., Paraschivoiu, M., Reggio, M., Camarero, R.: A conservative shock fitting method on unstructured grids. Journal of Computational Physics 126(2), 421–433 (1996)
Paciorri, R., Bonfiglioli, A.: A shock-fitting technique for 2d unstructured grids. Computers & Fluids 38(3), 715–726 (2009)
Huang, W., Ren, Y., Russell, R.D.: Moving mesh partial differential equations (mmpdes) based on the equidistribution principle. SIAM Journal on Numerical Analysis 31(3), 709–730 (1994)
Zegeling, P.: Moving grid techniques. In: Handbook of Grid Generation, pp. 37-1–37-18 (1999)
Stockie, J.M., Mackenzie, J.A., Russell, R.D.: A moving mesh method for one-dimensional hyperbolic conservation laws. SIAM Journal on Scientific Computing 22(5), 1791–1813 (2001)
Cao, W., Huang, W., Russell, R.D.: A moving mesh method based on the geometric conservation law. SIAM Journal on Scientific Computing 24(1), 118–142 (2002)
Shewchuk, J.R.: Delaunay Refinement Mesh Generation. Ph. D. thesis, School of Computer Science, Carnegie Mellon University (May 1997)
Ollivier-Gooch, C.: Grummp version 0.5.0 user’s guide. Tech. rep., Department of Mechanical Engineering, The University of British Columbia (2010)
Ong, B., Russell, R., Ruuth, S.: An h-r moving mesh method for one-dimensional time-dependent PDEs. In: Jiao, X., Weill, J.-C. (eds.) Proceedings of the 21st International Meshing Roundtable, vol. 123, pp. 39–54. Springer, Heidelberg (2013)
Ollivier-Gooch, C.F., Boivin, C.: Guaranteed-quality simplicial mesh generation with cell size and grading control 17(3), 269–286 (2001)
Freitag, L.A., Ollivier-Gooch, C.F.: Tetrahedral mesh improvement using swapping and smoothing 40(21), 3979–4002 (1997)
Cao, W., Huang, W., Russell, R.D.: Anr-adaptive finite element method based upon moving mesh PDEs. Journal of Computational Physics 149(2), 221–244 (1999)
Crestel, B.: Moving meshes on general surfaces. Master’s thesis, Simon Fraser University (2011)
Pagnutti, D.: Anisotropic adaptation: Metrics and meshes. Master’s thesis (2008)
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Zaide, D.W., Ollivier-Gooch, C.F. (2014). Inserting a Curve into an Existing Two Dimensional Unstructured Mesh. In: Sarrate, J., Staten, M. (eds) Proceedings of the 22nd International Meshing Roundtable. Springer, Cham. https://doi.org/10.1007/978-3-319-02335-9_6
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DOI: https://doi.org/10.1007/978-3-319-02335-9_6
Publisher Name: Springer, Cham
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Online ISBN: 978-3-319-02335-9
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