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Anisotropic mesh adaptation for evolving triangulated surfaces

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Abstract

Dynamic surfaces arise in many applications, such as free surfaces in multiphase flows and moving interfaces in fluid–solid interaction. In many engineering applications, an explicit surface triangulation is often used to represent dynamic surfaces, posing significant challenges in adapting their meshes, especially if large curvatures and sharp features may dynamically emerge or vanish as the surfaces evolve. In this paper, we present an anisotropic mesh adaptation technique to meet these challenges. Our technique strives for optimal aspect ratios of the triangulation to reduce positional errors and to capture geometric features of dynamic surfaces based on a novel extension of the quadrics. Our adaptation algorithm combines the operations of vertex redistribution, edge flipping, edge contraction, and edge splitting. Experimental results demonstrate the effectiveness of our anisotropic adaptation technique for static and dynamic surfaces.

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Acknowledgments

This work was supported by NSF and DARPA under CARGO grant #0310446. X. Jiao was also supported by a subcontract from the Center for Simulation of Advanced Rockets of the University of Illinois at Urbana-Champaign funded by the U.S. Department of Energy through the University of California under subcontract B523819.

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Author notes

  1. Xinlai Ni

    Present address: Google, Mountain View, CA, USA

Authors and Affiliations

  1. Department of Applied Mathematics and Statistics, Stony Brook University, Stony Brook, NY, 11794, USA

    Xiangmin Jiao

  2. Department of Computer Science, University of Illinois at Urbana-Champaign, Urbana, IL, 61801, USA

    Andrew Colombi, Xinlai Ni & John Hart

Authors
  1. Xiangmin Jiao
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  2. Andrew Colombi
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  3. Xinlai Ni
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  4. John Hart
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Correspondence to Xiangmin Jiao.

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Jiao, X., Colombi, A., Ni, X. et al. Anisotropic mesh adaptation for evolving triangulated surfaces. Engineering with Computers 26, 363–376 (2010). https://doi.org/10.1007/s00366-009-0170-1

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