Topological regularization on numerical simulations of the advection equation

DOI Web Site 4 References Open Access
  • Takeda Kota
    Department of Mathematics, Kyoto University RIKEN Center for Computational Science
  • Kaji Shizuo
    Institute of Mathematics for Industry, Kyushu University
  • Miyoshi Takemasa
    RIKEN Center for Computational Science

Description

<p>Numerical simulation of the one-dimensional advection equations is known to be difficult with discontinuous initial states. The initial shape undergoes distortion due to high-frequency fluctuations, exemplifying a prevalent challenge in discretizing dynamics: the violation of conservation laws. In addressing this issue, our study introduces a topological regularization method for numerical simulations, leveraging persistent homology. The effectiveness of our approach is demonstrated through numerical simulations of the one-dimensional advection equation with a rectangular initial state. The results highlight the potential of our method to improve the accuracy and fidelity of simulations, especially in scenarios where maintaining topological conservation is critical.</p>

Journal

  • JSIAM Letters

    JSIAM Letters 16 (0), 53-56, 2024

    The Japan Society for Industrial and Applied Mathematics

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