Signal processing approach to mesh refinement in simulations of axisymmetric droplet dynamics

JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS

卷:383

Article

Koga, Kazuki¹ 

[1] Kyoto Univ, Dept Adv Math Sci, Sakyo Ku, Yoshida Hommachi, Kyoto 6068501, Japan

关键词: Axisymmetric droplet;    Surface tension;    Vortex sheet;    Mesh refinement;    Signal processing;    Non-uniform fast Fourier transform;   

DOI  :  10.1016/j.cam.2020.113131

来源: Elsevier

【 摘 要 】

We propose a novel mesh refinement scheme based on signal processing for boundary integral simulations of inviscid droplet dynamics with axial symmetry. A key idea is to directly access the Fourier coefficients of a principal curvature as a function of the arclength through a natural change of variables. The trapezoidal rule is applied to those Fourier-type integrals and the resulting formula fits in the framework of the non-uniform fast Fourier transform. This observation enables to efficiently use an envelope analysis and smoothing filter to generate guidelines for mesh refinement in two singularity formation scenarios. Applications also include a non-iterative construction of the uniform parametrization for an important class of plane curves, which is used in a convergence study of the time-stepping procedure implemented in the previous work by Nitsche and Steen (2004). (C) 2020 Elsevier B.V. All rights reserved.

【 授权许可】

Free