A regularization method for solving the Poisson equation for mixed unbounded-periodic domains

Henrik Juul Spietz*, Mads Mølholm Hejlesen, Jens Honoré Walther

*Corresponding author for this work

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Abstract

Abstract Regularized Green's functions for mixed unbounded-periodic domains are derived. The regularization of the Green's function removes its singularity by introducing a regularization radius which is related to the discretization length and hence imposes a minimum resolved scale. In this way the regularized unbounded-periodic Green's functions can be implemented in an FFT-based Poisson solver to obtain a convergence rate corresponding to the regularization order of the Green's function. The high order is achieved without any additional computational cost from the conventional FFT-based Poisson solver and enables the calculation of the derivative of the solution to the same high order by direct spectral differentiation. We illustrate an application of the FFT-based Poisson solver by using it with a vortex particle mesh method for the approximation of incompressible flow for a problem with a single periodic and two unbounded directions.
Original languageEnglish
JournalJournal of Computational Physics
Volume356
Pages (from-to)439–447
ISSN0021-9991
DOIs
Publication statusPublished - 2018

Keywords

  • The Poisson equation
  • Unbounded and periodic domains
  • Mixed boundary conditions
  • Regularization methods
  • Green's function solution
  • Vortex methods

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