Journal article
A regularization method for solving the Poisson equation for mixed unbounded-periodic domains
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.
Language: | English |
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Year: | 2018 |
Pages: | 439-447 |
ISSN: | 10902716 and 00219991 |
Types: | Journal article |
DOI: | 10.1016/j.jcp.2017.12.018 |
ORCIDs: | Walther, Jens Honoré , Spietz, Henrik Juul and Mølholm Hejlesen, Mads |