EPIC : the Elliptical Parcel-In-Cell method
Abstract
We present a novel approach to simulating general two-dimensional flows, which could also be applied to other areas of continuum mechanics. The approach generalises the Particle-In-Cell (PIC) method, originally used to model two-dimensional hydrodynamics, by representing fluid elements by elliptical parcels. The rotation and deformation of these parcels are calculated, and parcels split beyond a critical aspect ratio. Conversely, small parcels are eliminated by merging them with larger ones. The elliptical parcels well represent the flow deformation and have excellent conservation properties. In contrast to earlier work that combined PIC with elliptical parcels that split and merge, a vorticity-based framework is used, and accurate integration over ellipses is performed efficiently by two-point Gaussian quadrature. The small-scale mixing associated with parcel splitting and merging is shown to be strongly convergent with grid resolution. The robustness, versatility, accuracy and efficiency of the new Elliptical Parcel-In-Cell (EPIC) method is demonstrated for a variety of standard test cases, and compared with a standard pseudo-spectral method. The results indicate that EPIC is a promising, Lagrangian-based alternative to grid-based methods.
Citation
Frey , M , Dritschel , D & Böing , S 2022 , ' EPIC : the Elliptical Parcel-In-Cell method ' , Journal of Computational Physics: X , vol. 14 , 100109 . https://doi.org/10.1016/j.jcpx.2022.100109
Publication
Journal of Computational Physics: X
Status
Peer reviewed
ISSN
2590-0552Type
Journal article
Rights
Copyright © 2022 The Authors. Published by Elsevier Inc. This is an open access article under the CC BY license (http://creativecommons.org/licenses/by/4.0/).
Description
Funding: This research is supported by the UK Engineering and Physical Sciences Research Council (grant numbers EP/T025301/1 and EP/T025409/1 ).Collections
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