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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.
Original language | English |
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Article number | 100109 |
Number of pages | 43 |
Journal | Journal of Computational Physics: X |
Volume | 14 |
Early online date | 6 Jun 2022 |
DOIs | |
Publication status | Published - 2022 |
Keywords
- Density stratified flows
- Elliptical parcels
- Lagrangian methods
- PIC
- Turbulent flows
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Dive into the research topics of 'EPIC: the Elliptical Parcel-In-Cell method'. Together they form a unique fingerprint.Projects
- 1 Finished
Datasets
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daviddritschel/2D_stratifiedflow_pseudospectral: PS version 0.0.4
Frey, M. (Contributor) & daviddritschel (Contributor), Zenodo, 2022
Dataset: Software
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matt-frey/epic: EPIC (all versions)
Frey, M. (Creator) & sjboeing (Creator), Zenodo, 2023
Dataset: Software