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Title: An interface reconstruction method based on an analytical formula for 3D arbitrary convex cells

Abstract

In this study, we are interested in an interface reconstruction method for 3D arbitrary convex cells that could be used in multi-material flow simulations for instance. We assume that the interface is represented by a plane whose normal vector is known and we focus on the volume-matching step that consists in finding the plane constant so that it splits the cell according to a given volume fraction. We follow the same approach as in the recent authors' publication for 2D arbitrary convex cells in planar and axisymmetrical geometries, namely we derive an analytical formula for the volume of the specific prismatoids obtained when decomposing the cell using the planes that are parallel to the interface and passing through all the cell nodes. This formula is used to bracket the interface plane constant such that the volume-matching problem is rewritten in a single prismatoid in which the same formula is used to find the final solution. Finally, the proposed method is tested against an important number of reproducible configurations and shown to be at least five times faster.

Authors:
ORCiD logo [1];  [1]
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  1. Los Alamos National Lab. (LANL), Los Alamos, NM (United States). Fluid Dynamics and Solid Mechanics (T-3)
Publication Date:
Research Org.:
Los Alamos National Laboratory (LANL), Los Alamos, NM (United States)
Sponsoring Org.:
USDOE National Nuclear Security Administration (NNSA), Office of Defense Programs (DP)
OSTI Identifier:
1325632
Alternate Identifier(s):
OSTI ID: 1359282
Report Number(s):
LA-UR-15-20420
Journal ID: ISSN 0021-9991
Grant/Contract Number:  
AC52-06NA25396
Resource Type:
Accepted Manuscript
Journal Name:
Journal of Computational Physics
Additional Journal Information:
Journal Volume: 305; Journal ID: ISSN 0021-9991
Publisher:
Elsevier
Country of Publication:
United States
Language:
English
Subject:
97 MATHEMATICS AND COMPUTING; Interface reconstruction; Arbitrary 3D convex cells; Analytical formula; VOF method; Non-iterative technique

Citation Formats

Diot, Steven, and François, Marianne M. An interface reconstruction method based on an analytical formula for 3D arbitrary convex cells. United States: N. p., 2015. Web. doi:10.1016/j.jcp.2015.10.011.
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Diot, Steven, & François, Marianne M. An interface reconstruction method based on an analytical formula for 3D arbitrary convex cells. United States. https://doi.org/10.1016/j.jcp.2015.10.011
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Diot, Steven, and François, Marianne M. Thu . "An interface reconstruction method based on an analytical formula for 3D arbitrary convex cells". United States. https://doi.org/10.1016/j.jcp.2015.10.011. https://www.osti.gov/servlets/purl/1325632.
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@article{osti_1325632,
title = {An interface reconstruction method based on an analytical formula for 3D arbitrary convex cells},
author = {Diot, Steven and François, Marianne M.},
abstractNote = {In this study, we are interested in an interface reconstruction method for 3D arbitrary convex cells that could be used in multi-material flow simulations for instance. We assume that the interface is represented by a plane whose normal vector is known and we focus on the volume-matching step that consists in finding the plane constant so that it splits the cell according to a given volume fraction. We follow the same approach as in the recent authors' publication for 2D arbitrary convex cells in planar and axisymmetrical geometries, namely we derive an analytical formula for the volume of the specific prismatoids obtained when decomposing the cell using the planes that are parallel to the interface and passing through all the cell nodes. This formula is used to bracket the interface plane constant such that the volume-matching problem is rewritten in a single prismatoid in which the same formula is used to find the final solution. Finally, the proposed method is tested against an important number of reproducible configurations and shown to be at least five times faster.},
doi = {10.1016/j.jcp.2015.10.011},
journal = {Journal of Computational Physics},
number = ,
volume = 305,
place = {United States},
year = {Thu Oct 22 00:00:00 EDT 2015},
month = {Thu Oct 22 00:00:00 EDT 2015}
}
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Publisher's Version of Record
https://doi.org/10.1016/j.jcp.2015.10.011
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Works referenced in this record:

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journal, May 2006

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    Works referencing / citing this record:

    Analytical interface reconstruction algorithms in the PLIC‐VOF method for 3D polyhedral unstructured meshes
    journal, June 2019

    • Dai, Dezhi; Tong, Albert Y.
    • International Journal for Numerical Methods in Fluids, Vol. 91, Issue 5
    • DOI: 10.1002/fld.4750

    Discontinuous Galerkin method for incompressible two-phase flows
    preprint, January 2020

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