An interface reconstruction method based on an analytical formula for 3D arbitrary convex cells
In this study, we are interested in an interface reconstruction method for 3D arbitrary convex cells that could be used in multimaterial flow simulations for instance. We assume that the interface is represented by a plane whose normal vector is known and we focus on the volumematching 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 volumematching 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:

^{[1]}
;
^{[1]}
 Los Alamos National Lab. (LANL), Los Alamos, NM (United States). Fluid Dynamics and Solid Mechanics (T3)
 Publication Date:
 Report Number(s):
 LAUR1520420
Journal ID: ISSN 00219991
 Grant/Contract Number:
 AC5206NA25396
 Type:
 Accepted Manuscript
 Journal Name:
 Journal of Computational Physics
 Additional Journal Information:
 Journal Volume: 305; Journal ID: ISSN 00219991
 Publisher:
 Elsevier
 Research Org:
 Los Alamos National Lab. (LANL), Los Alamos, NM (United States)
 Sponsoring Org:
 USDOE National Nuclear Security Administration (NNSA), Office of Defense Programs (DP) (NA10)
 Country of Publication:
 United States
 Language:
 English
 Subject:
 97 MATHEMATICS AND COMPUTING; Interface reconstruction; Arbitrary 3D convex cells; Analytical formula; VOF method; Noniterative technique
 OSTI Identifier:
 1325632
 Alternate Identifier(s):
 OSTI ID: 1359282
Diot, Steven, and François, Marianne M. An interface reconstruction method based on an analytical formula for 3D arbitrary convex cells. United States: N. p.,
Web. doi:10.1016/j.jcp.2015.10.011.
Diot, Steven, & François, Marianne M. An interface reconstruction method based on an analytical formula for 3D arbitrary convex cells. United States. doi:10.1016/j.jcp.2015.10.011.
Diot, Steven, and François, Marianne M. 2015.
"An interface reconstruction method based on an analytical formula for 3D arbitrary convex cells". United States.
doi:10.1016/j.jcp.2015.10.011. https://www.osti.gov/servlets/purl/1325632.
@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 multimaterial flow simulations for instance. We assume that the interface is represented by a plane whose normal vector is known and we focus on the volumematching 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 volumematching 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 = {2015},
month = {10}
}