Imposing jump conditions on nonconforming interfaces for the Correction Function Method: A least squares approach
Name
1710.11016.pdf
Description
Submitted version
Size
3.15 MB
Format
Adobe PDF
Checksum (MD5)
9163d2675bf60b72f3816e2ff0ab1af0
Author(s)
Marques, Alexandre N.
Rosales, Rodolfo
Date Issued
November 2019
Journal
Journal of computational physics
Publisher
Elsevier BV
Citation
Marques, Alexandre Noll, Jean-Christophe Nave and Rodolfo Ruben Rosales. “Imposing jump conditions on nonconforming interfaces for the Correction Function Method: A least squares approach.” Journal of computational physics, vol. 397, 2019, article 108869 © 2019 The Author(s)
Version
Original manuscript
Abstract
We introduce a technique that simplifies the problem of imposing jump conditions on interfaces that are not aligned with a computational grid in the context of the Correction Function Method (CFM). The CFM offers a general framework to solve Poisson's equation in the presence of discontinuities to high order of accuracy, while using a compact discretization stencil. A key concept behind the CFM is enforcing the jump conditions in a least squares sense. This concept requires computing integrals over sections of the interface, which is a challenge in 3-D when only an implicit representation of the interface is available (e.g., the zero contour of a level set function). The technique introduced here is based on a new formulation of the least squares procedure that relies only on integrals over domains that are amenable to simple quadrature after local coordinate transformations. We incorporate this technique into a fourth order accurate implementation of the CFM, and show examples of solutions to Poisson's equation with imposed jump conditions computed in 2-D and 3-D.
MIT Department
Massachusetts Institute of Technology. Department of Aeronautics and Astronautics
Massachusetts Institute of Technology. Department of Mathematics
Terms of Use
Creative Commons Attribution-NonCommercial-NoDerivs License
Persistent DSpace Link
DOI of Published Version
https://doi.org/10.1016/j.jcp.2019.108869
