@inproceedings{1a006f24c5ee40cca421849346ac9e88,
title = "Investigation of interpolation schemes for a class of nonlinear finite volume methods",
abstract = "The robustness and accuracy of a class of nonlinear finite volume methods (NFVM) for discretizing the heterogeneous and anisotropic pressure equation is investigated in this work. The formulation of NFVM requires the construction of one-sided fluxes, which involves interpolating pressure at auxiliary points. Grid vertices and harmonic averaging are two popular candidates. The principle of Enriched Multi-point Flux Approximation (EMPFA) is employed as an interpolating algorithm to interpolate pressure at grid vertices. To improve the robustness of interpolation using harmonic averaging point, a correction algorithm is proposed to modify those ill-placed harmonic averaging points so that all the co-normal vectors can be decomposed with non-negative coefficients successfully. Numerical tests demonstrate that the resulting NFVM has significantly improved robustness compared to NFVM utilizing the original harmonic averaging point and therefore can be applied to more general problems.",
keywords = "Anisotropic diffusion equation, Harmonic averaging point, Nonlinear finite volume method",
author = "Wenjuan Zhang and \{Al Kobaisi\}, Mohammed and Huafeng Sun",
note = "Funding Information: Funding of this work by the Abu Dhabi National Oil Company (ADNOC) is greatly appreciated. Publisher Copyright: {\textcopyright} 2018 Society for Modeling \& Simulation International (SCS).; 50th Summer Computer Simulation Conference, SCSC 2018, Part of the 2018 Summer Simulation Multi-Conference, SummerSim 2018 ; Conference date: 09-07-2018 Through 12-07-2018",
year = "2018",
language = "British English",
isbn = "9781510860131",
series = "Simulation Series",
number = "10",
pages = "303--314",
editor = "Padilla, \{Jose J.\} and Lynch, \{Christopher J.\}",
booktitle = "Simulation Series",
edition = "10",
}