University of Oulu

Aarne Pohjonen 2021 J. Phys.: Conf. Ser. 2090 012069,

Solving partial differential equations in deformed grids by estimating local average gradients with planes

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Author: Pohjonen, Aarne1
Organizations: 1Materials and Mechanical Engineering Faculty of Technology University of Oulu PL4200, 90014 Oulun Yliopisto Oulu, Finland
Format: article
Version: published version
Access: open
Online Access: PDF Full Text (PDF, 1.4 MB)
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Language: English
Published: IOP Publishing, 2021
Publish Date: 2022-01-10


For constructing physical science based models in irregular numerical grids, an easy-to-implement method for solving partial differential equations has been developed and its accuracy has been evaluated by comparison to analytical solutions that are available for simple initial and boundary conditions. The method is based on approximating the local average gradients of a field by fitting equation of plane to the field quantities at neighbouring grid positions and then calculating an estimate for the local average gradient from the plane equations. The results, comparison to analytical solutions, and accuracy are presented for 2-dimensional cases.

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Series: Journal of physics. Conference series
ISSN: 1742-6588
ISSN-E: 1742-6596
ISSN-L: 1742-6588
Volume: 2090
Article number: 012069
DOI: 10.1088/1742-6596/2090/1/01206
Host publication: Journal of Physics : Conference Series, Volume 2090, 10th International Conference on Mathematical Modeling in Physical Sciences (IC-MSQUARE 2021), 6-9 September 2021, Greece (Virtual)
Conference: International Conference on Mathematical Modeling in Physical Sciences
Type of Publication: A4 Article in conference proceedings
Field of Science: 216 Materials engineering
114 Physical sciences
111 Mathematics
Copyright information: Content from this work may be used under the terms of the Creative Commons Attribution 3.0 licence. Any further distribution of this work must maintain attribution to the author(s) and the title of the work, journal citation and DOI. Published under licence by IOP Publishing Ltd.