Moving iso-contour method for solving partial differential equations
Pohjonen, Aarne (2023-12-21)
IOP publishing
21.12.2023
Aarne Pohjonen 2023 J. Phys.: Conf. Ser. 2675 012031, DOI 10.1088/1742-6596/2675/1/012031
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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.
https://creativecommons.org/licenses/by/3.0/
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.
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Julkaisun pysyvä osoite on
https://urn.fi/URN:NBN:fi:oulu-202401221395
https://urn.fi/URN:NBN:fi:oulu-202401221395
Tiivistelmä
Abstract
The numerical solution of partial differential equations is often performed on a numerical grid, where the grid points are used for estimating the partial derivatives. The grid can be fully static as in Eulerian type of solution method, or the grid points can move during the solution, which is the case in Lagrangian type of method. In the current article, a numerical solution method is presented, where the grid points are located on iso-contours of the two-dimensional field. The method calculates the local movement of the iso-contours according to an evolution equation described by the PDE, and the solution proceeds by moving the grid points towards the calculated direction. Additional stability is obtained by setting the grid points to move along the iso-contour line. To exemplify the application of the method, numerical examples are calculated for the two-dimensional diffusion equation.
The numerical solution of partial differential equations is often performed on a numerical grid, where the grid points are used for estimating the partial derivatives. The grid can be fully static as in Eulerian type of solution method, or the grid points can move during the solution, which is the case in Lagrangian type of method. In the current article, a numerical solution method is presented, where the grid points are located on iso-contours of the two-dimensional field. The method calculates the local movement of the iso-contours according to an evolution equation described by the PDE, and the solution proceeds by moving the grid points towards the calculated direction. Additional stability is obtained by setting the grid points to move along the iso-contour line. To exemplify the application of the method, numerical examples are calculated for the two-dimensional diffusion equation.
Kokoelmat
- Avoin saatavuus [38841]
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