SIMULATION OF NONLINEAR DIFFUSION ON A SPHERE

Yuri N. Skiba, Denis M. Filatov

Abstract

A new numerical technique for the simulation of nonlinear diffusion processes on a sphere is developed. The core of our approach is to split the original equation's operator, thus reducing the two-dimensional problem to two one-dimentional problems. Further, we apply two different coordinate grids to cover the entire sphere for solving the split 1D problems. This allows avoiding the question of imposing adequate boundary conditions near the poles, which is always a serious problem when modelling on a sphere. Yet, therefore we can employ finite difference schemes of any even approximation order in space. The developed approach is cheap to implement from the computational point of view. Numerical experiments prove the suggested technique, simulating several diffusion phenomena with high accuracy.

References

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Paper Citation


in Harvard Style

N. Skiba Y. and M. Filatov D. (2011). SIMULATION OF NONLINEAR DIFFUSION ON A SPHERE . In Proceedings of 1st International Conference on Simulation and Modeling Methodologies, Technologies and Applications - Volume 1: SIMULTECH, ISBN 978-989-8425-78-2, pages 24-30. DOI: 10.5220/0003574500240030


in Bibtex Style

@conference{simultech11,
author={Yuri N. Skiba and Denis M. Filatov},
title={SIMULATION OF NONLINEAR DIFFUSION ON A SPHERE},
booktitle={Proceedings of 1st International Conference on Simulation and Modeling Methodologies, Technologies and Applications - Volume 1: SIMULTECH,},
year={2011},
pages={24-30},
publisher={SciTePress},
organization={INSTICC},
doi={10.5220/0003574500240030},
isbn={978-989-8425-78-2},
}


in EndNote Style

TY - CONF
JO - Proceedings of 1st International Conference on Simulation and Modeling Methodologies, Technologies and Applications - Volume 1: SIMULTECH,
TI - SIMULATION OF NONLINEAR DIFFUSION ON A SPHERE
SN - 978-989-8425-78-2
AU - N. Skiba Y.
AU - M. Filatov D.
PY - 2011
SP - 24
EP - 30
DO - 10.5220/0003574500240030