Year: 2012
Author: J. Mortensen, S. Olsen, J.-Y. Parlange, A. S. Telyakovskly
International Journal of Numerical Analysis and Modeling, Vol. 9 (2012), Iss. 1 : pp. 105–114
Abstract
In this article we construct an approximate similarity solution to a nonlinear diffusion equation in spherical coordinates. In hydrology this equation is known as the Boussinesq equation when written in planar or cylindrical coordinates. Recently Li et al. [8] obtained an approximate similarity solution to the Boussinesq equation in cylindrical coordinates. Here we consider the same problem in spherical coordinates with the prescribed power law point source boundary condition. The resulting scaling function has a power law singularity at the origin versus a logarithmic singularity in the cylindrical case.
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Journal Article Details
Publisher Name: Global Science Press
Language: English
DOI: https://doi.org/2012-IJNAM-614
International Journal of Numerical Analysis and Modeling, Vol. 9 (2012), Iss. 1 : pp. 105–114
Published online: 2012-01
AMS Subject Headings: Global Science Press
Copyright: COPYRIGHT: © Global Science Press
Pages: 10
Keywords: Approximate solutions similarity solutions Boussinesq equation nonlinear diffusion.