The paper studies mesh dependent numerical solution of groundwater problems with singularities, caused by boreholes represented as points, instead of a real radius. We show on examples, that the numerical solution of the borehole pumping problem with point source (singularity) can be related to the exact solution of a regular problem with adapted geometry of a finite borehole radius. The radius providing the fit is roughly proportional to the mesh step. Next we define a problem of fracture-rock coupling, with one part equivalent to the singular point source problem and the second part with a uniform flow. It is a regularized problem, but with the mesh dependence similar to the radial flow, in a certain range of steps. The behavior is explained by comparing the numerical solution with the analytical solution of a simplified problem. It also captures the effects of varying physical parameters.
@article{702996,
title = {Numerical studies of groundwater flow problems with a singularity},
booktitle = {Programs and Algorithms of Numerical Mathematics},
series = {GDML\_Books},
publisher = {Institute of Mathematics CAS},
address = {Prague},
year = {2017},
pages = {37-45},
url = {http://dml.mathdoc.fr/item/702996}
}
Hokr, Milan; Balvín, Aleš. Numerical studies of groundwater flow problems with a singularity, dans Programs and Algorithms of Numerical Mathematics, GDML_Books, (2017), pp. 37-45. http://gdmltest.u-ga.fr/item/702996/