# Numerical studies of groundwater flow problems with a singularity

• Programs and Algorithms of Numerical Mathematics, Publisher: Institute of Mathematics CAS(Prague), page 37-45

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## Abstract

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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.

## How to cite

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Hokr, Milan, and Balvín, Aleš. "Numerical studies of groundwater flow problems with a singularity." Programs and Algorithms of Numerical Mathematics. Prague: Institute of Mathematics CAS, 2017. 37-45. <http://eudml.org/doc/288165>.

@inProceedings{Hokr2017,
abstract = {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.},
author = {Hokr, Milan, Balvín, Aleš},
booktitle = {Programs and Algorithms of Numerical Mathematics},
keywords = {finite elements; mesh dependence; borehole; radial flow},
location = {Prague},
pages = {37-45},
publisher = {Institute of Mathematics CAS},
title = {Numerical studies of groundwater flow problems with a singularity},
url = {http://eudml.org/doc/288165},
year = {2017},
}

TY - CLSWK
AU - Hokr, Milan
AU - Balvín, Aleš
TI - Numerical studies of groundwater flow problems with a singularity
T2 - Programs and Algorithms of Numerical Mathematics
PY - 2017
CY - Prague
PB - Institute of Mathematics CAS
SP - 37
EP - 45
AB - 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.
KW - finite elements; mesh dependence; borehole; radial flow
UR - http://eudml.org/doc/288165
ER -

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