In some countries, underground waters are the most important sources to provide drinking water. So it is necessary to make scheme and to do high protection of to achieve maximum beneficiary. Necessity of this management is going to be felt by developing these sources and human's interference. However, in the past overtopping phenomenon was the first reason of dam's destruction, but nowadays by increasing of spate design's period, the significant problem that researchers are interfere with, is seepage problem. The purpose of solving the underground problems is to procure height of water as a function of coordinate and time. In observation of practical industries, we can use the mathematical models that simulate the water flow in porous media. Often, in large areas, examinations are impossible and too expensive. So, with computer simulation, more areas are going to be studied. In this paper, mathematical model of moving water under concrete dam in porous media is discussed. In this case, according to discretization methods of the governing equations in porous media such as finite difference and finite element, finite volume techniques, the last one was selected. The present model shows the amount of water that seep under the concrete dam. Herein, to possibility of solving the problem with this method, the media is simplified. For solving the equations, unstructured mesh is used. The effect of underrelaxation coefficient to increase the rate of convergence is illustrated. This factor was calculated and found equal to 0.995 that shows 10 percent improvement in rate of convergence. The results of seepage discharges by using 3 powerful seepage codes (Seep/w, Mseep and Plaxis) that are based on finite element method are compared with results of FVseep model which is based on finite volume method and shows 5.1 percent improvement in accuracy.
[1]
R. Eymard,et al.
Finite Volume Methods
,
2019,
Computational Methods for Fluid Dynamics.
[2]
A. Weiser,et al.
On convergence of block-centered finite differences for elliptic-problems
,
1988
.
[3]
E. Bender.
Numerical heat transfer and fluid flow. Von S. V. Patankar. Hemisphere Publishing Corporation, Washington – New York – London. McGraw Hill Book Company, New York 1980. 1. Aufl., 197 S., 76 Abb., geb., DM 71,90
,
1981
.
[4]
Josef Stoer,et al.
Numerische Mathematik 1
,
1989
.
[5]
Pascal Omnes,et al.
A FINITE VOLUME METHOD FOR THE LAPLACE EQUATION ON ALMOST ARBITRARY TWO-DIMENSIONAL GRIDS
,
2005
.
[6]
E. Bertolazzi,et al.
A CELL-CENTERED SECOND-ORDER ACCURATE FINITE VOLUME METHOD FOR CONVECTION–DIFFUSION PROBLEMS ON UNSTRUCTURED MESHES
,
2004
.
[7]
S. Patankar.
Numerical Heat Transfer and Fluid Flow
,
2018,
Lecture Notes in Mechanical Engineering.
[8]
J. Maître,et al.
Connection between finite volume and mixed finite element methods
,
1996
.
[9]
Thomas A. Manteuffel,et al.
The numerical solution of second-order boundary value problems on nonuniform meshes
,
1986
.
[10]
Robert Eymard,et al.
A mixed finite volume scheme for anisotropic diffusion problems on any grid
,
2006,
Numerische Mathematik.
[11]
Peter A. Forsyth,et al.
Quadratic convergence for cell-centered grids
,
1988
.