Abstract
To describe the two-dimensional flow of water in unsaturated soil, the governing equation is solved on a mesh constructed from small area elements. A transformation is introduced with which these possibly distorted rectangular elements of the physical plane are mapped into computational squares. Thus, irregularly shaped regions, which present difficulties when attempting to describe their geometry on an orthogonal computational mesh, can be more easily modelled. Using this methodology, here called the finite volume method, numerical results are obtained showing the ability of the method to describe transient unsaturated flow.
Similar content being viewed by others
References
Celia, M. A., Ahuja, L. R., and Pinder, G. F., 1987, Orthogonal collocation and alternating direction procedures for unsaturated flow problems,Adv. Water Resour. 10(4), 178–187.
Jeppson, R. W., 1968, Seepage from ditches - Solution by finite differences,J. Hydraul. Div., ASCE 94,259–294.
Jameson, A. and Caughey, D. A., 1988, A finite volume method for transonic potential flow equations, AIAA paper No. 77-635.
Philip, J. R., 1969, Theory of infiltration,Adv. Hydrosci. 5, 215–305.
Selim, H. M. and Kirkham, D., 1973, Unsteady two-dimensional flow of water in unsaturated soils above an impervious barrier,Soil Sci. Soc. Am. Proc. 37, 489–495.
Soulis, J. V., 1983, A finite volume method for two-dimensional transonic potential flow through turbomachinery blade tows,Int. J. Heat Fluid Flow 4, 229–237.
Taghavi, S. A., Marino, M. A., and Rolston, D. E., 1984, Infiltration from trickle irrigation source,J. Irrig. Drainage Engng., ASCE 110(4), 331–341.
Thomson, J. F., Thames, F. C., and Mastin, C. W., 1974, Automatic numerical generation of body-fitted curvilinear coordinates system for a field containing any number of arbitrary two-dimensional bodies,J. Comput. Phys. 15, 299–319.
Thomson, J. F. and Warsi, Z. V., 1982, Boundary-fitted coordinates systems for numerical solution of partial differential equations - A review,J. Comput. Phys. 47, 1–108.
Tolikas, P., 1981, Analytical solutions of the horizontal and vertical infiltration of water, Aristotelian Univ. of Thessaloniki, Post doctoral thesis (in Greek).
Van Genunchten, M. T., 1983, An Hermitian finite element solution of the two-dimensional saturated-unsaturated flow equation,Adv. Water Resour. 6, 106–111.
Vinokur, M., 1974, Conservation equations of gas dynamics in curvilinear coordinate systems,J. Comput. Phys. 14, 104–125.
Warrick, A. W. and Lomen, D. O., 1977, Flow from a line source above a shallow water table,Soil Sci. Soc. Am. J. 41, 849–852.
Zyvoloski, G., Bruch, J. C., and Sloss, J. M., 1976, Solution of equation for two-dimensional infiltration problems,Soil Sci. 122(2), 65–70.
Author information
Authors and Affiliations
Rights and permissions
About this article
Cite this article
Tsakiris, G.P., Soulis, J.V. & Bellos, C.V. Two-dimensional unsaturated flow in irregularly shaped regions using a finite volume method. Transp Porous Med 6, 1–12 (1991). https://doi.org/10.1007/BF00136819
Received:
Revised:
Issue Date:
DOI: https://doi.org/10.1007/BF00136819