The use of a high-speed digital computer in the study of the hydrodynamics of geologic basins

In order to predict the migration of hydrocarbons, and also in the estimation of water supply and water conservation requirements, it is important to be able to evaluate quantitatively the magnitude and direction of steady-state flows in aquifer systems and geologic basins. In many areas, sufficient information is available on topography, water tables, structure, stratigraphy, and permeabilities to make numerical solution possible on a digital computer. The equations governing steady-state flow are discussed, and the relevant aspects of the numerical analysis necessary for a proper solution are indicated. Results are given of the use of an experimental program applied to a three-dimensional model. A special algorithm for estimating the successive overrelaxation factor used in the numerical procedure is discussed.

[1]  L. Richardson,et al.  The Deferred Approach to the Limit. Part I. Single Lattice. Part II. Interpenetrating Lattices , 1927 .

[2]  J. Crank,et al.  A practical method for numerical evaluation of solutions of partial differential equations of the heat-conduction type , 1947 .

[3]  W. Wasow,et al.  On the Truncation Error in the Solution of Laplace's Equation by Finite Differences1 , 1952 .

[4]  D. Young,et al.  On the Degree of Convergence of Solutions of Difference Equations to the Solution of the Dirichlet Problem , 1954 .

[5]  D. Young Iterative methods for solving partial difference equations of elliptic type , 1954 .

[6]  H. H. Rachford,et al.  The Numerical Solution of Parabolic and Elliptic Differential Equations , 1955 .

[7]  H. H. Rachford,et al.  On the numerical solution of heat conduction problems in two and three space variables , 1956 .

[8]  L. D. Gates,et al.  A Method of Block Iteration , 1956 .

[9]  Adrian E. Scheidegger,et al.  The physics of flow through porous media , 1957 .

[10]  Richard S. Varga,et al.  A Comparison of the Successive Overrelaxation Method and Semi-Iterative Methods Using Chebyshev Polynomials , 1957 .

[11]  R. V. Viswanathan Solution of Poisson’s equation by relaxation method—normal gradient specified on curved boundaries , 1957 .

[12]  On the Truncation Error in a Numerical Solution of the Neumann Problem for a Rectangle , 1958 .

[13]  Helene E. Kulsrud,et al.  A practical technique for the determination of the optimum relaxation factor of the successive over-relaxation method , 1961, Commun. ACM.