Determination of optimum relaxation coefficient using finite difference method for groundwater flow

作者：Salmasi Farzin^*; Azamathulla Hazi Mohammad

来源：Arabian Journal of Geosciences, 2013, 6(9): 3409-3415.

DOI：10.1007/s12517-012-0591-9

• Laplace equation
• Numerical
• Successive over-relaxation (SOR)
• Explicit
• Finite difference
• Groundwater

Solution of Laplace%26apos;s equation can be done by iteration methods likes Jacobi, Gauss-Seidel, and successive over-relaxation (SOR). There is no new knowledge about the relaxation coefficient (omega) in SOR method. In this paper, we used SOR for solving Laplace%26apos;s differential equation with emphasis to obtaining the optimum (minimum) number of iterations with variations of the relaxation coefficient (omega). For this purpose, a code in FORTRAN language has been written to show the solution of a set of equations and its number of iterations. The results demonstrate that the optimum value of omega with minimum iterations is achieved between 1.7 and 1.9. Also, with increasing beta=Delta x/Delta y from 0.25 to 10, the number of iterations reduced and the optimum value is obtained for beta=2.

• 出版日期2013-9