Numerical solution of 2d seepage flow problem using discrete singular convolution method

Abstract

Purpose

The purpose of this paper is to describe the implementation of discrete singular convolution (DSC) method to steady seepage flow while presenting one of the possible uses of DSC method in geotechnical engineering. It also aims to present the implementation of DSC to the problems with mixed boundary conditions.

Design/methodology/approach

Second order spatial derivatives of potential and stream functions in Laplace's equation are discretized using the DSC method in which the regularized Shannon's delta kernel is used as an approximation to delta distribution. After implementation of boundary conditions, the system of equations is solved for the unknown terms.

Findings

The results are compared with those obtained from the finite element method and the finite difference method.

Originality/value

The method is applied to the flow problem through porous medium for the first time.

Citation

Alyavuz, B. (2012), "Numerical solution of 2d seepage flow problem using discrete singular convolution method", International Journal of Numerical Methods for Heat & Fluid Flow, Vol. 22 No. 5, pp. 607-621. https://doi.org/10.1108/09615531211231262