Numerical Simulation of Groundwater Flow and Pollution Transport Using the Dual Reciprocity and RBF Method

Karel Kovarik

doi:10.26552/com.c.2010.3a.5-10

Abstract

Transport of pollution is strongly influenced by groundwater flow. All numerical models of transport equation must be based on the groundwater flow models. The most of them suffer from numerical diffusion and/or oscillations of solution. Both phenomena lower the quality of results of these models. Plenty of authors are working on improving the quality of the numerical simulation. This paper presents the connection between a dual reciprocity method used to model groundwater flow and the meshless radial basis function methods used for a transport model. Both methods are one of the latest tools for modeling these phenomena.

Highlights

At the dawn of the use of numerical models, they were mostly used to study a groundwater flow in porous media
boundary element method (BEM) is not very suitable to solve time-dependent groundwater flow and, we decided to use the dual reciprocity method (DRM) which was developed like an enhancement of BEM
Equation (1) of groundwater flow is solved by a dual reciprocity method; the transport of pollution (Eq 4) is solved by the local radial basis function method (RBF) collocation method

Summary

Introduction

At the dawn of the use of numerical models, they were mostly used to study a groundwater flow in porous media. BEM is not very suitable to solve time-dependent groundwater flow and, we decided to use the dual reciprocity method (DRM) which was developed like an enhancement of BEM (see [6], [4]). The groundwater velocity caused an advection and increased the dispersion in porous media (see [1]). The advection can cause severe problems in numerical models of pollution transport. These problems were solved by different methods such as Galerkin characteristic method (see [5]) or random walk method [4]. The radial basis function method (RBF) was used for simulation of pollutant transport and this method seems to be quite successful

Basic equations

Dual Reciprocity Method

Local RBF Method

Numerical examples

Conclusions