Remediation of contaminated groundwater by meshless local weak forms

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• 作者：Mohammad Ilati ^{m.ilati@aut.ac.ir" class="auth_mail" title="E-mail the corresponding author} ; Mehdi Dehghan ; ^{mdehghan@aut.ac.ir" class="auth_mail" title="E-mail the corresponding author} ; ^{mdehghan.aut@gmail.com" class="auth_mail" title="E-mail the corresponding author}
• 关键词：Groundwater model ; Coupled non-linear advection&ndash ; diffusion&ndash ; reaction system ; Direct meshless local Petrov&ndash ; Galerkin method (DMLPG) ; Meshless local Petrov&ndash ; Galerkin method (MLPG) ; Local weak radial point interpolation method (LWRPIM) ; Local weak moving kriging method (LWMK)
• 刊名：Computers & Mathematics with Applications
• 出版年：2016
• 出版时间：November 2016
• 年：2016
• 卷：72
• 期：9
• 页码：2408-2416
• 全文大小：3779 K

文摘

In this paper, four meshless local weak form methods such as direct meshless local Petrov–Galerkin method (DMLPG), meshless local Petrov–Galerkin method (MLPG), local weak radial point interpolation method (LWRPIM) and local weak moving kriging method (LWMK) are applied to find the numerical solution of coupled non-linear advection–diffusion–reaction system arising in the prevention of groundwater contamination problem. A comparison between these methods is done from the perspective of accuracy and computational efficiency. An efficient fourth-order exponential time differencing Runge–Kutta method is utilized for the time discretization. The computational efficiency is the most significant advantage of the DMLPG method in comparison with the other meshless local weak form methods, because DMLPG reduces the computational costs, significantly. This is due to the fact that DMLPG shifts the numerical integrations over low-degree polynomials rather than over complicated shape functions. The main aim of this paper is to show that the meshless local weak form methods can be used for solving the system of non-linear partial differential equations especially coupled non-linear advection–diffusion–reaction system. The numerical results confirm the good efficiency of the proposed methods for solving our model.