Improved localized radial basis function collocation method for multi-dimensional convection-dominated problems

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• 作者：D.F. Yun^a ; ^b ; ^{dongfayun2-c@my.cityu.edu.hk" class="auth_mail" title="E-mail the corresponding author} ; Y.C. Hon^b ; ^{maychon@cityu.edu.hk" class="auth_mail" title="E-mail the corresponding author}
• 关键词：Localized radial basis function collocation method ; Convection-dominated ; Upwind scheme ; Burger׳s equation ; Singular perturbation
• 刊名：Engineering Analysis with Boundary Elements
• 出版年：2016
• 出版时间：June 2016
• 年：2016
• 卷：67
• 期：Complete
• 页码：63-80
• 全文大小：3912 K

文摘

In this paper, the localized radial basis function collocation method (LRBFCM) is combined with the partial upwind scheme for solving convection-dominated fluid flow problems. The localization technique adopted in LRBFCM has shown to be effective in avoiding the well known ill-conditioning problem of traditional meshless collocation method with globally defined radial basis functions (RBFs). For convection–diffusion problems with dominated convection, stiffness in the form of boundary/interior layers and shock waves emerge as convection overwhelms diffusion. We show in this paper that these kinds of stiff problems can be well tackled by combining the LRBFCM with partial upwind scheme. For verification, several numerical examples are given to demonstrate that this scheme improves the LRBFCM in providing stable, accurate, and oscillation-free solutions to one- and two-dimensional Burgers׳ equations with shock waves and singular perturbation problems with turning points and boundary layers.