Slope limiters for radial basis functions applied to conservation laws with discontinuous flux function

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• 作者：Fayssal Benkhaldoun^a ; ^{fayssal@math.univ-paris13.fr" class="auth_mail" title="E-mail the corresponding author} ; A. Halassi^b ; ^{halassi.abdoul@gmail.com" class="auth_mail" title="E-mail the corresponding author} ; Driss Ouazar^c ; ^{ouazar@emi.ac.ma" class="auth_mail" title="E-mail the corresponding author} ; Mohammed Seaid^d ; ^{m.seaid@durham.ac.uk" class="auth_mail" title="E-mail the corresponding author} ; Ahmed Taik^b ; ^{taik_ahmed@yahoo.fr" class="auth_mail" title="E-mail the corresponding author}
• 关键词：Conservation laws ; Discontinuous flux function ; Radial basis functions ; Slope limiters ; Meshless method ; Traffic flow
• 刊名：Engineering Analysis with Boundary Elements
• 出版年：2016
• 出版时间：May 2016
• 年：2016
• 卷：66
• 期：Complete
• 页码：49-65
• 全文大小：2366 K

文摘

We present slope limiters in meshless radial basis functions for solving nonlinear equations of conservation laws with flux function that depends on discontinuous coefficients. The method is based on the local collocation formulation and does not require either generation of a grid or evaluation of an integral. Upwind techniques are used to allocate collocation points within the characteristic solutions and different slope limiter functions are investigated. The main advantages of this approach are neither mesh generations nor Riemann problem solvers are required during the solution process. Numerical results are shown for several test examples including models on vehicular traffic and two-phase flows. The main focus is to examine the performance of the proposed meshless method for shock-capturing property in conservation laws with discontinuous flux function. The obtained results demonstrate its ability to capture the main solution features.