Higher-order finite volume method with semi-Lagrangian scheme for one-dimensional conservation laws

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• 作者：Lang Wu (1)
  Songsong Li (1) (2)
  Boying Wu (1)
  
  1. Department of Mathematics ; Harbin Institute of Technology ; No. 92 ; West Da-Zhi Street ; Harbin ; 150001 ; China
  2. School of Management ; Harbin Institute of Technology ; No. 92 ; West Da-Zhi Street ; Harbin ; 150001 ; China
  
• 关键词：semi ; Lagrangian method ; WENO reconstructions ; Taylor expansion ; Euler system
• 刊名：Advances in Difference Equations
• 出版年：2015
• 出版时间：December 2015
• 年：2015
• 卷：2015
• 期：1
• 全文大小：1,313 KB
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• 刊物主题：Difference and Functional Equations; Mathematics, general; Analysis; Functional Analysis; Ordinary Differential Equations; Partial Differential Equations;
• 出版者：Springer International Publishing
• ISSN：1687-1847

文摘

In this paper, a high-order, semi-Lagrangian finite volume (SL-FV) method based on the WENO approach is proposed in order to manage one-dimensional conservation laws. The proposed method successfully integrates WENO reconstructions and the semi-Lagrangian method. More specifically, the Taylor expansion of time is used to approximate the time integration, deployed to boost temporal accuracy. Next, characteristic curves are applied to replace the time level by points in the semi-Lagrangian method. The value of these points can then be reconstructed by WENO schemes to increase their accuracy in space. Both high-order accuracies in space and time, respectively, are achieved. Moreover, computational experiments allow for a weaker CFL condition, provided in detail to validate the performance of the proposed SL-FV-based WENO method.