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

Advances in Difference Equations

Songsong Li¹  Lang Wu¹  Boying Wu² 

[1] Department of Mathematics, Harbin Institute of Technology, Harbin, China;School of Management, Harbin Institute of Technology, Harbin, China

关键词: semi-Lagrangian method;    WENO reconstructions;    Taylor expansion;    Euler system;   

DOI  :  10.1186/s13662-014-0353-y

学科分类：数学（综合）

来源: SpringerOpen

【 摘 要 】

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.

【 授权许可】

CC BY