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arXiv 1812.00530math.NAcs.NA
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一种用于超保量守恒律的准拉格朗日移动网格不连续伽辽金方法

A quasi-Lagrangian moving mesh discontinuous Galerkin method for hyperbolic conservation laws

Xiamen University(厦门大学);University of Kansas(堪萨斯大学)

Dongmi Luo, Weizhang Huang, Jianxian Qiu

AI总结:

本文提出了一种结合不连续伽辽金方法和移动网格策略的移动网格不连续伽辽金方法,用于求解超保量守恒律。该方法在时间上连续移动网格,在空间上有序排列,通过准拉格朗日方式在移动网格上离散超保量守恒律,无需对物理变量进行插值。引入了两个对流项,并在DG格式中自然地进行了离散化。数值结果表明,该方法在光滑解问题中达到理论预测的收敛阶,并能捕捉激波并在非光滑区域集中网格点。其优势在于优于均匀网格,并且对网格光滑性不敏感。

摘要:

本文提出了一种用于超保量守恒律数值求解的移动网格不连续伽辽金方法。该方法结合了不连续伽辽金方法和基于移动网格偏微分方程方法的网格运动策略,能够在时间和空间上连续、有序地移动网格。该方法以准拉格朗日方式在移动网格上离散超保量守恒律,其中网格运动被连续处理,无需从旧网格到新网格对物理变量进行插值。由网格运动诱导出两个对流项,其离散化自然地包含在DG格式中。展示了若干一维和二维标量及系统守恒律的数值结果。证明了移动网格DG方法在具有光滑解的问题中达到理论预测的收敛阶,并能够捕捉激波并在非光滑区域集中网格点。还展示了其优于均匀网格以及对网格光滑性不敏感的优势。

英文摘要:

A moving mesh discontinuous Galerkin method is presented for the numerical solution of hyperbolic conservation laws. The method is a combination of the discontinuous Galerkin method and the mesh movement strategy which is based on the moving mesh partial differential equation approach and moves the mesh continuously in time and orderly in space. It discretizes hyperbolic conservation laws on moving meshes in the quasi-Lagrangian fashion with which the mesh movement is treated continuously and no interpolation is needed for physical variables from the old mesh to the new one. Two convection terms are induced by the mesh movement and their discretization is incorporated naturally in the DG formulation. Numerical results for a selection of one- and two-dimensional scalar and system conservation laws are presented. It is shown that the moving mesh DG method achieves the theoretically predicted order of convergence for problems with smooth solutions and is able to capture shocks and concentrate mesh points in non-smooth regions. Its advantage over uniform meshes and its insensitiveness to mesh smoothness are also demonstrated.

机构、总结、中文摘要均由AI分析而来,可能存在错误,请以论文正文为准。

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