BSLM内共享特征曲线耦合Burgers方程的算法

IF 2.3 Q1 MATHEMATICS
Soyoon Bak, Yonghyeon Jeon
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引用次数: 0

摘要

摘要本文介绍了后向半拉格朗日方法(BSLM)中耦合Burgers方程中各物理粒子速度的传统观点的新视角。所提出的方法减少了通过观察单个具有速度的虚拟特征曲线来求解柯西问题的数量。这可以大大减少确定出发点的计算成本。然后,求解由单个虚特性曲线反映的导出系统。此外,还给出了一种有效的求解线性方程组的策略。通过四个算例验证了该方法的适应性和有效性。实验结果表明,该方法在时间和空间上分别具有三阶和四阶精度。此外,与现有沿两个不同速度粒子求解问题的方法相比,我们证实了该方法在保持精度的同时显著降低了计算成本。
本文章由计算机程序翻译,如有差异,请以英文原文为准。

Algorithms for coupled Burgers’ equations by sharing characteristic curves within BSLM

Algorithms for coupled Burgers’ equations by sharing characteristic curves within BSLM
Abstract This paper introduces a new perspective of the traditional view on the velocity of each physical particle in the coupled Burgers’ equation in the backward semi-Lagrangian method (BSLM). The proposed methods reduce the number of Cauchy problems to be solved by observing a single virtual characteristic curve with a velocity. This can drastically reduce the computational cost of determining the departure point. Then, we solve the derived system reflected by the single virtual characteristic curve. Moreover, an efficient strategy for the derived linear system of equations is provided. Four examples are tested to demonstrate the adaptability and efficiency of the proposed method. The test results show that the proposed method has third- and fourth-order accuracy in time and space, respectively. In addition, compared with the existing method of solving the problem along two particles with different velocities, we confirm that the proposed method significantly reduces computational cost while maintaining accuracy well.
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CiteScore
2.30
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