用立方赫尔墨特 B 样条法模拟修正等宽波方程的新视角

IF 2.1 3区 物理与天体物理 Q2 ACOUSTICS Wave Motion Pub Date : 2024-05-06 DOI:10.1016/j.wavemoti.2024.103342
Selçuk Kutluay, Nuri Murat Yağmurlu, Ali Sercan Karakaş
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引用次数: 0

摘要

在当前的研究中,将采用一种新技术对修正等宽(MEW)方程进行数值处理,该技术采用了搭配有限元法,其中使用了立方赫米特 B-样条函数作为试验函数。为了测试该方法的准确性和效率,将研究四个不同的实验问题,即单个孤波的运动、两个孤波的相互作用、三个孤波的相互作用以及具有 Maxwellian 初始条件的孤子的产生。为了验证所提方法的有效性和可靠性,将新得到的误差规范 L2 和 L∞ 以及三个守恒常数与文献中给出的相同参数下的一些其他数值结果进行了比较。此外,还给出了新获得的数值结果的一些波形,以证明每个测试问题都展示了精确的物理模拟。与其他方法相比,拟议方法的优势在于使用 Legendre 和 Chebyshev 多项式根处的内点。这一优势使得空间方向上的元素数量更少,精度更高。数值实验结果清楚地表明,即使网格相对较粗,所提出的方案也能产生更精确的结果。
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A novel perspective for simulations of the Modified Equal-Width Wave equation by cubic Hermite B-spline collocation method

In the current study, the Modified Equal-Width (MEW) equation will be handled numerically by a novel technique using collocation finite element method where cubic Hermite B-splines are used as trial functions. To test the accuracy and efficiency of the method, four different experimental problems; namely, the motion of a single solitary wave, interaction of two solitary waves, interaction of three solitary waves and the birth of solitons with the Maxwellian initial condition will be investigated. In order to verify, the validity and reliability of the proposed method, the newly obtained error norms L2 and L as well as three conservation constants have been compared with some of the other numerical results given in the literature at the same parameters. Furthermore, some wave profiles of the newly obtained numerical results have been given to demonstrate that each test problem exhibits accurate physical simulations. The advantage of the proposed method over other methods is the usage of inner points at Legendre and Chebyshev polynomial roots. This advantage results in better accuracy with less number of elements in spatial direction. The results of the numerical experiments clearly reveal that the presented scheme produces more accurate results even with comparatively coarser grids.

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来源期刊
Wave Motion
Wave Motion 物理-力学
CiteScore
4.10
自引率
8.30%
发文量
118
审稿时长
3 months
期刊介绍: Wave Motion is devoted to the cross fertilization of ideas, and to stimulating interaction between workers in various research areas in which wave propagation phenomena play a dominant role. The description and analysis of wave propagation phenomena provides a unifying thread connecting diverse areas of engineering and the physical sciences such as acoustics, optics, geophysics, seismology, electromagnetic theory, solid and fluid mechanics. The journal publishes papers on analytical, numerical and experimental methods. Papers that address fundamentally new topics in wave phenomena or develop wave propagation methods for solving direct and inverse problems are of interest to the journal.
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