Lie Symmetry Analysis, Optimal Systems, and Conservation Laws for Two-Dimensional Compressible Euler Equations With Chaplygin Gas

IF 1.8 3区 数学 Q1 MATHEMATICS, APPLIED
Dia Zeidan, Sandhya Maurya, Manoj Pandey
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引用次数: 0

Abstract

In this paper, we employ Lie classical symmetries to analyze the two-dimensional isentropic Euler equations system for Chaplygin gas. Adjoint operators play an essential part in deriving an optimal system of subalgebras. Introducing a novel approach, we present a method for constructing a two-dimensional optimal system through strategic adjoint actions which is using the largest chain of removal operators. By employing the vector fields obtained from the optimal system, we efficiently transform the governing model into a collection of ordinary differential equations. Consequently, we attain group invariant solutions and elucidate their graphical behavior. Moreover, we obtain conservation laws for the governing model by utilizing it is nonlinear self-adjoint properties and employing the direct multiplier method.

李氏对称分析,最优系统,和守恒定律的二维可压缩欧拉方程与Chaplygin气体
本文利用李经典对称理论对二维等熵欧拉方程组进行了分析。伴随算子在导出子代数的最优系统中起着重要的作用。引入一种新的方法,提出了一种利用最大移除算子链,通过策略伴随作用构造二维最优系统的方法。利用从最优系统得到的向量场,我们有效地将控制模型转化为常微分方程的集合。因此,我们得到了群不变解,并阐明了它们的图形行为。利用控制模型的非线性自伴随性质,采用直接乘子法,得到了控制模型的守恒律。
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来源期刊
CiteScore
4.90
自引率
6.90%
发文量
798
审稿时长
6 months
期刊介绍: Mathematical Methods in the Applied Sciences publishes papers dealing with new mathematical methods for the consideration of linear and non-linear, direct and inverse problems for physical relevant processes over time- and space- varying media under certain initial, boundary, transition conditions etc. Papers dealing with biomathematical content, population dynamics and network problems are most welcome. Mathematical Methods in the Applied Sciences is an interdisciplinary journal: therefore, all manuscripts must be written to be accessible to a broad scientific but mathematically advanced audience. All papers must contain carefully written introduction and conclusion sections, which should include a clear exposition of the underlying scientific problem, a summary of the mathematical results and the tools used in deriving the results. Furthermore, the scientific importance of the manuscript and its conclusions should be made clear. Papers dealing with numerical processes or which contain only the application of well established methods will not be accepted. Because of the broad scope of the journal, authors should minimize the use of technical jargon from their subfield in order to increase the accessibility of their paper and appeal to a wider readership. If technical terms are necessary, authors should define them clearly so that the main ideas are understandable also to readers not working in the same subfield.
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