Lie symmetry and variational analysis of a blood flow model with body forces

IF 2.8 3区工程技术 Q2 MECHANICS

International Journal of Non-Linear Mechanics Pub Date : 2025-06-28 DOI:10.1016/j.ijnonlinmec.2025.105191

Debendra Prasad Panda, Manoj Pandey

引用次数: 0

Abstract

This work presents a comprehensive analysis of a one-dimensional nonlinear blood flow model that incorporates a body force term, using both Eulerian and Lagrangian descriptions. By introducing Lagrangian coordinates, the system is reformulated as a single second-order partial differential equation derived from a variational principle. Lie symmetry analysis is performed in both coordinate systems, leading to the construction of one-dimensional optimal systems and exact invariant solutions. Variational symmetries satisfying Noether’s criterion are identified, and the associated conservation laws are obtained using Noether’s theorem. Finally, the evolution of weak discontinuity waves is investigated using an exact solution, revealing important nonlinear effects such as wave steepening and shock formation. The results highlight the role of symmetries and conservation laws in understanding wave behavior in physiological flow models.

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具有身体力的血流模型的Lie对称性和变分分析

这项工作提出了一个综合分析的一维非线性血流模型，其中包括一个身体的力项，使用欧拉和拉格朗日的描述。通过引入拉格朗日坐标，将系统重新表述为由变分原理导出的单一二阶偏微分方程。在两种坐标系下进行李对称分析，得到一维最优系统和精确不变解。对满足诺特准则的变分对称进行了识别，并利用诺特定理得到了相应的守恒定律。最后，用精确解研究了弱不连续波的演化，揭示了重要的非线性效应，如波浪陡增和激波形成。这些结果突出了对称性和守恒定律在理解生理流动模型中的波动行为方面的作用。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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来源期刊

International Journal of Non-Linear Mechanics 物理-力学

CiteScore

5.50

自引率

9.40%

发文量

192

审稿时长

67 days

期刊介绍： The International Journal of Non-Linear Mechanics provides a specific medium for dissemination of high-quality research results in the various areas of theoretical, applied, and experimental mechanics of solids, fluids, structures, and systems where the phenomena are inherently non-linear. The journal brings together original results in non-linear problems in elasticity, plasticity, dynamics, vibrations, wave-propagation, rheology, fluid-structure interaction systems, stability, biomechanics, micro- and nano-structures, materials, metamaterials, and in other diverse areas. Papers may be analytical, computational or experimental in nature. Treatments of non-linear differential equations wherein solutions and properties of solutions are emphasized but physical aspects are not adequately relevant, will not be considered for possible publication. Both deterministic and stochastic approaches are fostered. Contributions pertaining to both established and emerging fields are encouraged.