IDEAS home Printed from https://ideas.repec.org/a/eee/chsofr/v198y2025ics0960077925005259.html

Shock wave dynamics via symmetry-driven analysis of a two-phase flow with the Chaplygin pressure law

Author

Listed:
  • Sharma, Aniruddha Kumar
  • Shagolshem, Sumanta
  • Arora, Rajan

Abstract

This article investigates wave propagation in a two-phase flow with Chaplygin pressure law, an equation where pressure inversely depends on density. The study employs Lie symmetries and symmetry-driven analysis to derive one-dimensional optimal subalgebras using the adjoint transformation and the invariant functions. Symmetry reductions yield several new exact solutions, and their physical behavior is examined graphically. Further, solutions such as peak-on waves, kinks, and parabolic solitons are identified using traveling wave transformation. Next, a framework of non-locally related PDE, including potential system and inverse potential systems (IPS), is designed to classify non-local symmetries and discover more non-trivial exact solutions for the model. Then, novel conservation laws are constructed using the non-linear self-adjointness property of the model. Finally, the research explores the dynamic evolution of characteristic shock, weak discontinuity, and their interactions using one of the developed solutions. It contributes to understanding two-phase flow, offering practical implications for astrophysics, high-speed aerodynamics, and energy systems with unconventional pressure laws.

Suggested Citation

  • Sharma, Aniruddha Kumar & Shagolshem, Sumanta & Arora, Rajan, 2025. "Shock wave dynamics via symmetry-driven analysis of a two-phase flow with the Chaplygin pressure law," Chaos, Solitons & Fractals, Elsevier, vol. 198(C).
    • Handle: RePEc:eee:chsofr:v:198:y:2025:i:c:s0960077925005259
    DOI: 10.1016/j.chaos.2025.116512
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0960077925005259
    Download Restriction: Full text for ScienceDirect subscribers only
    File URL: https://libkey.io/10.1016/j.chaos.2025.116512?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    As the access to this document is restricted, you may want to

    for a different version of it.

    References listed on IDEAS

    as
    1. Sil, Subhankar & Raja Sekhar, T. & Zeidan, Dia, 2020. "Nonlocal conservation laws, nonlocal symmetries and exact solutions of an integrable soliton equation," Chaos, Solitons & Fractals, Elsevier, vol. 139(C).
    2. Sil, Subhankar & Raja Sekhar, T., 2023. "Nonclassical potential symmetry analysis and exact solutions for a thin film model of a perfectly soluble anti-surfactant solution," Applied Mathematics and Computation, Elsevier, vol. 440(C).
    Full references (including those not matched with items on IDEAS)

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Mandal, Sougata & Sil, Subhankar & Ghosh, Sukhendu, 2024. "Lie symmetries and optimal classifications with certain modal approaches for the three-dimensional gas-dynamical equations," Chaos, Solitons & Fractals, Elsevier, vol. 181(C).
    2. Shagolshem, Sumanta & Bira, B. & Zeidan, D., 2023. "Optimal subalgebras and conservation laws with exact solutions for biological population model," Chaos, Solitons & Fractals, Elsevier, vol. 166(C).
    3. Simon, S. Gimnitz & Bira, B. & Zeidan, Dia, 2023. "Optimal systems, series solutions and conservation laws for a time fractional cancer tumor model," Chaos, Solitons & Fractals, Elsevier, vol. 169(C).
    4. Karna, Ashutosh Kumar & Satapathy, Purnima, 2023. "Lie symmetry analysis for the Cargo–Leroux model with isentropic perturbation pressure equation of state," Chaos, Solitons & Fractals, Elsevier, vol. 177(C).
    5. Sil, Subhankar & Raja Sekhar, T., 2023. "Nonclassical potential symmetry analysis and exact solutions for a thin film model of a perfectly soluble anti-surfactant solution," Applied Mathematics and Computation, Elsevier, vol. 440(C).
    6. Shagolshem, Sumanta & Bira, B. & Sil, Subhankar, 2022. "Conservation laws and some new exact solutions for traffic flow model via symmetry analysis," Chaos, Solitons & Fractals, Elsevier, vol. 165(P1).
    7. Mandal, Sougata & Sil, Subhankar & Ghosh, Sukhendu, 2025. "On the Lie symmetry analysis of three-dimensional perturbed shear flows," Chaos, Solitons & Fractals, Elsevier, vol. 191(C).
    8. Silambarasan, Rathinavel & Baskonus, Haci Mehmet & Vijay Anand, R. & Dinakaran, M. & Balusamy, Balamurugan & Gao, Wei, 2021. "Longitudinal strain waves propagating in an infinitely long cylindrical rod composed of generally incompressible materials and its Jacobi elliptic function solutions," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 182(C), pages 566-602.
    9. Manjit Singh & Shou-Fu Tian, 2023. "Lie symmetries, group classification and conserved quantities of dispersionless Manakov–Santini system in (2+1)-dimension," Indian Journal of Pure and Applied Mathematics, Springer, vol. 54(2), pages 312-329, June.

    More about this item

    Keywords

    ;
    ;
    ;
    ;
    ;
    ;
    ;

    Statistics

    Access and download statistics

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:eee:chsofr:v:198:y:2025:i:c:s0960077925005259. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Thayer, Thomas R. (email available below). General contact details of provider: https://www.journals.elsevier.com/chaos-solitons-and-fractals .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.