IDEAS home Printed from https://ideas.repec.org/a/wly/jnlamp/v2023y2023i1n8963904.html

A Finite Difference Method for Solving Unsteady Fractional Oldroyd‐B Viscoelastic Flow Based on Caputo Derivative

Author

Listed:
  • Fang Wang
  • Yu Wang

Abstract

In this paper, the effect of a fractional constitutive model on the rheological properties of fluids and its application in numerical simulation are investigated, which is important to characterize the rheological properties of fluids and physical characteristics of materials more accurately. Based on this consideration, numerical simulation and analytical study of unsteady fractional Oldroyd‐B viscoelastic flow are carried out. In order to improve the degree of accuracy, the mixed partial derivative including the fractional derivative in the differential equation is converted effectively by integrating by parts instead of by direct discretization. Then, the stability, convergence, and unique solvability of the difference scheme are verified. The validity of the finite difference method is tested by making comparisons with analytical solutions for two kinds of fractional Oldroyd‐B viscoelastic flow. Numerical results obtained using the finite difference method are in good agreement with analytical solutions obtained via the variable separation method. Viscoelastic characteristics of the unsteady Poiseuille flow are similar to the second‐order fluid or integer‐order Oldroyd‐B fluid when the parameter is close to 0 or to 1. Oscillation characteristics of fractional viscoelastic oscillatory flow are similar to those of the classical viscoelastic fluid under the same condition. Compared with the previous research, the present work studies the rheological properties of fluids with the finite difference method, and the application of fractional constitutive models in describing the rheological properties of fluids is developed. Meanwhile, more cases reflecting the fractional‐order characteristics are given. The present method can accurately capture the flow characteristics of unsteady fractional Oldroyd‐B viscoelastic fluid and is applicable for the generalized fractional fluid.

Suggested Citation

  • Fang Wang & Yu Wang, 2023. "A Finite Difference Method for Solving Unsteady Fractional Oldroyd‐B Viscoelastic Flow Based on Caputo Derivative," Advances in Mathematical Physics, John Wiley & Sons, vol. 2023(1).
    • Handle: RePEc:wly:jnlamp:v:2023:y:2023:i:1:n:8963904
    DOI: 10.1155/2023/8963904
    as

    Download full text from publisher

    File URL: https://doi.org/10.1155/2023/8963904
    Download Restriction: no
    File URL: https://libkey.io/10.1155/2023/8963904?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
    ---><---

    References listed on IDEAS

    as
    1. Dassios, Ioannis K. & Baleanu, Dumitru I., 2018. "Caputo and related fractional derivatives in singular systems," Applied Mathematics and Computation, Elsevier, vol. 337(C), pages 591-606.
    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. Tawfik, Ashraf M. & Abdelhamid, Hamdi M., 2021. "Generalized fractional diffusion equation with arbitrary time varying diffusivity," Applied Mathematics and Computation, Elsevier, vol. 410(C).
    2. Dassios, Ioannis & Vaca, Angel & Milano, Federico, 2024. "On hybrid dynamical systems of differential–difference equations," Chaos, Solitons & Fractals, Elsevier, vol. 187(C).
    3. Dassios, Ioannis & Tzounas, Georgios & Liu, Muyang & Milano, Federico, 2022. "Singular over-determined systems of linear differential equations," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 197(C), pages 396-412.
    4. Liao, Xiaozhong & Wang, Yong & Yu, Donghui & Lin, Da & Ran, Manjie & Ruan, Pengbo, 2023. "Modeling and analysis of Buck-Boost converter with non-singular fractional derivatives," Chaos, Solitons & Fractals, Elsevier, vol. 169(C).
    5. Fabio Tramontana & Laura Gardini, 2021. "Revisiting Samuelson’s models, linear and nonlinear, stability conditions and oscillating dynamics," Journal of Economic Structures, Springer;Pan-Pacific Association of Input-Output Studies (PAPAIOS), vol. 10(1), pages 1-15, December.
    6. Dassios, Ioannis & Tzounas, Georgios & Milano, Federico, 2019. "The Möbius transform effect in singular systems of differential equations," Applied Mathematics and Computation, Elsevier, vol. 361(C), pages 338-353.
    7. Su, Guangwang & Lu, Liang & Tang, Bo & Liu, Zhenhai, 2020. "Quasilinearization technique for solving nonlinear Riemann-Liouville fractional-order problems," Applied Mathematics and Computation, Elsevier, vol. 378(C).
    8. Fernando Ortega & Maria Filomena Barros, 2020. "The Samuelson macroeconomic model as a singular linear matrix difference equation," Journal of Economic Structures, Springer;Pan-Pacific Association of Input-Output Studies (PAPAIOS), vol. 9(1), pages 1-10, December.
    9. Alijani, Zahra & Baleanu, Dumitru & Shiri, Babak & Wu, Guo-Cheng, 2020. "Spline collocation methods for systems of fuzzy fractional differential equations," Chaos, Solitons & Fractals, Elsevier, vol. 131(C).
    10. Maria Filomena Barros & Fernando Ortega, 2019. "An optimal equilibrium for a reformulated Samuelson economic discrete time system," Journal of Economic Structures, Springer;Pan-Pacific Association of Input-Output Studies (PAPAIOS), vol. 8(1), pages 1-10, December.

    More about this item

    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:wly:jnlamp:v:2023:y:2023:i:1:n:8963904. 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: Wiley Content Delivery (email available below). General contact details of provider: https://onlinelibrary.wiley.com/journal/3197 .

    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.