IDEAS home Printed from https://ideas.repec.org/a/gam/jmathe/v10y2022i20p3881-d946886.html
   My bibliography  Save this article

An Improved Component-Wise WENO-NIP Scheme for Euler System

Author

Listed:
  • Ruo Li

    (CAPT, LMAM and School of Mathematical Sciences, Peking University, Beijing 100871, China
    These authors contributed equally to this work.)

  • Wei Zhong

    (School of Mathematical Sciences, Peking University, Beijing 100871, China
    Northwest Institute of Nuclear Technology, Xi’an 710024, China
    These authors contributed equally to this work.)

Abstract

As is well known, due to the spectral decomposition of the Jacobian matrix, the WENO reconstructions in the characteristic-wise fashion (abbreviated as CH-WENO) need much higher computational cost and more complicated implementation than their counterparts in the component-wise fashion (abbreviated as CP-WENO). Hence, the CP-WENO schemes are very popular methods for large-scale simulations or situations whose full characteristic structures cannot be obtained in closed form. Unfortunately, the CP-WENO schemes usually suffer from spurious oscillations badly. The main objective of the present work is to overcome this drawback for the CP-WENO-NIP scheme, whose counterpart in the characteristic-wise fashion was carefully studied and well-validated numerically. The approximated dispersion relation (ADR) analysis is performed to study the spectral property of the CP-WENO-NIP scheme and then a negative-dissipation interval which leads to a high risk of causing spurious oscillations is discovered. In order to remove this negative-dissipation interval, an additional term is introduced to the nonlinear weights formula of the CP-WENO-NIP scheme. The improved scheme is denoted as CP-WENO-INIP. Accuracy test examples indicate that the proposed CP-WENO-INIP scheme can achieve the optimal convergence orders in smooth regions even in the presence of the critical points. Extensive numerical experiments demonstrate that the CP-WENO-INIP scheme is much more robust compared to the corresponding CP-WENO-NIP or even CH-WENO-NIP schemes for both 1D and 2D problems modeled via the Euler equations.

Suggested Citation

  • Ruo Li & Wei Zhong, 2022. "An Improved Component-Wise WENO-NIP Scheme for Euler System," Mathematics, MDPI, vol. 10(20), pages 1-21, October.
    • Handle: RePEc:gam:jmathe:v:10:y:2022:i:20:p:3881-:d:946886
    as

    Download full text from publisher

    File URL: https://www.mdpi.com/2227-7390/10/20/3881/pdf
    Download Restriction: no
    File URL: https://www.mdpi.com/2227-7390/10/20/3881/
    Download Restriction: no
    ---><---

    References listed on IDEAS

    as
    1. Wei Guo & Guang Lin & Andrew J. Christlieb & Jingmei Qiu, 2016. "An Adaptive WENO Collocation Method for Differential Equations with Random Coefficients," Mathematics, MDPI, vol. 4(2), pages 1-14, May.
    2. Sabir, Zulqurnain & Saoud, Sahar & Raja, Muhammad Asif Zahoor & Wahab, Hafiz Abdul & Arbi, Adnène, 2020. "Heuristic computing technique for numerical solutions of nonlinear fourth order Emden–Fowler equation," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 178(C), pages 534-548.
    3. Feng, Hui & Huang, Cong & Wang, Rong, 2014. "An improved mapped weighted essentially non-oscillatory scheme," Applied Mathematics and Computation, Elsevier, vol. 232(C), pages 453-468.
    4. Li, Ruo & Zhong, Wei, 2023. "A robust and efficient component-wise WENO scheme for Euler equations," Applied Mathematics and Computation, Elsevier, vol. 438(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. Hajipour, Mojtaba & Jajarmi, Amin & Malek, Alaeddin & Baleanu, Dumitru, 2018. "Positivity-preserving sixth-order implicit finite difference weighted essentially non-oscillatory scheme for the nonlinear heat equation," Applied Mathematics and Computation, Elsevier, vol. 325(C), pages 146-158.
    2. Naz, Sidra & Raja, Muhammad Asif Zahoor & Kausar, Aneela & Zameer, Aneela & Mehmood, Ammara & Shoaib, Muhammad, 2022. "Dynamics of nonlinear cantilever piezoelectric–mechanical system: An intelligent computational approach," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 196(C), pages 88-113.
    3. Jadoon, Ihtesham & Raja, Muhammad Asif Zahoor & Junaid, Muhammad & Ahmed, Ashfaq & Rehman, Ata ur & Shoaib, Muhammad, 2021. "Design of evolutionary optimized finite difference based numerical computing for dust density model of nonlinear Van-der Pol Mathieu’s oscillatory systems," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 181(C), pages 444-470.
    4. Huang, Cong & Chen, Li Li, 2021. "A simple WENO-AO method for solving hyperbolic conservation laws," Applied Mathematics and Computation, Elsevier, vol. 395(C).
    5. Tang, Shujiang & Feng, Yujie & Li, Mingjun, 2022. "Novel weighted essentially non-oscillatory schemes with adaptive weights," Applied Mathematics and Computation, Elsevier, vol. 420(C).
    6. Umar, Muhammad & Sabir, Zulqurnain & Raja, Muhammad Asif Zahoor & Baskonus, Haci Mehmet & Ali, Mohamed R. & Shah, Nehad Ali, 2023. "Heuristic computing with sequential quadratic programming for solving a nonlinear hepatitis B virus model," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 212(C), pages 234-248.
    7. Sabir, Zulqurnain & Raja, Muhammad Asif Zahoor & Guirao, Juan L.G. & Saeed, Tareq, 2021. "Meyer wavelet neural networks to solve a novel design of fractional order pantograph Lane-Emden differential model," Chaos, Solitons & Fractals, Elsevier, vol. 152(C).
    8. Zhang, Xin & Huang, Lintao & Qin, Xueyu & Qu, Feng & Yan, Chao, 2023. "An efficient finite difference IFWENO-THINC hybrid scheme for capturing discontinuities," Applied Mathematics and Computation, Elsevier, vol. 446(C).
    9. Huang, Cong, 2016. "WENO scheme with new smoothness indicator for Hamilton–Jacobi equation," Applied Mathematics and Computation, Elsevier, vol. 290(C), pages 21-32.
    10. Katta, Kiran K. & Nair, Ramachandran D. & Kumar, Vinod, 2015. "High-order finite volume shallow water model on the cubed-sphere: 1D reconstruction scheme," Applied Mathematics and Computation, Elsevier, vol. 266(C), pages 316-327.
    11. Li, Ruo & Zhong, Wei, 2023. "A robust and efficient component-wise WENO scheme for Euler equations," Applied Mathematics and Computation, Elsevier, vol. 438(C).
    12. Uroosa Arshad & Mariam Sultana & Ali Hasan Ali & Omar Bazighifan & Areej A. Al-moneef & Kamsing Nonlaopon, 2022. "Numerical Solutions of Fractional-Order Electrical RLC Circuit Equations via Three Numerical Techniques," Mathematics, MDPI, vol. 10(17), pages 1-16, August.

    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:gam:jmathe:v:10:y:2022:i:20:p:3881-:d:946886. 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: MDPI Indexing Manager (email available below). General contact details of provider: https://www.mdpi.com .

    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.