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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
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    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. 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.
    3. Li, Ruo & Zhong, Wei, 2023. "A robust and efficient component-wise WENO scheme for Euler equations," Applied Mathematics and Computation, Elsevier, vol. 438(C).
    4. 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.
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