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A New Smoothness Indicator of Adaptive Order Weighted Essentially Non-Oscillatory Scheme for Hyperbolic Conservation Laws

Author

Listed:
  • Omer Musa

    (College of Energy and Power Engineering, Nanjing University of Aeronautics and Astronautics, Nanjing 210016, China
    These authors contributed equally to this work.)

  • Guoping Huang

    (College of Energy and Power Engineering, Nanjing University of Aeronautics and Astronautics, Nanjing 210016, China
    These authors contributed equally to this work.)

  • Mingsheng Wang

    (College of Energy and Power Engineering, Nanjing University of Aeronautics and Astronautics, Nanjing 210016, China)

Abstract

Adaptive order weighted essentially non-oscillatory scheme (WENO-AO(5,3)) has increased the computational cost and complexity of the classic fifth-order WENO scheme by introducing a complicated smoothness indicator for fifth-order linear reconstruction. This smoothness indicator is based on convex combination of three third-order linear reconstructions and fifth-order linear reconstruction. Therefore, this paper proposes a new simple smoothness indicator for fifth-order linear reconstruction. The devised smoothness indicator linearly combines the existing smoothness indicators of third-order linear reconstructions, which reduces the complexity of that of WENO-AO(5,3) scheme. Then WENO-AO(5,3) scheme is modified to WENO-O scheme with new and simple formulation. Numerical experiments in 1-D and 2-D were run to demonstrate the accuracy and efficacy of the proposed scheme in which WENO-O scheme was compared with original WENO-AO(5,3) scheme along with WENO-AO-N, WENO-Z, and WENO-JS schemes. The results reveal that the proposed WENO-O scheme is not only comparable to the original scheme in terms of accuracy and efficacy but also decreases its computational cost and complexity.

Suggested Citation

  • Omer Musa & Guoping Huang & Mingsheng Wang, 2020. "A New Smoothness Indicator of Adaptive Order Weighted Essentially Non-Oscillatory Scheme for Hyperbolic Conservation Laws," Mathematics, MDPI, vol. 9(1), pages 1-31, December.
    • Handle: RePEc:gam:jmathe:v:9:y:2020:i:1:p:69-:d:472236
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    References listed on IDEAS

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    1. Huang, Cong, 2016. "WENO scheme with new smoothness indicator for Hamilton–Jacobi equation," Applied Mathematics and Computation, Elsevier, vol. 290(C), pages 21-32.
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