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The Finite Volume WENO with Lax–Wendroff Scheme for Nonlinear System of Euler Equations

Author

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  • Haoyu Dong

    (College of Mathematics and Systems Science, Shandong University of Science and Technology, Qingdao 266590, China)

  • Changna Lu

    (School of Mathematics and Statistics, Nanjing University of Information Science and Technology, Nanjing 210044, China)

  • Hongwei Yang

    (College of Mathematics and Systems Science, Shandong University of Science and Technology, Qingdao 266590, China)

Abstract

We develop a Lax–Wendroff scheme on time discretization procedure for finite volume weighted essentially non-oscillatory schemes, which is used to simulate hyperbolic conservation law. We put more focus on the implementation of one-dimensional and two-dimensional nonlinear systems of Euler functions. The scheme can keep avoiding the local characteristic decompositions for higher derivative terms in Taylor expansion, even omit partly procedure of the nonlinear weights. Extensive simulations are performed, which show that the fifth order finite volume WENO (Weighted Essentially Non-oscillatory) schemes based on Lax–Wendroff-type time discretization provide a higher accuracy order, non-oscillatory properties and more cost efficiency than WENO scheme based on Runge–Kutta time discretization for certain problems. Those conclusions almost agree with that of finite difference WENO schemes based on Lax–Wendroff time discretization for Euler system, while finite volume scheme has more flexible mesh structure, especially for unstructured meshes.

Suggested Citation

  • Haoyu Dong & Changna Lu & Hongwei Yang, 2018. "The Finite Volume WENO with Lax–Wendroff Scheme for Nonlinear System of Euler Equations," Mathematics, MDPI, vol. 6(10), pages 1-17, October.
    • Handle: RePEc:gam:jmathe:v:6:y:2018:i:10:p:211-:d:176572
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    References listed on IDEAS

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    3. Changna Lu & Luoyan Xie & Hongwei Yang, 2018. "The Simple Finite Volume Lax-Wendroff Weighted Essentially Nonoscillatory Schemes for Shallow Water Equations with Bottom Topography," Mathematical Problems in Engineering, Hindawi, vol. 2018, pages 1-15, February.
    4. Shaowei Zhou & Weihai Zhang, 2012. "Discrete-Time Indefinite Stochastic LQ Control via SDP and LMI Methods," Journal of Applied Mathematics, Hindawi, vol. 2012, pages 1-14, February.
    5. Lu, Changna & Fu, Chen & Yang, Hongwei, 2018. "Time-fractional generalized Boussinesq equation for Rossby solitary waves with dissipation effect in stratified fluid and conservation laws as well as exact solutions," Applied Mathematics and Computation, Elsevier, vol. 327(C), pages 104-116.
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    Cited by:

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    2. Runhuan Sun & Li Tang & Yanjun Liu, 2022. "Boundary Controller Design for a Class of Horizontal Belt Transmission System with Boundary Vibration Constraint," Mathematics, MDPI, vol. 10(9), pages 1-19, April.

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