High-order finite-volume weighted essentially non-oscillatory WENO-THETA6 method for the unsteady euler equations in one-dimensional computational fluid dynamics simulations

https://doi.org/10.31130/ud-jst.2025.23(6A).211E

Abstract: 164 | PDF: 76

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Author

  • Nguyen Minh Hieu Pham
    Computational Engineering Study Program, Vietnamese-German University, Vietnam
    Thien Binh Nguyen
    Computational Engineering Study Program, Vietnamese-German University, Vietnam

Keywords:

WENO-THETA6
Finite Volume Method
Euler equations
Hyperbolic conservation laws
Computational fluid dynamics

Abstract

A sixth-order finite-volume WENO method is proposed for one-dimensional problems with shocks in computational fluid dynamics simulations in which the hyperbolic Euler system are the governing equations. Finite-volume spatial discretization is a natural approach for hyperbolic problems, thanks to its conservation property. Adaptively switching between high-order and low-order reconstructed solutions at the finite-volume cell interfaces using a new set of symmetric smoothness indicators, the developed method excels in resolving small-scaled structures in smooth regions of the solution and sharply capturing shocks and discontinuities without introducing non-physical oscillatory disturbances in the numerical approximation in the vicinity of shocks. Numerical comparisons with other latest WENO methods demonstrate the outperformance of our proposed method.

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Published

Jun 30, 2025
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How to Cite
Pham, N. M. H., and T. B. Nguyen. “High-Order Finite-Volume Weighted Essentially Non-Oscillatory WENO-THETA6 Method for the Unsteady Euler Equations in One-Dimensional Computational Fluid Dynamics Simulations”. The University of Danang - Journal of Science and Technology, vol. 23, no. 6A, June 2025, pp. 74-80, doi:10.31130/ud-jst.2025.23(6A).211E.

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