High-order weno-θ6 finite volume method for two-dimensional compressible euler equations
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Đã chọn:High-order finite-volume WENO-θ6 scheme
Finite Volume Method
Shock Capturing
Riemann problems
Computational Fluid Dynamics
Tóm tắt
A high-order finite-volume WENO-θ6 method is proposed for two-dimensional compressible Euler equations. The method employs θ-adaptive weighting to combine fifth-order upwind and sixth-order central reconstructions based on local smoothness indicators, performed in characteristic fields to enhance stability near sharp gradients and discontinuities. The conservation property is naturally preserved within the finite-volume framework. We validate the proposed scheme against WENO-Z5 and WENO-Z6 on standard benchmark problems in computational fluid dynamics, including shock tube problems, Rayleigh–Taylor and Kelvin–Helmholtz instabilities, Double Mach Reflection, Forward-Facing Step, and 2D Riemann problems. Results demonstrate that WENO-θ6 achieves sixth-order accuracy in smooth regions, captures shocks sharply without spurious oscillations, resolves fine vortical structures with lower numerical dissipation, and maintains solution symmetry, proving the method a reliable, strictly conservative tool for compressible flow simulations.
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Jun 30, 2026
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Pham, N. M. H., và T. B. Nguyen. “High-Order Weno-θ6 Finite Volume Method for Two-Dimensional Compressible Euler Equations”. Tạp Chí Khoa học Và Công nghệ Đại học Đà Nẵng, vol 24, số p.h 6A, Tháng Sáu 2026, tr 40-49, doi:10.31130/ud-jst.2026.24(6A).112E.
