基于有限体积HWENO格式的二维溃坝流模拟

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应用有限体积HWENO(Hermite Weighted Essentially Non-Oscillatory)格式、TVD(Total Variation Dimin-ishing)型Runge-Kutta法,建立了溃坝流模型,模拟了二维局部溃坝流和圆型溃坝流.HWENO格式的重构思想源于WENO重构,区别在于前者在其运算过程中同时涉及函数值及其一阶导数值.其优点是:在收敛阶相同的情况下,HWENO重构需要较少的点,因而HWENO重构较WENO重构更紧凑.二维局部溃坝流的计算结果显示波前间断波在靠近决口一侧的岸边形成雍水,决口两端形成2个非对称的漩涡,部分水位等高线尾部呈锯齿状,而这些结果恰恰与决口位置及决口两侧不对称、堤坝瞬间溃决产生的溃坝波向后推进产生的实际物理现象相吻合,并与已报道结果相一致.圆型溃坝的计算结果显示水位和流场均保持较好的对称性.以上结果表明本文模型适合处理类似溃坝流的浅水间断流运动. The finite volume HWENO (Hermite Weighted Essentially Non-Oscillatory) format and the TVD (Total Variation Dimin-ishing) Runge-Kutta method were used to establish the dam-break flow model and simulate the 2D local dam-break flow and the circular dam-break flow. The reconstruction idea of ​​HWENO is derived from WENO reconstruction, the difference lies in that the former involves both the function value and its first derivative value in its operation. The advantage is that the HWENO reconstruction requires less Therefore, the reconstruction of HWENO is more compact than that of WENO. The calculation results of two-dimensional local dam-break flow show that the wavefront discontinuity wave forms Yong water near the bank near the ripple, and two asymmetric eddies form at both ends of the ripple. Some of the water level contour lines have a serrated tail, and these results coincide with the actual physical phenomena caused by the unsteady bursting position and the two sides of the bursting burst, and the dam break waves caused by the instantaneous collapse of the dam, and are consistent with the reported results The results of circular dam - break show that the water level and the flow field all maintain good symmetry.The above results show that the model is suitable for dealing with the discontinuous flow of shallow water such as dam - break flow.
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