高分辨率熵相容算法在二维溃坝问题中的应用

High-resolution entropy consistent algorithm for the two-dimensional dam-break flows

该文将高分辨率熵相容算法推广应用于二维浅水波方程的数值求解问题中。该算法空间方向采用三阶中心加权基本无振荡(CWENO)重构,时间方向采用具有强稳定特点的优化三阶Runge-Kutta方法,数值通量采用总熵恰当耗散的高分辨率熵相容函数。用该算法实现了几个典型的二维溃坝问题的数值求解,并通过对所得结果的分析与讨论研究算法的性能。数值结果显示,高分辨率熵相容算法适用于二维溃坝问题的数值求解,且该算法具有分辨率高和数值稳定性强等优势。

The high-order, high-resolution entropy consistent algorithm is popularized to the two-dimensional shallow water equations. The scheme is reconstructed by the third-order central weighted essentially non-oscillatory （CWENO） reconstruction in space, the third-order optimal Runge-Kutta method in time and the new high-resolution entropy consistent flux function with the proper dissipation of the total entropy. The algorithm is utilized for analyzing the several special dam-break flows. Moreover, the numerical results are analyzed for the algorithm＇s property, which show that the new method is feasible for two-dimensional dam-break flows with high-resolution and strong-stability.