基于高精度WENO格式的二维溃坝波数值模拟

Numerical simulation of two-dimensional dam break wave based on high-accuracy WENO scheme

以浅水波方程组建立二维溃坝洪水模型,对经典WENO格式计算模板重新选取,得到各计算模板上重构多项式,对各个模板的局部光滑因子进行组合得到更高阶的全局光滑因子,建立相应的非线性权,将各模板上重构多项式加权处理得到计算单元界面数值通量的一个新高精度WENO格式,泰勒级数展开证明了该格式的非线性权比经典WENO格式的非线性权更接近理想权。将该格式、Lax-Friedrich通量分裂方法和局部特征分解方法相结合用于二维浅水方程的离散求解,模拟二维局部溃坝流和圆形溃坝流洪水的演进过程,模拟结果与实际流动符合较好,表明采用高精度WENO格式所建立的高分辨率溃坝模型能很好地模拟溃坝波的演进过程。

This paper presents a model of two-dimensional dam break flow based on shallow water equation.The reconstructed polynomial of each computational stencils is obtained by reelecting the classical WENO computational stencils and the global smoothness indicator is got by combining local smoothness indicators,and the corresponding nonlinear weights are established.A new high-accuracy WENO scheme for the numerical flux at the cell interface is obtained by weighting the reconstructed polynomials on each stencil.By expanding the Taylor series of smooth factors,it is proved that the nonlinear weight of this scheme is closer to the ideal weight than that of the classical WENO.The new scheme,Lax-Friedrich flux splitting method and local characteristic decomposition method are combined to solve the two-dimensional shallow water equation,and simulated 2 D partial dam-break flow and circular dam-break flow,the results agree well with the physical flow.Present numerical experiments show that the high-resolution dam break model can well simulate the evolution process of dam break wave.