一维不恒定明流计算的三种高性能差分格式

本文首先讨论了从物理上对差分格式提出的四项要求,即守恒性、逆风性,正性(或保持单调性)和对间断的高分辨率.最近十多年来,在空气动力学领域中已提出许多满足这些要求的高性能格式.本文将其中广泛应用的三类格式,即通量向量分裂格式、通量差分裂格式及通量校正输运格式,移用到一维不恒定明流计算中.结合圣维南方程组的具体形式,并考虑天然河道的几何不规则性,导出了有关公式.最后通过一个溃坝算例对各种方法进行了验证,其结果十分接近,说明这些方法具有广阔的应用前景.

Three High-performance Difference Schemes for One- dimensional Unsteady Open Channel Flow Computations

This paper first summarizes four physically-posed requirements on the difference scheme used, i. e., conservation, upwindn}ss, positivity (or monotonicity-preserving), and high-resolution in discontinuities. In the recent over one decade, a lot of schemes satisfying these requirements have been proposed and widely used in gas dynamics. Among them, three types of schemes, including the flux-vector splitting (FVS), flux-difference splitting (FDS), and flux-corrected transport (FCT), are transferred to the computations for one-dimensional unsteady open channel flows, and related formulas are derived based on the concrete form of the Saint-Venant system of equations in consideration of the geometric irregulKrity of natural rivers. Finally, these methods are verified through a dam-break case study, yelding results that are close to each other, so that brilliant prospects of their applications can be foreseen.