泥沙传输方程广义初边值问题的解析解与差分解比较

Comparison Results between the Analytical Solution and the Difference Numerical Solution for the Sediment Transport Equation

Cheng提出了泥沙传输问题的广义底边界条件并导出了具有复杂形式的解析解 ,解析解的求解过程中还需求解两个超越方程。本文一方面分析了解析解的复杂性 ,简化了超越方程根的搜索区间 ,另一方面 ,通过数值试验 ,得到了一类稳定的差分格式 ,格式参数为 0 .48≤Θ ≤ 1 ,数值例子表明 :对于稳定的差分格式 ,差分数值解具有很好的逼近效果。

Based on the generalized bottom boundary condition proposed by Cheng,Cheng derived an analytical solution with complicated form and we need to solve two transcend equations in order to get the analytical solution.In this paper,we analyse the difficulties in the analytical solution calculation.We reduce the searching regions for finding roots of the transcend equations easily.On the other hand,according to the numerical results,we found that the constructed difference schemes with scheme parameter 0.48≤Θ≤1 are stable and identify with the analytical solution.