We derive boundary conditions and estimates based on the energy and entropy analysis of systems of the nonlinear shallow water equations in two spatial dimensions. It is shown that the energy method provides more details, but is fully consistent with the entropy analysis. The details brought forward by the nonlinear energy analysis allow us to pinpoint where the difference between the linear and nonlinear analysis originate. We find that the result from the linear analysis does not necessarily hold in the nonlinear case. The nonlinear analysis leads in general to a different minimal number of boundary conditions compared with the linear analysis. In particular, and contrary to the linear case, the magnitude of the flow does not influence the number of required boundary conditions.
翻译:我们根据对两个空间维度的非线性浅水方程式系统的能量和酶分析得出边界条件和估计,显示能源方法提供了更多细节,但与酶分析完全一致,非线性能源分析提出的细节使我们能够确定线性和非线性分析的起源点,我们发现线性分析的结果不一定在非线性案件中有效,非线性分析的结果一般导致与线性分析相比的边界条件数量少得多,特别是,与线性分析相反,流动的规模并不影响所需边界条件的数量。