一维明渠非定常流数值计算稳定性分析

Stability Analysis on Numerical Calculation for One-dimensional Unsteady Open Channel Flow

通过分析明渠非定常流物理现象对差分格式稳定性的具体要求,提出通过非定常流微分方程组的无量纲形式建立差分格式的稳定性判别公式的方法。并通过对Lax格式的稳定性分析,得到含佛汝德数Fr和斯托罗哈数St的稳定性判别条件。并通过理论分析和数值计算验证了该条件的正确。从而证明通过圣·维南方程组的无量纲形式建立差分格式的稳定性条件是切实可行的且更精确的方法。

This paper investigates the specific requirements for the stability of the difference scheme which is required by the physical phenomenon of unsteady flow and advances a new method for setting the stability conditions of the difference schemes by using the non-dimensional form of Saint-Venant equations. the stability criterion of the diffusion difference scheme which contains Fr and St is obtained by means of stability analysis .The theoretical analysis and the numerical testing show that this stability criterion is correct and is more accurate than CFL condition. It is proved that the stability criterion set by using S. V non-dimensional equations is practicable and quite exact.