Preissmann四点隐格式对计算混合流动的适定性分析

普赖斯曼(Preissmann)四点隐格式为双对角隐式有限差分方法,具有结构简单、无条件稳定及对时间步长没有限制等优点,因而在河道、渠道、管道、河口潮流及管网、河网等非恒定缓流计算中,广泛用于数值求解圣维南方程组。针对四点隐格式应用于混合流模拟时的适定性进行了研究分析。结果表明,当采用激波捕捉法时,应用四点隐格式求解急缓混合流动在数学上为不适定。线性稳定性分析结果表明,如果计算域内存在临界流动,则四点隐格式为临界稳定。

Study on the Invalidity of Preissmann Scheme for Transcritical Flow

The Preissmann four-point scheme is a bi-diagonal implicit finite-difference method for solution of the St.Venant equations.It is unconditionally stable and extremely robust,and thus is widely used in the numerical simulation of one-dimensional unsteady sub-critical flow.The purpose is to study the limitations of Preissmann scheme when applied to trans-critical flow.The analysis results indicate that the Preissmann scheme cannot be used to simulate trans-critical flow using the shock capturing method.