摘要
圣维南方程组是工程实践中应用广泛的一类流体动力学方程组,4点线性隐格式亦是目前较为成熟的计算圣维南方程组的差分格式.依据非线性稳定性的定义,提出用增长因子M(τ)判别非线性差分格式的稳定性,针对圣维南方程组的4点线性隐式差分格式,给出了计算增长因子M(τ)切实可行的方法,并结合算例得到了增长因子M(τ)的一些近似数据.稳定性研究结果将有助于更好地选择时步长τ和网格步长Δx,对改善计算格式的稳定性具有指导意义.
Saint-Venant equations are a kind of fluid dynamics equations,which is widely used in engineering practice.Four-point linear implicit scheme is a common difference scheme for solving Saint-Venant equations at present.According to the definition of nonlinear stability,increase factor M（τ） is proposed to discriminate the stability of nonlinear difference schemes.A feasible method for calculating increase factor M（τ） of four-point linear implicit scheme of Saint-Venant equations is provided.Some approximate data of increase factor M（τ） are obtained through a case study.The results of stability studies will help make a better choice of time step τ and grid step Δx,which is of significance in improving the stability of calculation scheme.
出处
《河海大学学报（自然科学版）》
CAS
CSCD
北大核心
2011年第4期397-401,共5页
Journal of Hohai University(Natural Sciences)
基金
河海大学自然科学基金(理科类)(2008431411)
