不规则地形上浅水模拟平衡性的实现

天然河道地形复杂而无规律,采用守恒型浅水方程进行水流运动数值模拟时往往会出现不平衡现象。本文在任意四边形网格的基础上采用Roe方法对守恒型浅水方程进行离散,针对连续方程离散后所出现的不平衡性,从原方程及离散方法的物理实质出发提出了局部水位法,使该问题得以解决;参照数值通量构造方法采用有限体积法构造了底坡项的离散方式,消除了动量方程底坡项离散后可能出现的虚假流动现象,同时保证了物理量的守恒性。将模型应用于松花江佳木斯河段的水流模拟中,其计算结果表现出了良好的守恒性、收敛性和平衡性。     

GLOBAL ANALYSIS OF SIS EPIDEMIC MODEL WITH A SIMPLE VACCINATION AND MULTIPLE ENDEMIC EQUILIBRIA

An SIS epidemic model with a simple vaccination is investigated in this article. The efficiency of vaccine, the disease-related death rate and population dynamics are also considered in this model. The authors find two threshold R0 and Rc (Rc may not exist). There is a unique endemic equilibrium for R0 > 1 or Rc = R0; there are two endemic equilibria for Rc < R0 < 1; and there is no endemic equilibrium for R0 < Rc < 1. When Rc exists, there is a backward bifurcation from the disease-free equilibrium for R0 = 1. They analyze the stability of equilibria and obtain the globally dynamic behaviors of the model. The results acquired in this article show that an accurate estimation of the efficiency of vaccine is necessary to prevent and controll the spread of disease.