Analytical Analysis of Linear Discretization Strategies in Unsteady Open Channel Flows

The equations governing unsteady flow in channels are ([8], [7], [1], [2]) (1)$$\frac{{\partial v}}{{\partial t}} + v\frac{{\partial v}}{{\partial x}} + \frac{{\partial y}}{{\partial x}}+g\left({{S_1} - {S_0}} \right) + \frac{{vq}}{A} = 0$$(2)$$T\frac{{\partial y}}{{\partial t}} + vT\frac{{\partial y}}{{\partial x}} + A\frac{{\partial v}}{{\partial x}} - q = 0$$ in which t = time, x = distance along the channel, v(x, t) = the average velocity, …