Semi Discrete Scheme for the Solution of Flow in River Tinnelva
Chapter, Peer reviewed
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Original versionDissanayake, S., Sharma, R. & Lie, B. (2016) Semi Discrete Scheme for the Solution of Flow in River Tinnelva. 2016 9th EUROSIM Congress on Modelling and Simulation Oulu, Finland 12-16 September. 134-139. 10.1109/EUROSIM.2016.142
The Saint-Venant equation is a mathematical model which could be used to study water flow in an open channel, river etc. The Kurganov-Petrova (KP) method, which is a second order scheme, is used to solve the Saint-Venant equations with good stability. Water flow of a river between two hydropower stations in Norway has been simulated in this study using MATLAB and OpenModelica. The KP scheme has been used to discretize the Saint-Venant equations in spatial domain, yielding a collection of Ordinary Differential Equations (ODEs). These are then integrated with time using the variable step-length solvers in MATLAB: ode23t, ode23s, ode45, and fixed step-length solvers: The Euler method, the second and fourth order Runge Kutta method (RK2 and RK4). In OpenModelica built-in, variable step-length DASSL solver has been used. From the simulation, it was observed that all solvers produce more or less similar results. Volumetric flowrate calculation indicated numerical oscillation with variable step-length solvers in MATLAB. The results indicated that it is reasonable to match the order of the space and time discretization.