Third Order Reconstruction of the KP Scheme for Model of River Tinneselva

Abstract

The Saint-Venant equation/Shallow Water Equation is used to simulate ow of river, ow of liquid in an open channel, tsunami etc. The Kurganov-Petrova (KP) scheme which was developed based on the local speed of discontinuity propagation, can be used to solve hyperbolic type partial di_erential equations (PDEs), hence can be used to solve the Saint-Venant equation. The KP scheme is semi discrete: PDEs are discretized in the spatial domain, resulting in a set of Ordinary Di_erential Equations (ODEs). In this study, the common 2nd order KP scheme is extended into 3rd order scheme while following the Weighted Essentially Non-Oscillatory (WENO) and Central WENO (CWENO) reconstruction steps. Both the 2nd order and 3rd order schemes have been used in simulation in order to check the suitability of the KP schemes to solve hyperbolic type PDEs. The simulation results indicated that the 3rd order KP scheme shows some better stability compared to the 2nd order scheme. Computational time for the 3rd order KP scheme for variable step-length ode solvers in MATLAB is less compared to the computational time of the 2nd order KP scheme. In addition, it was con_rmed that the order of the time integrators essentially should be lower compared to the order of the spatial discretization. However, for computation of abrupt step changes, the 2nd order KP scheme shows a more accurate solution.