Semi-implicit WENO schemes for the shallow water equations

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Abstract

Recent studies have shown that first order semi-implicit well-balanced numerical schemes for open-channel flow equations appear to be very stable and efficient especially when performing long numerical simulations. The main reason for the semi-implicit schemes' efficiency lies in the fact that, unlike explicit schemes, they are not limited with the CFL stability condition. On the other hand, a class of explicit numerical schemes for hyperbolic balance laws, which include the weighted essentially non-oscillatory (WENO) reconstruction, although computationally demanding, have good shock capturing properties and achieve high order of accuracy. In this work we combine the WENO reconstruction with the semi-implicit approach in order to obtain a stable, efficient and accurate numerical scheme. The scheme properties are then analyzed through several test problems. We investigate the scheme stability and its behavior for different CFL numbers.

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