A consistent finite difference local inertial model for shallow water simulation

Tomohiro Tanaka, Hidekazu Yoshioka, Sokly Siev, Hideto Fujii, Sarann Ly, Chihiro Yoshimura
Received 2018/12/11, Accepted 2019/04/09, Published 2019/05/29

Tomohiro Tanaka1), Hidekazu Yoshioka2), Sokly Siev3)4), Hideto Fujii4), Sarann Ly5), Chihiro Yoshimura6)

1) Graduate School of Global Environmental Studies, Kyoto University, Japan
2) Graduate School of Natural Science and Technology, Shimane University, Japan
3) Department of Global Engineering for Development, Environment and Society, Tokyo Institute of Technology, Japan
4) Faculty of Agriculture, Yamagata University, Japan
5) Faculty of Hydrology and Water Resources Engineering, Institute of Technology of Cambodia, Cambodia
6) Department of Civil and Environmental Engineering, Tokyo Institute of Technology, Japan

Hydrological-hydraulic modeling is a core technique in assessing surface water dynamics of rivers, lakes, and floodplains. The local inertial model (LIM) as a physically simplified model of the shallow water equations is essential for efficient numerical simulator of surface water dynamics. In this paper, we point out that the conventional semi-implicit finite difference scheme for the friction slope terms, despite being convenient, is not consistent in the sense that it may lead to incorrect numerical solutions if the temporal resolution is not high. We propose an alternative discretization to resolve this issue, which is more accurate and stable, and has comparable computational efficiency. The new numerical scheme is implemented into a modern hydrological-hydraulic model, demonstrating reasonable accuracy. The new scheme is also compared with a recently-proposed implicit scheme, demonstrating comparable theoretical and computational performances. The results indicate that the proposed scheme potentially serves as a new central core for numerical simulation with the LIM.

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Copyright (c) 2019 The Author(s) CC-BY 4.0

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