Abstract
The two-dimensional local inertial equation (2D LIE) is a system of nonlinear hyperbolic partial differential equations describing shallow surface water flows. It is a central tool for modeling and analysis in hydraulics and hydrology and has been applied to a variety of numerical simulations of surface water flows. In this chapter, we review the physical basis of 2D LIE and present its modern numerical scheme. The key points in this scheme are the use of a space-time staggered discretization for efficient computation and the knowledge of local exact solutions to avoid the instability issue that the friction slope terms may cause. We also describe the accuracy, stability, and consistency of numerical schemes for 2D LIE, supporting the applicability of 2D LIE to simulating the flow field of Tonle Sap Lake.
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Yoshioka, H., Tanaka, T. (2022). Mathematics and Numerics of a Two-Dimensional Local Inertial Equation. In: Yoshimura, C., Khanal, R., Sovannara, U. (eds) Water and Life in Tonle Sap Lake. Springer, Singapore. https://doi.org/10.1007/978-981-16-6632-2_13
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DOI: https://doi.org/10.1007/978-981-16-6632-2_13
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