Application of shallow water equations to analyze runoff processes in hilly farmlands

Abstract

Analysis of runoff processes in farmlands during storm events in particular is an important engineering topic. The shallow water equations describing the physical conservation laws are attractive tools for understanding motion of surface water. A numerical model is developed to reproduce surface water flows during storm events, using the finite element method and the finite volume method applied to the one-dimensional shallow water equations. The numerical model has the advantage of dealing with transcritical flows, wet, and dry processes, irregular channel bed slopes, and channel junctions involving multiply connected networks. Standard numerical tests demonstrated some of these features. Runoff processes from farmlands in a Japanese hilly area is analyzed with the numerical model coupled with another runoff model of black-box type. Parameters of the models are calibrated and validated using observed series of rainfall and runoff discharge data. Simulated results included submergence of hydraulic jumps and flood storage in farming plots, which are very informative in terms of assessing diverse functions of the farmlands.

Comparative Numerical Analysis on Momentum Flux Evaluation Schemes for Shallow Water Flows in Open Channel Networks

“…1 Doctoral Student, Research Fellow of Japan Society for the Promotion of Science, Graduate School of Agriculture, Kyoto University, Kitashirakawa-Oiwake-cho, Sakyo-ku, Kyoto 606-8502, Japan (Corresponding Author): E-mail: yoshih@kais.kyoto-u.ac.jp 2 Associate Professor, Graduate School of Agriculture, Kyoto University, Kitashirakawa-Oiwake-cho, Sakyo-ku, Kyoto 606-8502, Japan 3 Professor, Graduate School of Agriculture, Kyoto University, Kitashirakawa-Oiwake-cho, Sakyo-ku, Kyoto 606-8502, Japan the ability to consider the geometrical information of the domain (the contact angle of a channel bend and those of the reaches meeting at a junction) in evaluating the momentum flux, which has not been implemented in the other 1-D models (Szymkiewicz, 1991;Laugering and Schmidt, 2002;Carling et al, 2010;Roggensack, 2011). A similar but slightly reduced FEVM was proposed by Ishida et al (2011) and has been applied to the runoff analysis in irrigated paddy. Yoshioka and Unami (2012) developed a finite volume counterpart of the FEVM, referred to as Dual-FVM (DFVM).…”

Numerical comparison of shallow water models in multiply connected open channel networks

“…The authors developed spatially staggered numerical schemes for solving the 1-D SWEs based on both the FEM and FVM techniques with the heuristic upwind methods for handling the momentum equation [18,19,20], which are referred to as the Finite Element/Volume Methods (FEVMs). There also exists an FVM counterpart of the FEVMs, which is referred to as the Dual-Finite Volume Method (DFVM) [21].…”

“…These numerical methods assume different IBCs in handling the momentum equation at junctions, which are considered to have significant impacts on simulated hydraulic processes. However, their qualitative and quantitative comparisons have not been performed so far except for Yoshioka et al [20] who focused on steady problems and Yoshioka et al [23] [18], that of Unami and Alam [19], and that of Yoshioka et al [20]. This paper is an extended version of Yoshioka et al [23] that focused only on applications of the numerical schemes to dam break flash floods.…”

A finite element/volume method model of the depth‐averaged horizontally 2D shallow water equations

“…This study develops a new FEVM model of 2D SWEs, referred to as 2D FEVM model for subcritical, supercritical, and transcritical flows with horizontally 2D structures such that 1D models cannot appropriately capture. The 2D FEVM model is a 2D counterpart of the 1D FEVM models . Spatial discretization of the model is based on triangular mesh.…”

“…The 1D FEVM models are sufficiently accurate and robust for a wide range of problems; however, clearly, the models cannot be applied to the flows having horizontally 2D structures.This study develops a new FEVM model of 2D SWEs, referred to as 2D FEVM model for subcritical, supercritical, and transcritical flows with horizontally 2D structures such that 1D models cannot appropriately capture. The 2D FEVM model is a 2D counterpart of the 1D FEVM models [47][48][49]. Spatial discretization of the model is based on triangular mesh.…”