Mathematical Modeling of Sediment-Laden shallow water flow using finite volume method

Carlo Arturo S.J. Mondonedo

Thesis (M.S. Civil Engineering)-University of the Philippines Diliman

Abstract

This study presents a two-dimensional hydraulic model of sediment-laden flow using finite volume method (FVM). The hydraulic equations used are the depth-integrated conservation equations of mass, momentum (longitudinal and transverse), suspended sediment, and total sediment. In the finite volume method, the mass, momentum, and suspended sediment fluxes of the conservation equations are calculated for each side of a finite volume based on an approximate Riemann problem solution. This Riemann problem solution involves approximating the fluxes by the characteristics solution of the governing equations. To solve the total sediment conservation equation, similar fluxes are generated using physically based, empirical, or semi-empirical sediment transport equations. The selection of sediment transport equation was based on field conditions.

The model was tested using data from physical model studies. The physical model was used to represent a real world channel with a bend. A sensitivity analysis for the transport mode exchange parameter was performed, which revealed a value of δ = 0.9. Limited simulation of water elevations showed that flow elevations in the prototype varied from 79.179 to 64.919 compared to 78.600 to 61.300 in the prototype. It may be noted that flow depths in the mathematical model were severely greater than those in the prototype. However, as shown in this study, the 2D sediment flow model developed using FVM shows satisfactory results for real world applications. Formulation are general enough for applications on other rivers in the country.