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Error Analysis of Control Volume Finite Element for Overland flow Shallow-Water Equations (SWE)

Published by the American Society of Agricultural and Biological Engineers, St. Joseph, Michigan

Citation:  Paper number  053082,  2005 ASAE Annual Meeting . (doi: 10.13031/2013.19084) @2005
Authors:   Rabi H. Mohtar, Jagadeesh Anmala
Keywords:   numerical stability, time step, finite volume method, amplification factor, wave number, Courant number, consistent, square element

A new control volume finite element (CVFE) method is formulated from integral form of conservation laws, i.e. conservation of mass, for overland flows under kinematic wave assumption. With an approximation m v h = , the system becomes a nonlinear system with unknowns such as flow velocity and flow depth. The differential system of error equations is obtained by linearization of conservation laws in their discrete form for a control volume and an error analysis is obtained using Fourier or von Neumann method. Four nodal quadrilateral or bilinear rectangular shape functions are used to evaluate local and global matrices in the resulting control volume finite element (CVFE) formulation. The nodal amplification factors using coefficient method are compared with those obtained using exact method or eigen-value analysis. The nodal amplification factors show a straight line behavior for all of the wavenumbers for explicit, semi-implicit, and implicit control volume finite element schemes.

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