A robust numerical scheme for transcritical flow simulation in a Braided river

Abstract

Flow simulation over a braided channel is a challenging task as in the monsoon season flow moves over an undulating bed while as in non-monsoon season or in lean period it moves through several sub-channel. Therefore a more robust scheme is necessary for simulating such kind flow particularly when transcritical flow occurs in river reach. Shallow water equations can be derived by depth integration of the Navier Stokes equation and assuming hydrostatic pressure distribution. These equations are basically based upon the conservation of mass and momentum approach. Shallow water equations are a set of a first-order nonlinear hyperbolic partial differential equation and do not have closed form of analytical solution without considering a large number of approximation because of which these equation needs to be solved by different numerical techniques like finite difference, finite element, and finite volume. The hyperbolic nature of the equations results in a generation of numerical dispersion in the solution domain because of which proper shock capturing methods need to be implemented along with the scheme. The presence of bed slope term in the governing equations causes some difficulty to apply them in complex bathymetry. Researchers have modified the original form of governing equations so that these equations can be implemented in a complex topography with proper mass conservation. In this paper, the modified form of the 2D governing equation is combined with the proper shock capturing technique to investigate the applicability of the scheme in complex bathymetry. This scheme is used as an integral part of BRAHMA model (Braided River Aid: Hydro-Morphological Analyser) developed by IIT-Guwahati in collaboration with Brahmaputra Board. Governing equations solved by Mac Cormack predictor-corrector scheme and the scheme has been tested with some classical problem including dam break, quiescent water above an irregular bed, steady flow over an irregular bed, transcritical flow over a bump etc. For each test case numerical results are compared with the analytical result and found satisfactory.