Title: A simple and efficient two-dimensional hydrodynamic model for unsteady flow simulation in undulating bathymetry

Authors: Anupal Baruah; Arup Kumar Sarma

Addresses: Department of Civil Engineering, IIT – Guwahati, Assam, 781039, India ' Department of Civil Engineering, IIT – Guwahati, Assam, 781039, India

Abstract: Two-dimensional modelling in a river having undulating bathymetry is challenging in terms of numerical stability, accuracy and robustness. The main reason behind the model stability is the oscillations in the solutions due to nonlinear and hyperbolic form of the flow equations. Sometimes, it is observed that using of primitive variables as temporal derivatives in conservation equation is a source of model instability, especially in a braided river. In this work, the surface form of two-dimensional hydrodynamic equations of shallow water is solved using a five-point TVD Mac-Cormack predictor-corrector scheme. The water surface gradient is used as a gravitational force component in the source term to overcome the possible error that may occur during bed slope discretisation in case of undulating bathymetry. Model is then applied over a wide range of problems including irregular bed, dam breach flow and mix flow with a hydraulic jump. Model outputs are validated with the available experimental data.

Keywords: total variation diminishing; TVD; complex topography; mix flow; water surface slope; two-dimensional shallow water equation; unsteady flow.

DOI: 10.1504/PCFD.2021.119256

Progress in Computational Fluid Dynamics, An International Journal, 2021 Vol.21 No.6, pp.369 - 377

Received: 27 Apr 2020
Accepted: 29 Nov 2020
Published online: 30 Nov 2021 *

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