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Numerical Methods for Studying Self-similar Propagation of Viscous Gravity Currents

<div>A strongly implicit, nonlinear Crank-Nicolson-based finite-difference scheme was constructed for the numerical study of the self-similar behavior of viscous gravity currents. Viscous gravity currents are low Reynolds number flow phenomena in which a dense, viscous fluid displaces a lighter (usually immiscible) fluid. Under the lubrication approximation, the mathematical description of the spreading of these fluids is reduced to solving a nonlinear parabolic partial differential equation for the shape of the fluid interface. This thesis focuses on the finite-speed propagation of a power-law non-Newtonian current in a variable width channel-like geometry (a "Hele-Shaw cell'') subject to a given mass conservation/balance constraint. The proposed numerical scheme was implemented on a uniform but staggered grid. It is shown to be strongly stable, while possessing formal truncation error that is of second-order in space and it time. The accuracy of the scheme was verified by benchmarking it against established analytical solutions, which were obtained via a first-kind self-similarity transformation. A series of numerical simulations confirmed that the proposed scheme accurately respects the mass conservation/balance constraint. Next, the numerical scheme was used to study the second-kind self-similar behaviour of Newtonian viscous gravity currents flowing towards the end of a converging channel. Second-kind self-similar transformations are not fully specified without further information from simulation or experiment. Thus, using the proposed numerical scheme, the self-similar spreading and leveling leveling of the current was definitively addressed. The numerical results showed favorable comparison with experimental data.</div>

  1. 10.25394/pgs.8044457.v1
Identiferoai:union.ndltd.org:purdue.edu/oai:figshare.com:article/8044457
Date14 May 2019
CreatorsAditya Avinash Ghodgaonkar (6635993)
Source SetsPurdue University
Detected LanguageEnglish
TypeText, Thesis
RightsCC BY 4.0
Relationhttps://figshare.com/articles/Numerical_Methods_for_Studying_Self-similar_Propagation_of_Viscous_Gravity_Currents/8044457

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