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On Mathematical Balancing of a Two-Layer Shallow Flow Model

Author(s): Wei-Koon Lee; Alistair G. L. Borthwick; Paul H. Taylor

Linked Author(s): Alistair G. L. Borthwick

Keywords: No Keywords

Abstract: Two-layer shallow flow models offer an apparently cheap computational means of simulating density-stratified free surface flows. In the present study, we extend an algebraic method for balancing flux gradient and source terms proposed by Rogers et al. [Rogers B. D., Borthwick A. G. L., and Taylor P. H. 2003 Mathematical balancing of flux gradient and source terms prior to using Roe’s approximate Riemann solver, J. of Computational Physics, 192 (2): 422-451]to a two-layer shallow flow of distinct and immiscible liquids. It is found that the resulting scheme is well balanced for the steady state at rest but produces unwanted spurious oscillations in the presence of interface perturbation. We show that the imbalance is associated with the Bernoulli-type functions in the expanded form of the equations of motion after the elimination of the depth evolution terms.


Year: 2010

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