Lattice Boltzmann approach to simulating a wetting–drying front in shallow flows

• Published in: Journal of fluid mechanics Vol. 743; pp. 32 - 59
• Main Authors: Liu, H., Zhou, J. G.
• Format: Journal Article
• Language: English
• Published: Cambridge, UK Cambridge University Press 25.03.2014
• Subjects: Beaches; Computational methods in fluid dynamics; Drying; Exact sciences and technology; Flow velocity; Fluid dynamics; Fluid mechanics; Fundamental areas of phenomenology (including applications); Hydrodynamic waves; Lattices; Mathematical analysis; Mathematical models; Physics; Planes; Shallow water; Simulation; Solitary waves; Tidal waves; Two dimensional; Water depth; Water flow; computational methods; solitary waves; hydraulics; Solitary wave; Boltzmann equation; Hydraulics; Digital simulation; Lattice model; Free surface flow; Modelling; Shallow-water equations
• ISSN: 0022-1120; 1469-7645
• DOI: 10.1017/jfm.2013.682

The paper reports a new lattice Boltzmann approach to simulating wetting–drying processes in shallow-water flows. The scheme is developed based on the Chapman–Enskog analysis and the Taylor expansion, which is consistent with the theory of the lattice Boltzmann method. All the forces, such as bed slope and bed friction, are taken into account naturally in determining the wet–dry interface, without the use of either the spurious assumption of a thin water film on a dry bed or the non-physical extrapolation of certain variables such as water depth or velocity. This offers a simple and general model for simulating wetting–drying processes in complex flows involving external forces. Its verification is carried out by modelling several one-dimensional (1D) and two-dimensional (2D) flows: (i) 1D sloshing over a parabolic container; (ii) a 1D tidal wave over three adverse bed slopes; (iii) a 1D solitary wave run up on a plane sloping beach; (iv) a tsunami run up on a plane beach; (v) a 2D stationary case with wet–dry boundaries; (vi) a 2D long-wave resonance over a parabolic basin; and (vii) a 2D solitary wave run up on a conical island. The numerical results agree well with analytical solutions, other numerical results and experimental data, demonstrating the effectiveness and accuracy of the new approach.