Generalized transformation of the lattice Boltzmann method for shallow water flows. Issue 4 (3rd July 2016)

• Record Type: Journal Article
• Authors: Hedjripour, Amir H.; Callaghan, David P.; Baldock, Tom E.
• Is Part Of: Journal of hydraulic research. Volume 54:Issue 4(2016)
• Page Start: 371
• Page End: 388
• Publication Date: 2016-07-03
• Subjects: Asymmetric scheme -- Galilean transformation -- lattice Boltzmann method -- shallow water equations -- supercritical flow; Hydraulics -- Research -- Periodicals; Hydraulic engineering -- Periodicals; Hydraulic engineering; Electronic journals; Periodicals; 621.2
• DOI: 10.1080/00221686.2016.1168881
• Languages: English
• ISSNs: 0022-1686

Abstract

ABSTRACT: A one-dimensional lattice Boltzmann model is developed to solve the shallow water equations for steady and unsteady flows within both the subcritical and supercritical regimes. Previous work is extended through a generalized Galilean transformation applied to the standard scheme. The transformation yields a general asymmetric lattice Boltzmann model scheme which can successfully model a wide range of both subcritical and supercritical flow regimes, and enables implementation of the asymmetric model for practical purposes. In current work, a new set of equilibrium functions, boundary conditions and the external force weights are derived for the generalized transformed scheme. A new stability region is also defined, allowing selection of a lattice speed that maintains numerical stability for a wider range of sub- and supercritical flows and combinations of those flow conditions, compared to the previous scheme with fixed asymmetry. The model is validated against a range of benchmark cases in open-channel hydraulics that demonstrate the applicability of the new model.