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Lattice Boltzmann simulation of free-surface temperature dispersion in shallow water flows.

Seaid, M.; Thömmes, G.

Authors

G. Thömmes



Abstract

We develop a lattice Boltzmann method for modeling free-surface temperature dispersion in the shallow water flows. The governing equations are derived from the incompressible Navier-Stokes equations with assumptions of shallow water flows including bed frictions, eddy viscosity, wind shear stresses and Coriolis forces. The thermal effects are incorporated in the momentum equation by using a Boussinesq approximation. The dispersion of free-surface temperature is modelled by an advection-diffusion equation. Two distribution functions are used in the lattice Boltzmann method to recover the flow and temperature variables using the same lattice structure. Neither upwind discretization procedures nor Riemann problem solvers are needed in discretizing the shallow water equations. In addition, the source terms are straightforwardly included in the model without relying on well-balanced techniques to treat flux gradients and source terms. We validate the model for a class of problems with known analytical solutions and we also present numerical results for sea-surface temperature distribution in the Strait of Gibraltar.

Citation

Seaid, M., & Thömmes, G. (2009). Lattice Boltzmann simulation of free-surface temperature dispersion in shallow water flows. Advances in applied mathematics and mechanics, 1(3), 415-437

Journal Article Type Article
Publication Date 2009
Journal Advances in Applied Mathematics and Mechanics
Print ISSN 2070-0733
Electronic ISSN 2075-1354
Publisher Global Science Press
Peer Reviewed Peer Reviewed
Volume 1
Issue 3
Pages 415-437
Public URL https://durham-repository.worktribe.com/output/1555673
Publisher URL http://www.global-sci.org/intro/articles_list.html?journal=aamm&volume_id=1278