@Article{AAMM-1-415,
author = {Seaïd , Mohammed and Thömmes , Guido},
title = {Lattice Boltzmann Simulation of Free-Surface Temperature Dispersion in Shallow Water Flows},
journal = {Advances in Applied Mathematics and Mechanics},
year = {2009},
volume = {1},
number = {3},
pages = {415--437},
abstract = {<p style="text-align: justify;">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.</p>},
issn = {2075-1354},
doi = {https://doi.org/},
url = {http://global-sci.org/intro/article_detail/aamm/8379.html}
}