Lattice Boltzmann Simulation of Free-Surface Temperature Dispersion in Shallow Water Flows (Advances in Applied Mathematics and Mechanics, 2018)
We develop a lattice Boltzmann method for modeling free-surfacetemperature dispersion in the shallow water flows. The governingequations are derived from the incompressible Navier-Stokesequations with assumptions of shallow water flows including bedfrictions, eddy viscosity, wind shear stresses and Coriolis forces.The thermal effects are incorporated in the momentum equation byusing a Boussinesq approximation. The dispersion of free-surfacetemperature is modelled by an advection-diffusion equation. Twodistribution functions are used in the lattice Boltzmann method torecover the flow and temperature variables using the same latticestructure. Neither upwind discretization procedures nor Riemannproblem solvers are needed in discretizing the shallow waterequations. In addition, the source terms are straightforwardlyincluded in the model without relying on well-balanced techniques totreat flux gradients and source terms. We validate the model for aclass of problems with known analytical solutions and we alsopresent numerical results for sea-surface temperature distributionin the Strait of Gibraltar.