A new collision operator for lattice Boltzmann shallow water model: a convergence and stability study. (January 2020) - Venturi, Sara; Di Francesco, Silvia; Geier, Martin; Manciola, Piergiorgio
Highlights: A method solving shallow water equations based on a cumulant collision operator. Accuracy of the new method comparable to the accuracy of the classical BGK approach. Overcoming of stability problems of BGK method also for low viscosity values. Conservation of the correct viscosity and phase with second order convergence. Allowing simulations of natural phenomena involving the water propagation. Abstract: This work presents a new lattice Boltzmann model for steady and unsteady two-dimensional shallow water flows. Compared to previous lattice Boltzmann based shallow water models, the proposed method uses a consistent characteristic speed in the pressure term and in the viscosity. To preserve the isotropy of viscosity, the relaxation rates for the different cumulants have to be decoupled. This is only possible by using multiple relaxation rates. The recovery of the correct viscosity is investigated by a convergence study based on the decay of a Taylor Green Vortex. Results from shallow water models using the proposed collision operator are then compared to those derived from standard BGK approach and from a continuous model.