On the effect of the intrinsic viscosity in a two-layer shallow water lattice Boltzmann model of axisymmetric density currents

Abstract

In this work, a numerical assessment of the suitability of a Single Relaxation Time (SRT) Lattice Boltzmann Method (LBM) model to simulate axisymmetric gravity currents is carried out. The model results are compared with both experimental data and other numerical models. The particular SRT formulation employed is known to converge, in the limit of low Knudsen number, to the two-layer 2D Shallow Water Equations (SWEs) set with a viscosity term featuring a closed theoretical formulation. Even with the lowest viscosity achievable by the method, its effect is shown to become important in most of the cases analysed, thus posing some serious constraints on possible application of the single relaxation time LBM method to simulate the lock-release generated-type gravity currents analysed here. The comparison with classical numerical models shows that the the viscous effects in the LBM model can be well reproduced employing coefficients derived from the above-mentioned theoretical formulation.

Keywords:

• Axisymmetric gravity currents
• gravity currents
• LBM
• shallow water
• two-layer flows
• viscosity

Acknowledgement

The research has been supported by the Italian national project “Hydroelectric energy by osmosis in coastal areas”, PRIN 2010-211.