Corner transport upwind lattice Boltzmann model for bubble cavitation

TL;DR

This paper introduces a third-order lattice Boltzmann model with corner transport upwind scheme to simulate bubble cavitation in 2D fluids, accurately capturing bubble dynamics in quiescent and sheared liquids.

Contribution

It develops a high-accuracy off-lattice LB model with CTU scheme for nonideal fluids, enabling detailed study of cavitation phenomena and bubble deformation under shear.

Findings

Accurate phase diagram of nonideal fluid obtained.

Reproduction of Rayleigh-Plesset bubble growth solution.

Linear and nonlinear bubble deformation behaviors identified.

Abstract

Aiming to study the bubble cavitation problem in quiescent and sheared liquids, a third-order isothermal lattice Boltzmann (LB) model that describes a two-dimensional ($2D$) fluid obeying the van der Waals equation of state, is introduced. The evolution equations for the distribution functions in this off-lattice model with 16 velocities are solved using the corner transport upwind (CTU) numerical scheme on large square lattices (up to $6144 \times 6144$ nodes). The numerical viscosity and the regularization of the model are discussed for first and second order CTU schemes finding that the latter choice allows to obtain a very accurate phase diagram of a nonideal fluid. In a quiescent liquid, the present model allows to recover the solution of the $2D$ Rayleigh-Plesset equation for a growing vapor bubble. In a sheared liquid, we investigated the evolution of the total bubble area, the bubble deformation and the bubble tilt angle, for various values of the shear rate. A linear relation between the dimensionless deformation coefficient $D$ and the capillary number $Ca$ is found at small $Ca$ but with a different factor than in equilibrium liquids. A non-linear regime is observed for $Ca \gtrsim 0.2$.