Isotropic color gradient for simulating very high-density ratios with a two-phase flow lattice Boltzmann model

Multiphase lattice Boltzmann simulations for porous media applications

“…Leclaire et al [94] conducted a numerical comparison of the recoloring operators A1 and A2 for an immiscible twophase flow by a series of benchmark cases and concluded that the recoloring operator A2 greatly increases the rate of convergence, improves the numerical stability and accuracy of the solutions over a broad range of model parameters, and significantly reduces spurious velocities and relieves the lattice pinning problem. Several recent numerical studies [81,95] indicated that, for a combination of Eq. 17 and the recoloring algorithm A2, the simulated density ratio and viscosity ratio can be up to O(10 3 ) for stationary bubble/droplet tests, whereas for dynamic problems the simulated density ratio is restricted to O(10) due to numerical instability.…”

Convolution Kernel for Fast CPU/GPU Computation of 2D/3D Isotropic Gradients on a Square/Cubic Lattice

“…And, by supposing that F = F(r) is rotationally invariant, it is possible to show (after a lengthy algebraic manipulation) that the vector that results when the differential operator E (2) is applied to F(r) will have a Euclidean norm that is a function of θ and r,e x c e p ti f F(r) is a constant. This result, that is, the norm || E (2) F(r)|| ≡ f (r, θ), is an equation that takes up almost a page, and so is not presented here.…”

“…[2] and without loss of generality, the function F is expressed using a 2D Taylor series expansion around the zero vector:…”

“…The method is based on a filter which is generally not split along any direction, and there is no need to make the assumption of a continuous filter to reach isotropy, as done by [3]. We also believe that optimal or maximal isotropy can only be reached with a discrete filter when the error terms of Taylor's series expansion are isotropic, as explained in detail by [1,2].…”

“…To address this issue, we present an efficient computational method for obtaining discrete isotropic gradients that was previously applied to simulate two-phase flows within the lattice Boltzman framework [1,2]. This "omnidirectional" approach makes it possible to improve the limitations inherent in handling high density ratios between the phases and to significantly reduce spurious currents at the interface.…”