Lattice Boltzmann methods are numerical schemes derived as a kinetic approximation of an underlying lattice gas. A numerical convergence theory for nonlinear convective-diffusive lattice Boltzmann methods is established. Convergence, consistency, and stability are defined through truncated Hilbert expansions. In this setting it is shown that consistency and stability imply convergence. Monotone...

[1] This paper introduces new methods for simulating subsurface solute and heat transport in heterogeneous media using large‐scale lattice‐Boltzmann models capable of representing both macroscopically averaged porous media and open channel flows. Previous examples of macroscopically averaged lattice‐Boltzmann models for solute and heat transport are only applicable to homogeneous media. Here, w...

We introduce a mesoscale approach for the simulation of multicomponent flows to model direct-writing printing process, along with early stage ink deposition. As an application scenario, alginate solutions at different concentrations are numerically investigated alongside processing parameters, such as apparent viscosity, extrusion rate, and print head velocity. The present offers useful insight...

Recently, several methods were proposed to accelerate a time integrator that uses a time step that is much smaller than the dominant slow time scales of the dynamics of the system. In this paper, we apply these methods to accelerate the lattice Boltzmann BGK model for the one-dimensional FitzHugh-Nagumo reaction-diffusion system. We compare the projective method proposed by Gear and Kevrekidis ...