Related papers: Well-balanced lattice Boltzmann equation for two-p…
The problem of energy conservation in the lattice Boltzmann method is solved. A novel model with energy conservation is derived from Boltzmann's kinetic theory. It is demonstrated that the full thermo-hydrodynamics pertinent to the…
Conventional lattice Boltzmann models for the simulation of fluid dynamics are restricted by an error in the stress tensor that is negligible only for vanishing flow velocity and at a singular value of the temperature. To that end, we…
We computationally study the spontaneous phase separation of ternary fluid mixtures using the lattice Boltzmann method, both when all the surface tensions are equal and when they have different values. Previous theoretical works typically…
In this work, we consider a general consistent and conservative phase-field model for the incompressible two-phase flows. In this model, not only the Cahn-Hilliard or Allen-Cahn equation can be adopted, but also the mass and the momentum…
The lattice Boltzmann (LB) method intrinsically links to the Boltzmann equation with the Bhatnagar-Gross-Krook collision operator; however, it has been questioned to be able to simulate noncontinuum bounded gas flows at the micro and…
Recently, we notice that a pressure-based lattice Boltzmann (LB) method was established to recover the volume-averaged Navier-Stokes equations (VANSE), which serve as the cornerstone of various fluid-solid multiphase models. It decouples…
The local balance equations for the density, momentum, and energy of a dilute gas of elastic or inelastic hard spheres, strongly confined between two parallel hard plates are obtained. The starting point is a Boltzmann-like kinetic…
We consider a mono-dimensional two-velocities scheme used to approximate the solutions of a scalar hyperbolic conservative partial differential equation. We prove the convergence of the discrete solution toward the unique entropy solution…
In this paper, a double multiple-relaxation-time lattice Boltzmann model is developed for simulating transient solid-liquid phase change problems in porous media at the representative elementary volume scale. The model uses two different…
We establish the notion of limit consistency as a modular part in proving the consistency of lattice Boltzmann equations (LBEs) with respect to a given partial differential equation (PDE) system. The incompressible Navier--Stokes equations…
Lattice kinetic equations incorporating the effects of external/internal force fields via a shift of the local fields in the local equilibria, are placed within the framework of continuum kinetic theory. The mathematical treatment reveals…
Under the condition of partial surface wettability, thin liquid films can be destabilized by small perturbations and rupture into droplets. As successfully predicted by the thin film equation (TFE), the rupture dynamics are dictated by the…
The particles model, the collision model, the polynomial development used for the equilibrium distribution, the time discretization and the velocity discretization are factors that let the lattice Boltzmann framework (LBM) far away from its…
We revisit the classical stability versus accuracy dilemma for the lattice Boltzmann methods (LBM). Our goal is a stable method of second-order accuracy for fluid dynamics based on the lattice Bhatnager--Gross--Krook method (LBGK). The LBGK…
Adaptive lattice Boltzmann methods (LBMs) are based on velocity discretizations that self-adjust to local macroscopic conditions such as velocity and temperature. While this feature improves the accuracy and the stability of LBMs for large…
We investigate the coupled dynamics of quantized vortices and normal fluid in superfluid $^4$He at finite temperatures using a numerical approach based on the vortex filament model (VFM) and lattice Boltzmann method (LBM). The LBM allows us…
Discrete particle simulations are widely used to study large-scale particulate flows in complex geometries where particle-particle and particle-fluid interactions require an adequate representation but the computational cost has to be kept…
A method is described for embedding a deformable, elastic, membrane within a lattice Boltzmann fluid. The membrane is represented by a set of massless points which advect with the fluid and which impose forces on the fluid which are derived…
Finite-difference Lattice Boltzmann (LB) models are proposed for simulating gas flows in devices with microscale geometries. The models employ the roots of half-range Gauss-Hermite polynomials as discrete velocities. Unlike the standard LB…
The phase-field-based lattice Boltzmann (LB) model has been developed to perform high fidelity multiphase flow simulations. Its ability to accurately handle high density ratio and surface tension effects is expected to be beneficial for…