Related papers: Equivalent partial differential equations of a lat…
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…
Rooted from the gas kinetics, the lattice Boltzmann method is a powerful tool in modeling hydrodynamics. In the past decade, it has been extended to simulate the rarefied gas flow beyond the Navier-Stokes level, either by using the…
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…
The birth of the lattice Boltzmann method (LBM) fulfils a dream that simple arithmetic calculations can simulate complex fluid flows without solving complicated partial differential flow equations. Its power and potential of resolving more…
Thermal fluctuations play a central role in fluid dynamics at mesoscopic scales and must be incorporated into numerical schemes in a manner consistent with statistical mechanics. In this work, we develop a fluctuating lattice Boltzmann…
In this paper, we are concerned about the lattice Boltzmann methods (LBMs) based on vector-kinetic models for hyperbolic partial differential equations. In addition to usual lattice Boltzmann equation (LBE) derived by explicit…
In this work, we first develop a general mesoscopic multiple-relaxation-time lattice Boltzmann (MRT-LB) model for the two-dimensional diffusion equation with the constant diffusion coefficient and source term, where the D2Q5 (five discrete…
A new description of the binary fluid problem via the lattice Boltzmann method is presented which highlights the use of the moments in constructing two equilibrium distribution functions. This offers a number of benefits, including better…
We present a multi-scale lattice Boltzmann scheme, which adaptively refines particles' velocity space. Different velocity sets, i.e., higher- and lower-order lattices, are consistently and efficiently coupled, allowing us to use the…
Lattice Boltzmann schemes are efficient numerical methods to solve a broad range of problems under the form of conservation laws. However, they suffer from a chronic lack of clear theoretical foundations. In particular, the consistency…
A unified framework to derive discrete time-marching schemes for coupling of immersed solid and elastic objects to the lattice Boltzmann method is presented. Based on operator splitting for the discrete Boltzmann equation, second-order…
The lattice Boltzmann algorithm efficiently simulates the Navier Stokes equation of isothermal fluid flow, but ignores thermal fluctuations of the fluid, important in mesoscopic flows. We show how to adapt the algorithm to include noise,…
Starting from Boltzmann equation with relaxation time approximation for the collision term and using Chapman-Enskog like expansion for distribution function close to equilibrium, we derive hydrodynamic evolution equations for the…
The lattice dynamics in $\mathbb{Z}^d$, $d\ge1$, is considered. The initial data are supposed to be random function. We introduce the family of initial measures $\{\mu_0^\epsilon,\epsilon>0\}$ depending on a small scaling parameter…
We show that the asymptotic properties of the link-wise artificial compressibility method are not compatible with a correct approximation of fluid properties. We propose to adapt the previous method through a framework suggested by the…
Conventional lattice Boltzmann models only satisfy moment isotropy up to fourth order. In order to accurately describe improtant physical effects beyond the isothermal Navier-Stokes fluid regime, higher order isotropy is required. In this…
Most biological fluids are viscoelastic, meaning that they have elastic properties in addition to the dissipative properties found in Newtonian fluids. Computational models can help us understand viscoelastic flow, but are often limited in…
We present a systematic procedure for the construction of relativistic lattice Boltzmann models (R-SLB) appropriate for the simulation of flows of massless particles. Quadrature rules are used for the discretization of the momentum space in…
We derive the Enskog equation utilizing orthonormal vielbein fields, enabling the utilization of arbitrary coordinate systems to characterize spatial geometry. Additionally, we employ an adapted coordinate system in the momentum space,…
We re-derive the equations of motion of dissipative relativistic fluid dynamics from kinetic theory. In contrast to the derivation of Israel and Stewart, which considered the second moment of the Boltzmann equation to obtain equations of…