Related papers: A new lattice Boltzmann scheme for linear elastic …
The relation between Latttice Boltzmann Method, which has recently become popular, and the Kinetic Schemes, which are routinely used in Computational Fluid Dynamics, is explored. A new discrete velocity model for the numerical solution of…
We introduce a structured approach to the construction of linear BGK-type collision operators ensuring that the resulting Lattice-Boltzmann methods are stable with respect to a weighted $L^2$-norm. The results hold for particular boundary…
We present a systematic account of recent developments of the relativistic Lattice Boltzmann method (RLBM) for dissipative hydrodynamics. We describe in full detail a unified, compact and dimension-independent procedure to design…
Multi-component lattice Boltzmann models operating in a wide range of fluid viscosity values are developed and examined. The algorithm is constructed with the goal to enable engineering applications without sacrificing simplicity and…
The Lattice Boltzmann method (LBM) is a well-established mesoscopic approach for simulating fluid dynamics by evolving particle distribution functions on discrete lattices. While the LBM is highly parallelizable on classical hardware, its…
The Lattice Boltzmann Method (LBM) has emerged as a powerful tool in computational fluid dynamics and material science. However, standard LBM formulation imposes some limitations on the applications of the method, particularly compressible…
We show that when we formulate the lattice Boltzmann equation with a small time step $\Delta$t and an associated space scale $\Delta$x, a Taylor expansion joined with the so-called equivalent equation methodology leads to establish…
We present a general methodology for constructing lattice Boltzmann models of hydrodynamics with certain desired features of statistical physics and kinetic theory. We show how a methodology of linear programming theory, known as…
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…
We consider the problem of ''energy conserving'' lattice Boltzmann models. A major difficulty observed in previous studies is the coupling between the viscous and thermal waves even at moderate wave numbers. We propose a theoretical…
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…
Electroconvective flow between two infinitely long parallel electrodes is investigated via a multiphysics computational model. The model solves for spatiotemporal flow properties using two-relaxation-time Lattice Boltzmann Method for fluid…
We propose to extend the multiresolution relaxation times lattice Boltzmann schemes with an additional projection step. For the explicit example of the D2Q9 scheme, we define this extended method. We prove that in general the projection…
In spite of the large number of papers appeared in the past which are devoted to the lattice Boltzmann (LB) methods, basic aspects of the theory still remain unchallenged. An unsolved theoretical issue is related to the construction of a…
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…
We present a robust scheme for solving the electrokinetic equations. This goal is achieved by combining the lattice-Boltzmann method (LB) with a discrete solution of the convection-diffusion equation for the different charged and neutral…
In the paper arXiv:1708.02289 we have introduced new solvability methods for strongly elliptic second order systems in divergence form on a domains above a Lipschitz graph, satisfying $L^p$-boundary data for $p$ near $2$. The main novel…
We consider a class of nonlinear elliptic problems associated with models in biophysics, which are described by the Poisson-Boltzmann equation (PBE). We prove mathematical correctness of the problem, study a suitable class of…
We develop and implement a novel lattice Boltzmann scheme to study multicomponent flows on curved surfaces, coupling the continuity and Navier-Stokes equations with the Cahn-Hilliard equation to track the evolution of the binary fluid…
A quadrature-based finite-difference lattice Boltzmann model is developed that is suitable for simulating relativistic flows of massless particles. We briefly review the relativistc Boltzmann equation and present our model. The quadrature…