Related papers: Finite Difference formulation of any lattice Boltz…
A lattice Boltzmann method (LBM) with enhanced stability and accuracy is presented for various Hermite tensor-based lattice structures. The collision operator relies on a regularization step, which is here improved through a recursive…
A new lattice Boltzmann (LB) model is introduced, based on a regularization of the pre-collision distribution functions in terms of the local density, velocity, and momentum flux tensor. The model dramatically improves the precision and…
Lattice-Boltzmann methods are known for their simplicity, efficiency and ease of parallelization, usually relying on uniform Cartesian meshes with a strong bond between spatial and temporal discretization. This fact complicates the crucial…
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…
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…
In this contribution, a new class of lattice Boltzmann schemes is introduced and studied. These schemes are presented in a framework that generalizes the multiple relaxation times method of d'Humi\`eres. They extend also the Geier's…
Differential equations arising in fluid mechanics are usually derived from the intrinsic properties of mechanical systems, in the form of conservation laws, and bear symmetries, which are not generally preserved by a finite difference…
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…
The monotonicity and stability of difference schemes for, in general, hyperbolic systems of conservation laws with source terms are studied. The basic approach is to investigate the stability and monotonicity of a non-linear scheme in terms…
Fourth-order accurate compact schemes for variable coefficient convection diffusion equations are considered. A sufficient condition for the stability of the fully discrete problem is derived using a difference equation based approach. The…
Spurious velocities arising from the imperfect offset of the undesired term at the discrete level are frequently observed in numerical simulations of equilibrium multiphase flow systems using the lattice Boltzmann equation (LBE) method. To…
Lattice Boltzmann Models (LBM) and Phase Field Models (PFM) are two of the most widespread approaches for the numerical study of multicomponent fluid systems. Both methods have been successfully employed by several authors but, despite…
The pseudopotential model within the Lattice Boltzmann Method (LBM) framework has emerged as a prominent approach in computational fluid dynamics due to its dual strengths in physical intuitiveness and computational tractability. However,…
In this work, we improve the accuracy and stability of the lattice Boltzmann model for the Kuramoto-Sivashinsky equation proposed in \cite{2017_Otomo}. This improvement is achieved by controlling the relaxation time, modifying the…
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…
Numerical simulation results of basic exactly solvable fluid flows using the previously proposed Lattice Boltzmann Method (LBM) formulated on a general curvilinear coordinate system are presented. As was noted in the theoretical work of H.…
We propose a formal expansion of multiple relaxation times lattice Boltzmann schemes in terms of a single infinitesimal numerical variable. The result is a system of partial differential equations for the conserved moments of the lattice…
We present a novel framework for the development of fourth-order lattice Boltzmann schemes to tackle multidimensional nonlinear systems of conservation laws. As for other numerical schemes for hyperbolic problems, high-order accuracy…
A class of finite difference schemes for solving a fractional anti-diffusive equation, recently proposed by Andrew C. Fowler to describe the dynamics of dunes, is considered. Their linear stability is analyzed using the standard Von Neumann…
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…