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Vortex lattices -- highly ordered arrays of vortices -- are known to arise in quantum systems such as type II superconductors and Bose-Einstein condensates. More recently, similar arrangements have been reported in classical rotating…

Fluid Dynamics · Physics 2025-10-09 Julián Amette Estrada , Alexandros Alexakis , Marc E. Brachet , Pablo D. Mininni

A general derivation is proposed for several boundary conditions arisen in the lattice Boltzmann simulations of various physical problems. Pair-wise moment conservations are proposed to enforce the boundary conditions with given macroscopic…

Computational Physics · Physics 2025-10-16 Jun Li , Wai Hong Ronald Chan , Zhe Feng , Chenglei Wang

In this paper, we first present a multiple-relaxation-time lattice Boltzmann (MRT-LB) model for one-dimensional diffusion equation where the D1Q3 (three discrete velocities in one-dimensional space) lattice structure is considered. Then…

Numerical Analysis · Mathematics 2021-08-04 Yuxin Lin , Ning Hong , Baochang Shi , Zhenhua Chai

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…

Fluid Dynamics · Physics 2007-05-23 Jonas Latt , Bastien Chopard

We demonstrate how to produce a stable multispeed lattice Boltzmann method (LBM) for a wide range of velocity sets, many of which were previously thought to be intrinsically unstable. We use non-Gauss--Hermitian cubatures. The method…

Statistical Mechanics · Physics 2007-05-23 R. A. Brownlee , A. N. Gorban , J. Levesley

The Lattice Boltzmann Method (LBM), e.g. in [ 1] and [2 ], can be interpreted as an alternative method for the numerical solution of partial differential equations. Consequently, although the LBM is usually applied to solve fluid flows, the…

Numerical Analysis · Mathematics 2023-01-03 Alexander Schlüter , Henning Müller , Sikang Yan , Erik Faust , Ralf Müller

A lattice Boltzmann scheme able to model the hydrodynamics of phase separation and two-phase flow is described. Thermodynamic consistency is ensured by introducing a non-ideal pressure tensor directly into the collision operator. We also…

comp-gas · Physics 2009-10-28 Michael R. Swift , W. R. Osborn , J. M. Yeomans

In this article we are interested in the boundary stabilization in finite time of one-dimensional linear hyperbolic balance laws with coefficients depending on time and space. We extend the so called "backstepping method" by introducing…

Optimization and Control · Mathematics 2020-11-30 Jean-Michel Coron , Long Hu , Guillaume Olive , Peipei Shang

Boundary problem for linear partial differential algebraic equations system with multiple characteristic curves is considered. It is supposed that matrix-functions pencil of the system under consideration is smoothly equivalent to special…

Numerical Analysis · Mathematics 2013-03-27 Svetlana Gaidomak

In this contribution, we study the theoretical and numerical stability of a bidimensional relative velocity lattice Boltzmann scheme. These relative velocity schemes introduce a velocity field parameter called "relative velocity" function…

Numerical Analysis · Mathematics 2015-06-09 François Dubois , Tony Février , Benjamin Graille

A system of partial differential equations representing stochastic neural fields was recently proposed with the aim of modelling the activity of noisy grid cells when a mammal travels through physical space. The system was rigorously…

Analysis of PDEs · Mathematics 2023-07-18 José Antonio Carrillo , Pierre Roux , Susanne Solem

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…

Computational Physics · Physics 2017-09-20 Christophe Coreixas , Gauthier Wissocq , Guillaume Puigt , Jean-François Boussuge , Pierre Sagaut

This paper proposes an improved lattice Boltzmann scheme for incompressible axisymmetric flows. The scheme has the following features. First, it is still within the framework of the standard lattice Boltzmann method using the…

Computational Physics · Physics 2010-06-07 Q. Li , Y. L. He , G. H. Tang , W. Q. Tao

The lattice Boltzmann (LB) method has gained much success in a variety of fields involving fluid flow and/or heat transfer. In this method, the bounce-back scheme is a popular boundary scheme for treating nonslip boundaries. However, this…

Computational Physics · Physics 2020-07-01 Y. Yu , Q. Li , Z. X. Wen

A lattice Boltzmann scheme that is close to pure upwind, low diffusive and entropy satisfying Engquist-Osher scheme has been formulated for hyperbolic scalar conservation laws. A model for source terms, with scalar conservation laws, is…

Numerical Analysis · Mathematics 2021-11-17 Megala A , S. V. Raghurama Rao

In this paper we analyze the boundary treatment of the lattice Boltzmann method (LBM) for simulating 3D flows with free surfaces. The widely used free surface boundary condition of K\"orner et al. (2005) is shown to be first order accurate.…

Numerical Analysis · Mathematics 2015-09-29 Simon Bogner , Regina Ammer , Ulrich Rüde

We examine robustness of exponential dichotomies of boundary value problems for general linear first-order one-dimensional hyperbolic systems. The boundary conditions are supposed to be of types ensuring smoothing solutions in finite time,…

Analysis of PDEs · Mathematics 2025-12-10 I. Kmit , L. Recke , V. Tkachenko

We propose a kinetic framework for single-component non-ideal isothermal flows. Starting from a kinetic model for a non-ideal fluid, we show that under conventional scaling the Navier-Stokes equations with a non-ideal equation of state are…

Fluid Dynamics · Physics 2022-12-14 S. A. Hosseini , B. Dorschner , I. V. Karlin

We discuss in details a modified variational matrix-product-state algorithm for periodic boundary conditions, based on a recent work by P. Pippan, S.R. White and H.G. Everts, Phys. Rev. B 81, 081103(R) (2010), which enables one to study…

Quantum Physics · Physics 2015-03-19 Davide Rossini , Vittorio Giovannetti , Rosario Fazio

We consider the nonlinear boundary layers of the Boltzmann equation in a three-dimensional half-space by perturbing around a Maxwellian, under the assumption that the Mach number of the Maxwellian satisfies ${\cal M}_{\infty} < -1$. In…

Analysis of PDEs · Mathematics 2020-09-17 Shota Sakamoto , Masahiro Suzuki , Katherine Zhiyuan Zhang