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Related papers: Stability Analysis of Lattice Boltzmann Methods

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A novel polar coordinate lattice Boltzmann kinetic model for detonation phenomena is presented and applied to investigate typical implosion and explosion processes. In this model, the change of discrete distribution function due to local…

Soft Condensed Matter · Physics 2015-06-16 Chuandong Lin , Aiguo Xu , Guangcai Zhang , Yingjun Li

Lattice Boltzmann models are briefly introduced together with references to methods used to predict their ability for simulations of systems described by partial differential equations that are first order in time and low order in space…

Numerical Analysis · Mathematics 2024-11-15 Pierre Lallemand , François Dubois , Li-shi Luo

The Lattice Boltzmann Method (LBM) is widely recognized as an efficient algorithm for simulating fluid flows in both single-phase and multi-phase scenarios. In this research, a quantum Carleman Linearization formulation of the Lattice…

Quantum Physics · Physics 2024-03-05 Bastien Bakker , Thomas W. Watts

We explore the Carlemann linearization of the collision term of the lattice Boltzmann formulation, as a first step towards formulating a quantum lattice Boltzmann algorithm. Specifically, we deal with the case of a single, incompressible…

Fluid Dynamics · Physics 2021-11-23 Wael Itani , Sauro Succi

A linear stability analysis of the hydrodynamic equations with respect to the homogeneous cooling state is performed to study the conditions for stability of a suspension of solid particles immersed in a viscous gas. The dissipation in such…

Statistical Mechanics · Physics 2017-03-28 Rubén Gómez González , Vicente Garzó

In this contribution, we study a stability notion for a fundamental linear one-dimensional lattice Boltzmann scheme, this notion being related to the maximum principle. We seek to characterize the parameters of the scheme that guarantee the…

Analysis of PDEs · Mathematics 2019-11-28 François Dubois , Benjamin Graille , S. V. Raghurama Rao

We study a generic class of inelastic soft sphere models with a binary collision rate $g^\nu$ that depends on the relative velocity $g$. This includes previously studied inelastic hard spheres ($\nu=1$) and inelastic Maxwell molecules…

Statistical Mechanics · Physics 2007-05-23 M. H. Ernst , E. Trizac , A. Barrat

The simulation of geometrically resolved rigid particles in a fluid relies on coupling algorithms to transfer momentum both ways between the particles and the fluid. In this article, the fluid flow is modeled with a parallel Lattice…

Fluid Dynamics · Physics 2021-03-22 Lukas Werner , Christoph Rettinger , Ulrich Rüde

We study the velocity distribution function for inelastic Maxwell models, characterized by a Boltzmann equation with constant collision rate, independent of the energy of the colliding particles. By means of a nonlinear analysis of the…

Statistical Mechanics · Physics 2009-11-07 Matthieu H. Ernst , Ricardo Brito

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…

Fluid Dynamics · Physics 2026-03-11 Yang Liu , Xuan Zhang , Jingchun Min , Xiaomin Wu

One of the central challenges in kinetic theory is the derivation of macroscopic evolution equations--describing, for example, the dynamics of an electron gas--from the underlying fundamental microscopic laws of classical or quantum…

Mathematical Physics · Physics 2017-08-23 Jens Marklof

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…

Fluid Dynamics · Physics 2023-11-21 Long Ju , Peiyao Liu , Bicheng Yan , Jin Bao , Shuyu Sun , Zhaoli Guo

A linear stability analysis of the hydrodynamic equations with respect to the homogeneous cooling state is carried out to identify the conditions for stability of a granular gas of rough hard spheres. The description is based on the results…

Soft Condensed Matter · Physics 2018-05-10 Vicente Garzó , Andrés Santos , Gilberto M. Kremer

A theoretical formulation of lattice Boltzmann models on a general curvilinear coordinate system is presented. It is based on a volumetric representation so that mass and momentum are exactly conserved as in the conventional lattice…

Fluid Dynamics · Physics 2024-01-31 Hudong Chen

We present a mathematical theory of dynamical fluctuations for the hard sphere gas in the Boltzmann-Grad limit. We prove that: (1) fluctuations of the empirical measure from the solution of the Boltzmann equation, scaled with the square…

Analysis of PDEs · Mathematics 2022-08-26 Thierry Bodineau , Isabelle Gallagher , Laure Saint-Raymond , Sergio Simonella

A detailed derivation of the Lattice Boltzmann (LB) scheme for relativistic fluids recently proposed in Ref. [1], is presented. The method is numerically validated and applied to the case of two quite different relativistic fluid dynamic…

Solar and Stellar Astrophysics · Physics 2010-12-28 M. Mendoza , B. M. Boghosian , H. J. Herrmann , S. Succi

Rayleigh-Taylor (RT) instability commonly arises in compressible systems with time-dependent acceleration in practical applications. To capture the complex dynamics of such systems, a two-component discrete Boltzmann method is developed to…

Fluid Dynamics · Physics 2025-04-08 Huilin Lai , Chuandong Lin , Hao Xu , Hailong Liu , Demei Li , Bailing Chen

The profiles of narrow lattice solitons are calculated analytically using perturbation analysis. A stability analysis shows that solitons centered at a lattice (potential) maximum are unstable, as they drift toward the nearest lattice…

Pattern Formation and Solitons · Physics 2009-11-13 Y. Sivan , G. Fibich , N. K. Efremidis , S. Bar-Ad

Analytical solutions to the lattice Boltzmann Equation make it possible to study the method itself, explore the properties of its collision operator, and identify implementations of boundary conditions. In this paper, we propose a method to…

Fluid Dynamics · Physics 2025-06-02 Jordan Larson , Alexander J. Wagner

In this paper, we aim to address several important issues about the recently developed lattice Boltzmann (LB) model for relativistic hydrodynamics [M. Mendoza et al., Phys. Rev. Lett. 105, 014502 (2010); Phys. Rev. D 82, 105008 (2010)].…

Computational Physics · Physics 2012-11-15 Q. Li , K. H. Luo , X. J. Li