Optimal stability of advection-diffusion lattice Boltzmann models with two relaxation times for positive/negative equilibrium

DOI10.1007/s10955-010-9969-9zbMath1205.82049OpenAlexW2025723755MaRDI QIDQ612008

Irina Ginzburg, Dominique d'Humières, Alexander Kuz'min

Publication date: 3 January 2011

Published in: Journal of Statistical Physics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s10955-010-9969-9

zbMATH Keywords

lattice Boltzmann equationadvection-diffusion equationBGKnecessary and sufficient stability conditionsvon Neumann stability analysisforward time finite-difference schemestwo-relaxation-time model

Mathematics Subject Classification ID

Stability in context of PDEs (35B35) Rarefied gas flows, Boltzmann equation in fluid mechanics (76P05) Lattice systems (Ising, dimer, Potts, etc.) and systems on graphs arising in equilibrium statistical mechanics (82B20)

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Uses Software

• Mathematica

Cites Work

• The role of the kinetic parameter in the stability of two-relaxation-time advection-diffusion lattice Boltzmann schemes
• Lattice Boltzmann modeling with discontinuous collision components: hydrodynamic and advection-diffusion equations
• Three-dimensional multi-relaxation time (MRT) lattice-Boltzmann models for multiphase flow
• Stability and multiscale analysis of an advective lattice Boltzmann scheme
• Viscosity independent numerical errors for lattice Boltzmann models: from recurrence equations to ``magic collision numbers
• Non-negativity and stability analyses of lattice Boltzmann method for advection-diffusion equation
• Variably saturated flow described with the anisotropic lattice Boltzmann methods
• Finite Boltzmann schemes
• An evaluation of lattice Boltzmann schemes for porous medium flow simulation
• Diffusion lattice Boltzmann scheme on a orthorhombic lattice
• Lattice-gas cellular automata and lattice Boltzmann models. An introduction
• The stability of explicit Euler time-integration for certain finite difference approximations of the multi-dimensional advection-diffusion equation
• NUMERICAL SCHEMES OBTAINED FROM LATTICE BOLTZMANN EQUATIONS FOR ADVECTION DIFFUSION EQUATIONS
• Lattice BGK Models for Navier-Stokes Equation
• Multiple–relaxation–time lattice Boltzmann models in three dimensions
• A Stability Notion for Lattice Boltzmann Equations
• On the Location of Zeros of Certain Classes of Polynomials with Applications to Numerical Analysis
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