Equivalent finite difference and partial differential equations for the lattice Boltzmann method

DOI10.1016/j.camwa.2021.03.014OpenAlexW3143134528WikidataQ115359479 ScholiaQ115359479MaRDI QIDQ2019604

Radek Fučík, Robert Straka

Publication date: 21 April 2021

Published in: Computers \& Mathematics with Applications (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.camwa.2021.03.014

zbMATH Keywords

cascaded lattice Boltzmann methodequivalent finite difference schemeequivalent partial difference equationmatrix lattice Boltzmann method

Mathematics Subject Classification ID

Navier-Stokes equations for incompressible viscous fluids (76D05) Diffusion (76R50) Rarefied gas flows, Boltzmann equation in fluid mechanics (76P05) Particle methods and lattice-gas methods (76M28) Probabilistic methods, particle methods, etc. for initial value and initial-boundary value problems involving PDEs (65M75)

Related Items

Hydrodynamic limits and numerical errors of isothermal lattice Boltzmann schemes, Finite difference formulation of any lattice Boltzmann scheme, Truncation errors and modified equations for the lattice Boltzmann methodviathe corresponding Finite Difference schemes, Lattice Boltzmann method analysis tool (LBMAT), Revisiting the second-order convergence of the lattice Boltzmann method with reaction-type source terms

Uses Software

• GiNaC

Cites Work

• Optimal relaxation collisions for lattice Boltzmann methods
• Truncation effect on Taylor-Aris dispersion in lattice Boltzmann schemes: accuracy towards stability
• Equivalent partial differential equations of a lattice Boltzmann scheme
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• Parametrization of the cumulant lattice Boltzmann method for fourth order accurate diffusion. I: Derivation and validation
• The cumulant lattice Boltzmann equation in three dimensions: theory and validation
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• Asymptotic analysis of the lattice Boltzmann equation
• Towards higher order lattice Boltzmann schemes
• NUMERICAL SCHEMES OBTAINED FROM LATTICE BOLTZMANN EQUATIONS FOR ADVECTION DIFFUSION EQUATIONS
• STABILITY AND ACCURACY OF LATTICE BOLTZMANN SCHEMES FOR ANISOTROPIC ADVECTION-DIFFUSION EQUATIONS
• Truncation Errors, Exact And Heuristic Stability Analysis Of Two-Relaxation-Times Lattice Boltzmann Schemes For Anisotropic Advection-Diffusion Equation
• LATTICE BOLTZMANN METHOD FOR FLUID FLOWS
• An accurate multi-level finite difference scheme for 1D Diffusion equations derived from the lattice Boltzmann method