Volumetric formulation for a class of kinetic models with energy conservation

2010/04/28 by Mauro Sbragaglia, M. Sbragaglia, K. Sugiyama +1
Engineering · Mathematics · Physics and Astronomy · #Fluid Dynamics and Turbulent Flows #Gas Dynamics and Kinetic Theory #Lattice Boltzmann Simulation Studies #cond-mat.soft

paper · pdf · doi:10.1103/physreve.82.046709

published as Physical Review E 82, 046709 (2010) · 8 figures

arxiv created 2010/04/28 · openalex publication_date 2010/10/22 · arxiv updated 2015/05/18 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/01

Abstract

We analyze a volumetric formulation of lattice Boltzmann for compressible thermal fluid flows. The velocity set is chosen with the desired accuracy, based on the Gauss-Hermite quadrature procedure, and tested against controlled problems in bounded and unbounded fluids. The method allows the simulation of thermohydrodyamical problems without the need to preserve the exact space-filling nature of the velocity set, but still ensuring the exact conservation laws for density, momentum, and energy. Issues related to boundary condition problems and improvements based on grid refinement are also investigated.

Citations

• Large scale dynamics in turbulent Rayleigh-Benard convection
• Lattice Boltzmann method for thermal flow simulation on standard lattices
• New Statistical Models for Kinetic Theory: Methods of Construction
• Lattice Boltzmann model for simulating flows with multiple phases and components
• Theory of the lattice Boltzmann method: From the Boltzmann equation to the lattice Boltzmann equation
• Fluctuating lattice Boltzmann
• LATTICE BOLTZMANN METHOD FOR FLUID FLOWS
• Hydrodynamics beyond Navier-Stokes: Exact Solution to the Lattice Boltzmann Hierarchy