2014/03/31 by Aiguo Xu, Xu, Aiguo, Guangcai Zhang +3
Engineering · Physics and Astronomy · #Computational Physics (physics.comp-ph) #FOS: Physical sciences #Fluid Dynamics (physics.flu-dyn) #Fluid Dynamics and Turbulent Flows #Fluid Dynamics and Vibration Analysis #Lattice Boltzmann Simulation Studies #Statistical Mechanics (cond-mat.stat-mech) #cond-mat.stat-mech #physics.comp-ph #physics.flu-dyn
paper · pdf · doi:10.48550/arxiv.1403.7859
49 pages
arxiv created 2014/03/31 · openalex publication_date 2014/03/31 · arxiv updated 2014/04/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
To study simultaneously the hydrodynamic and thermodynamic behaviors in compressible flow systems with spherical or cylindrical symmetry, we present a theoretical framework for constructing Discrete Boltzmann Model(DBM) with spherical or cylindrical symmetry in spherical or cylindrical coordinates. To this aim, a key technique is to use local Cartesian coordinates to describe the particle velocity in the kinetic model. Thus, the geometric effects, like the divergence and convergence, are described as a \textquotedblleft force term\textquotedblright . Even though the hydrodynamic models are one- or two-dimensional, the DBM needs a Discrete Velocity Model(DVM) with 3 dimensions. We use a DVM with 26 velocities to formulate the DBM which recovers the Navier-Stokes equations with spherical or cylindrical symmetry in the hydrodynamic limit. For the system with global cylindrical symmetry, we formulated also a DBM based on a DVM with 2 dimensions and 16 velocities. In terms of the nonconserved moments, we define two sets of measures for the deviations of the system from its thermodynamic equilibrium state. The extension of current model to the multiple-relaxation-time version is straightforward.