Lattice Boltzmann Method for Compressible Navier-Stokes-Fourier Equations

Abstract

A lattice Boltzmann scheme for the three-dimensional compressible Navier--Stokes--Fourier equations, derived automatically from the declared system by a symbolic compiler, is validated against exact solutions and published reference data. The declared system carries the viscous stress and the heat flux as transported state, and is discretized on a D3Q7 lattice in single precision. Against the exact Sod and Becker solutions the captured shock thickness converges at first order. On the supersonic Taylor-Green vortex at $M_0 = 1.25$ the scheme at $512^3$ matches the reference dilatational dissipation more closely than seven compared solvers, by thirty percent over the next best. Every operator in this solver, the generated collision and constitutive closure and the added shock sensor alike, reads only the cell it acts on, and data reaches a neighbor only by streaming along the lattice characteristics.