2026 Bukreev Compressible Lattice Boltzmann

This paper presents a lattice Boltzmann scheme for the three-dimensional compressible Navier–Stokes–Fourier equations, which is derived automatically from the declared system using a symbolic compiler. The validation of the scheme is performed against exact solutions and published reference data, demonstrating its capabilities in capturing viscous stress and heat flux as transported states on a D3Q7 lattice in single precision. Results indicate that for the exact Sod and Becker solutions, the captured shock thickness converges at first order. Additionally, in the case of the supersonic Taylor–Green vortex at M0 = 1.25, our scheme at 5123 resolution achieves a higher accuracy in matching reference dilatational dissipation than seven comparison solvers, being thirty percent superior over the next best performing solver. Every operator in this solver, including the generated collision, constitutive closure, and shock sensor, acts solely on the cell it processes, with data transmission to neighboring cells occurring exclusively through streaming along the lattice characteristics.