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.Comment: 8 figure
