Compound waves in a thermohydrodynamic lattice BGK scheme using non-perturbative equilibria

A previously proposed thermohydrodynamic lattice BGK scheme using non-perturbative, or non-polynomial, equilibria is found to simulate continuum equations that differ from the Euler equations of gas dynamics at leading order. Shock tube simulations with this BGK scheme coincide with solutions obtained by solving these different continuum equations with conventional methods. Both sets of solutions contain unphysical compound waves, shocks attached to rarefactions, where the Euler equations contain contact discontinuities.