TRT lattice Boltzmann schemes converge to the unique entropy solution of a scalar nonlinear conservation law when the relaxation parameters satisfy two explicit monotonicity inequalities.
Bouchut, Construction of BGK models with a family of kinetic entropies for a given system of conservation laws , Journal of Statistical Physics, 95 (1999), pp
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Monotonicity and convergence of two-relaxation-times lattice Boltzmann schemes for a non-linear conservation law
TRT lattice Boltzmann schemes converge to the unique entropy solution of a scalar nonlinear conservation law when the relaxation parameters satisfy two explicit monotonicity inequalities.