A blended first- and second-order vectorial lattice Boltzmann scheme with convex limiters provably preserves density and internal energy positivity in two-dimensional compressible Euler simulations.
Bouchut , Construction of BGK models with a family of kinetic entropies for a given system of conservation laws., Journal of Statistical Physics, 95 (1999)
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A positive- and bound-preserving vectorial lattice Boltzmann method in two dimensions
A blended first- and second-order vectorial lattice Boltzmann scheme with convex limiters provably preserves density and internal energy positivity in two-dimensional compressible Euler simulations.