Gorban, Alexander N. and Karlin, Iliya V.
Invariance correction to Grad's equations: where to go beyond approximations?
Continuum Mechanics and Thermodynamics, 17, (4), . (doi:10.1007/s00161-005-0202-z).
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We review some recent developments of Grad's approach to solving the Boltzmann equation and creating a reduced description. The method of the invariant manifold is put forward as a unified principle to establish corrections to Grad's equations. A consistent derivation of regularized Grad's equations in the framework of the method of the invariant manifold is given. A new class of kinetic models to lift the finite-moment description to a kinetic theory in the whole space is established. Relations of Grad's approach to modern mesoscopic integrators such as the entropic lattice Boltzmann method are also discussed.
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