Abstract
Using the method of moments to approximate the solution of kinetic equations has become a standard technique especially in the context of solving the Boltzmann equation to model rarefied gases. One attractive example is the maximum-entropy closure, which, however, is computationally barely affordable. In this paper, we will combine the maximum-entropy approach with the quadrature method of moments (QMOM) – two methods which have in some sense diametric properties, thereby introducing the “Entropic Quadrature” (EQ) closure. EQ calculates a sparse quadrature-based reconstruction of the unknown velocity distribution like the QMOM where the physical meaningful maximum-entropy principle is employed as a criterion for selecting a quadrature among different quadratures fitting the given moments. We will discuss the construction of the closure and give several numerical examples of its performance in one and two dimensions.
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