Related papers: Convergence Analysis of the Grad's Hermite Approxi…
We propose a necessary and sufficient condition for the well-posedness of the linear non-homogeneous Grad moment equations in half-space. The Grad moment system is based on Hermite expansion and regarded as an efficient reduction model of…
Despite the progress achieved by kinetic theory, the search of possible exact kinetic equations remains elusive to date. This concerns, specifically, the issue of the validity of the conjecture proposed by Grad (Grad, 1972) and developed in…
While Pad\'e approximation is a general method for improving convergence of series expansions, Gell-Mann--Low renormalization group normally relies on the presence of special symmetries. We show that in the single-variable case, the latter…
We introduce a numerical method for solving Grad's moment equations or regularized moment equations for arbitrary order of moments. In our algorithm, we do not need explicitly the moment equations. As an instead, we directly start from the…
This paper derives transport equations for medium rarefied gases from the Bhatnagar-Gross-Krook (BGK) model kinetic equation using a Hermite polynomial approximation for the monoatomic gas distribution function. We apply the Chapman-Enskog…
We point out an equivalence between the discrete velocity method of solving the Boltzmann equation, of which the lattice Boltzmann equation method is a special example, and the approximations to the Boltzmann equation by a Hermite…
The aim of this paper is to investigate the quality of approximation of almost time and band limited functions by its expansion in the Hermite and scaled Hermite basis. As a corollary, this allows us to obtain the rate of convergence of the…
We obtain a formal integral solution to the 3+1 D Boltzmann Equation in relaxation time approximation. The gradient series obtained from this integral solution contains exponentially decaying non-hydrodynamic terms. It is shown that this…
Any numerical method fails to provide us with acceptable results if not equipped with appropriate boundary conditions. Catering to more realistic applications, in the present article we have extended the work done on the one plus one…
We review some recent developments of Grad's approach to solving the Boltzmann equation and creating reduced description. The method of invariant manifold is put forward as a unified principle to establish corrections to Grad's equations. A…
In this paper, we propose a first second-order scheme based on arbitrary non-Euclidean norms, incorporated by Bregman distances. They are introduced directly in the Newton iterate with regularization parameter proportional to the square…
In this work, we have theoretically analyzed and numerically evaluated the accuracy of high-order lattice Boltzmann (LB) models for capturing non-equilibrium effects in rarefied gas flows. In the incompressible limit, the LB equation is…
We suggest simple implementable modifications of conditional gradient and gradient projection methods for smooth convex optimization problems in Hilbert spaces. Usually, the custom methods attain only weak convergence. We prove strong…
We study linear closure relations for the moments' method applied to simple kinetic equations. The equations are linear collisional models (velocity jump processes) which are well suited to this type of approximation. In this simplified, 1…
A description of Orthogonal Tensor Hermite Polynomials in 3-D is presented. These polynomials, as introduced by Grad in 1949 [1], can be used to obtain a series solution to the Boltzmann Transport Equation. The properties that are explored…
We make a brief historical review to the moment model reduction to the kinetic equations, particularly the Grad's moment method for Boltzmann equation. The focus is on the hyperbolicity of the reduced model, which is essential to the…
High order accurate Hermite methods for the wave equation on curvilinear domains are presented. Boundaries are treated using centered compatibility conditions rather than more standard one-sided approximations. Both first-order-in-time…
We examine the last-iterate convergence rate of Bregman proximal methods - from mirror descent to mirror-prox and its optimistic variants - as a function of the local geometry induced by the prox-mapping defining the method. For generality,…
This paper is devoted to the numerical analysis of the Hermite spectral method proposed in [14], which provides, in the semiclassical limit, an asymptotic preserving approximation of the von Neumann equation. More precisely, it relies on…
Grad's moment models for Boltzmann equation were recently regularized to globally hyperbolic systems, and thus the regularized models attain local well-posedness for Cauchy data. The hyperbolic regularization is only related to the…