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On Stable Wall Boundary Conditions for the Hermite Discretization of the Linearised Boltzmann Equation

Journal Article · · Journal of Statistical Physics
;  [1]
  1. RWTH Aachen University, Center for Computational Engineering & Department of Mathematics, Mathematics (CCES) (Germany)
We define certain criteria, using the characteristic decomposition of the boundary conditions and energy estimates, which a set of stable boundary conditions for a linear initial boundary value problem, involving a symmetric hyperbolic system, must satisfy. We first use these stability criteria to show the instability of the Maxwell boundary conditions proposed by Grad (Commun Pure Appl Math 2(4):331–407, 1949). We then recognise a special block structure of the moment equations which arises due to the recursion relations and the orthogonality of the Hermite polynomials; the block structure will help us in formulating stable boundary conditions for an arbitrary order Hermite discretization of the Boltzmann equation. The formulation of stable boundary conditions relies upon an Onsager matrix which will be constructed such that the newly proposed boundary conditions stay close to the Maxwell boundary conditions at least in the lower order moments.
OSTI ID:
22784065
Journal Information:
Journal of Statistical Physics, Journal Name: Journal of Statistical Physics Journal Issue: 1 Vol. 170; ISSN JSTPBS; ISSN 0022-4715
Country of Publication:
United States
Language:
English