Paper Info
Title
A positive and stable L2-minimization based moment method for the Boltzmann equation of gas dynamics
Abstract
We consider the method-of-moments approach to solve the Boltzmann equation of rarefied gas dynamics, which results in the following moment-closure problem. Given a set of moments, find the underlying probability density function. The moment-closure problem has infinitely many solutions and requires an additional optimality criterion to single-out a unique solution. Motivated from a discontinuous Galerkin velocity discretization, we consider an optimality criterion based upon L2-minimization. To ensure a positive solution to the moment-closure problem, we enforce positivity constraints on L2-minimization. This results in a quadratic optimization problem with moments and positivity constraints. We show that a (Courant-Friedrichs-Lewy) CFL-type condition ensures both the feasibility of the optimization problem and the L2-stability of the space-time discrete moment approximation. We provide an extension of our method to multi-dimensional space-velocity domains and perform several numerical experiments to showcase its accuracy.
Year
DOI
Venue
2021
10.1016/j.jcp.2021.110428
Journal of Computational Physics
Keywords
DocType
Volume
Moment methods,Positive L2-minimization,Boltzmann equation
Journal
440
ISSN
Citations 
PageRank 
0021-9991
0
0.34
References 
Authors
0
1
Name
Order
Citations
PageRank
Neeraj Sarna100.34