Convergence Analysis of Grad's Hermite Expansion for Linear Kinetic Equations

DOI10.1137/19M1270884zbMath1436.65150arXiv1809.08213MaRDI QIDQ4960452

Manuel Torrilhon, Neeraj Sarna, Jan Giesselmann

Publication date: 16 April 2020

Published in: SIAM Journal on Numerical Analysis (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1809.08213

zbMATH Keywords

convergence analysisinitial boundary value problemkinetic equationsGrad's expansion

Mathematics Subject Classification ID

Rarefied gas flows, Boltzmann equation in fluid mechanics (76P05) Stability and convergence of numerical methods for initial value and initial-boundary value problems involving PDEs (65M12) Spectral, collocation and related methods for initial value and initial-boundary value problems involving PDEs (65M70) Kinetic theory of gases in time-dependent statistical mechanics (82C40) Applications to the sciences (65Z05) Boltzmann equations (35Q20)

Related Items (6)

Projective integration schemes for hyperbolic moment equations ⋮ The solvability of mixed value problem for the first and second approximations of one-dimensional nonlinear system of moment equations with microscopic boundary conditions ⋮ A positive and stable L2-minimization based moment method for the Boltzmann equation of gas dynamics ⋮ Moment method as a numerical solver: challenge from shock structure problems ⋮ Moment method for the Boltzmann equation of reactive quaternary gaseous mixture ⋮ Investigation of aerodynamic characteristics of aircrafts in a rarefied gas flow using the moment method

Cites Work

• Convergence of filtered spherical harmonic equations for radiation transport
• Entropy stable Hermite approximation of the linearised Boltzmann equation for inflow and outflow boundaries
• Macroscopic transport equations for rarefied gas flows. Approximation methods in kinetic theory.
• Abstract time-dependent transport equations
• The Boltzmann equation and its applications
• On regularity of twisted spherical means and special Hermite expansions
• Discrete-velocity models and numerical schemes for the Boltzmann-BGK equation in plane and axisymmetric geometries
• Hierarchical Boltzmann simulations and model error estimation
• On stable wall boundary conditions for the Hermite discretization of the linearised Boltzmann equation
• Galerkin-Petrov approach for the Boltzmann equation
• Boundary-layer behavior in the fluid-dynamic limit for a nonlinear model Boltzmann equation
• Two-dimensional time dependent Riemann solvers for neutron transport
• A MIXED VARIATIONAL FRAMEWORK FOR THE RADIATIVE TRANSFER EQUATION
• A class of Galerkin Schemes for Time-Dependent Radiative Transfer
• Numerical Regularized Moment Method of Arbitrary Order for Boltzmann-BGK Equation
• The Linearized Boltzmann Collision Operator for Cut-Off Potentials
• A Quasi-Projection Analysis of Galerkin Methods for Parabolic and Hyperbolic Equations
• Convergence of Moment Methods for Linear Kinetic Equations
• Moment Methods for the Semiconductor Boltzmann Equation on Bounded Position Domains
• NUMERICAL METHODS FOR THE SEMICONDUCTOR BOLTZMANN EQUATION BASED ON SPHERICAL HARMONICS EXPANSIONS AND ENTROPY DISCRETIZATIONS
• Existence of Solutions to the Stationary Linear Boltzmann Equation
• Convergence Study of Moment Approximations for Boundary Value Problems of the Boltzmann-BGK Equation
• $L^2 $-Estimates for Galerkin Methods for Second Order Hyperbolic Equations
• Asymptotic Theory of the Boltzmann Equation
• On the kinetic theory of rarefied gases

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