Numerical simulation of microflows using moment methods with linearized collision operator

DOI10.1007/s10915-017-0442-7zbMath1404.65082OpenAlexW2609538046MaRDI QIDQ1703062

Manuel Torrilhon, Zhenning Cai

Publication date: 1 March 2018

Published in: Journal of Scientific Computing (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s10915-017-0442-7

zbMATH Keywords

linearized collision operatorBurnett's expansionhyperbolic moment equationsMaxwell's boundary condition

Mathematics Subject Classification ID

Rarefied gas flows, Boltzmann equation in fluid mechanics (76P05) Finite difference methods for initial value and initial-boundary value problems involving PDEs (65M06) Kinetic theory of gases in time-dependent statistical mechanics (82C40) Boltzmann equations (35Q20)

Related Items (18)

Moment method as a numerical solver: challenge from shock structure problems ⋮ Numerical Solver for the Boltzmann Equation with Self-Adaptive Collision Operators ⋮ Entropy bounds for the space-time discontinuous Galerkin finite element moment method applied to the BGK-Boltzmann equation ⋮ Burnett spectral method for the spatially homogeneous Boltzmann equation ⋮ Construction of boundary conditions for hyperbolic relaxation approximations II: Jin-Xin relaxation model ⋮ An Efficient Nonlinear Multigrid Solver for the Simulation of Rarefied Gas Cavity Flow ⋮ Representation theory based algorithm to compute Boltzmann's bilinear collision operator in the irreducible spectral Burnett ansatz efficiently ⋮ Construction of boundary conditions for Navier-Stokes equations from the moment system ⋮ Regularized 13-moment equations for inverse power law models ⋮ Hyperbolic Model Reduction for Kinetic Equations ⋮ Construction of boundary conditions for hyperbolic relaxation approximations I: The linearized Suliciu model ⋮ Burnett Spectral Method for High-Speed Rarefied Gas Flows ⋮ A Nonlinear Hyperbolic Model for Radiative Transfer Equation in Slab Geometry ⋮ Approximation to Singular Quadratic Collision Model in Fokker--Planck--Landau Equation ⋮ A hybrid moment method for multi-scale kinetic equations based on maximum entropy principle ⋮ Numerical Simulation of Microflows Using Hermite Spectral Methods ⋮ Hermite spectral method for multi-species Boltzmann equation ⋮ High-Order Non-Conservative Simulation of Hyperbolic Moment Models in Partially-Conservative Form

Uses Software

• HLLE

Cites Work

• Model reduction of kinetic equations by operator projection
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• Boundary conditions for regularized 13-moment-equations for micro-channel-flows
• A numerical study of the heat transfer through a rarefied gas confined in a microcavity
• A Framework on Moment Model Reduction for Kinetic Equation
• Numerical Regularized Moment Method of Arbitrary Order for Boltzmann-BGK Equation
• Regularization of Grad’s 13 moment equations: Derivation and linear analysis
• On Upstream Differencing and Godunov-Type Schemes for Hyperbolic Conservation Laws
• Maximisation of the entropy in non-equilibrium
• Boundary conditions for hyperbolic systems with stiff source terms
• Derivation of 13 Moment Equations for Rarefied Gas Flow to Second Order Accuracy for Arbitrary Interaction Potentials
• Convergence Study of Moment Approximations for Boundary Value Problems of the Boltzmann-BGK Equation
• Globally Hyperbolic Regularization of Grad's Moment System
• Initial boundary value problems for hyperbolic systems
• The Distribution of Molecular Velocities and the Mean Motion in a Non-Uniform Gas
• On the kinetic theory of rarefied gases

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