A relaxation scheme for solving the Boltzmann equation based on the Chapman-Enskog expansion

DOI10.1007/s102550200003zbMath0998.82027OpenAlexW1975639216MaRDI QIDQ1611081

Lorenzo Pareschi, Marshall Slemrod, Shih Jin

Publication date: 12 September 2002

Published in: Acta Mathematicae Applicatae Sinica. English Series (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s102550200003

zbMATH Keywords

Boltzmann equationrelaxationChapman-Enskog expansionBurnett equationscentral schemes

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)

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A high-order moment approach for capturing non-equilibrium phenomena in the transition regime ⋮ Comparing macroscopic continuum models for rarefied gas dynamics: a new test method ⋮ Scaling and expansion of moment equations in kinetic theory ⋮ Multiple temperature kinetic model and gas-kinetic method for hypersonic non-equilibrium flow computations ⋮ Regularization of Grad’s 13 moment equations: Derivation and linear analysis ⋮ Stable transport equations for rarefied gases at high orders in the Knudsen number ⋮ Grossly determined solutions for a Boltzmann-like equation ⋮ Numerical methods for kinetic equations ⋮ A computational strategy for the regularized 13 moment equations with enhanced wall-boundary conditions ⋮ On hyperbolicity of 13-moment system

Cites Work

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• A high order staggered grid method for hyperbolic systems of conservation laws in one space dimension
• Non-oscillatory central differencing for hyperbolic conservation laws
• On the domain space for constitutive laws in linear viscoelasticity
• Fluid dynamics of viscoelastic liquids
• The Boltzmann equation and its applications
• Implicit-explicit Runge-Kutta methods for time-dependent partial differential equations
• Moment closure hierarchies for kinetic theories.
• In the Chapman-Enskog expansion the Burnett coefficients satisfy the universal relation \(\omega _{3} + \omega _{4} + \theta _{3} = 0\)
• Constitutive relations for monatomic gases based on a generalized rational approximation to the sum of the Chapman-Enskog expansion
• Central Schemes for Balance Laws of Relaxation Type
• An introduction to Monte Carlo method for the Boltzmann equation
• Uniformly High-Order Accurate Nonoscillatory Schemes. I
• The Gaussian Moment Closure for Gas Dynamics
• Relaxation of Energy and Approximate Riemann Solvers for General Pressure Laws in Fluid Dynamics
• Hyperbolic conservation laws with stiff relaxation terms and entropy
• Time-derivatives and frame-invariance beyond Newtonian fluids
• Central Differencing Based Numerical Schemes for Hyperbolic Conservation Laws with Relaxation Terms
• The relaxation schemes for systems of conservation laws in arbitrary space dimensions
• On the Construction and Comparison of Difference Schemes
• Asymptotic Theory of the Boltzmann Equation
• Regularization of the Burnett equations for rapid granular flows via relaxation
• Regularization of the Burnett equations via relaxation

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