A direct method for the Boltzmann equation based on a pseudo-spectral velocity space discretization
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Publication:348621
DOI10.1016/j.jcp.2013.10.055zbMath1349.76207arXiv1303.6825OpenAlexW2068302555MaRDI QIDQ348621
Gian Pietro Ghiroldi, Livio Gibelli
Publication date: 5 December 2016
Published in: Journal of Computational Physics (Search for Journal in Brave)
Full work available at URL: https://arxiv.org/abs/1303.6825
Galerkin methodBoltzmann equationdeterministic solutiongaussian quadraturehalf- and full-range Hermite polynomials
Rarefied gas flows, Boltzmann equation in fluid mechanics (76P05) Finite element methods applied to problems in fluid mechanics (76M10) Spectral, collocation and related methods for initial value and initial-boundary value problems involving PDEs (65M70)
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Cites Work
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- Deterministic solution of the spatially homogeneous Boltzmann equation using discontinuous Galerkin discretizations in the velocity space
- Solving model kinetic equations on GPUs
- Application of the Boltzmann kinetic equation to the eddy problems
- A hybrid method for hydrodynamic-kinetic flow. I: A particle-grid method for reducing stochastic noise in kinetic regimes
- Gas kinetic algorithm using Boltzmann model equation
- Implicit-explicit Runge-Kutta schemes and applications to hyperbolic systems with relaxation
- Numerical properties of high order discrete velocity solutions to the BGK kinetic equation
- A numerical model of the Boltzmann equation related to the discontinuous Galerkin method
- Boundary value problems in kinetic theory of gases
- Molecular gas dynamics. Theory, techniques, and applications.
- A Galerkin method for the simulation of the transient 2-D/2-D and 3-D/3-D linear Boltzmann equation
- A multiscale kinetic-fluid solver with dynamic localization of kinetic effects
- Spectral-Lagrangian methods for collisional models of non-equilibrium statistical states
- Semilagrangian schemes applied to moving boundary problemsfor the BGK model of rarefied gas dynamics
- Some observations on grid convergence
- A Gaussian quadrature procedure for use in the solution of the Boltzmann equation and related problems
- The linearized Boltzmann equation: Concise and accurate solutions to basic flow problems
- Discrete-velocity models and numerical schemes for the Boltzmann-BGK equation in plane and axisymmetric geometries
- High order numerical methods for the space non-homogeneous Boltzmann equation.
- Statistical error in particle simulations of hydrodynamic phenomena.
- Fast methods for the Boltzmann collision integral
- Modeling and computational methods for kinetic equations
- A stochastic weighted particle method for the Boltzmann equation
- Solving the Boltzmann equation on GPUs
- A moment method for low speed microflows
- A low-variance deviational simulation Monte Carlo for the Boltzmann equation
- Implicit-explicit schemes for BGK kinetic equations
- Solving the Boltzmann Equation in N log2N
- Variance-reduced Monte Carlo solutions of the Boltzmann equation for low-speed gas flows: A discontinuous Galerkin formulation
- Ghost effect of infinitesimal curvature in the plane Couette flow of a gas in the continuum limit
- The driven cavity flow over the whole range of the Knudsen number
- Temperature jump and Knudsen layer in a rarefied gas over a plane wall: Numerical analysis of the linearized Boltzmann equation for hard-sphere molecules
- Structure of normal shock waves: Direct numerical analysis of the Boltzmann equation for hard-sphere molecules
- Exact solutions of the Boltzmann equation
- Numerical Solution of the Boltzmann Equation I: Spectrally Accurate Approximation of the Collision Operator
- A new consistent discrete-velocity model for the Boltzmann equation
- Finite Volume Methods for Hyperbolic Problems
- Velocity slip coefficients based on the hard-sphere Boltzmann equation
- A Finite-Difference Lattice Boltzmann Approach for Gas Microflows
- Convolutive decomposition and fast summation methods for discrete-velocity approximations of the Boltzmann equation
- Direct methods for solving the Boltzmann equation and study of nonequilibrium flows
