A stochastic weighted particle method for the Boltzmann equation
Journal of Computational Physics
SIAM Journal on Numerical Analysis
Journal of Computational Physics
The linearized Boltzmann equation: concise and accurate solutions to basic flow problems
Zeitschrift für Angewandte Mathematik und Physik (ZAMP)
High order numerical methods for the space non-homogeneous Boltzmann equation
Journal of Computational Physics
Statistical error in particle simulations of hydrodynamic phenomena
Journal of Computational Physics
Implicit---Explicit Runge---Kutta Schemes and Applications to Hyperbolic Systems with Relaxation
Journal of Scientific Computing
Solving the Boltzmann Equation in N log2 N
SIAM Journal on Scientific Computing
A Galerkin Method for the Simulation of the Transient 2-D/2-D and 3-D/3-D Linear Boltzmann Equation
Journal of Scientific Computing
Implicit—Explicit Schemes for BGK Kinetic Equations
Journal of Scientific Computing
A low-variance deviational simulation Monte Carlo for the Boltzmann equation
Journal of Computational Physics
Spectral-Lagrangian methods for collisional models of non-equilibrium statistical states
Journal of Computational Physics
A multiscale kinetic-fluid solver with dynamic localization of kinetic effects
Journal of Computational Physics
Numerical properties of high order discrete velocity solutions to the BGK kinetic equation
Applied Numerical Mathematics
Journal of Computational Physics
Hi-index | 31.45 |
A deterministic method is proposed for solving the Boltzmann equation. The method employs a Galerkin discretization of the velocity space and adopts, as trial and test functions, the collocation basis functions based on weights and roots of a Gauss-Hermite quadrature. This is defined by means of half- and/or full-range Hermite polynomials depending whether or not the distribution function presents a discontinuity in the velocity space. The resulting semi-discrete Boltzmann equation is in the form of a system of hyperbolic partial differential equations whose solution can be obtained by standard numerical approaches. The spectral rate of convergence of the results in the velocity space is shown by solving the spatially uniform homogeneous relaxation to equilibrium of Maxwell molecules. As an application, the two-dimensional cavity flow of a gas composed of hard-sphere molecules is studied for different Knudsen and Mach numbers. Although computationally demanding, the proposed method turns out to be an effective tool for studying subsonic slightly rarefied gas flows.