Second-order Boltzmann schemes for compressible Euler equations in one and two space dimensions
SIAM Journal on Numerical Analysis
Numerical recipes in FORTRAN (2nd ed.): the art of scientific computing
Numerical recipes in FORTRAN (2nd ed.): the art of scientific computing
Journal of Computational Physics
Numerical Approximations of Pressureless and Isothermal Gas Dynamics
SIAM Journal on Numerical Analysis
Journal of Computational Physics
A quadrature-based moment method for dilute fluid-particle flows
Journal of Computational Physics
Efficient kinetic schemes for steady and unsteady flow simulations on unstructured meshes
Journal of Computational Physics
Journal of Computational Physics
A comparative study of the LBE and GKS methods for 2D near incompressible laminar flows
Journal of Computational Physics
A DGBGK scheme based on WENO limiters for viscous and inviscid flows
Journal of Computational Physics
A quadrature-based third-order moment method for dilute gas-particle flows
Journal of Computational Physics
Journal of Computational Physics
Accuracy of higher-order lattice Boltzmann methods for microscale flows with finite Knudsen numbers
Journal of Computational Physics
Realizable high-order finite-volume schemes for quadrature-based moment methods
Journal of Computational Physics
Conditional quadrature method of moments for kinetic equations
Journal of Computational Physics
A multivariate quadrature based moment method for LES based modeling of supersonic combustion
Journal of Computational Physics
Journal of Computational Physics
Journal of Computational Physics
Journal of Computational and Applied Mathematics
Hi-index | 31.47 |
Kinetic equations containing terms for spatial transport, body forces, and particle-particle collisions occur in many applications (e.g., rarefied gases, dilute granular gases, fluid-particle flows). The direct numerical solution of the kinetic equation is usually intractable due to the large number of independent variables. A useful alternative is to reformulate the problem in terms of the moments of the velocity distribution function. Closure of the moment equations is challenging for flows sufficiently far away from the Maxwellian limit. In previous work, a quadrature-based third-order moment closure was derived for approximating solutions to the kinetic equation for arbitrary Knudsen number. A key component of quadrature-based closures is the moment-inversion algorithm used to find the non-negative weights and velocity abscissas. Here, a robust inversion procedure is proposed for three-component velocity moments up to ninth order. By reconstructing the velocity distribution function, the spatial fluxes in the moment equations are treated using a kinetic-based finite-volume solver. Because the quadrature-based moment method employs the moment transport equations directly instead of a discretized form of the kinetic equation, the mass, momentum and energy are conserved for arbitrary Knudsen and Mach numbers. The computational algorithm is tested for the Riemann shock problem and, for increasing Knudsen numbers (i.e. larger deviations from the Maxwellian limit), the accuracy of the moment closure is shown to be determined by the discrete representation of the spatial fluxes.