A Quadrature-Based Kinetic Model for Dilute Non-Isothermal Granular Flows (Communications in Computational Physics, 2011)
A moment method with closures based on Gaussian quadrature formulas isproposed to solve the Boltzmann kinetic equation with a hard-sphere collision kernelfor mono-dispersed particles. Different orders of accuracy in terms of the moments ofthe velocity distribution function are considered, accounting for moments up to seventhorder. Quadrature-based closures for four different models for inelastic collision theBhatnagar-Gross-Krook, ES-BGK, the Maxwell model for hard-sphere collisions,and the full Boltzmann hard-sphere collision integral-are derived and compared. Theapproach is validated studying a dilute non-isothermal granular flow of inelastic particlesbetween two stationary Maxwellian walls. Results obtained from the kineticmodels are compared with the predictions of molecular dynamics (MD) simulationsof a nearly equivalent system with finite-size particles. The influence of the number ofquadrature nodes used to approximate the velocity distribution function on the accuracyof the predictions is assessed. Results for constitutive quantities such as the stresstensor and the heat flux are provided, and show the capability of the quadrature-basedapproach to predict them in agreement with the MD simulations under dilute conditions.