On the Anisotropic Gaussian Velocity Closure for Inertial-Particle Laden Flows (Communications in Computational Physics, 2018)
The accurate simulation of disperse two-phase flows, where a discrete particulatecondensed phase is transported by a carrier gas, is crucial for many applications;Eulerian approaches are well suited for high performance computations of suchflows. However, when the particles from the disperse phase have a significant inertiacompared to the time scales of the flow, particle trajectory crossing (PTC) occurs i.e. theparticle velocity distribution at a given location can become multi-valued. To properlyaccount for such a phenomenon many Eulerian moment methods have been recentlyproposed in the literature. The resulting models hardly comply with a full set of desiredcriteria involving: 1- ability to reproduce the physics of PTC, at least for a givenrange of particle inertia, 2- well-posedness of the resulting set of PDEs on the chosenmoments as well as guaranteed realizability, 3- capability of the model to be associatedwith a high order realizable numerical scheme for the accurate resolution of particlesegregation in turbulent flows. The purpose of the present contribution is to introducea multi-variate Anisotropic Gaussian closure for such particulate flows, in the spiritof the closure that has been suggested for out-of-equilibrium gas dynamics and whichsatisfies the three criteria. The novelty of the contribution is three-fold. First we derivethe related moment system of conservation laws with source terms, and justify the useof such a model in the context of high Knudsen numbers, where collision operatorsplay no role. We exhibit the main features and advantages in terms of mathematicalstructure and realizability. Then a second order accurate and realizable MUSCL/HLLscheme is proposed and validated. Finally the behavior of the method for the descriptionof PTC is thoroughly investigated and its ability to account accurately for inertialparticulate flow dynamics in typical configurations is assessed.