Comparison Between Grad’s and Quadrature-Based Methods of Moments for the Numerical Simulation of Unsteady Particle-Laden Flows Available to Purchase

We present here a new method of moments for the numerical simulation of particle-laden flows. The closure needed in Eulerian methods relies on writing the kinetic descriptor, the velocity destribution function, as a sum of delta-functions instead of the one-delta-function or close-to-Maxwellian assumption in existing methods. The closure velocity distribution function parameters are computed from the transported moments using a quadrature method. Simulation results are compared to those of a close-to-Maxwellian-based Eulerian method and those of a reference Lagrangian simulation, considering only transport and drag of particles in a Taylor-Green fluid flow. For a particular Stokes number of 1 the velocity distribution function is far from equilibrium and particle trajectory crossing is an important feature. We find that the quadrature-based method performs better than the close-to-equilibrium-based method, giving moment profiles closer to those of the Lagrangian reference simulation. However significant differences still remain between quadrature-based and Lagrangian methods results.