Comparison of realizable schemes for the eulerian simulation of disperse phase flows

Abstract

In the framework of fully Eulerian simulation of disperse phase flows, the use of a monokinetic closure for the kinetic based moment method is of high importance since it accurately reproduces the physics of low inertia particles with a minimum number of moments. The free transport part of this model leads to a pressureless gas dynamics system which is weakly hyperbolic and can generate δ-shocks. These singularities are difficult to handle numerically, especially without globally degenerating the order or disrespecting the realizability constraints. A comparison between three second order schemes is conducted in the present work. These schemes are: a realizableMUSCL/HLL finite volume scheme, a finite volume kinetic scheme, and a convex state preserving Runge-Kutta discontinuous Galerkin scheme. Even though numerical computations have already been led in 2D and 3D with this model and numerical methods, the present contribution focuses on 1D results for a full understanding of the trade off between robustness and accuracy and of the impact of the limitation procedures on the numerical dissipation. Advantages and drawbacks of each of these schemes are eventually discussed. 1 Introduction