Adam Larat

On the Development of High Order Realizable Schemes for the Eulerian Simulation of Disperse Phase Flows: A Convex-State Preserving Discontinuous Galerkin Method

In the present work, a high order realizable scheme for the Eulerian simulation of disperse phase flows on unstructured grids is developed and tested. In the Eulerian modeling framework two approaches are studied: the monokinetic (MK) [1] and the Gaussian closures [2, 3]. The former leads to a pressureless gas dynamics system (PGD). It accurately reproduces the physics of such flows at low Stokes number, but is challenging for numerics since the resulting system is weakly hyperbolic. The latter deals with higher Stokes numbers by accounting for particle trajectory crossings (PTC) [4]. Compared to the MK closure, the resulting system of equation is hyperbolic but has a more complex structure; realizability conditions are satisfied at the continuous level, which imply a precise framework for numerical methods. To achieve the goals of accuracy, robustness and realizability, the Discontinuous Galerkin method (DG) is a promising numerical approach [5, 6, 7, 8]. Based on the recent work of Zhang et al. [6], the...

Comparison of Realizable Schemes for the Eulerian Simulation of Disperse Phase Flows

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 \(\delta \)-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 realizable MUSCL/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.