Projection methods for two velocity–two pressure models for flows of heterogeneous mixtures

In this paper, a numerical analysis of two velocity–two pressure models for flows of solid particles and fluids is presented. First, a formal exploitation of the weak formulation of such models asserts that they are amenable to integration via projection methods. The challenging issues in the algorithm development for these models are then documented and suitable numerical methodologies for their remedy are devised. Subsequently, an algorithm for the integration of the models of interest is proposed. This is a two-phase projection method on collocated grids that utilizes a fractional-step time-marching scheme. It is further endowed with an interface detection-and-treatment methodology to properly account for the stiffness induced by the presence of moving and deforming material interfaces. The efficiency and robustness of the proposed numerical method are assessed in a series of numerical experiments that are delineated in the last part of this paper.