An ALE numerical method with HLLC-2D solver for the two-phase flow ejecta transporting model

TL;DR

This paper introduces an ALE numerical method combined with an HLLC-2D Riemann solver to accurately simulate two-phase flow ejecta transporting, emphasizing particle-flow interactions and conservation properties.

Contribution

It develops a novel ALE approach with an improved HLLC-2D solver for better modeling of particle and flow phase interactions in two-phase flows.

Findings

The method maintains conservation of momentum and energy.

Numerical tests validate robustness and accuracy.

The approach effectively models particle influence on fluid dynamics.

Abstract

This work presents an arbitrary Lagrangian Eulerian (ALE) method for the compressible two-phase flow ejecta transporting model with the HLLC-2D Riemann solver. We focus on researching the precise equation to describe the interactions between particle phase and flow phase. The calculation of the momentum and energy exchange across two phases is the key point during the procedure, which can be capable of maintaining the conservation of this system. For particles, tracking their trajectories within the mesh and elements is essential. Thereafter an ALE method instead of Lagrangian scheme is derived for the discretization of the equation to perform better with the complex motion of particles and flow. We apply the HLLC-2D Riemann solver to substitute the HLLC solver which relaxes the limitation for continuous fluxes along the edge. Meanwhile we propose a method for searching particles and provide a CFL-like condition based on this. Finally, we show some numerical tests to analysis the influence of particles on fluid and get a following effect between two phases. The model and the numerical method are validated through numerical tests to show its robustness and accuracy.