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

Jianqiao Zhang, Wei Yan, Xianggui Li

TL;DR

The paper develops an ALE-based numerical framework for a compressible two-phase ejecta transport problem, coupling gas dynamics to dispersed particles via drag and convective heat transfer. It advances a 2D HLLC-2D Riemann solver on moving, unstructured meshes with a nodal solver to preserve local conservation, and includes a detailed particle-searching and time-step strategy to handle interphase interactions. Numerical tests across particle transport scenarios and a multiphase Sod shock-tube demonstrate the method’s robustness, accuracy, and sensitivity to viscosity and interphase coupling. The work provides a practical tool for simulating ejecta transport in high-speed flows with moving bodies, highlighting the importance of accurate interphase momentum/energy exchange and mesh adaptation.

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.

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

TL;DR

The paper develops an ALE-based numerical framework for a compressible two-phase ejecta transport problem, coupling gas dynamics to dispersed particles via drag and convective heat transfer. It advances a 2D HLLC-2D Riemann solver on moving, unstructured meshes with a nodal solver to preserve local conservation, and includes a detailed particle-searching and time-step strategy to handle interphase interactions. Numerical tests across particle transport scenarios and a multiphase Sod shock-tube demonstrate the method’s robustness, accuracy, and sensitivity to viscosity and interphase coupling. The work provides a practical tool for simulating ejecta transport in high-speed flows with moving bodies, highlighting the importance of accurate interphase momentum/energy exchange and mesh adaptation.

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.
Paper Structure (24 sections, 43 equations, 14 figures, 1 table)

This paper contains 24 sections, 43 equations, 14 figures, 1 table.

Table of Contents

  1. Introduction
  2. Particle Trajectory Model
  3. Problem statement, Notation and Assumptions
  4. Governing Equations
  5. Numerical Scheme
  6. ALE scheme
  7. Notations on a generic polygonal grid
  8. Flux formula of HLLC-2D on moving mesh
  9. Nodal Solver
  10. Boundary Condition
  11. Time discretization and particle searching
  12. Particle searching
  13. Time step limitation
  14. CFL condition
  15. Criterion on the variation of volume
  16. ...and 9 more sections

Figures (14)

  • Figure 1: Notations on a grid
  • Figure 2: Particle searching
  • Figure 3: Drag model
  • Figure 4: Different radius comparison in a quiescent fluid
  • Figure 5: Different radius comparison in a constant acceleration fluid
  • ...and 9 more figures

Theorems & Definitions (2)

  • Remark 3.1
  • Remark 5.1