An ALE Framework with an HLLC-2D Riemann Solver for Reactive Gas–Particle Flows

We propose a coupled gas–particle two-phase model for particle transport in a compressible carrier gas with interphase momentum and energy exchange, and we incorporate a diffusion-based mechanism to represent gas–particle reactions. The governing equations are discretized in an Arbitrary Lagrangian–Eulerian (ALE) finite-volume framework using an HLLC-type two-dimensional Riemann solver (HLLC-2D). The solver employs a nodal-conservation construction that enforces consistency between numerical fluxes and nodal contact velocities, which helps reduce spurious oscillations near discontinuities on moving meshes. In addition, a particle-search-based Courant–Friedrichs–Lewy(CFL)-like time-step restriction is introduced to enhance robustness in coupled simulations. Numerical tests are presented to assess the method and to illustrate particle-induced modifications of wave dynamics, as well as reaction-driven variations in velocity and temperature fields.