A compressible semi-resolved computational fluid dynamics-discrete element method coupling model for fluid–solid systems with heat transfer.

This article presents the development and validation of a compressible semi-resolved computational fluid dynamics-discrete element method (CFD-DEM) coupling model with heat transfer for simulating compressible fluid–solid systems. The model integrates the volume-averaged Navier–Stokes equations for the fluid phase and Newton's second law for particle motion, incorporating a diffusion-based smoothing method and volume-averaged weighted function interpolation to overcome grid size restrictions relative to particle diameter. Validation cases include single-particle sedimentation in liquid, gas–solid fluidized beds with and without heat transfer, particle dispersion induced by shock waves, and shock wave interaction with dense particle curtains, demonstrating the model's accuracy and computational efficiency across dilute to dense flow regimes and low to high-speed conditions. The study highlights the model's capability to bridge the gap between fully resolved and unresolved CFD-DEM approaches, offering improved accuracy over unresolved methods while maintaining greater efficiency than fully resolved simulations.