A Technique for Computing Dense Granular Compressible Flows with Shock Waves

TL;DR

This paper introduces a high-order, low-dissipation numerical method for simulating compressible granular multiphase flows with shocks, capable of handling wide particle volume fractions and sharp interfaces.

Contribution

It develops a novel algorithm that separates gas and solid phases for independent Riemann problem solutions, enabling accurate shock and interface modeling in granular flows.

Findings

Converges under grid refinement even with dense granular interfaces.

Accurately models shock interactions and granular material interfaces.

Reproduces known shock tube and wave transmission phenomena.

Abstract

A numerical procedure was developed for solving equations for compressible granular multiphase flows in which the particle volume fraction can range dynamically from very dilute to very dense. The procedure uses a low-dissipation and high-order numerical method that can describe shocks and incorporates a particulate model based on kinetic theory. The algorithm separates edges of a computational cell into gas and solid sections where gas- and granular-phase Riemann problems are solved independently. Solutions from these individual Riemann problems are combined to assemble the fully coupled convective fluxes and nonconservative terms for both phases. The technique converges under grid refinement even with very high volume fraction granular interfaces. The method can advect sharp granular material interfaces that coincide with multi-species gaseous contact surfaces without violating the pressure nondisturbing condition. The procedure also reproduces known features from multiphase shock tube problems, granular shocks, transmission angles of compaction waves, and shock wave and dust-layer interactions. This approach is relatively straightforward to use in an existing code based on Godunov's method and can be constructed from standard compressible solvers for the gas-phase and a modified AUSM$^+$-up scheme for the particle phase.