A Split-Flux Method for Dust-Gas Two-Fluid Simulations from Strong to Weak Coupling

We develop a new method for simulating pressureless fluids of neutral dust coupled to magnetohydrodynamic gas through dust-gas drag. It has been pointed out that, in the strong-coupling regime, dust-gas multifluid methods suffer from artificial variations in the dust-to-gas mass ratio when the dust and gas are evolved with independent numerical fluxes. This problem arises from inconsistencies between the dust and gas mass fluxes. In the strong-coupling limit, the dust-to-gas mass ratio is advected with the local gas velocity. Recently, a new method based on the Harten-Lax-van Leer (HLL) solver was proposed. This method constructs the dust mass flux so that it is consistent with the gas mass flux, and successfully reduces artificial variations in the dust-to-gas mass ratio. Here, we develop a Split-Flux method that can be coupled to an HLLD gas solver. Through various numerical experiments, we show that the Split-Flux method suppresses artificial variations in the dust-to-gas mass ratio, while preserving the low numerical diffusivity of the HLLD solver.