Comparison between two Riemann solvers for the dust fluid: HLLgd and H&B22, the solver from Huang & Bai (2022). Gas density map in the first column (HLL solver) at t = 60.6 kyr, dust-to-gas ratio maps from the two Riemann solvers (HLLgd in the second column and H&B22 in the third column), and resolution of the recoupling length expressed as Δx/(c_st_{s,1 mm}), with mesh-refinement levels indicated by contours, in the last column. Zoom-in of the collapse region (upper panels) to the disk scale (lower panels). Dust feedback has been deactivated to ease the comparison between the two solvers.