The radius of the cylinder is also set to 500 AU. Particles that flow outside the computational domain are removed from the simulation. The inflow consists of new particles. The parameters we have adopted are listed in Table \[tb:parameters\_eda1\].

  **Parameter**                                            **Value** **Description**
  ------------------------- ---------------------------------------- --------------------------------
  $n$                            $5 \times 10^6 \, \mathrm{cm^{-3}}$ Number density of ISM
  $v_{\rm ISM}$                           $20\,\mathrm{km\, s^{-1}}$ 
  $\mu$                                                          2.3 Mean molecular weight
  $M_*$                         $0.4\,{\mbox{$\mathrm{M}_{\odot}$}}$ 
  $M_{\rm disc}$              $0.004\,{\mbox{$\mathrm{M}_{\odot}$}}$ 
  $R_{\rm disc, inner}$                                         10AU 
  $R_{\rm disc, outer}$                                        100AU 
  EoS                                                     Isothermal Equation of state
  $T$                                                            25K Temperature of gas particles
  $c_s$                                  $0.3\,\mathrm{km\, s^{-1}}$ Sound speed
  $R_{\rm sink}$                                              0.09AU Sink particle radius
  $N_{\rm neighbours}$                                      $64\pm2$ 
  $\epsilon_{\rm grav}$                       $10^{-2}\,\mathrm{AU}$ Gravitational softening length
  $\alpha_{\rm SPH}$                                             0.1 Artificial viscosity parameter
  $\mathrm{N_{\rm disc}}$                              $4000-128000$ Number of disc particles

  : Initial values of the parameters in our simulations. The parameters are the same for every simulation, except for the number of disc particles which may vary from simulation to simulation.[]{data-label="tb:parameters_eda1"}

Initial conditions and parameters
---------------------------------

We adopt equal mass particles for the flow and the disc in order to prevent spurious forces on the interface between the ISM and the disc. We set the number of neighbours in the SPH codes to $64 \pm 2$ and use an 