A hybrid scheme for gas–dust systems stiffly coupled via viscous drag

We present a stable and convergent method for studying a system of gas and dust, coupled through viscous drag in both non-stiff and stiff regimes. To account for the effects of dust drag in the update of the fluid quantities, we employ a fluid description of the dust component and study the modified gas-dust hyperbolic system following the approach in Miniati and Colella [19]. In addition to two entropy waves for the gas and dust components, respectively, the extended system includes three waves driven partially by gas pressure and partially by dust drift, which, in the limit of vanishing coupling, tend to the two original acoustic waves and the unhindered dust streaming. Based on this analysis we formulate a predictor step providing first order accurate reconstruction of the time-averaged state variables at cell interfaces, whence a second order accurate estimate of the conservative fluxes can be obtained through a suitable linearized Riemann solver. The final source term update is carried out using a one-step, second order accurate, L-stable, predictor corrector asymptotic method (the αα-QSS method suggested by Mott et al. [21]). This procedure completely defines a two-fluid method for gas-dust system. Using the updated fluid solution allows us to then advance the individual particle solutions, including self-consistently the time evolution of the gas velocity in the estimate of the drag force. This is done with a suitable particle scheme also based on the αα-QSS method. A set of benchmark problems shows that our method is stable and convergent. When dust is modeled as a fluid (two-fluid) second order accuracy is achieved in both stiff and non-stiff regimes, whereas when dust is modeled with particles (hybrid) second order is achieved in the non-stiff regime and first order otherwise.