Complex wave patterns in dilute gas-particle flows based on a novel discontinuous Galerkin scheme

The present work investigates complex wave patterns in dilute gas-particle flows based on a novel discontinuous Galerkin (DG) method. For this purpose, a high order DG method was for the first time applied to two-fluid model equations for dusty gas flows. The new DG scheme not only meets the demand for high order accuracy and the positivity/monotonicity preserving property for accurately simulating dusty gas flows, but it can also handle the numerically problematic source terms efficiently, without resorting to the complicated operator splitting method commonly employed in the conventional finite volume method (FVM). For verification, several benchmark problems in one- and two-dimensional space were calculated. Special attention was then paid to the complex mechanisms of wave patterns in the dusty gas flows, which have rarely been studied in previous works, and to the physical justifications of such abnormal behaviors. In particular, it was shown that when a dust contact discontinuity is present in the flow, a pseudo-compound wave (a reflected shock attached to the rarefaction wave) as well as a composite wave (a contact discontinuity attached to the relaxation zone) can form.