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 …