A positivity-preserving HLLC-based discontinuous Galerkin method for weakly compressible two-phase flows

In this study, we present a novel robust discontinuous Galerkin (DG) method based on the Harten-Lax-van Leer-contact (HLLC) approximate Riemann solver for weakly compressible two-phase flows governed by a three-equation model. The proposed method satisfies the mechanical equilibrium criterion which states that uniform velocity and pressure should be remained uniform during the simulation. It also maintains a positive density solution and an oscillation-free material interface by employing a positivity-preserving limiter and a compact multi-resolution weighted essentially non-oscillatory (MRWENO) limiter without violating the mechanical equilibrium criterion. A series of one- and two-dimensional numerical results are presented to demonstrate the exceptional accuracy and robustness of the proposed method. More importantly, based on the extensive numerical results, we successfully derive a suitable choice on the linear weight of the MRWENO limiter, which plays an important role in both accuracy and robustness in simulating weakly compressible two-phase flows.