Using the composite Riemann problem solution for capturing interfaces in compressible two-phase flows

摘要

The paper addresses a novel interface-capturing approach for two-phase flows governed by the five-equation model. In this model, two fluids separated with an interface are treated as a homogenous fluid with a characteristic function (volume fraction) determining the location of the fluids and the interface. To suppress the numerical diffusion of the interface, we reconstruct the discontinuity of the volume fraction in each composite (mixed) cell that contains two materials. This sub-cell reconstruction gives rise to the Composite Riemann Problem (CRP) whose solution is used to calculate the numerical flux through cell faces which bound mixed cells. The HLLC method is incorporated to approximate the solution of the CRP. The CRP method is shown to reduce the interface numerical diffusion without introducing spurious oscillations. Its performance and robustness is examined by a variety of 1D and 2D numerical tests, such as the shock-bubble interaction problem, the triple-point problem, and the Richtmyer–Meshkov instability problem.