A high-fidelity interface sharpening method for the five-equation model in compressible multiphase flows

The five-equation model is commonly utilized for simulating compressible multiphase flows. Conventional high-resolution schemes, however, frequently suffer from excessive numerical dissipation that leads to interface smearing, thereby compromising simulation accuracy in interfacial flow characterization. In this work, we propose an improved multi-material artificial compression method with extreme interface sharpening (MMACM-Ex), a novel high-fidelity numerical method specifically designed for solving the five-equation model. The method discretizes the equations within a standard finite volume framework and calculates the numerical fluxes with two components: an upwind Riemann flux derived through the Harten-Lax van Leer contact (HLLC) Riemann solver, combined with an interface sharpening flux formulated using a downwind scheme adapted from the flux-corrected transport volume-of-fluid (FCT-VOF) method. Besides, a characteristic function is strategically designed to ensure that the interface sharpening flux can effectively counteract numerical dissipation generated by Riemann flux computations while preserving rigorous interface sharpness. The proposed numerical method is versatile and applicable to a wide range of one-, two-, and three-dimensional problems. Numerical validations demonstrate the method's ability to capture material interfaces with high resolution, highlighting its superiority over the original MMACM in simulating compressible multiphase flows.