A simplified and efficient weakly-compressible FV-WENO scheme for immiscible two-phase flows

The present paper proposes a simplified and efficient FV-WENO scheme for simulating weakly-compressible multi-phase flows. Comparing with a classic FV-WENO scheme, the computational accuracy and efficiency are improved by two choices: (i) reconstructing the primitive variables instead of the conservative ones; (ii) performing the WENO reconstruction only once per direction. Although these choices lead to a formally 2nd -order accurate scheme, it is still different from conventional 2nd-order schemes and can be expected to provide higher-order accuracies far from interfaces. An HLLC-type Riemann flux solver is proposed, which appears to be more robust than the linearized Riemann flux solver, allowing the use of smaller artificial sound speeds. The proposed scheme is proven to have the oscillation-free property in the advection of isolated interfaces. A series of validation test-cases have been carried out, in which a good agreement can be observed with references. It is shown that the proposed scheme can give accurate results with little numerical diffusion in the simulations involving weakly-compressible multi-phase flows.