State-of-the-art finite-volume discretisation of Kapila's two-fluid flow model

In preparation of the study of liquefied natural gas (LNG) sloshing in ships and vehicles, we model and numerically analyse compressible two-fluid flow. We consider a five-equation two-fluid flow model, assuming velocity and pressure continuity across two-fluid interfaces, with a separate equation to track the interfaces. The system of partial differential equations is hyperbolic and quasi-conservative. It is discretised in space with a tailor-made third-order accurate finite-volume method, employing an HLLC approximate Riemann solver. The third-order accuracy is obtained through spatial reconstruction with a limiter function, for which a novel formulation is presented. The non-homogeneous term is handled in a way consistent with the HLLC method. We study the one-dimensional case of a liquid column impacting onto a gas pocket entrapped at a solid wall. It mimics the impact of a breaking wave in an LNG containment system, where a gas pocket is entrapped at the tank wall below the wave crest. Furthermore, the impact of a shock wave on a gas bubble containing the heavy gas R22, immersed in air, is simulated and compared with experimental results. The computational results are consistent with the experimental results.