An Enhanced Momentum Conservation Treatment for FDM Simulation of Two-Phase Flows with Large Density Ratio

The differences of the fluid properties across a fluid interface in two-phase flow often bring difficulties into computational simulations, as the conservation of mass, momentum and energy requires careful consideration at the interfacial region. Velocity advection and unsynchronised variables lead to loss of conservation of momentum across the interface, which results in an unphysical interface deformation and spurious interfacial currents. In this study, we investigate the numerical errors and instabilities in the interfacial region, and propose a new algorithm with strong temporal coupling and momentum-based velocity reconstruction, to enhance its conservation properties. The capability of the proposed algorithm is demonstrated with two idealised cases including a one-dimensional convection case of a dense droplet and a standing wave case, and one laboratory dambreak case. Results are compared with theoretical results, experimental data or existing simulations, which demonstrate the advantages of the proposed algorithm on the conservation of mass, momentum and energy, and the mitigation of unphysical interfacial transport. Without modification of any numerical methods or discretization schemes, the algorithm keeps its simplicity and can work with the existing methods, and it is straightforward to implement.