arXiv2026
Flows with high density ratios, such as wave breaking and air entrainment in maritime applications, remain challenging to simulate due to their energetic and strongly nonlinear nature. In such regimes, maintaining numerical robustness is difficult when using the commonly adopted velocity-based formulation. The Consistent Mass-Momentum (CMOM) transport framework improves numerical robustness by enforcing fundamental physical properties, most notably momentum conservation and semi-discrete energy-conserving. However, CMOM replaces the advection of a continuous velocity field with that of a discontinuous momentum field. When combined with sharp interface methods, this leads to severe momentum shocks, for which conventional shock-capturing schemes are ineffective. To reconcile physical fidelity with numerical robustness, this work proposes a Synchronized Donor-Region of Momentum fluxes (SynDRoM) that enforces monotonicity of the transported velocity field. The resulting algorithm effectively eliminates spurious velocity oscillations without sacrificing physical fidelity, as demonstrated through scalar transport and interfacial shear instability test cases. Beyond difficulties from large density ratio, improper estimation of viscosity in the vicinity of the interface can introduce numerical instabilities at finite time steps, thereby undermining overall robustness. To address this issue, a viscosity limiter based on the bounded kinetic viscosity concept is introduced and validated using a gravity-driven plane shear flow. Finally, a breaking wave simulation is performed to assess the combined performance of the proposed physics-preserving numerical schemes for multiphase flows.