A low-dissipation SPH Riemann solver for multiphase flows with arbitrary density ratios

A low-dissipation Riemann-based WCSPH formulation is proposed for the simulation of multiphase flows with arbitrary density ratios. The method combines a Riemann-solver-based formulation with a parameter-free dissipation coefficient and a continuum surface-tension model to accurately capture interfacial dynamics. In addition, a consistent treatment of fluid–boundary interactions based on a partial Riemann problem is introduced to improve the robustness of high-impact simulations. A key feature of the proposed approach is the use of an identical numerical speed of sound for both phases, which enhances computational efficiency while maintaining numerical stability in high-density-ratio configurations. The method is implemented within the open-source DualSPHysics framework and is applicable to a wide range of flow regimes, from surface-tension-dominated to inertia-dominated flows. The proposed formulation is validated against several benchmark problems, including square droplet relaxation, rising and merging bubbles, and wave impact on a rigid plate. The results demonstrate that the method accurately captures sharp interfaces, pressure discontinuities, and complex interfacial dynamics, while avoiding spurious mixing and unphysical void formation. Good agreement with analytical, numerical, and experimental reference data is obtained across a wide range of density ratios and flow conditions.