An accurate SPH Volume Adaptive Scheme for modeling strongly-compressible multiphase flows. Part 1: Numerical scheme and validations with basic 1D and 2D benchmarks

Abstract In the present work, the single-phase and weakly-compressible δ-SPH  model is further extended to simulate multiphase and strongly-compressible flows. This is motivated by the fact that traditional SPH models can meet some difficulties when modeling strongly-compressible flows with large volume variations (e.g. expansion and collapse of cavitation bubbles). Due to the strong compressibility of the fluid, the energy equation should be considered in the governing equations. In that case, the pressure is solved based on both density and internal energy. To stabilize the pressure field, density and energy diffusive terms should be applied. Large variations of particle volumes in the compressible phase would result in large variations of particle spacing. Therefore, particle smoothing lengths are adjusted in time to maintain appropriate neighboring particles. To ensure good properties of accuracy and conservation when particles with different smoothing lengths interact, corrected SPH operators are utilized to discretize the governing equations. Moreover, in order to limit the particle volume variations and maintain a homogeneous volume distribution in the entire flow field, especially near the interface between different phases of different compressibility, a new volume adaptive scheme is proposed to control particle volumes. The volumes which are over-expanded or over-compressed will be split or merged with others, maintaining a small particle volume variation in the flow. Finally, the proposed SPH model is validated with several challenging benchmarks including expansion and collapse of underwater-explosion bubbles or cavitation bubbles. All the SPH results are compared with other numerical solutions with good agreements.