An accurate thermodynamic Riemann-SPH model for multiphase flows with applications in bubble dynamics

In the present work, an accurate thermodynamic Riemann-SPH model for multiphase flows is developed. This model considers the effect of the thermal diffusivity ratio on the transient heat transfer, and more importantly, the Riemann approximation is introduced to deal with the discontinuous temperature field. Through several one- and two-dimensional heat conduction benchmarks, the accuracy and convergence of the developed model are firstly validated by comparing with the results of conventional SPH heat conduction models and analytical solutions. Subsequently, based on the developed SPH model and considering the heat-fluid coupling effect, several cases of rising bubbles are simulated, and the influence of the initial fluid temperature on the kinematic properties of the rising bubble is investigated. On this basis, the thermodynamic Riemann-SPH model is further refined by developing a thermal radiation SPH model and considering the effect of strong fluid compressibility on the temperature field. Finally, using the refined model, the oscillation of the cavitation bubble is simulated, and the heat conduction and radiation process is analyzed.