An active learning SPH method for generalized Newtonian free surface flows

Abstract

This paper presents an active learning smoothed particle hydrodynamics (ALSPH) method to simulate generalized Newtonian free surface flows. First, an improved smoothed particle hydrodynamics (ISPH) method is established to obtain more reliable results for free surface flows by coupling the modified kernel gradient, the artificial viscosity, the density diffusive term, and the optimized particle shifting technique. Second, based on data and Gaussian process regression (GPR), an active learning strategy is developed to provide an effective constitutive relation. It is the first time that the ISPH method is combined with GPR to simulate generalized Newtonian free surface flows. Not only can the constitutive relation of any generalized Newtonian fluid in nature be accurately predicted, but a small amount of sampling data is also able to ensure accuracy over a wide range of the shear deformation rate. The challenging droplet impact and dam break are first modeled to validate the ISPH method. Due to the lack of an analytical constitutive relation for an arbitrary generalized Newtonian fluid in nature, the Cross model is then adopted and offers the required data to validate the ALSPH method. The results indicate that the learned constitutive relation is quite consistent with the analytical one and the simulation results match well. In addition, predictive accuracy and time consumption are proven. Furthermore, to verify the applicability of the learned constitutive relation, the jet buckling case and the jet entering the static fluid case are modeled. The good performance demonstrates the ALSPH method has a promising prospect of applications in simulating complex flows in nature.