A data-driven smoothed particle hydrodynamics method for fluids

The rheological properties of emerging novel complex fluids are usually governed by multiple variables, which is challenging for traditional parameterized rheological models in the context of hydrodynamics modelling. In this paper, we propose a novel Data-Driven Smoothed Particle Hydrodynamics (DDSPH) method that, instead of applying the empirical rheological models, utilizes discrete experimental datasets to close the Navier-Stokes equations for hydrodynamics modelling. To this end, a DDSPH solver is introduced to search for the best data points that minimize a distance-based penalty function while satisfying the velocity constraints obtained from the previous timestep. In order to improve the computational efficiency of data retrieval, a large volume of experimental rheological data is pre-sectioned into several labelled subgroups so that the data retrieval can be carried out in a small span of data. The robustness of the proposed method with respect to noisy data is achieved via adding a variable, namely the data probability, to qualify the relevance of data points to the clusters. The convergence and robustness of the proposed DDSPH method are investigated through the examples for both Newtonian and non-Newtonian fluids. The numerical examples have demonstrated that the proposed DDSPH is effective and efficient for both Newtonian and non-Newtonian fluids. The proposed DDSPH will open a new avenue for hydrodynamics modelling though some further studies are required in the future.