Simulation of Fluid Flows based on the Data-driven Evolution of Vortex Particles
Fluid solvers that provide accurate and fast fluid simulations are of great importance in many scientific and engineering disciplines. Conventional numerical solvers based on the Eulerian description of the flow provide highly accurate solutions to the Navier-Stokes equations. However, there is typically a significant amount of computational effort is required to execute such Eulerian simulations. On the other hand, fluid solvers built on the Lagrangian description of the flow are more appealing in terms of its vicinity to the true physics, since it treats the actual fluid particles as the primary computational elements. A particular group of Lagrangian particle methods based on vorticity, instead of velocity, as the primary flow variable, delivers velocity field solutions, which are always divergence-free. These vortex methods have an inherent advantage that the particles need to be present only in the regions where vorticity exists, and therefore fewer fluid particles are required to execute simulations as compared to their counterparts with velocity-based formulations.
Recently, deep learning solutions for fluid dynamics problems by the application of artificial neural networks has become more prominent. Neural networks encode the information about the governing laws of fluid dynamics in its parameters using the knowledge extracted from data samples during training. The aim of this work is to use deep learning to learn fluid dynamics with Lagrangian vortex particles as the primary flow representation. Solution strategies to train and evaluate the neural networks for predicting Lagrangian vortex particle dynamics for different flow scenarios are presented throughout this work. Conceptualization and implementation of an approach to model interaction between vortex particles based on the Taylor series expansion of the velocity form the core of this work. We demonstrate that our trained neural networks produce fluid simulations with reasonable accuracy for different flow scenarios while respecting appropriate constraints pertaining to fluid dynamics.