This paper aims to introduce a particle trickle release (PTR) algorithm for implementing an inlet velocity boundary condition in graph network simulators (GNS) and explore the ability of GNS to extrapolate and apply the learned fluid dynamics to unseen, out-of-distribution examples.
The study uses the “WaterRamps” training data set, which provides essential parameters for fluid particles. The training of the GNS is conducted using both the existing dynamics bootstrapping method and a sequential training approach to assess their effectiveness in capturing fluid dynamics accurately. The PTR algorithm is introduced to ensure realistic particle inflows at boundaries, calculated using a binomial distribution based on inflow velocity and inlet boundary length.
The PTR algorithm demonstrated realistic particle release with minimal errors in particle count and area consistency compared to theoretical values. Sequential training resulted in a mean squared error of 13.9 × 10–3, slightly higher than the 12.9 × 10–3 achieved with dynamics bootstrapping. The study also highlights challenges in maintaining incompressibility conditions and the tendency to learn excessive wall friction, which leads to undesired boundary layer development, particularly in out-of-distribution simulations such as the “WaterVortex” example and flow over a backward-facing step.
This paper contributes to the field of graph network-based fluid flow modelling by facilitating the implementation of inlet velocity conditions through the PTR algorithm and evaluating the effectiveness of sequential training. The degree of compressibility is assessed using a newly proposed velocity divergence term, and a “push particle” algorithm is introduced to improve the quality of particle distribution.
