Domain-Decomposed Finite-Difference PINNs for Lid-Driven Cavity Flow
A physics-informed neural network method for solving the incompressible Navier-Stokes equations that computes the equation's spatial derivatives with finite differences on a grid instead of automatic differentiation, and splits the spatial domain into subdomains each handled by its own network (domain decomposition). This combination captures the counter-rotating secondary corner vortices of the lid-driven cavity benchmark at higher Reynolds numbers (Re = 400 and 1000) and improves near-wall accuracy, without requiring a reference solution from a classical solver as training data.
Finite difference physics-informed neural networks enable improved solution accuracy of the
Generating an accurate solution of the Navier--Stokes equations using physics--informed neural networks (PINNs) for higher Reynolds numbers in the corners of a lid--driven cavity problem is challengi…