An artificial viscosity augmented physics-informed neural network for incompressible flow

Y He, Z Wang, H Xiang, X Jiang, D Tang - Applied Mathematics and …, 2023 - Springer
Y He, Z Wang, H Xiang, X Jiang, D Tang
Applied Mathematics and Mechanics, 2023Springer
Physics-informed neural networks (PINNs) are proved methods that are effective in solving
some strongly nonlinear partial differential equations (PDEs), eg, Navier-Stokes equations,
with a small amount of boundary or interior data. However, the feasibility of applying PINNs
to the flow at moderate or high Reynolds numbers has rarely been reported. The present
paper proposes an artificial viscosity (AV)-based PINN for solving the forward and inverse
flow problems. Specifically, the AV used in PINNs is inspired by the entropy viscosity method …
Abstract
Physics-informed neural networks (PINNs) are proved methods that are effective in solving some strongly nonlinear partial differential equations (PDEs), e.g., Navier-Stokes equations, with a small amount of boundary or interior data. However, the feasibility of applying PINNs to the flow at moderate or high Reynolds numbers has rarely been reported. The present paper proposes an artificial viscosity (AV)-based PINN for solving the forward and inverse flow problems. Specifically, the AV used in PINNs is inspired by the entropy viscosity method developed in conventional computational fluid dynamics (CFD) to stabilize the simulation of flow at high Reynolds numbers. The newly developed PINN is used to solve the forward problem of the two-dimensional steady cavity flow at Re = 1 000 and the inverse problem derived from two-dimensional film boiling. The results show that the AV augmented PINN can solve both problems with good accuracy and substantially reduce the inference errors in the forward problem.
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