An artificial-compressibility relaxation lets PINNs solve smooth incompressible flows with sub-0.5% velocity error, while vortex shedding is only recovered when sparse data from a finite-element reference is assimilated.
On the artificial compressibility method for the Navier Stokes Fourier system
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abstract
This paper deals with the approximation of the weak solutions of the incompressible Navier Stokes Fourier system. In particular it extends the artificial compressibility method for the Leray weak solutions of the Navier Stokes equation, used by Temam, in the case of a bounded domain and later in the case of the whole space. By exploiting the wave equation structure of the pressure of the approximating system the convergence of the approximating sequences is achieved by means of dispersive estimate of Strichartz type. It will be proved that the projection of the approximating velocity fields on the divergence free vectors is relatively compact and converges to a weak solution of the incompressible Navier Stokes Fourier system.
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physics.flu-dyn 1years
2026 1verdicts
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An Artificial-Compressibility Physics-Informed Neural Network for the Unsteady Incompressible Navier--Stokes Equations
An artificial-compressibility relaxation lets PINNs solve smooth incompressible flows with sub-0.5% velocity error, while vortex shedding is only recovered when sparse data from a finite-element reference is assimilated.