Physics-informed neural networks for high-speed flows

@article{Mao2020PhysicsinformedNN,
  title={Physics-informed neural networks for high-speed flows},
  author={Zhiping Mao and Ameya Dilip Jagtap and George Em Karniadakis},
  journal={Computer Methods in Applied Mechanics and Engineering},
  year={2020},
  volume={360},
  pages={112789}
}
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177 Citations
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5
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52
Methods Citations
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177 Citations

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, We present a novel physics-informed deep learning framework for solving steady-state incompressible flow on multiple sets of irregular geometries by incorporating two main elements: using a…
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References

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Physics-informed neural networks: A deep learning framework for solving forward and inverse problems involving nonlinear partial differential equations
Adaptive activation functions accelerate convergence in deep and physics-informed neural networks
fPINNs: Fractional Physics-Informed Neural Networks
TLDR
This work extends PINNs to fractional PINNs (fPINNs) to solve space-time fractional advection-diffusion equations (fractional ADEs), and demonstrates their accuracy and effectiveness in solving multi-dimensional forward and inverse problems with forcing terms whose values are only known at randomly scattered spatio-temporal coordinates (black-box forcing terms).
The solution of the compressible Euler equations at low Mach numbers using a stabilized finite element algorithm
Numerical Methods for High-Speed Flows
We review numerical methods for direct numerical simulation (DNS) and large-eddy simulation (LES) of turbulent compressible flow in the presence of shock waves. Ideal numerical methods should be…
A discontinuous Galerkin method for the Navier-Stokes equations
TLDR
The foundations of a new discontinuous Galerkin method for simulating compressible viscous flows with shocks on standard unstructured grids are presented and monotonicity is enforced by appropriately lowering the basis order and performing h-refinement around discontinuities.
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