Data-free Physics-Informed Neural Networks for Compressible Flows with Shocks

This repository implements Physics-Informed Neural Networks (PINNs) for solving the compressible Euler equations in the presence of shock waves.

The framework incorporates a learnable global artificial viscosity model, enabling robust, data-free shock capturing without requiring labeled training data.

The code includes standard 1D and 2D Riemann benchmark problems, which are widely used to validate numerical methods for compressible flows.

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📂 Repository Structure

.
├── 1DRiemann
│   ├── main.py
│   └── src.py
│
├── 2DRiemann
│   ├── main.py
│   └── src.py
│
└── README.md

---

▶ Running the Code

1D Riemann Problems

Navigate to the 1DRiemann directory and run:

python main.py --case SST

or

python main.py --case LST

Available cases:
	•	SST → Sod Shock Tube
	•	LST → Lax Shock Tube

2D Riemann Problems

Navigate to the 2DRiemann directory and run:

python main.py --case CONFIG1

or

python main.py --case CONFIG2

or

python main.py --case CONFIG3

Each case corresponds to a distinct 2D Riemann initial configuration.

📖 Citation

If you use this code in your research, please cite:

@article{kumar2026shocks,
  title = {A Robust Data-Free Physics-Informed Neural Network for Compressible Flows with Shocks}},
  author = {Prashant Kumar and Rajesh Ranjan},
  doi = {https://doi.org/10.1016/j.compfluid.2026.106975},
  url = {https://www.sciencedirect.com/science/article/pii/S0045793026000174},
  year = {2026},
  journal = {Computer & Fluids}
}