🧪 Probabilistic Simulation Framework for 2D PDEs

This project implements a Monte Carlo simulation framework for solving divergence-dependent partial differential equations (PDEs) in 2D domains. It models stochastic particle dynamics with reflecting boundary conditions and supports coordinate mapping for solving PDEs in simplified geometries.

🚧 This repository is a public-facing subset of a larger research codebase developed as part of graduate work at UNC Chapel Hill. Some core components have been omitted or abstracted for confidentiality.

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📁 Project Structure

project_root/
├── config.py                   # Defines simulation parameters, initial conditions, and domain setup
├── diffusion_simulator.py      # Core simulation function for 2D advection-diffusion processes
├── geometry.py                 # Wall definitions, intersection logic, and reflection angle computation
├── ititial_conditions.py       # Helper functions for setting particle initial positions and values
├── main.py                     # Entry point for running a simulation using the config and simulator
├── utils/
│   ├── io.py                   # Functions to save simulation data (.csv, .npz) and configs (.json)
│   └── __init__.py             # Marks the utils folder as a package
├── step_models.py              # Modular diffusion step generators (e.g., constant, mapped)
├── vector_utils.py             # Vector rotation and linear algebra utilities
├── results/                    # Directory where simulation outputs are saved
└── README.md                   # Project overview, instructions, and documentation

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📈 Features

• Simulates 2D advection-diffusion PDEs with divergence-dependent drift
• Supports reflecting walls and arbitrary polygonal geometries
• Allows custom coordinate mappings (e.g., half-plane, quarter-plane, L-shaped)
• Modular structure: plug in different step models and reflection rules
• Outputs .npz, .csv, and .json formats for easy analysis and reproducibility

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🧪 Example Usage

Run the simulation from the terminal:

python Main.py

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🔒 Access & License

This repository is for demonstration purposes only. Some files and methods have been withheld for confidentiality.
Please do not reuse or redistribute without written permission.

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📬 Contact:
If you'd like to learn more or discuss the project in a technical interview, feel free to reach out via LinkedIn or email.