This project is part of Jedd (Cheng-Chun Yang)'s master's thesis titled "Developing Stabilized Material Point Method for Free Surface Flow Modeling" (開發穩態物質點法應用於自由表面流建模), advised by Prof. Tsung-Hui Huang at National Tsing Hua University, 2024. The work is set to be published in 2025. For more information about this work, please visit Prof. Tsung-Hui Huang's personal website.

• config.py: Specifies the numerical settings for the simulation.
• fields.py: Declares the Taichi fields used in the simulation.
• exec.py: The entry point where the iteration of the simulation takes place.
• functionsConfidential.py: Contains the innovative algorithm for the Concurrent Material Point Method (MPM), specifically demonstrated in the subStep() function.

This simulation is powered by the Taichi runtime environment, a high-performance computational framework developed by Prof. Yuanming Hu and colleagues. The implementation of the algorithm is inspired by the Affine Particle-In-Cell (APIC) method (Jiang et al., 2015) and the Fluid Implicit Particle (FLIP) method.

• Innovative algorithm under material point method scheme for computational fluid dynamics.
• A practical programming implementation using Taichi's computational capabilities.

We hope to contribute to the community's understanding and application of stabilized numerical methods in fluid dynamics.

The file functionsConfidential.py is not uploaded due to laboratory policy regarding confidential research materials. This file contains proprietary implementations that cannot be publicly shared. However, this repository includes a simplified demo showcasing the core concepts and techniques. For more information, please contact National Tsing Hua University, Extreme Event Computation Lab.

We first validate our concept in the c++ source code using Taichi. The simulation yields a stable solution, as shown below.

We them proceed to develop our methods in Python for better maintenance.

(Will be uploaded in the near future.)

• Updated Lagrangian Mechanics: Decomposes acceleration, velocity, and position updates for improved simulation efficiency.
• Material Mixing: Demonstrates the blending of different velocity solvers for versatile material behavior.
• Taichi-Powered Simulation: Utilizes Taichi's capabilities for high-performance numerical computation.

• Taichi Framework: https://taichi.graphics
• APIC Method: Jiang et al. (2015), The Affine Particle-In-Cell Method

Feel free to explore the provided demo and experiment with the Taichi-based implementation.