HyFlow1D

HyFlow1D is a lightweight, high-performance research code implementing a Hybrid Finite Volume (FV) / Discontinuous Galerkin (DG) solver for 1D aerodynamic flows.

It serves as a Proof of Concept (PoC) for coupling robust low-order industrial schemes with high-order accurate methods to achieve superior fidelity in transient simulations.

🚀 Features

• Hybrid Coupling: Seamlessly couples 1st-order FV (robust near-field) with High-Order DG (accurate far-field).
• High-Order Accuracy: Arbitrary polynomial order DG implementation (default $P=3$).
• Efficient Numerics: Uses Gauss-Legendre quadrature and optimized Legendre basis evaluation.
• Simple & Modular: Written in clean C++17 with no external dependencies (standard library only).
• Visualization: Python scripts included for immediate result analysis.

🛠️ Build & Install

Prerequisites

• C++ Compiler: GCC 7+, Clang 5+, or MSVC (C++17 support required).
• CMake: Version 3.10 or higher.
• Python: For plotting (optional, requires matplotlib and pandas).

Compilation

# Clone the repository
git clone https://github.com/username/HyFlow1D.git
cd HyFlow1D

# Create build directory
mkdir build && cd build

# Configure and Build
cmake ..
make

🏃 Usage

Running the Solver

After building, run the executable from the build directory:

./hyflow1d

The simulation propagates a Gaussian pulse through the domain. The domain $[0, 0.5]$ uses Finite Volume, and $[0.5, 1.0]$ uses Discontinuous Galerkin.

Output files (solution_*.csv) will be generated in the current directory.

Visualizing Results

To see the wave move through the hybrid interface:

python3 ../scripts/plot_results.py

(Ensure matplotlib and pandas are installed: pip install matplotlib pandas)

🧪 Testing

The project includes unit tests for numerical integration and solver logic.

cd build
make test
# Output:
#     Start 1: numerics_test
# 1/2 Test #1: numerics_test ....................   Passed    0.00 sec
#     Start 2: solvers_test
# 2/2 Test #2: solvers_test .....................   Passed    0.00 sec

📄 License

This project is licensed under the MIT License - see the LICENSE file for details.

📚 Theory

The Hybrid Strategy:

1. Near-Field (FV): Uses standard Finite Volume methods ($P=0$). This handles complex geometries and discontinuities robustly but is dissipative.
2. Far-Field (DG): Uses Discontinuous Galerkin methods ($P=k$). This preserves wave shape and energy over long distances (low dispersion/dissipation).
3. Interface: Fluxes are exchanged by treating the neighbor's state as a boundary condition. Reconstruction is performed to pass high-order information to the FV cells and vice-versa.

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