Heat Equation

1次元・2次元の熱伝導方程式を Python と Fortran で解くための作業ディレクトリです。

Directory Layout

heat_equation/
├── src/
│   ├── python/      # Python source files
│   ├── fortran/     # Fortran source files
│   └── julia/       # Julia source files
├── scripts/         # Plotting and helper scripts
├── figure/          # Figures and animations
├── output/          # Simulation output files
└── bin/             # Executable files

Top-Level Commands

make build        # Build Fortran executables
make run-python   # Run Python 1-D and 2-D solvers
make run-fortran  # Run Fortran 1-D and 2-D solvers
make animation    # Create Python/Fortran animations
make clean        # Remove generated output, figures, and Fortran binaries

Python Solvers

python3 src/python/run_1d.py --initial gaussian --boundary neumann
python3 src/python/run_2d.py --initial sine --boundary periodic

Available initial conditions:

• 1-D: semicircle, gaussian, sine
• 2-D: square, gaussian, sine

Available boundary conditions:

• dirichlet
• neumann
• periodic

Default outputs:

• output/python/1d/temp.0000, temp.0000.vtk, ...
• output/python/2d/field.0000, field.0000.vtk, ...
• output/python/2d/result.dat
• output/python/2d/result.vtk

The .vtk files can be opened in ParaView.

Create Animations

python3 scripts/animate_heat_1d.py
python3 scripts/animate_heat_2d.py

Default outputs:

• figure/heat_1d.mp4
• figure/heat_1d.gif
• figure/heat_2d.mp4
• figure/heat_2d.gif

Fortran Solvers

make build
./bin/heat_1d output/fortran/1d gaussian neumann
./bin/heat_2d output/fortran/2d sine periodic

Default build output:

• bin/heat_1d
• bin/heat_2d
• src/fortran/tmp/*.mod

Fortran positional arguments:

heat_1d [output_dir] [initial] [boundary] [no-vtk]
heat_2d [output_dir] [initial] [boundary] [no-vtk]