C++ source code to solve one-dimensional scalar advection equation. Problems are taken from [1].

1-D scalar advection equation with constant velocity

$$ \frac{\partial u}{\partial t} + c \frac{\partial u}{\partial x} = 0 $$

is solved by using the finie difference method. Currently, the following spacial reconstruction schemes are implemented:

• Lax-Wendroff scheme
• 1st-order upwind scheme
• Beam-Warming scheme
• Fromm scheme
• TVD scheme with minmod, Superbee, van Leer, and van Albada slope limiters.

In addition, periodic boundaries, the Roe-Riemann solver, and the explicit Euler scheme for time integration are used.

Please refer to [1] for the details of each scheme.

Run the following commands under the root directory of the project:

$ cmake -S . -B build
$ cmake --build build

Please note that the project depends on the Eigen library, which is automatically downloaded and built by CMake using the FetchContent module.

Then, run all simulators and get results. For Linux,

$ ./run_all.sh

For Windows,

$ .\run_all.ps1

To visualize results, open plot.ipynb with Jupyter Lab, and run all cells.

1. 肖鋒・長﨑孝夫　2020　数値流体解析の基礎 －Visual C++とgnuplotによる圧縮性・非圧縮性流体解析－　コロナ社