carlosal1015 / advectionsolver

A numeric code to solve the 1D advection equation using different slope limiter schemes.

AdvectionSolver

This code solves the 1D advection equation using a finite volume approach. It uses different numerical methods to approximate the flux between cells. It is meant as a showcase of the methods involved and should not be seen as a ready-to-use code for numerical simulation of physical systems described via the 1D adv. eq.

Features

-Switching between different Slope- and Fluxlimiters to get an easy side to side comparison of the methods used.

-Adjustments of simulation parameters like gridsize and courant number to see their effect on the quality of the solution.

-Periodic boundary conditions

-Custom initial conditions q(t=0, x) or a test problem that includes discontinuities as well as a wave.

Slope- and Fluxlimiters

1. Simple Upwind
2. Lax-Wendroff
3. Beam-Warming
4. Fromm
5. MinMod
6. SuperBee
7. MC
8. VanLeer

Code Manual

There are three parts to this program. createDist.cpp stands on it's own and can generate a customDistribution as the initial condition for the solver.

The main simulation uses CMake to build. It includes the main.cpp aswell as the headers and source files in include/ and src/. After compilation and execution of the binary, the resulting simulation data can be found in the data dir.

Now plotting.py can be run. This generates plots of the numerical versus the analytical solution in the results directory.