Convergence Tests (Euler Equations)

Table of Contents

• Prepare benchmark
• Compilation
• Postproccessing

This is a simple benchmark used to perform convergence tests for a solver.

It uses the Euler equations to advance a 2D setup where the density follows a sine wave, and the initial velocity is constant in the x direction. The domain is centred around the origin.

Prepare benchmark

Peano should be built with the following options:

--enable-exahype --enable-loadbalancing --enable-blockstructured

You will need to ensure that the Python environment variables are properly set:

export PYTHONPATH=<path-to-peano4-repository>/src

We are in the process of migrating all files into the src directory such that the Python directory should go. For the time being, the order in which we include remains important.

Compilation

The relevant mesh size and timestep size should be set in the python script directly. For the mesh size, \(p\) should be modified in the expression \(\frac{0.2}{p}\) where \(p\) is the number of cells that are desired in each coordinate direction.

Postproccessing

The output after a run will be 2 snapshots of teh solution, one at the start and one at the end (this can be modified), as Peano patch files. These can be converted to vtk files for visualisation in Paraview.

pvpython ../../../../python/peano4/visualisation/render.py --filter-fine-grid solution-CCZ4DG2RK2.peano-patch-file

The paraview module should be loaded where neccessary (system dependent) for this command.

In order to directly ocmpare results, my preferred method is to apply a plot over line filter in Paraview, with fixed spacing between plot points such that they are always at the centre of a cell for every resolution. This is converted to a csv file and read in Python using the csv library. Plots can then be generated using this data.