Smooth bump

Tutorial

chidg tutorial smooth_bump

Background

A canonical problem for verifying high-order solvers is the Euler smooth bump test case. In this example, the geometry is defined as a channel with a small smooth bump profile on the lower wall, as shown here:

The Euler equations are solved on this geometry, which for subsonic flow are isentropic. However, in the numerical solution, some entropy is generated due to the discretization. This gives us a quantity that we can measure in the numerical solution by which we can gauge the accuracy of the numerical scheme. The measure of the entropy error is integrated over the volume of the domain and computed as:

\[\text{Entropy Error} = \sqrt{ \frac{\int\Bigg( \frac{ \frac{p}{\rho^\gamma} - \frac{p_\infty}{\rho_\infty^\gamma} } { \frac{p_\infty}{\rho_\infty^\gamma} } \Bigg)^2 d\Omega} { \int d\Omega }}\]

Setup

smoothbump.tar.gz

Setup from scratch:

A Fortran code is attached that can be used to generate a Plot3D grid file for this case:

Step 1: compile the provided grid generator file using a Fortran compiler

Step 2: run the executable to produce an unformatted double precision Plot3D grid file

Step 3: convert the Plot3D grid file to a ChiDG-format grid file using chidg convert gridfile.x

Step 4: set boundary conditions on the ChiDG grid using the chidg edit gridfile.h5 action

Step 5: download a chidg.nml configuration file and place it in a run directory with the grid file

Step 6: change to the run directory and execute chidg from the command line

Step 7: once the simulation is converged, execute chidg post gridfile.h5 to write a Tecplot file for visualization

Use setup provided:

Alternatively, a ChiDG-formatted grid file is also provided with the boundary conditions already set:

Step 1: download the smoothbump.h5 grid file and the chidg.nml settings file

Step 2: place the grid and settings file in a new directory

Step 3: change to the run directory and execute chidg from the command line

Step 4: once the simulation is converged, execute chidg post smoothbump.h5 to write a Tecplot file for visualization

Results