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In order to test our simulation for convergence, we will refine the mesh. Refining the mesh will allow us to make sure that the results we are calculating are independent of the mesh. However, instead of refining the mesh everywhere (which would be wasteful, as most of the area of the domain far away from the shock has constant values), we will use our results to refine our mesh. Specifically, we are going to use the gradient of the pressure to determine where to refine the mesh.

<iframe width="560" height="315" src="https://www.youtube.com/embed/DPwK6W2e9RA49U2YxZ9JsA?rel=0" frameborder="0" allowfullscreen></iframe>

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Summary of the Above Video:

1. Display Current Mesh:
   1. Mesh>Setup>Display (In newer versions, this is found under the Setting Up Domain tab, then Mesh > Display.)
2. In the Menu
   1. Adapt>Gradient (In newer versions, this is found under Setting Up Domain tab, then Adapt > Mark/Adapt Cells > Gradient.)
      1. uncheck Coarsen in Options Box
      2. select Gradient in Method Box
      3. Gradients of > Pressure > Static Pressure
      4. Compute
3. View Contours 
   1. Contours > Contours of Adaption > Existing Value
   2. Compute
   3. Display
4. Under Contours 
   1. Uncheck Auto Range
   2. Change Min to 10000 
   3. Display
5. Under Refine Threshold enter 10000 
   1. Press Mark
   2. Press Adapt
6. Display the New Mesh

Notice that the area surrounding the shock was refined. Now, re-initialize the solution, (Solution Initialization > Compute From Farfield > Initialize), and rerun the solution (you will also need to increase the number of iterations – I recommend 150).

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In order to verify our simulation, we need to compare our results to either an analytical solution or an experiment. Below is a table comparing the values from the simulation with the calculations from the pre-analysis.

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