# Verification & Validation — Lesson 8

## Verification

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.

Below is a comparison of the Mach number results from the original mesh and the refined mesh.

Original Mesh

Refined Mesh

The most striking difference between the two results is the thickness of the shock. Notice that for the refined mesh, the shock is less thick that for the original mesh. This shows that the refined mesh is converging toward the real case.

### Comparison to Analytical Solution

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.

Mach Number Static Pressure (atm) Shock Angle (degrees)
Theory Value 2.254 2.824 32.22
Fluent Solution 2.243 2.803 34.99
Percent Difference 0.8% 0.7% 8.2%

As we can see from the table, we are getting a fairly good match between the computation and analytical approaches. From this we can build our trust in our simulation. Note that in this case, adaptive mesh refinement doesn't have a significant effect on the values behind the shock but makes the shock less smeared.

#### Save Project

Save the project using File > Save. Copy wedge.wbpj and the associated wedge_files folder to a flash drive. You will need both entities to resume the project.

Alternatively, you can select File > Archive and save the project as one file called wedge.wbpz. When prompted, select the option to save Result/Solution also. You will then need to save only this file. This is also convenient to e-mail the project. Double-clicking on the wedge.wbpz file will resume the project.  Note on some computers, double-clicking the wbpz file will open it in Ansys AIM (a different application) rather than Ansys Workbench. This is not right. The workaround is to start Workbench and then select File > Open.