The objective of a simulation is to predict physical phenomena. But the question is how can you make sure that your numerical model works well? And the other question is that what does it mean “works well”?

 

The first question can be answered through verification and validation steps. With the verification step, you make sure that your model is mathematically correct. And with the validation step, you ensure that your model is physically correct.

 

For instance in verification, you compare your simulation predictions with the predictions of an analytical model. Imagine that you want to model a beam by Finite Element (FE) simulation. Your FE model predicts the deformation of a cantilever beam under a uniform and static loading. Then, you also need to compute the beam deformation by analytical model of the Euler-Bernoulli beam or Timoshenko beam. You compare the predicted deformation by your FE simulation with the predicted deformation by the Euler-bernoli beam. If the error is less than your expected error, then you can say that Yes my model works well! (congratulations!).

 

Besides that, you also need to make sure that you have a fine mesh. So you should do a convergence study. In convergence study, you reduce the element size to have a converged system response quantity. For instance, in our case you reduce the element size (whether it’s solid element or beam element) and then you plot the deformation at the tip of the beam with respect to the total degrees of freedom.

 

​In validation, you compare the model’s predictions with the experimental measurement. This time, it is much more difficult. First, an experimental setup should be designed and it should be defined what and how you want to measure? Let’s say like the verification step, you want to measure the vertical displacement at the tip of the beam (it would be called system response quantity). Then, you should define how you want to measure and what is the accuracy of the measurement. It would matter whether you want to measure it with a three thousand dollar camera or with a three dollar plastic ruler. You will decide. And of course, your decision will affect your validation results.

 

The verification results and validation results indicate how your model performs. It can work well or not. Now the second question that was asked at the beginning should be answered. What does it mean that the model works well? Well, it depends again on you. There are no good or bad results. There are just numbers that describe the model performance. The results can be acceptable or not. If you want to design a blade in a jet engine the error of simulation should be less and 1 millimeter. If you want to do an assignment, maybe 10 mm is still ok (it depends on your TA). So the application of the modeling in fact determines the expected accuracy of the model.