2025 ASEE Annual Conference & Exposition

An oft-heard complaint from engineering students is that they are unable to see how the theory that they are learning is connected to practical applications. Simulation can help bridge the gap between theory and applications since it connects to both CAD and fundamental theory which usually are taught as different realms. A general framework to do this bridging -- using problem-based learning – has been developed and implemented in over a dozen Cornell engineering courses using industry-standard Ansys simulation software. Applications implemented include pressure vessel static behavior, wind turbine blade buckling, turbine vibration as well as turbulent flow over a car and an airplane.

For each application, the first step is to use physical reasoning and assumptions to build a mathematical model, which in most cases is a boundary value problem -- governing equations defined in a domain and boundary conditions defined at the edges of the domain. The second step is to review the numerical solution strategy used to solve the model and how to minimize the numerical errors introduced. Here, it is necessary to cover only the big ideas such as discretization and interpolation since the details are taken care of by the simulation tool. The third step is to perform hand calculations to predict expected results. These three steps comprise what is labeled as the “Pre-Analysis” stage.

Following Pre-Analysis, we move to Ansys or another tool and specify the mathematical model with the domain being defined through a CAD model which can be provided. Next, we obtain the numerical solution to the model in the tool using a mesh, a process that is highly automated. The numerical solution yields the primary unknowns at discrete points marked by the mesh. This sets the stage for post-processing where we obtain relevant results from the primary unknowns. The visualization of results can be highly effective in helping students develop physical intuition while also connecting the underlying theory to CAD models of practical applications.

The final step is verification and validation (V&V) where we undertake a systematic process to check the results. Verification steps include checking if the results are consistent with the physical principles in the mathematical model such as equilibrium, comparing results at the boundary against the boundary conditions, reduction of numerical error through mesh refinement, etc. This same set of steps, from problem specification to Pre-Analysis to V&V has been implemented in around 30 examples -- involving both simple and complex geometries -- in courses as well as my massive open online course or MOOC at edX.org. The MOOC -- entitled “A hands-on introduction to engineering simulations” – is one of the most popular free online engineering courses with an enrollment close to 300,000 from 173 countries. Assessment and student evaluation results show that this approach helps students connect theory to practice while also developing an expert-like approach to simulations.