Equations: Who needs them?
David Kan September 28, 2012
Most of us take mathematical modeling for granted. After all, we’re taught physics and calculus almost hand-in-hand. But we owe a lot to the early pioneers like Isaac Newton, who demonstrated and strongly promoted interpreting natural phenomena through equations. Differential equations are especially useful since most things change as time marches on. Since we live in 3D space, partial differential equations (i.e., equations that express change in more than one “direction”) arise as the prominent tool to express continuum level physics for engineering purposes.
For or Against Equations
But not everyone likes equations. In fact, many become engineers in spite of equations. Common complaints are that equations are too abstract, too complicated, and just too dull. They have little to do with actually putting things together and making them work, which is a big part of engineering.
On the other hand, some engineers are theoretical experts who are more comfortable with equations than with the actual thing they’re making or fixing. And in any engineering organization, you’ll likely both sorts of professionals at least to some degree.
COMSOL Caters to Both Sides
With COMSOL, we’re sympathetic to both points of view, and we believe we can satisfy both. You might be more comfortable describing things in terms of the physics: loads, constraints, fields, conductivity, currents, etc. For you, we use specialized terminology specific to the sort of your application. This goes for everything from the material properties to the boundary conditions and other model inputs.
Context menu for solid mechanics boundary conditions.
Or you might be like me, “just show me the equation and I’ll figure it out…” We have a section in the settings window (hidden so as not to scare anyone) just for you. It opens the “black box” of simulation and reveals exactly the system of equations that is being solved.
Governing equations for thermal stress.
So how about you? What category would you place yourself in? We welcome your comments and discussion in the comment field below.
In either case, it is our aim to make multiphysics modeling accessible to all serious engineers from researchers to designers and manufacturing. We still have some work to do, and we’ll continue to find new ways toward this goal. Your feedback is indeed important.
Note from the editor: A follow-up to this blog post titled Multiphysics versus FEA was published on 2/14/2013.