The FEATool GUI makes it easy to add and coupled multiphysics equations and complex expressions to your models. This post illustrates how to do this.

After starting to work with a physics mode it is easy to add one or
more other modes by going to the **+** tab in the **Equation
Settings** dialog box. There you can simply choose an additional
physics mode from the drop down combo box, select the dependent
variable names you want to use, and press **Add Physics >>>**
to add the additional mode. The new physics mode will now show up as a
new tab with its short abbreviated name on its tab. Once the new mode
has been added you can switch between the modes by clicking on the
corresponding tabs in the Equation and Boundary Settings dialog boxes.

The physics modes can be coupled by simply using the the dependent
variable names and derivatives in the coefficient expression dialog
boxes. For example, the Navier-Stokes equations physics mode shown
below uses the temperature variable **T** from the heat transfer mode
in the source term for the y-direction (**F_y**).

Moreover, the next step illustrates how to make a three way
multiphysics coupling. The convective velocities **u** and **v** are
coupled from the Navier-Stokes equations physics mode and at the same
time the temperature **T** and its two derivatives **Tx** and **Ty**
are simultaneously coupled to the reaction rate source term in the
convection and diffusion mode (**R**).

As we have seen, it is simple to set up multiphysics models in FEATool
Multiphysics. This is made possible by the expression parsing
functionality that allows entering and using complex expressions of
dependent variables (for example **u**, **v**, **T**, **c**), their
first derivatives (by just appending x or y to the variable names like
**Tx** and **Ty**), the space dimensions **x** and **y**, as well as
all common MATLAB expressions and constants like **pi**,
**sin**, **cos**, **log**, **sqrt**, **^2** etc.

Lastly, it is also possible to call user defined m-script functions.
If one for example has defined a m-file function called
**my_function.m** which takes two input arguments, then one can simply
enter `my_function(x,y)`

as an equation coefficient
expression which in this case will call the function script with the
evaluated values for **x** and **y**.