jerrodbouchard wrote

I was unable to find any examples (with time-dependency) in the documentation

Although probably not directly related to your application, there are several tutorials involving time-dependency, for example:

Quickstart > Wave Equation on a Circle Heat Transfer > Transient Heat Diffusion in a Rod Heat Transfer > Shrink Fitting of an Assembly Fluid Dynamics > Vortex Flow Multiphysics > Heat Induced Stress in a Brake Disc Multiphysics > Thermo-Mechanical Bending of a Beam Multiphysics > Fluid-Structure Interaction - Elastic Beam Multiphysics > Electro-Osmotic Flow Classic PDE > Shallow Water Equations
jerrodbouchard wrote

and keep getting the following error:

"High-order time stepping schemes not supported with integral constraints."

Any help you could lend would be greatly appreciated.

Without really knowing any details about your model it is hard to say, but I suspect you have set up a model with the Navier-Stokes equations without an outflow. In this case a integral pressure constraint (the integral of the pressure over the domain is zero) is added implicitly in order to mathematically ensure a well posed problem (define a unique pressure). As the error message indicates, such an integral constraint does not work with higher order time-discretization/stepping schemes, and a solution would be to select a low order/1st order time stepping scheme (such as Backward-Euler) in the solver settings. Alternatively, you can avoid having to use a pressure integral constraint by fixing the pressure with a point constraint at at least one point.

That said, if you are using the Navier-Stokes they are only valid for incompressible fluids, and as such would probably not apply to the problem you're investigating. But then again, I'm not sure what you have modeled exactly.