Total pressure jump at fluid-porous interface
 

In the superficial velocity formulation (without any resistance sources), velocity, pressure, and total-pressure are continuous at the fluid-porous interface.

In the physical velocity formulation (without any resistance sources), (true) velocity jumps at the fluid-porous interface. If static pressure is continuous at the interface that would mean that total pressure also jumps which is unphysical?

I haven't gone through the physical velocity formulation but my quick thoughts are this:

The fluid does not flow through the entire flow area/volume in the porous region (because of porosity). So the mean flow velocity is the same as before. You would need to compute the shape factors to see if there is any increase/decrease in total pressure. But keep in mind that more uniform profiles have lower shape factor.

Thanks LuckyTran!

Can you please explain what is the "shape factor" you alluded to.

You can compute the integral of the total pressure using the local pressure + velocity contour.

You can also compute the total pressure using mean pressure and mean velocity. This won't give you the correct total pressure. But you can define a shape factor as a correction factor that you multiply by this quantity that will give you the correct total pressure integral. It's called shape factor because the only difference between the two is the shape of the velocity profile. There are shape factors for various other fluid dynamics quantities (kinetic energy, temperature, etc) all based on the same principle. A uniform profile has a shape factor of unity. Just about any other profile will have a shape factor greater than one.

Thanks LuckyTran!