# zero pressure gradient flat plate CFD++

I'm trying to perform a trasient simulation of a subsonin flow over a flat plate in CFD++. I want to impose a ramp profile on the velocity at the inlet, like for instance a smooth step, and look at the evolution of the boundary layer over the plate due to this acceleration. I want to perform this simulation without pressure gradient so I'm imposing a back pressure value in outflow BC. The problem is that once I start the acceleration at the inlet it creates a pressure gradient that travels to the outlet, and since the pressure there is kept constant, the pressure wave bounces creating instabilities Does any one know how to perform this simulation without creating pressure gradients? Thanks

$$\frac{dp}{dx}=-\rho U \frac{dU}{dx}$$
where $U(x)$ is the x-direction velocity boundary condition at the top of the domain. This isn't true for unsteady flows, but if you ramp slowly, you may be able to have a nearly constant pressure during your ramp.