[fraser29]

I have a temporal dataset of velocity vectors in a 3D volume. I also have a reference pressure at t=0. My flow is incompressible.

I can calculate the pressure gradient and define a pressure field relative to my reference pressure at t=0, however how could I calculate pressure fields at t=1, t=2, t=i ... ?
(I have the pressure gradient fields at all these time points, but no reference pressure).

Any tips, resources would be helpful. I haven't been able to turn up anything in the literature.

Thanks,
Fraser

[leflix]

Did you solve the Navier-Stokes equations? if so ,necessary you have the pressure on each grid point of your computational domain.
If it is not the case,you need a spatial reference pressure for each time step (if you have the pressure gradient at each time step)

Originally Posted by fraser29

I have a temporal dataset of velocity vectors in a 3D volume. I also have a reference pressure at t=0. My flow is incompressible.

I can calculate the pressure gradient and define a pressure field relative to my reference pressure at t=0, however how could I calculate pressure fields at t=1, t=2, t=i ... ?
(I have the pressure gradient fields at all these time points, but no reference pressure).

Any tips, resources would be helpful. I haven't been able to turn up anything in the literature.

Thanks,
Fraser

[FMDenaro]

Originally Posted by fraser29

I have a temporal dataset of velocity vectors in a 3D volume. I also have a reference pressure at t=0. My flow is incompressible.

I can calculate the pressure gradient and define a pressure field relative to my reference pressure at t=0, however how could I calculate pressure fields at t=1, t=2, t=i ... ?
(I have the pressure gradient fields at all these time points, but no reference pressure).

Any tips, resources would be helpful. I haven't been able to turn up anything in the literature.

Thanks,
Fraser

1) for any time, solve a Poisson equation with the source terme obtained taking the divergence of the momentum equation.
2) However, for incompressible flows be careful that you do not define a thermodicamic pressure

[fraser29]

Thanks for the reply.

Velocities are measured velocities. Pressure gradient is solved for from the momentum equations. I have no reference pressure for each time step.

Approach so far is an implicit discretisation based on SIMPLE

[agd]

Why can you not use the same reference pressure as at t = 0? What is causing the reference pressure to change?

[fraser29]

A beating heart

[agd]

But ordinarily the reference pressure is a quantity that primarily affects the non-dimensionalization of the equations of motion. The actual pressure in a heart chamber will vary in time, but the pressure levels will vary relative to the reference pressure. So I guess I still don't understand how or why the reference pressure is changing in time.

[FMDenaro]

the blood pressure is measured by the device with reference to a pressure value, you should use this one...

[fraser29]

Sorry - grant deadlines

The velocities are measured and thus should be non-divergent - solution of Poisson eqn not required.

I don't want to know pressures relative to single point at each time step. I want to know pressures relative to single point at time step one. All pressures, everywhere are time dep. Reusing ref pressure from t=0 would give me the former case.

Thus I need some sort of coupling of the pressure gradient to the unsteady component.

[FMDenaro]

Originally Posted by fraser29

Sorry - grant deadlines

The velocities are measured and thus should be non-divergent - solution of Poisson eqn not required.

I don't want to know pressures relative to single point at each time step. I want to know pressures relative to single point at time step one. All pressures, everywhere are time dep. Reusing ref pressure from t=0 would give me the former case.

Thus I need some sort of coupling of the pressure gradient to the unsteady component.

You can always write

Div (Grad p') = Div ( diffusion - convection - acceleration)

so, if you have a non divergence-free acceleration you can compute it (you have the velocity ad several time steps, right?) and consider it in the source term.