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 May 1, 2014, 23:05 Unsteady pressure calculation #1 New Member   Fraser Callaghan Join Date: Oct 2013 Posts: 4 Rep Power: 11 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

May 3, 2014, 19:33
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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)

Quote:
 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

May 4, 2014, 04:34
#3
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Filippo Maria Denaro
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Quote:
 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

 May 4, 2014, 18:58 #4 New Member   Fraser Callaghan Join Date: Oct 2013 Posts: 4 Rep Power: 11 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

 May 5, 2014, 00:11 #5 Senior Member   Join Date: Jul 2009 Posts: 333 Rep Power: 17 Why can you not use the same reference pressure as at t = 0? What is causing the reference pressure to change?

 May 5, 2014, 00:51 #6 New Member   Fraser Callaghan Join Date: Oct 2013 Posts: 4 Rep Power: 11 A beating heart

 May 5, 2014, 09:23 #7 Senior Member   Join Date: Jul 2009 Posts: 333 Rep Power: 17 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.

 May 5, 2014, 10:54 #8 Senior Member   Filippo Maria Denaro Join Date: Jul 2010 Posts: 6,255 Rep Power: 67 the blood pressure is measured by the device with reference to a pressure value, you should use this one...

 May 8, 2014, 21:34 #9 New Member   Fraser Callaghan Join Date: Oct 2013 Posts: 4 Rep Power: 11 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.

May 9, 2014, 04:24
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Filippo Maria Denaro
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Quote:
 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.