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May 1, 2014, 23:05 
Unsteady pressure calculation

#1 
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Fraser Callaghan
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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 

#2  
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Did you solve the NavierStokes 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:


May 4, 2014, 04:34 

#3  
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Filippo Maria Denaro
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Quote:
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 
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Fraser Callaghan
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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 

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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 
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Fraser Callaghan
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A beating heart


May 5, 2014, 09:23 

#7 
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But ordinarily the reference pressure is a quantity that primarily affects the nondimensionalization 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 
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Filippo Maria Denaro
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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 
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Fraser Callaghan
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Sorry  grant deadlines
The velocities are measured and thus should be nondivergent  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 

#10  
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Filippo Maria Denaro
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Quote:
You can always write Div (Grad p') = Div ( diffusion  convection  acceleration) so, if you have a non divergencefree acceleration you can compute it (you have the velocity ad several time steps, right?) and consider it in the source term. 

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incompressible, navierstokes, pressure, unsteady 
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