Open boundary condition in OpenFOAM

t.oliveira · March 15, 2017, 17:21

The question made short:
Is there any open boundary condition implemented in OpenFOAM? By that I mean a boundary condition such as the no boundary condition (Griffiths, 1997) and the free boundary condtion (Papanastasiou, 1992).

The problem I am trying to simulate is the unsteady advection-diffusion of a quantity $\phi$ along a tube. The velocity field is known. At

, $\phi=0$ . At the inlet face, the quantity is constantly $\phi_I$ . What would be the appropriate boundary condition for the outlet face?

The question made precise (in 1D):
Consider the advection-diffusion equation $\frac{\partial \phi}{\partial t} + u \frac{\partial \phi}{\partial x} = D \frac{\partial^2 \phi}{\partial x^2}$ on $0 < x < \infty$ ,

, with initial data $\phi(x,0)=0$ and the boundary condition $\phi(0,t) = \phi_I$

If, for simulation purposes, we restrict the domain to

, what is the appropriate boundary condition at

?

Best regards,
Thomas

piu58 · March 16, 2017, 02:07

> What would be the appropriate boundary condition for the outlet face?

For the flow, use zero gradient. This is a free outflow. I recommend to set the pressure at the outflow to 0 to have a reference pressure.

t.oliveira · March 16, 2017, 10:16

Quote:

Originally Posted by piu58

For the flow, use zero gradient. This is a free outflow. I recommend to set the pressure at the outflow to 0 to have a reference pressure.

Thank you for your comment. I don't need to solve for the flow, as the velocity field is known a priori and the pressure is irrelevant for the problem.

As for the transport, $\frac{\partial \phi}{\partial x} (x=L)=0$ would not be a free outflow because it makes the diffusion of $\phi$ outward of the domain impossible.

t.oliveira · December 6, 2017, 10:59

I recommend this post by Eugene de Villiers:

Second Derivative Zero - Boundary Condition

March 15, 2017, 17:21	Open boundary condition in OpenFOAM	#1
t.oliveira Senior Member Thomas Oliveira Join Date: Apr 2015 Posts: 114 Rep Power: 12	The question made short: Is there any open boundary condition implemented in OpenFOAM? By that I mean a boundary condition such as the no boundary condition (Griffiths, 1997) and the free boundary condtion (Papanastasiou, 1992). The problem I am trying to simulate is the unsteady advection-diffusion of a quantity $\phi$ along a tube. The velocity field is known. At , $\phi=0$ . At the inlet face, the quantity is constantly $\phi_I$ . What would be the appropriate boundary condition for the outlet face? The question made precise (in 1D): Consider the advection-diffusion equation $\frac{\partial \phi}{\partial t} + u \frac{\partial \phi}{\partial x} = D \frac{\partial^2 \phi}{\partial x^2}$ on $0 < x < \infty$ , , with initial data $\phi(x,0)=0$ and the boundary condition $\phi(0,t) = \phi_I$ If, for simulation purposes, we restrict the domain to , what is the appropriate boundary condition at ? Best regards, Thomas

March 16, 2017, 02:07		#2
piu58 Senior Member Uwe Pilz Join Date: Feb 2017 Location: Leipzig, Germany Posts: 744 Rep Power: 15	> What would be the appropriate boundary condition for the outlet face? For the flow, use zero gradient. This is a free outflow. I recommend to set the pressure at the outflow to 0 to have a reference pressure. __________________ Uwe Pilz -- Die der Hauptbewegung überlagerte Schwankungsbewegung ist in ihren Einzelheiten so hoffnungslos kompliziert, daß ihre theoretische Berechnung aussichtslos erscheint. (Hermann Schlichting, 1950)

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December 6, 2017, 10:59		#4
t.oliveira Senior Member Thomas Oliveira Join Date: Apr 2015 Posts: 114 Rep Power: 12	I recommend this post by Eugene de Villiers: Second Derivative Zero - Boundary Condition