Non-Reflecting Boundary Conditions in OpenFOAM

What we want to achieve

When we simulate fluid flow, we have to cut a finite computational domain out of an entire flow region. For accurate simulation, we need to let fluid and sound wave flow smoothly out of the domain through the boundary.

The reflection at the boundary has a larger effect on the solution especially when we perform a compressible flow simulation as can be seen in the following movie (Upper: With reflection, Lower: Without reflection of sound wave).

In OpenFOAM, we can use two approximate non-reflecting boundary conditions:

They determine the boundary value by solving the following equation

\frac{D \phi}{D t} = \frac{\partial \phi}{\partial t} + \boldsymbol{U} \cdot \nabla \phi = 0, \tag{1} \label{eq:advection}

where \(D/Dt\) is the material derivative and \(\boldsymbol{U}(\boldsymbol{x}, t)\) is the advection velocity.

We assume that the advection velocity \(\boldsymbol{U}\) is parallel to the boundary (face) normal direction and rewrite the eqn. \eqref{eq:advection} as

\frac{D \phi}{Dt} \approx \frac{\partial \phi}{\partial t} + U_{n} \cdot \frac{\partial \phi}{\partial \boldsymbol{n}}= 0, \tag{2} \label{eq:advection2}

where \(\boldsymbol{n}\) is the outward-pointing unit normal vector.

These boundary conditions are different in how the advection speed (scalar quantity) \(U_{n}\) is calculated and it is calculated in advectionSpeed() member function.

advective B.C.

The advection speed is the component of the velocity normal to the boundary

U_n = u_n. \tag{3} \label{eq:advectiveUn}

waveTransmissive B.C.

The advection speed is the sum of the component of the velocity normal to the boundary and the speed of sound \(c\)

U_n = u_n + c = u_n + \sqrt{\gamma/\psi}, \tag{4} \label{eq:waveTransmissiveUn}

where \(\gamma\) is the ratio of specific heats \(C_p/C_v\) and \(\psi\) is compressibility.

What do lInf and fieldInf mean?

Coming soon.

Author: fumiya

CFD engineer in Japan

9 thoughts on “Non-Reflecting Boundary Conditions in OpenFOAM”

  1. I think what you published was actually very reasonable.
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    1. Hi Betway88,

      Thanks for your valuable feedback!
      I’ll try to make my blog more visually understandable.

  2. I really like your website and it explain many useful topics
    do you have further explaination for lInf and fieldInf ?
    Also what is the connection between mixedFvPatchField and equation (1)?

  3. Hello Fumiya,
    Very nice explanation by you.
    I am doing an axisymmetric simulation of bubble collapse in OpenFOAM. I want to make one of the boundary as non-reflective. Even after using Wavetransmissive/ Advective condition I am not able get the non-reflective boundary. The pressure wave is still reflecting and affecting the shape of bubble.
    I request you to please guide me what to do?
    Your help in this regards will be highly solicited.

    Thank you,
    Arjun Garva

  4. Dear,
    This link is really helpful to understand the concept of waveTransmissive boundary conditions with respect to OpenFOAM. I want to request you if possible please help me with the test case as a simulation and show above in the blog.

    This will help us to understand the problem in greater depth.

    Best regards,
    Thank you for providing a better explanation of science.

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