##### 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

\begin{align}

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

\end{align}

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

\begin{align}

\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}

\end{align}

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

\begin{align}

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

\end{align}

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template<class Type> Foam::tmp<Foam::scalarField> Foam::advectiveFvPatchField<Type>::advectionSpeed() const { const surfaceScalarField& phi = this->db().objectRegistry::template lookupObject<surfaceScalarField> (phiName_); fvsPatchField<scalar> phip = this->patch().template lookupPatchField<surfaceScalarField, scalar> ( phiName_ ); if (phi.dimensions() == dimDensity*dimVelocity*dimArea) { const fvPatchScalarField& rhop = this->patch().template lookupPatchField<volScalarField, scalar> ( rhoName_ ); return phip/(rhop*this->patch().magSf()); } else { return phip/this->patch().magSf(); } } |

##### waveTransmissive B.C.

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

\begin{align}

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

\end{align}

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

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template<class Type> Foam::tmp<Foam::scalarField> Foam::waveTransmissiveFvPatchField<Type>::advectionSpeed() const { // Lookup the velocity and compressibility of the patch const fvPatchField<scalar>& psip = this->patch().template lookupPatchField<volScalarField, scalar>(psiName_); const surfaceScalarField& phi = this->db().template lookupObject<surfaceScalarField>(this->phiName_); fvsPatchField<scalar> phip = this->patch().template lookupPatchField<surfaceScalarField, scalar>(this->phiName_); if (phi.dimensions() == dimDensity*dimVelocity*dimArea) { const fvPatchScalarField& rhop = this->patch().template lookupPatchField<volScalarField, scalar>(this->rhoName_); phip /= rhop; } // Calculate the speed of the field wave w // by summing the component of the velocity normal to the boundary // and the speed of sound (sqrt(gamma_/psi)). return phip/this->patch().magSf() + sqrt(gamma_/psip); } |

##### What do lInf and fieldInf mean?

Coming soon.

I think what you published was actually very reasonable.

However, what about this? suppose you were to create a awesome post title?

I ain’t suggesting your information is not solid, however what if

you added something to maybe grab people’s attention? I mean Non-Reflecting Boundary Conditions

in OpenFOAM | Fumiya Nozaki's CFD Blog is

a little boring. You should peek at Yahoo’s home page and

note how they create post headlines to grab viewers to click.

You might try adding a video or a pic or two to get readers

interested about everything’ve got to say. Just my opinion, it would bring your

website a little livelier.

Hi Betway88,

Thanks for your valuable feedback!

I’ll try to make my blog more visually understandable.

Amazing!

Hi plunge,

Thanks!

Thank you for your work this is really helpful!

Hi natalie,

Thank you for your comment!

I’m glad to be of your help.

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)?