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dokeun July 3, 2013 10:12

Alternative boundary treatment on cell-centered scheme
 
Dear all

I used ghost cell concept for euler solver but confused how can I compute gradient of flow properties at boundary face for viscous flux.

Because I need gradients of velocity and Temperature at ghost cell for face centered properties, but I have no idea about this.

For your understanding I'd like to use modified gradient described in Blazek's

Is there any alternative or breakthrough?

FMDenaro July 3, 2013 11:35

Quote:

Originally Posted by dokeun (Post 437582)
Dear all

I used ghost cell concept for euler solver but confused how can I compute gradient of flow properties at boundary face for viscous flux.

Because I need gradients of velocity and Temperature at ghost cell for face centered properties, but I have no idea about this.

For your understanding I'd like to use modified gradient described in Blazek's

Is there any alternative or breakthrough?


In a FV method is quite natural to prescribe the flux at a boundary. FOr example

mass:
zero flux on a not-permeable wall, prescribed flow rate on inflow, etc

momentum:
zero convective flux a not-permeable wall, prescribed flux for fixed flow rate. The diffusive flux is imposed such that the velocity on a boundary is prescribed, for example, at first order, a normal derivatives of the velocity on a wall is
mu*du/dy|wall -> mu * (u(wall+1) - u(wall-1))/(2*dy) = mu*u(wall+1)/dy

temperature:
quite natural if you have adiabatic or fixed heat flux q = -k*Grad T

and so on ...

dokeun July 11, 2013 09:59

Quote:

Originally Posted by FMDenaro (Post 437614)
In a FV method is quite natural to prescribe the flux at a boundary. FOr example

mass:
zero flux on a not-permeable wall, prescribed flow rate on inflow, etc

momentum:
zero convective flux a not-permeable wall, prescribed flux for fixed flow rate. The diffusive flux is imposed such that the velocity on a boundary is prescribed, for example, at first order, a normal derivatives of the velocity on a wall is
mu*du/dy|wall -> mu * (u(wall+1) - u(wall-1))/(2*dy) = mu*u(wall+1)/dy

temperature:
quite natural if you have adiabatic or fixed heat flux q = -k*Grad T

and so on ...

Dear FMDenaro.

Thank you for your kind reply with example.

I guess I understood your explanation. But I'd like to be checked the thought below and get some more about boundary condition.

Quote:

Supersonic inlet [gradients are zero]
  • Inviscid flux \rightarrow directly obtained on boundary
  • Viscous flux \rightarrow needs only care about heat conduction terms, k \frac{\partial T}{\partial x_i}
Supersonic outlet[gradients are zero]
  • Inviscid flux \rightarrow directly obtained on boundary
  • Viscous flux \rightarrow needs only care about heat conduction terms, k \frac{\partial T}{\partial x_i}
Inviscid wall
  • Inviscid flux \rightarrow need only care about pressure\left( p_w \right) at wall
Viscous wall
  • Viscous flux \rightarrow needs only care about heat conduction terms, k \frac{\partial T}{\partial  x_i}
Subsonic inlet
  • Inviscid flux \rightarrow use (*)
  • Viscous flux \rightarrow ??
Subsonic outlet
  • Inviscid flux \rightarrow use (*)
  • Viscous flux \rightarrow ??
(*)'Three-Dimensional Unsteady Euler Equations Solution Using Flux vector Splitting'. AIAA Paper 84-1552
I have no idea how can I dealing Viscous flux for subsonic inlet/outlet.

How can I implement viscous flux for subsonic boundary condition?

Thank you in advance :)


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