# Alternative boundary treatment on cell-centered scheme

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 July 3, 2013, 10:12 Alternative boundary treatment on cell-centered scheme #1 Member   Dokeun, Hwang Join Date: Apr 2010 Posts: 71 Rep Power: 8 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?

July 3, 2013, 11:35
#2
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Filippo Maria Denaro
Join Date: Jul 2010
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Quote:
 Originally Posted by dokeun 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 ...

July 11, 2013, 09:59
#3
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Dokeun, Hwang
Join Date: Apr 2010
Posts: 71
Rep Power: 8
Quote:
 Originally Posted by FMDenaro 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.

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 directly obtained on boundary Viscous flux needs only care about heat conduction terms, Supersonic outlet[gradients are zero]Inviscid flux directly obtained on boundary Viscous flux needs only care about heat conduction terms, Inviscid wallInviscid flux need only care about pressure at wall Viscous wallViscous flux needs only care about heat conduction terms, Subsonic inletInviscid flux use (*) Viscous flux ?? Subsonic outletInviscid flux use (*) Viscous flux ?? (*)'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?