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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.

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.