Alternative boundary treatment on cell-centered scheme

dokeun · July 3, 2013, 11:12

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, 12:35

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 ...

dokeun · July 11, 2013, 10:59

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.

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

July 3, 2013, 11:12	Alternative boundary treatment on cell-centered scheme	#1
dokeun Member Dokeun, Hwang Join Date: Apr 2010 Location: Korea, Republic of Posts: 98 Rep Power: 16	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?

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