problem related to staggered grids
 

hi,all,

when staggered grids used in my code to simulate flow field around a wedge(structural grids),i met a problem,for u equ.,the frist u cell with it's south interface touching the wedge,half of this interface is the wall,another half of this interface is in the flow,i have to deal with this interface as wall,but the resiual of the incompressible equ.(continuous equ.for this cell is large,and what more,this residual donot change small as others inner cell.i donot know why,maybe this big residual comes from this treatment,because for v and p equ.no needs to deal with this kind of interface.i was mixed by this problem for a long time,and try again and again,but failed,i hope someone to help me.

thanks in advance

pendy

Re: problem related to staggered grids
 

See harmonic-mean gamma in Patankar, Numerical heat transfer and fluid flow

Re: problem related to staggered grids
 

(1). Twenty years ago, when I was using the code and method, it was very confusing to me about this method. (2). I have since stopped using this approach. (3). With the staggered grid, I think, you have to look at it in some approximate ways first. (that is, create your own tricks, to see how it works. or read more papers or get some helps from Prof. Patankar)

Re: problem related to staggered grids
 

hi,all

in my thread,i have said,that only half of this interface is the wall,another half of this interface is in the flow,NOT half of the cell is solid,i donot use the so called"block-off" method(in fact,i used it with projection method for incompressible flow without p in the momentum equ.but i failed,also because of the large residual of the continuous equ),so the harmonic_mean gamma isnot needed,and professor Patankar didnot show me how to deal with this problem in his book.

i think,this problem is related to the arithmetic-staggered grid,because the models used by u,v,and p equ.arenot the same.when incompressible flow is simulated,the stagged grids method is often used,so,i think this problem should be meet by too many CFD people.hope someone give my hints.

Re: problem related to staggered grids
 

Pendy,

Just split the surface integrals over the south face of this u-cell into a sum of two integrals. One will cover the flow part of the interface. The other will include the wall. Moreover, make sure that your discretization assures that once your solution conserves mass over scalar cells, mass will be conserved over staggered momentum cells.

Mark

Re: problem related to staggered grids
 

hi Zhu,

try gamma_u_s = (gamma_p*gamma_s)/(gamma_p+gamma_s) + (gamma_e*gamma_es)/(gamma_e+gamma_es)

gamma_es is inside the wall and set to a very small negative value.

Baetke, Werner & Wengle, Numerical simulation of trubulent flow over surface-mounted obstacles with sharp edges and corners, J. wing eng. ind. aerodyn.,1990

Re: problem related to staggered grids
 

thanks Capi for your help,but i didnot use the "block-off"method.

Re: problem related to staggered grids
 

thanks mark,

if i do just like what you said"split the surface integrals over the south face of this u-cell into a sum of two integrals. One will cover the flow part of the interface. The other will include the wall". there are some questions for me

1.how to locate the u,v and p in this u_cell with the help of staggered grids,does each half use itsown u,v and p?

2.i use 2nd order upwind scheme,how to calculate the flux on the 2 half parts of this interface?

3.the difference equ. for this cell will be of much diffence compared with other cell,it's willnot be convenient.

maybe i didnot catch what you said

best regards

Re: problem related to staggered grids
 

Pendy,

There is really no problem to split the south face into two surfaces. You still have only a single staggered U-cell. There are no half-cells involved with their U, V, P.

What concerns the convective flux through the open part of the south face, just use the mean value theorem for integrals. Then the convective flux will be equal to the mass flow rate times the value of the function (U in your case) in the middle of the open segment of your south face. The mass flow rate is known (half of the south mass flow rate for the left cell contributing to your U-cell). The value of U on the open segment can be obtained by the interpolation. The convective flux through the open part will modify the source term of your FV equation for the staggered U-cell.

The other half of the south face (the wall) should be implemented in a standard way, i.e. it will modify your matrix of the coefficients and the source term.

regards

Mark

Re: problem related to staggered grids
 

thanks Lipinski,i will try with your hints.

best regards

Re: problem related to staggered grids
 

dear Lipinski,

when i use FDM,I meet this problem again,i know how to deal with this problem in FVM,but i am sorry ,i donot know how to treat this half-control interface in FDM,CAN you give me some advice?

best regards