[baratian]

Hi every body
I have a problem with QUICK scheme
In a 2d pure convection for 2 cells when i apply the scheme ij cell property phi eliminates and only neighbors remain! So how can i calculate the ij cell ?
i.e. sigma"a(nb)×phi(nb)"=0 and there is no a(ij)×phi(ij) in the discretized equation for that two special cells which are near the boundary ! Versteeg dotted cells in pic attached
Thanks in advance
A11-ConvertImage.png

[FMDenaro]

Originally Posted by baratian

Hi every body
I have a problem with QUICK scheme
In a 2d pure convection for 2 cells when i apply the scheme ij cell property phi eliminates and only neighbors remain! So how can i calculate the ij cell ?
i.e. sigma"a(nb)×phi(nb)"=0 and there is no a(ij)×phi(ij) in the discretized equation for that two special cells which are near the boundary ! Versteeg dotted cells in pic attached
Thanks in advance
Attachment 71348

Sorry but I don't think to understand clearly your problem...

[baratian]

Originally Posted by FMDenaro

Sorry but I don't think to understand clearly your problem...

sorry u r right. i try to make it clear. the QUICK scheme as stated in versteeg book is as follow (for a cell downstream face):
2.png
1.png

there is a 2D pure convection problem in the book shown below:
3.png

when i do the discretization for different cells there is no problem except for the mentioned ones stated in the first post i.e. the cell of (2,N) shown below:
4.png

as u c the coefficient of the main cell (2,N) sum to zero!!! and only neighbors remain. so there is no explicit representation for the mentioned cell!!! what should i do to close the system of equations now?!

[FMDenaro]

Originally Posted by baratian

sorry u r right. i try to make it clear. the QUICK scheme as stated in versteeg book is as follow (for a cell downstream face):
Attachment 71354
Attachment 71353

there is a 2D pure convection problem in the book shown below:
Attachment 71356

when i do the discretization for different cells there is no problem except for the mentioned ones stated in the first post i.e. the cell of (2,N) shown below:
Attachment 71357

as u c the coefficient of the main cell (2,N) sum to zero!!! and only neighbors remain. so there is no explicit representation for the mentioned cell!!! what should i do to close the system of equations now?!

First of all, I would be sure about your test problem. You have the velocity components u and v constant and prescribed and you want to solve the transport equation


df/dt + d(u*f)/dx+d(v*f)/dy=0


right or not?

In such a case, owing to the hyperbolic character of the equation, you cannot prescribe a Dirichlet condition at the top and right edges of the domain.
How do you define the Finite Volume and its faces? Be also aware that the QUICK schemed in 2D is presented by Leonard in a multidimensional extension but it is formulated for steady flow.

[baratian]

Originally Posted by FMDenaro

First of all, I would be sure about your test problem. You have the velocity components u and v constant and prescribed and you want to solve the transport equation


df/dt + d(u*f)/dx+d(v*f)/dy=0


right or not?

In such a case, owing to the hyperbolic character of the equation, you cannot prescribe a Dirichlet condition at the top and right edges of the domain.
How do you define the Finite Volume and its faces? Be also aware that the QUICK schemed in 2D is presented by Leonard in a multidimensional extension but it is formulated for steady flow.

yes, u c all the equations are same as in the book they are true for this steady state pure convection problem in which u=v and dx=dy. but for the two cells stated the problem is lack of the phi(i,j) itself !!!
you mean i have done the discretizatin in the wrong way?

[FMDenaro]

Originally Posted by baratian

yes, u c all the equations are same as in the book they are true for this steady state pure convection problem in which u=v and dx=dy. but for the two cells stated the problem is lack of the phi(i,j) itself !!!
you mean i have done the discretizatin in the wrong way?

Immagine that the FV you are considering has the left face (w) at the inlet boundary and the top face (n) at the outlet boundary of the domain. Now you have that flux_w is prescribed as inlet value (u*f)_w but the flux (v*f)_n must be deduced from a convection condition from the interior, you cannot set to a value using a Dirichlet condition.


Could you show the picture of your cell arrangement?

[baratian]

Originally Posted by FMDenaro

Immagine that the FV you are considering has the left face (w) at the inlet boundary and the top face (n) at the outlet boundary of the domain. Now you have that flux_w is prescribed as inlet value (u*f)_w but the flux (v*f)_n must be deduced from a convection condition from the interior, you cannot set to a value using a Dirichlet condition.


Could you show the picture of your cell arrangement?

yeah, as for the QUICK scheme in this problem there are 16 kinds of cells to be treated differently as below,
5.png

the problem exists only for cells '6' and '8'

i have done this problem by upwind and central the results are alike the book, my problem is QUICK for '6' and '8'

[FMDenaro]

Ok, now could you write the expression of each one of the four fluxes for the cell 8? How do you insert the BCs?

[baratian]

Originally Posted by fmdenaro

ok, now could you write the expression of each one of the four fluxes for the cell 8? How do you insert the bcs?

5.png
4.png

[baratian]

for extrapolation as stated in book linearly:
7.png

[FMDenaro]

Originally Posted by baratian

Attachment 71362
Attachment 71363

- phi_top what is? You do not know it



- The left flux requires the inflow condition for a ghost node, why are you writing that relation?

[baratian]

Originally Posted by FMDenaro

- phi_top what is? You do not know it



- The left flux requires the inflow condition for a ghost node, why are you writing that relation?

phi_top=100 as stated in pic in last posts

ghost node (left of L boundary which phi_L=100) is extrapolates as suggested by the book, (the pic in last post)

[FMDenaro]

Originally Posted by baratian

phi_top=100 as stated in pic in last posts

ghost node (left of L boundary which phi_L=100) is extrapolates as suggested by the book, (the pic in last post)

As I wrote above, you are wrong in setting the BCs

[baratian]

Originally Posted by FMDenaro

As I wrote above, you are wrong in setting the BCs

where is the fault? are u sure, because i used this BCs for upwind and central and the results were exactly the same as in the book.

[arkie87]

Originally Posted by baratian

sorry u r right. i try to make it clear. the QUICK scheme as stated in versteeg book is as follow (for a cell downstream face):
Attachment 71354
Attachment 71353

there is a 2D pure convection problem in the book shown below:
Attachment 71356

when i do the discretization for different cells there is no problem except for the mentioned ones stated in the first post i.e. the cell of (2,N) shown below:
Attachment 71357

as u c the coefficient of the main cell (2,N) sum to zero!!! and only neighbors remain. so there is no explicit representation for the mentioned cell!!! what should i do to close the system of equations now?!

look up deferred correction scheme. basically, you use upwind to solve, and then add a source which is equal to (upwind - quick)