setting boundary condition for curvlinear grid

taw · February 5, 2010, 05:40

Dear fellows,

I am desperate for assistance please!!

I converted my FV Cartesian code for incompressible (primitive variable) Navier-Stokes solver to a general boundary fitted curvilinear coordinate system, written in a strong conservative form, with the physical velocity being directly solved.

I spend about 15 days on that and I am certain I did right on evaluating the metrics of the Jacobean (transformation matrix), the volume flux and pressure correction, etc. For instance I calculated the Jacobean as ja_i^j=\partial x_i/\partial \zeta_i; I find the area of the cell faces a_i^j=transpose(inverse(ja_i^j)).

I bench marked the code for rectangular grid using Ghia82 driven cavity flow. It works ok up to this.

Now I have some problem implementing Dirichlet boundary condition, trying to reproduce the skewed driven cavity problem.

I assume U1=A11*u1+A21*u2, U2=A12*uf1+A22*uf2, etc. with Ui and ufi being the volume flux and physical velocities at the faces of the cells respectively. For start I evaluated the cell face velocities using centered averages from consecutive grids, ie uf1=0.5(u1_i+u1_i+1), etc.

In many papers I came across, they don't discuss how to implement the bc, and I thought it is trivial. So I set u1=u2=0 at bottom , left and right faces of the cavity, u1=1, v1=0 at the top face.

But the result I got is different with Demirdzic92. I exhausted all avenues to find where I went wrong, with no avail.

By the way I used CDS and 2nd order UW (SOU) for the diffusive and convective and Rhie-chow for velocity/pressure coupling (collocated grid), in a fractional step manner. Since I tested this with Ghia I believe they are properly implemented

Can someone shade a light on this. I suspect I am stuffed with implementing the BC. For instance do we need to explicitly specify a BC for the corners. Normally, I don not set separate BC for the corners, since as the grid get refined the singularity from the corner fades away.

With best regards,

taw

taw · February 5, 2010, 08:03

apology for the urgency; can some one suggest an explanation.

taw · February 5, 2010, 18:23

Hi,

I think I figured out the problem. The continuity equation (cell face velocities) bc was the problem. I should have set one extra grid line to zero for vf_i, unlike the centre velocities bc, since the computational molecule with Rhie-chow is large. Or one sided differencing should have been implemted for the boundaries.

One more correction
a_i^j=transpose(cofactor(ja_i^j)).

Regards, TAW

February 5, 2010, 05:40	setting boundary condition for curvlinear grid	#1
taw New Member Join Date: Oct 2009 Posts: 29 Rep Power: 17	Dear fellows, I am desperate for assistance please!! I converted my FV Cartesian code for incompressible (primitive variable) Navier-Stokes solver to a general boundary fitted curvilinear coordinate system, written in a strong conservative form, with the physical velocity being directly solved. I spend about 15 days on that and I am certain I did right on evaluating the metrics of the Jacobean (transformation matrix), the volume flux and pressure correction, etc. For instance I calculated the Jacobean as ja_i^j=\partial x_i/\partial \zeta_i; I find the area of the cell faces a_i^j=transpose(inverse(ja_i^j)). I bench marked the code for rectangular grid using Ghia82 driven cavity flow. It works ok up to this. Now I have some problem implementing Dirichlet boundary condition, trying to reproduce the skewed driven cavity problem. I assume U1=A11u1+A21u2, U2=A12uf1+A22uf2, etc. with Ui and ufi being the volume flux and physical velocities at the faces of the cells respectively. For start I evaluated the cell face velocities using centered averages from consecutive grids, ie uf1=0.5(u1_i+u1_i+1), etc. In many papers I came across, they don't discuss how to implement the bc, and I thought it is trivial. So I set u1=u2=0 at bottom , left and right faces of the cavity, u1=1, v1=0 at the top face. But the result I got is different with Demirdzic92. I exhausted all avenues to find where I went wrong, with no avail. By the way I used CDS and 2nd order UW (SOU) for the diffusive and convective and Rhie-chow for velocity/pressure coupling (collocated grid), in a fractional step manner. Since I tested this with Ghia I believe they are properly implemented Can someone shade a light on this. I suspect I am stuffed with implementing the BC. For instance do we need to explicitly specify a BC for the corners. Normally, I don not set separate BC for the corners, since as the grid get refined the singularity from the corner fades away. With best regards, taw

February 5, 2010, 08:03	any suggestion from those online now	#2
taw New Member Join Date: Oct 2009 Posts: 29 Rep Power: 17	apology for the urgency; can some one suggest an explanation.

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February 5, 2010, 18:23		#3
taw New Member Join Date: Oct 2009 Posts: 29 Rep Power: 17	Hi, I think I figured out the problem. The continuity equation (cell face velocities) bc was the problem. I should have set one extra grid line to zero for vf_i, unlike the centre velocities bc, since the computational molecule with Rhie-chow is large. Or one sided differencing should have been implemted for the boundaries. One more correction a_i^j=transpose(cofactor(ja_i^j)). Regards, TAW