[AnhDL]

Dear expert,

I am writing my own CFD code using finite difference method.
The problem is the flow pass two cylinders. I created an O-type mesh with a cut line.
The boundary condition is non-slip at wall. And at the cut-line (points 1, 2, 3,...), simply, using the average value from two points (1'-1'', 2'-2'', 3'-3'',...) near to the grid point at the cut-line.

The problem is that it is difficult to choose boundary condition for grid point 0. I tried different boundary conditions:
1. P0=(Pa+Pa')/2
2. P0=(Pa+Pa')/2 and Ua=Ub/4, Va=Vb/4 and Ua'=Ub'/4, Va'=Vb'/4 (apply second order approximation)
But the solution got strange result with pressure jump at the cut-line and some points near the cut-line and wall.
Could you please give me advices to this problems? Thank you

[AnhDL]

Could anyone please help me?

[agd]

The indexing that you are using for your mesh seems odd to me. Topologically your cut line is part of the same surface as the cylinder wall in (I,J) space, but you appear to be treating those pieces as partly I and partly J. Your results are more than likely the result of an indexing issue with your grid, and you are sticking values in the cells from parts of the grid that you don't mean to. Formally, the surface of the cylinder is no-slip, and then if you use an average properly, the point on the cylinder that corresponds to the cut location will get its values from the adjacent wall points - then the average of the no-slip velocities returns the correct no-slip velocity at the first cut point (zero if the wall is not moving).

[AnhDL]

Originally Posted by agd

The indexing that you are using for your mesh seems odd to me. Topologically your cut line is part of the same surface as the cylinder wall in (I,J) space, but you appear to be treating those pieces as partly I and partly J. Your results are more than likely the result of an indexing issue with your grid, and you are sticking values in the cells from parts of the grid that you don't mean to. Formally, the surface of the cylinder is no-slip, and then if you use an average properly, the point on the cylinder that corresponds to the cut location will get its values from the adjacent wall points - then the average of the no-slip velocities returns the correct no-slip velocity at the first cut point (zero if the wall is not moving).

Thank you. My mistake. The simulation contains two cylinders. The grid point is indexed from the top cylinder to bottom cylinder with the cutline. Thus the point on the cutline is also indexed as (i,1). The velocity at the first cut point on the cylinder is zero. But, I wonder about the boundary condition at this point for pressure. There is a jump that I think somewhat strange.

[agd]

So the cylinder surfaces and cutline comprise the j=1 grid line, if I understand your figures. So the next question is - are you sure that you are assigning the computed boundary pressure to both sides of the cutline? It looks like you are only assigning it to one side.

[AnhDL]

Originally Posted by agd

So the cylinder surfaces and cutline comprise the j=1 grid line, if I understand your figures. So the next question is - are you sure that you are assigning the computed boundary pressure to both sides of the cutline? It looks like you are only assigning it to one side.

Yes, I assigned the boundary condition to both sides of the cutline. I tested for the tandem cylinders and side-by-side cylinders.
There is no problem with the tandem cylinders (pressure tendency on the cylinder surfaces fit the reference data) although the same boundary conditions were used.