[shovaliye2]

Hi. I have potential velocity for points on hydrofoil.
In other words:
for P1=(x1,y1,z1), the potential velocity is phi1
for P1=(x2,y2,z2), the potential velocity is phi2
for P1=(x3,y3,z3), the potential velocity is phi3
and
.
.
.
for Pn=(xn,yn,zn), the potential velocity is phin
(coordinates of points and magnitudes of potential velocities for each points are known values).

how can I obtain velocity in x,y and z direction for each point? I know u is derivative of phi with respect to x, v is derivative of phi with respect to y, w is derivative of phi with respect to z. But I don't have equation for phi in order to calculate derivative of phi. I just have phi magnitudes (in number) for each points.
In this case how can I obtain components of velocity (u, v, w)?
It is a long time that I am struggling with this problem.

[sbaffini]

Where do these values come from? They generally come from the solution of a linear system which is actually assembled using a singulalirity distribution. Is your a different case?

[FMDenaro]

Originally Posted by shovaliye2

Hi. I have potential velocity for points on hydrofoil.
In other words:
for P1=(x1,y1,z1), the potential velocity is phi1
for P1=(x2,y2,z2), the potential velocity is phi2
for P1=(x3,y3,z3), the potential velocity is phi3
and
.
.
.
for Pn=(xn,yn,zn), the potential velocity is phin
(coordinates of points and magnitudes of potential velocities for each points are known values).

how can I obtain velocity in x,y and z direction for each point? I know u is derivative of phi with respect to x, v is derivative of phi with respect to y, w is derivative of phi with respect to z. But I don't have equation for phi in order to calculate derivative of phi. I just have phi magnitudes (in number) for each points.
In this case how can I obtain components of velocity (u, v, w)?
It is a long time that I am struggling with this problem.

Your problem seems not well posed... you have a 3D spatial problem and only 3 spatial positions that define mathematically a plane generally oriented in x,y,z. You can interpolate the function phi on the triangle on this plane (csi, eta) but does the point xn,yn,zn lie on this plane??


You should provide more details.

[shovaliye2]

Originally Posted by sbaffini

Where do these values come from? They generally come from the solution of a linear system which is actually assembled using a singulalirity distribution. Is your a different case?

I evaluate these values from Boundary Element Method by using following equation:
https://pasteboard.co/JdWMk6w.png

[shovaliye2]

Originally Posted by FMDenaro

Your problem seems not well posed... you have a 3D spatial problem and only 3 spatial positions that define mathematically a plane generally oriented in x,y,z. You can interpolate the function phi on the triangle on this plane (csi, eta) but does the point xn,yn,zn lie on this plane??


You should provide more details.

sorry I didn't understand. can you explain your purpose more clearly?

[FMDenaro]

Your three nodes (x1,y1,z1), (x2,y2,z2),(x3,y3,z3) defines a plane in the x,y,z reference system. If not differently specified, such plane is generally oriented in this system. If you use a local reference system on the plane, (csi,eta,zeta), you can interpolate linearly only on the (csi,eta) plane but you need that the position xn,yn,zn belongs to the (csi,eta) plane. If so, you just compute the interpolation of phy on the planar triangle.


Again, write the details of what you are doing not the link to a software.

[sbaffini]

Originally Posted by shovaliye2

I evaluate these values from Boundary Element Method by using following equation:
https://pasteboard.co/JdWMk6w.png

So, you know who R is and how it is distributed on your body (B) and Wake (W), don't you? That's where everything comes from.

All these things are very well explained in the Katz & Plotkin book and, if you are working on a panel method, there is no substitution to reading it. Really, any attempt here is going to be approximate and, in the end, not effective.

If you already read it, you should be able to tell us which exact combination of sources, doublets and boundary conditions (dirichlet/neumann) you are using, so that we can be of help in pointing you to the correct procedure to follow to obtain velocity, potential, pressure, etc.

[FMDenaro]

Maybe I misunderstood the original question? Isn't an interpolation problem value from a set of known phi values?
If the issue is in the determination of a solution in a BEM then this is more a theory problem and yes, the textbook explains all the requirements.