[Sparsh]

What are the major similarities and dissimilarities between boundary element method and panel method?

[piu58]

There is no numerical difference. The panel method is the BEM applied to fluid dynamics.

It can be used for flow past bodies. The body needs to be divided in panels. The panels fulfil the Laplace differentialequation and give sources for the flow. The sources are calculated so that the no slip boundary condition is fulfilled.

[Sparsh]

Excerpt from the paper, "LIFTING AEROFOIL CALCULATION USING THE BOUNDARY ELEMENT METHOD"; G. F. CAmY AND S. W. KIM

The boundary element method and panel method have some strong similarities, principally due to their use of boundary integral relations and the classical ideas of potential theory. There are, however, some major conceptual distinctions; the panel method is based upon superposition using for instance sources, doublets or vortices with solution determined for example from the discrete satisfaction of boundary flux conditions; in the boundary element method we use a finite element expansion and a discrete approximation of the boundary integral equation.

[Sparsh]

Originally Posted by piu58

The sources are calculated so that the no slip boundary condition is fulfilled.

The Laplace equation is for potential flows which are inviscid in nature, so there wouldn't be no slip BC. Moreover the tangential velocity component exists for each collocation point on the surface thus ruling out the no-slip. Even the kutta condition requires the upper and the lower trailing edge tangential velocity components to be non-zero.

[FMDenaro]

Originally Posted by Sparsh

Excerpt from the paper, "LIFTING AEROFOIL CALCULATION USING THE BOUNDARY ELEMENT METHOD"; G. F. CAmY AND S. W. KIM

The boundary element method and panel method have some strong similarities, principally due to their use of boundary integral relations and the classical ideas of potential theory. There are, however, some major conceptual distinctions; the panel method is based upon superposition using for instance sources, doublets or vortices with solution determined for example from the discrete satisfaction of boundary flux conditions; in the boundary element method we use a finite element expansion and a discrete approximation of the boundary integral equation.

Also in the panel method you have practically a finite element representation ... the potential function is approximated like step-wise, linear, etc.

[piu58]

> wouldn't be no slip BC. Moreover the tangential velocity component exists

Thank you for that clarification.

[piu58]

> Also in the panel method you have practically a finite element representation

I do not fully understand how you meand that. There is a remarkably difference between FEM and BEM /panel.

In FEM you have to mesh the volume, similar to the FVM in openfoam and other cfd software. The panel method requires a meshing only of the surface(s) of the circulated body/ bodies. The solution in the field will be calculated from superposition of source elements of the flow connected with each panel (= element of the surface mesh).

[adrin]

"There are, however, some major conceptual distinctions; the panel method is based upon superposition using for instance sources, doublets or vortices with solution determined for example from the discrete satisfaction of boundary flux conditions; in the boundary element method we use a finite element expansion and a discrete approximation of the boundary integral equation."

If the above quote is not taken out of context by "sparsh", it supports the observation that just because a material is printed it doesn't automatically imply it's correct/accurate! The assertion above is complete hogwash! There is NO fundamental difference between BEM and Panel Methods, except for terminology (and specifics of applying the physics of fluids to BEM to get a Panel Method, such as the application of the Kutta condition).

I agree with Uwe Pilz on both (1) the fact that FEM/FVM/FDM are completely different solution strategies from BEM/Panel, as well as (2) his claim that no-slip condition is satisfied in BEM! Let me clarify below.

1) The FEM/FVM/FDM discretize the d-dimensional Laplacian in the "traditional" sense, whereas the BEM (panel method) uses the Green function for the Laplacian, which, upon manipulation, leads to a (d-1)-dimensional solution method. There is absolutely NO similarity between FEM and BEM/panel, whatsoever!

2) It is true that we apply a flux boundary condition for the Laplace equation (potential flow problem). But, depending on the choice of the panel (say, vortex sheets), satisfying the no-flux boundary condition also satisfies the no-slip boundary condition. Strictly speaking, if we evaluate the velocity field right *above* the panels (on the fluid side of the problem), then we would see a finite value of velocity, which is equal to the slip velocity (as we expect of inviscid and potential flow problems). However, if we evaluate the velocity field right *below* the panels (on the solid side of the problem), we would get zero, which implies no-slip boundary condition. In other words, these vortex sheets on the body are, really, fluid elements of zero thickness. Think of them as zero-thickness finite volumes that contain infinite vorticity but finite circulation!

3) It seems to me that the authors referred to by "sparsh" are confusing direct and indirect boundary element methods (which is where differences between sources, doublets, vortex panels, etc arise). Most, not all, "panel methods" are of the indirect variety of BEM (using sources and dipoles).

adrin

[FMDenaro]

Originally Posted by piu58

> Also in the panel method you have practically a finite element representation

I do not fully understand how you meand that. There is a remarkably difference between FEM and BEM /panel.

In FEM you have to mesh the volume, similar to the FVM in openfoam and other cfd software. The panel method requires a meshing only of the surface(s) of the circulated body/ bodies. The solution in the field will be calculated from superposition of source elements of the flow connected with each panel (= element of the surface mesh).

I wrote FEM but I referred as to BEM

[Sparsh]

We can't impose no-slip condition by the panel method. To satisfy the no-slip condition, we have to create voracity on the surface of the body, i.e. we have to create vortex sheet on the surface of the body. Thanks "adrin"!

[Sparsh]

Originally Posted by adrin

"no-slip condition is satisfied in BEM! adrin

When a solid is immersed in a flow, its effect can be summarized in two expressions of the boundary conditions: the flow cannot go through the solid wall, and the tangential velocity of the flow on the wall is zero. Common terminology refers to these conditions as the no-through and the no-slip boundary conditions.

[adrin]

The vortex sheet you "create" is the very vortex panel you use to discretize the body. In fact, you can apply either the no-flux or the no-slip boundary condition to the same system of equations to obtain the distribution of vortex sheet strengths on the body (it's really straight-forward in 2D, but somewhat more complicated in 3D, though still doable). There are errors involved when one uses low-order panels, but that's due to discretization; theoretically, the vortex sheets satisfy both no-slip and no-flux conditions. For details, see, for example, http://lhldigital.lindahall.org/util...lename/879.pdf.

When you say "panel method" you are implicitly assuming a very specific distribution of sources and doublets in an indirect BEM setting; nevertheless, the velocity induced by doublets can be shown to be equivalent to those induced by vortex sheets, which implies, once again, that you can impose both no-flux and no-slip (but it's a matter of what side of the panel you evaluate the velocity).

adrin

[barehull]

Such a fight for some text of OP's paper he's writing