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potential flow in 3D pipe using boundary element/panel methodhi guys, I'm trying to find articles about potential flow in 3D pipe using boundary element/panel method, but i can't find it..
anyone can tell me where i can find this kind of articles? or somebody can explain this to me? as i realized that it is different from external flow, whereas in external flow the potential is decomposed into 2 parts which is from free stream and from the body. is it the same for internal flow? |

Internal and external flow use the same equations, except that the latter has an additional freestream term. However, depending on the form of the integral equations, the internal flow problem is somewhat more difficult to solve in that the Neumann problem (the Laplace eqn with Neumann/flux boundary conditions) is not unique (or is unique up to an arbitrary constant). So, if you want to solve the internal flow problem in terms of the classical BEM, with the potential as the unknown and the potential normal fluxes as the known then my paper below discusses the issue of handling the above-mentioned uniqueness issue:
A. Gharakhani and A. F. Ghoniem, "BEM Solution of the 3D Internal Neumann Problem and A Regularized Formulation for the Potential Velocity Gradients," International Journal of Numerical Methods in Fluids, Vol. 24, No. 1, pp. 81-100, 1997 If on the other hand you want to use the panel method approach; i.e., the derivative BEM formulation with velocity sources and vortex sheets as the surface variables then there is little problem except that you'd have to assign u.n boundary conditions for the sources all around the boundary surface, and you'd have to solve an equation system for a 2D vectorial vortex sheet strength per panel (in 3D), which is a bigger matrix than in the previous case. See, for example: M. J. Stock and A. Gharakhani, "Graphics Processing Unit-Accelerated Boundary Element Method and Vortex Particle Method," Journal of Aerospace Computing, Information, and Communication, Vol. 8, No. 7, pp. 224-236, 2011. Hope these help adrin |

thanks for the reply Aldrin,
i wonder if i stick to potential formulation and I would like to extend to vortex methods. how do i get the vortex sheet for the non-slip bc? isn't that vortex sheet \gamma = \hat{n} \times \nabla \Phi_{total} for external flow? assuming without any body movement,and total means the total of boundary and freestream contributions. or is it only \gamma = \hat{n} \times \nabla \Phi_{boundary} i prefer the bem approach because it solves smaller matrix than the vectorial vortex sheet in panel method. |

The velocity field is the sum of all contributions (freestream, panel vortex, particle/filament vortex, other sources). You use all of them to find the panel strength such that the prescribed slip/flux BC is satisfied. Once that is available, you go back to the original statement that velocity is the sum effect of all terms. It doesn't matter whether you solve for the velocity directly or indirectly (as in the case of a Neumann problem)
Adrin |

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