Numerical Treatment of the Weakly Singular Integrals

Poiseuille flow of a Newtonian fluid in a circular tube. For a pressure driven flow of a Newtonian fluid in a circular tube, we can obtain an analytical solution as we already did in Chapter 5. Ignoring the entrance effects, the solution for the velocity field as a function of the radial direction (see Fig. 10.18) is as follows 

The BEM methodology listed in Algorithm 11 will be applied again with the exception of the matrices dimensions. The BEM matrices assembly will be performed in a similar way as in the scalar case. Algorithms 14 and 15 show the new assembly methodology for the matrices and the integral calculation of the components, including Telles transformation for matrix G. 

Algorithm 14 Assembling Boundary Element Matrices for the Stokes Momentum Equations.  

Algorithm 15 Small Boundary Element Matrices (Integrals). 

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