Laminar flow in polygonal conduits by the large singular finite element method

The three-step large singular finite element method (LSFEM) applied to the calculation of laminar flow in polygonal conduits (ducts). The mathematical formulation concerns a constant property, steady, fully developed laminar flow in a duct of constant polygonal cross-section with the axis of the duct in the z-direction. The first step of the method is diversion of the domain, the second step deals with solution of auxiliary problems, and the third step is patching of the auxiliary solutions. In three particular cases the numerical results obtained with the LSFEM are compared with those given by other methods. For equilateral triangular ducts the LSFEM provides the exact analytical solution. For square or pentagonal ducts the LSFEM proves to be much more efficient than Fourier's method and the finite element method.