Isogeometric Boundary Element Analysis of steady incompressible viscous flow, Part 2: 3-D problems

This is a sequel to a previous paper (Beer et al., 2017) [1] where a novel approach was presented to the 2-D Boundary Element analysis of steady incompressible viscous flow. Here the method is extended to three dimensions. NURBS basis functions are used for describing the geometry of the problem and for approximating the unknowns. In addition, the arising volume integrals are treated differently to published work and volumes are described by bounding NURBS surfaces instead of cells and only one mapping is used. The advantage of the present approach is that complex boundary shapes can be described with very few parameters and that no generation of cells is required. For the solution of the non-linear equations full and modified Newton-Raphson methods are used. A comparison of the two methods is made on the classical example of a forced cavity flow, where accurate two-dimensional solutions are available in the literature. Finally, it is shown on a practical example of an airfoil how more complex boundary shapes can be approximated with few parameters and a solution obtained with a small number of unknowns.