Isogeometric Boundary Element Analysis of steady incompressible viscous flow, Part 1: Plane problems

A novel approach is presented to the Boundary Element analysis of steady incompressible flow. 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, that is, volumes are described by bounding NURBS curves instead of cells and a mapping is used. The advantage of our approach is that non-trivial 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 both classical 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 solutions are available in the literature. The results obtained agree well with published ones for moderate Reynolds numbers using both methods, but it is found that the latter requires a relaxation scheme and considerably more iterations to converge. 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.