Condition of boundary integral equations arising from flow computations
The solution of potential flow problems in a given region is considered by producing a Fredholm integral equation around the boundary of the region. This integral equation is then discretized to produce a collocation solution. The authors conclude that (i) equations of the first kind with Cauchy singular kernels do not appear to be worse conditioned than equations of the second kind with regular kernels (ii) collocation points for such equations of the first kind are better placed between the knots, but for equations of the second kind they should be placed at the knots (iii) the circulation is mainly determined by equations of the first kind but the mean velocity by an equation of the second kind. The use of simultaneous equations generally improves the computed solution and permits the determination of flows near aerodynamic profiles of any thickness.
scientific article; zbMATH DE number 3924052
scientific article