A higher order boundary element method for fluid flow

An infinite system of higher order regular integral equations is obtained by using the first spatial derivative of the fundamental solution as kernel function with its singularity taken outside the domain of the problem. The resulting higher order kernels are everywhere regular over the boundary on discretizing the system in the usual manner. Two two-dimensional problems of inviscid laminar fluid flow are analyzed using constant elements for both conventional and higher order boundary integral methods. Results for flow past a circular obstacle in a channel and for flow past a plate in a channel show that the higher order method may be employed for both regular and singular problems. The use of higher order kernels is potentially advantageous because of improved diagonal dominance in the algebraic equations.