Optimising series solution methods for flow over topography---Part 1

Abstract

Series solution methods have recently been used to solve fully nonlinear flow over topography problems. These methods are iterative schemes that update an initial estimate of the fluid surface (a free boundary) using a cost function. Series solutions are obtained efficiently and accurately with exact error bounds immediately available. Critical to the speed of the procedure is the implementation of efficient computer code and numerical techniques. In this paper we discuss methods that improve the computational time of the original implementation by several orders of magnitude, without any loss of accuracy. The efficiency of the improved method is demonstrated by generating two dimensional solutions to subcritical flow over an isolated cosine shaped obstacle.