A Parallel Hierarchical-Element Method for Contour Dynamics Simulations

Many two-dimensional incompressible inviscid vortex flows can be simulated with high efficiency by means of the contour dynamics method. Several applications require the use of a hierarchical-element method (HEM), a modified version of the classical contour dynamics scheme by applying a fast multipole method, in order to accelerate the computations substantially. The HEM can be used, for example, to study the large-scale motion of coherent structures in geophysical fluid dynamics where the flow can be modelled by considering the motion in a thin layer of fluid in the presence of a non-uniform background vorticity (due to the latitudinal variation of the Coriolis force). Nevertheless, such simulations demand a substantial computational effort, even when the HEM is used. In this paper it is shown that the acceleration of contour dynamics simulations by means of the HEM can be increased further by parallelising the HEM algorithm. Speed-up, load balance and scalability are parallel performance features which are studied for several test examples. Furthermore, typical simulations are shown, including an application of vortex dynamics near the pole of a rotating sphere. The HEM has been parallelised using OpenMP and tested with up to 16 processors on an Origin 3800 cc-NUMA computer.