Improvements to the convection scheme in the vortex particle method using a semi-Lagrangian method

Abstract

This study focuses on the convection scheme in the vortex particle method. The usual two-step convection procedure for vortex elements, which comprises the convection of vortex elements on each grid point and redistribution of vorticity into each grid point, is extremely difficult to parallelize because of unavoidable memory-write conflictions in the redistribution step, thereby limiting the computational speed. We apply a semi-Lagrangian method called the cubic semi-Lagrangian method, as the convection scheme in the vortex particle method to improve space-time accuracy and accelerate computations. Two test problems, namely the Taylor-Green vortex and double shear flow, are simulated using the semi-Lagrangian vortex particle method proposed in this study to confirm its suitability. The results show that the accuracy of capturing standing vortices and the total amount of kinetic energy conservation are significantly improved. The performance measurements show that the average execution time for the convection of vortex elements is reduced to one-half, thus verifying the semi-Lagrangian method as a suitable convection scheme for the vortex particle method.