Abstract
This paper proposes a fast computation technique for particle (vortex element)-grid interpolations in the Vortex-in-Cell method (hereafter referred to as the VIC method). This technique is based on the incremental computation algorithm for the Gaussian, expressed as exp(–x2) in the recurrence formula, proposed by Turkowski to generate coefficient tables for the Gaussian blur filter used in image processing. The technique can reduce computational costs by replacing an exponential function call, exp(), with two floating-point multiplications per grid point, thus avoiding some expensive operations. The technique is applied to the vortex element-grid interpolation in the two-dimensional VIC method to simulate a plane mixing layer, and error evaluations and performance measurements are performed to confirm its suitability. The error evaluations show that the errors accumulated in computational directions do not affect the large-scale structures of the flow, although the errors do affect the time evolutions of the flow. The performance measurements show that the average execution time of the vortex element-grid interpolation is reduced to one-third and that the average total execution time is also significantly reduced, thus verifying the technique’s suitability for the VIC method.
