Analysis of the efficiency and accuracy of two adaptive partitioned time step schemes in Lagrangian particle tracking algorithms

Abstract

Simulations of particle trajectories on the ocean's surface usually involve thousands of releases. The efficiency and accuracy of Lagrangian trajectory algorithms, based on the velocities provided at the nodes of an Eulerian grid, depend mainly on the size of the time step (∆t) to calculate the movement between two consecutive points that make up the trajectory. Adaptive partitioned time step schemes are viable alternatives, as the ∆t can be divided into parts to increase accuracy when the speed is high, but, to maintain efficiency, preserve the original ∆t when the speed is low. This study proposed two algorithms with adaptive particle tracking formulations: in one of them, the particle cannot cross the edge of the grid cell in a single movement, and in the other, it can, but to a limited extent. They were compared in a hydrodynamic simulation of currents forced by winds and tides in a bay with channels, islands and obstacles, with large variations in grid cell size and surface velocity. The two algorithms showed similar accuracy and efficiency, with some differences in channels where velocity variations were greater. The size of the ∆t had a notable impact on computing time; the choice of the size should be decided taking into account the desired details for trajectories. In cases of continuous leakage, ∆t cannot be greater than the time interval between two consecutive releases.