A SUNTANS-based unstructured grid local exact particle tracking model

Abstract

A parallel particle tracking model, which employs the local exact integration method to achieve high accuracy, has been developed and embedded in an unstructured-grid coastal ocean model, Stanford Unstructured Nonhydrostatic Terrain-following Adaptive Navier–Stokes Simulator (SUNTANS). The particle tracking model is verified and compared with traditional numerical integration methods, such as Runge–Kutta fourth-order methods using several test cases. In two-dimensional linear steady rotating flow, the local exact particle tracking model is able to track particles along the circular streamline accurately, while Runge–Kutta fourth-order methods produce trajectories that deviate from the streamlines. In periodically varying double-gyre flow, the trajectories produced by local exact particle tracking model with time step of 1.0 × 10− 2 s are similar to those trajectories obtained from the numerical integration methods with reduced time steps of 1.0 × 10− 4 s. In three-dimensional steady Arnold–Beltrami–Childress (ABC) flow, the trajectories integrated with the local exact particle tracking model compares well with the approximated true path. The trajectories spiral upward and their projection on the x–y plane is a periodic ellipse. The trajectories derived with the Runge–Kutta fourth-order method deviate from the approximated true path, and their projections on the x–y plane are unclosed ellipses with growing long and short axes. The spatial temporal resolution needs to be carefully chosen before particle tracking models are applied. Our results show that the developed local exact particle tracking model is accurate and suitable for marine Lagrangian (trajectory-based)-related research.