A comparison of three Lagrangian approaches for extending near field mixing calculations

Lagrangian techniques have previously been employed to extend initial mixing calculations beyond the near field, either alone or in combination with Eulerian models. Computational efficiency and accuracy are of prime importance in designing these ‘hybrid’ approaches to simulating a pollutant discharge, and we characterize three relatively simple Lagrangian techniques in this regard: random walk particle tracking (RWPT), forward Gaussian puff tracking (FGPT), and backward Gaussian puff tracking (BGPT). RWPT is generally the most accurate, capable of handling complexities in the flow field and domain geometry. It is also the most computationally expensive, as a large number of particles are generally required to generate a smooth concentration distribution. FGPT and BGPT offer dramatic savings in computational expense, but their applicability is limited by accuracy concerns in the presence of spatially variable flow or diffusivity fields or complex no-flux or open boundary conditions. For long simulations, particle and/or puff methods can transition to an Eulerian model if appropriate, since the relative computational expense of Lagrangian methods increases with time for continuous sources. Although we focus on simple Lagrangian models that are not suitable to all environmental applications, many of the implementation and computational efficiency concerns outlined herein would also be relevant to using higher order particle and puff methods to extend the near field.