The application of adaptive mesh techniques to numerical simulations of gravity current flows

Abstract

The performance of unstructured adaptive meshes (adaptive meshes) in simulations of gravity current flows is evaluated in order to assess their utility for ocean modelling. Adaptive mesh models aim to capture transient and complex dynamics in an efficient manner by refining or coarsening the mesh as the flow evolves. Gravity currents that exhibit such behaviour therefore present an ideal test case to investigate the promise of the adaptive mesh approach. The prime focus is on gravity currents generated in the idealised lock-exchange set-up and simulated with the Imperial College Ocean Model (Fluidity-ICOM). The Froude number (non-dimensional front speed) and background potential energy (a measure of the mixing) are used to evaluate the performance of fixed and adaptive meshes. Adaptive mesh simulations produce comparable values of the diagnostics to the higher resolution fixed mesh simulations whilst using at least one order of magnitude fewer nodes. The results also compare well with published values. Here, the metrics that guide the mesh adapt are formed from a modified Hessian and a user-defined weight for selected solution fields. The best performing of these simple metrics (denoted M2) incorporates a scaling by the determinant of the modified Hessian. This gives greater weighting to smaller-scale fluctuations leading to better representation of these features. Simulations of a gravity current on an incline are also presented that showcase the strength of M2 and progress the modelled scenario towards a realistic ocean overflow. The choice of metric is fundamental to the ability of the adaptive mesh to represent the flow. This decision will remain key for ocean models, from idealised studies to scenarios of increasing complexity. The potential for good representation of the flow and efficiency gains with adaptive meshes demonstrated here offers a promising outlook for their use in ocean modelling.