High-order accurate finite-volume formulations for the pressure gradient force in layered ocean models.

Discretisation of the horizontal pressure gradient force in layered ocean models is a challenging task, with non-trivial interactions between the thermodynamics of the fluid and the geometry of the layers often leading to numerical difficulties. We present two new finite-volume schemes for the pressure gradient operator designed to address these issues. In each case, the horizontal acceleration is computed as an integration of the contact pressure force that acts along the perimeter of an associated momentum control-volume. A pair of new schemes are developed by exploring different control-volume geometries. Non-linearities in the underlying equation-of-state definitions and thermodynamic profiles are treated using a high-order accurate numerical integration framework, designed to preserve hydrostatic balance in a non-linear manner. Numerical experiments show that the new methods achieve high levels of consistency, maintaining hydrostatic and thermobaric equilibrium in the presence of strongly-sloping layer geometries, non-linear equations-of-state and non-uniform vertical stratification profiles. These results suggest that the new pressure gradient formulations may be appropriate for general circulation models that employ hybrid vertical coordinates and/or terrain-following representations.

On the formulation of environmental fugacity models and their numerical solutions.

Multimedia models based on chemical fugacity, solved numerically, play an important role in investigating and quantifying the environmental fate of chemicals such as persistent organic pollutants. These models have been used extensively in studying the local and global distribution of chemicals in the environment. The present study describes potential sources of error that may arise from the formulation and numerical solution of environmental fugacity models. The authors derive a general fugacity equation for the rate of change of mass in an arbitrary volume (e.g., an environmental phase). Deriving this general equation makes clear several assumptions that are often not articulated but can be important for successfully applying multimedia fugacity models. It shows that the homogeneity of fugacity and fugacity capacity in a volume (the homogeneity assumption) is fundamental to formulating discretized fugacity models. It also shows that when using the fugacity rather than mass as the state-variable, correction terms may be necessary to accommodate environmental factors such as varying phase temperatures and volume. Neglecting these can lead to conservation errors. The authors illustrate the manifestation of these errors using heuristic multimedia fugacity models. The authors also show that there are easily avoided errors that can arise in mass state-variable models if variables are not updated appropriately in the numerical integration scheme. Environ Toxicol Chem 2016;35:2182-2191. © 2016 SETAC.