Accurate numerical representation of advection has always been a major research area in computational fluid dynamics. In MITgcm we have many schemes available so that the most appropriate for a particular problem can be used.

In addition to conventional schemes (linear 2nd, 3rd and 4th order) we have developed some higher order non-linear methods in the class of flux-limited methods. Flux limited methods are highly non-linear and can be constructed to guarantee monotonicity and to optimize shape preserving properties. In multiple dimensions we use a technique that retains these qualities for three dimensional flow.

An example of how the advection scheme can impact the solution is shown in the figure below; a gravity plume, forced by deep water formation on the shelf (left), flows and accelerates down the slope. The shear between the plume and ambient fluid leads to Kelvin-Helmholtz billows which lead to detrainment and entrainment of plume fluid.

More details can be found here.

The upper panel was calculated using conventional centered second order methods while the lower panel used third order interpolation with a Sweby flux-limiter. The latter has denser water in the plume and stronger contrasts in the billows, all indicative of lower levels of numerical diffusion.