Lagrangian Numerical Methods for Ocean Biogeochemical Simulations

TL;DR

This paper introduces two Lagrangian numerical methods tailored for simulating ocean biogeochemical processes involving advection, reaction, and diffusion, especially in high Péclet number flows where resolving all scales is impractical.

Contribution

The paper develops two novel Lagrangian methods that combine characteristics with particle couplings to effectively model diffusion and small-scale transport in ocean flows.

Findings

Methods conserve mass and obey the maximum principle.

They allow tuning of diffusive effects down to zero.

Suitable for high Péclet number ocean flow simulations.

Abstract

We propose two closely--related Lagrangian numerical methods for the simulation of physical processes involving advection, reaction and diffusion. The methods are intended to be used in settings where the flow is nearly incompressible and the P\'eclet numbers are so high that resolving all the scales of motion is unfeasible. This is commonplace in ocean flows. Our methods consist in augmenting the method of characteristics, which is suitable for advection--reaction problems, with couplings among nearby particles, producing fluxes that mimic diffusion, or unresolved small-scale transport. The methods conserve mass, obey the maximum principle, and allow to tune the strength of the diffusive terms down to zero, while avoiding unwanted numerical dissipation effects.