Lagrangian numerical methods for ocean biogeochemical simulations

Francesco Paparella, Marina Popolizio

Research output: Contribution to journalArticlepeer-review


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 Péclet 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.

Original languageEnglish (US)
Pages (from-to)229-246
Number of pages18
JournalJournal of Computational Physics
StatePublished - May 1 2018


  • Advection reaction diffusion
  • Lagrangian methods
  • Ocean biogeochemistry
  • Unresolved flows

ASJC Scopus subject areas

  • Numerical Analysis
  • Modeling and Simulation
  • Physics and Astronomy (miscellaneous)
  • General Physics and Astronomy
  • Computer Science Applications
  • Computational Mathematics
  • Applied Mathematics


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