• discretisation;
  • finite volume;
  • kinematic equation;
  • mass conservation;
  • trajectory


When the trajectory equation is discretised in semi-Lagrangian models, the departure points can be spuriously located outside the model domain. Historically this has been addressed in an ad hoc manner by relocating any such departure point to the domain boundary. This procedure, whilst convenient, is not physically justified and is inaccurate. It is of particular concern for mass-conserving, finite-volume, semi-Lagrangian schemes that use the locations of departure points to determine upstream volumes, since it can lead to spuriously massless or near-massless volumes, and large errors in mass transport. This weakness of current discretisations is discussed. An improved near-boundary discretisation of the trajectory equation is then proposed and analysed via an example. Crown Copyright © 2009. Reproduced with the permission of HMSO. Published by John Wiley & Sons Ltd.