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Adaptive time stepping algorithm for Lagrangian transport models: theory and idealised test cases
Shah, S.H.A.M.; Heemink, A.W.; Grawe, U.; Deleersnijder, E. (2013). Adaptive time stepping algorithm for Lagrangian transport models: theory and idealised test cases. Ocean Modelling 68: 9-21. dx.doi.org/10.1016/j.ocemod.2013.04.001
In: Ocean Modelling. Elsevier: Oxford. ISSN 1463-5003, more
Peer reviewed article  

Available in Authors 
    VLIZ: Open Repository 279374 [ OMA ]

Keyword
    Marine
Author keywords
    Lagrangian modelling; Non-flat isopycnal surfaces; Shallow-sea model;Vertical diffusivity; Stochastic differential equations

Authors  Top 
  • Shah, S.H.A.M.
  • Heemink, A.W.
  • Grawe, U.
  • Deleersnijder, E., more

Abstract
    Random walk simulations have an excellent potential in marine and oceanic modelling. This is essentially due to their relative simplicity and their ability to represent advective transport without being plagued by the deficiencies of the Eulerian methods. The physical and mathematical foundations of random walk modelling of turbulent diffusion have become solid over the years. Random walk models rest on the theory of stochastic differential equations. Unfortunately, the latter and the related numerical aspects have not attracted much attention in the oceanic modelling community. The main goal of this paper is to help bridge the gap by developing an efficient adaptive time stepping algorithm for random walk models. Its performance is examined on two idealised test cases of turbulent dispersion; (i) pycnocline crossing and (ii) non-flat isopycnal diffusion, which are inspired by shallow-sea dynamics and large-scale ocean transport processes, respectively. The numerical results of the adaptive time stepping algorithm are compared with the fixed-time increment Milstein scheme, showing that the adaptive time stepping algorithm for Lagrangian random walk models is more efficient than its fixed step-size counterpart without any loss in accuracy.

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