Why the Euler scheme in particle tracking is not enough: the shallow-sea pycnocline test case
Gräwe, U.; Deleersnijder, E.; Shah, S.H.A.M.; Heemink, A.W. (2012). Why the Euler scheme in particle tracking is not enough: the shallow-sea pycnocline test case. Ocean Dynamics 62(4): 501-514. http://dx.doi.org/10.1007/s10236-012-0523-y
In: Ocean Dynamics. Springer-Verlag: Berlin; Heidelberg; New York. ISSN 1616-7341; e-ISSN 1616-7228, more
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| Keyword |
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| Author keywords |
Particle tracking; Milstein scheme; Pycnocline; Diffusion; Residence time |
| Authors | | Top |
- Gräwe, U.
- Deleersnijder, E., more
- Shah, S.H.A.M.
- Heemink, A.W.
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| Abstract |
During the last decades, the Euler scheme was the common “workhorse” in particle tracking, although it is the lowest-order approximation of the underlying stochastic differential equation. To convince the modelling community of the need for better methods, we have constructed a new test case that will show the shortcomings of the Euler scheme. We use an idealised shallow-water diffusivity profile that mimics the presence of a sharp pycnocline and thus a quasi-impermeable barrier to vertical diffusion. In this context, we study the transport of passive particles with or without negative buoyancy. A semi-analytic solutions is used to assess the performance of various numerical particle-tracking schemes (first- and second-order accuracy), to treat the variations in the diffusivity profile properly. We show that the commonly used Euler scheme exhibits a poor performance and that widely used particle-tracking codes shall be updated to either the Milstein scheme or second-order schemes. It is further seen that the order of convergence is not the only relevant factor, the absolute value of the error also is. |
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