{"refrec":{"BRefID":220490,"RR":"<b>Gräwe, U.; Deleersnijder, E.; Shah, S.H.A.M.; Heemink, A.W.</b> (2012). Why the <i>Euler</i> scheme in particle tracking is not enough: the shallow-sea pycnocline test case. <i>Ocean Dynamics 62(4)</i>: 501-514. <a href=\"http://dx.doi.org/10.1007/s10236-012-0523-y\" target=\"_blank\">http://dx.doi.org/10.1007/s10236-012-0523-y</a>","BEntID":212223,"PublicFlag":1,"CheckedFlag":1,"wosflag":1,"vabbflag":null,"RefStringPartII":". <i>Ocean Dynamics 62(4)</i>: 501-514. <a href=\"http://dx.doi.org/10.1007/s10236-012-0523-y\" target=\"_blank\">http://dx.doi.org/10.1007/s10236-012-0523-y</a>","DocTypID":8,"DocType":"Journal article","MarineFlag":1,"FreshFlag":0,"BrackishFlag":0,"TerrestrialFlag":0,"Authorstring":"Gräwe, U.; Deleersnijder, E.; Shah, S.H.A.M.; Heemink, A.W.","OrigTitleTranslFlag":0,"Authorstringtrunc":"Gräwe, U. <i>et al.</i>","Englishabstract":"During the last decades, the <i>Euler</i> 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 <i>Euler</i> 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 <i>Euler</i> scheme exhibits a poor performance and that widely used particle-tracking codes shall be updated to either the <i>Milstein</i> 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.","AbstractOtherLang":null,"BibLvlCode":"AS","StandardTitle":"Why the <i>Euler</i> scheme in particle tracking is not enough: the shallow-sea pycnocline test case","OrigTitleLangCode":"en","OrigTitleLangCodeExtended":"eng","OrigTitleLangID":15,"DateLastModified":{"date":"2024-12-10 01:33:17.368041","timezone_type":1,"timezone":"+01:00"},"UserAccessRight":null,"UserAccID":null,"AuthorKeywords":"Particle tracking; Milstein scheme; Pycnocline; Diffusion; Residence time","OtherDescriptors":null,"Notes":null,"AnaPub":2012,"MonPub":null,"DateUpdate":"2018-05-17","DateCreate":"2012-11-27","SecASFANote":null,"ConfID":null,"PeerRev":1,"VlizCoreFlag":1,"WoScode":"WOS:000302103800001","VABBcode":null,"OpenAcc":0,"DOI":"10.1007/s10236-012-0523-y"},"refs":null,"anarec":{"AnaID":220490,"PubliDate":2012,"Pagination":"501-514","XtraPublOfAnaID":null,"ISBN":null,"Volume":"62","Issue":"4","BRefMon":null,"BRefMonRR":null,"BRefXtra":null,"BRefXtraRR":null,"SerBRefID":45486,"SerRR":"Ocean Dynamics. 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