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  5.     <title>UTas ePrints - On the use of random walk models with spatially variable diffusivity</title>
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  14. <meta content="Craig, P.D." name="eprints.creators_name" />
  15. <meta content="Phillips, Helen E." name="eprints.creators_name" />
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  33. <meta content="The random walk technique is commonly used to model diffusion in
  34. the environment. For a constant diffusivity K and model time-step dt.
  35. the random step should be chosen from a distribution with variance
  36. 2Kdt. However, if K varies spatially, this choice of step leads to the
  37. accumulation of particles in regions of low diffusivity. This problem
  38. may be overcome either by the incorporation of an apparent advection
  39. velocity, or by transforming to a coordinate system in which the
  40. diffusivity is constant. The latter technique requires no immediate
  41. approximations, is applicable to any reasonable diffusivity field and is
  42. therefore the preferred approach. In this case, as with constant K, the
  43. random step should be chosen from a normal distribution, for reasons
  44. of both theoretical accuracy and computational efficiency. Three
  45. important aspects of model design are discussed: the selection of the
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  72. accumulation of particles in regions of low diffusivity. This problem
  73. may be overcome either by the incorporation of an apparent advection
  74. velocity, or by transforming to a coordinate system in which the
  75. diffusivity is constant. The latter technique requires no immediate
  76. approximations, is applicable to any reasonable diffusivity field and is
  77. therefore the preferred approach. In this case, as with constant K, the
  78. random step should be chosen from a normal distribution, for reasons
  79. of both theoretical accuracy and computational efficiency. Three
  80. important aspects of model design are discussed: the selection of the
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  196.     <h1 class="ep_tm_pagetitle">On the use of random walk models with spatially variable diffusivity</h1>
  197.     <p style="margin-bottom: 1em" class="not_ep_block"><span class="person_name">Hunter, J.A.</span> and <span class="person_name">Craig, P.D.</span> and <span class="person_name">Phillips, Helen E.</span> (1993) <xhtml:em>On the use of random walk models with spatially variable diffusivity.</xhtml:em> Journal of Computational Physics, 106 (2). pp. 366-376. ISSN 0021-9991</p><p style="margin-bottom: 1em" class="not_ep_block"></p><table style="margin-bottom: 1em" class="not_ep_block"><tr><td valign="top" style="text-align:center"><a href="http://eprints.utas.edu.au/815/1/hunter1993jcp.pdf"><img alt="[img]" src="http://eprints.utas.edu.au/style/images/fileicons/application_pdf.png" border="0" class="ep_doc_icon" /></a></td><td valign="top"><a href="http://eprints.utas.edu.au/815/1/hunter1993jcp.pdf"><span class="ep_document_citation">PDF</span></a> - Full text restricted - Requires a PDF viewer<br />1059Kb</td><td><form method="get" accept-charset="utf-8" action="http://eprints.utas.edu.au/cgi/request_doc"><input value="817" name="docid" accept-charset="utf-8" type="hidden" /><div class=""><input value="Request a copy" name="_action_null" class="ep_form_action_button" onclick="return EPJS_button_pushed( '_action_null' )" type="submit" /> </div></form></td></tr></table><p style="margin-bottom: 1em" class="not_ep_block">Official URL: <a href="http://dx.doi.org/10.1016/S0021-9991(83)71114-9">http://dx.doi.org/10.1016/S0021-9991(83)71114-9</a></p><div class="not_ep_block"><h2>Abstract</h2><p style="padding-bottom: 16px; text-align: left; margin: 1em auto 0em auto">The random walk technique is commonly used to model diffusion in&#13;
  198. the environment. For a constant diffusivity K and model time-step dt.&#13;
  199. the random step should be chosen from a distribution with variance&#13;
  200. 2Kdt. However, if K varies spatially, this choice of step leads to the&#13;
  201. accumulation of particles in regions of low diffusivity. This problem&#13;
  202. may be overcome either by the incorporation of an apparent advection&#13;
  203. velocity, or by transforming to a coordinate system in which the&#13;
  204. diffusivity is constant. The latter technique requires no immediate&#13;
  205. approximations, is applicable to any reasonable diffusivity field and is&#13;
  206. therefore the preferred approach. In this case, as with constant K, the&#13;
  207. random step should be chosen from a normal distribution, for reasons&#13;
  208. of both theoretical accuracy and computational efficiency. Three&#13;
  209. important aspects of model design are discussed: the selection of the&#13;
  210. random number generator, the time step and the total number of&#13;
  211. particles.</p></div><table style="margin-bottom: 1em" border="0" cellpadding="3" class="not_ep_block"><tr><th valign="top" class="ep_row">Item Type:</th><td valign="top" class="ep_row">Article</td></tr><tr><th valign="top" class="ep_row">Additional Information:</th><td valign="top" class="ep_row">http://www.elsevier.com/wps/find/homepage.cws_home</td></tr><tr><th valign="top" class="ep_row">Keywords:</th><td valign="top" class="ep_row">diffusivity&#13;
  212. eddy&#13;
  213. random walk&#13;
  214. </td></tr><tr><th valign="top" class="ep_row">Subjects:</th><td valign="top" class="ep_row"><a href="http://eprints.utas.edu.au/view/subjects/260403.html">260000 Earth Sciences &gt; 260400 Oceanography &gt; 260403 Physical Oceanography</a><br /><a href="http://eprints.utas.edu.au/view/subjects/230116.html">230000 Mathematical Sciences &gt; 230100 Mathematics &gt; 230116 Numerical Analysis</a></td></tr><tr><th valign="top" class="ep_row">Collections:</th><td valign="top" class="ep_row">UNSPECIFIED</td></tr><tr><th valign="top" class="ep_row">ID Code:</th><td valign="top" class="ep_row">815</td></tr><tr><th valign="top" class="ep_row">Deposited By:</th><td valign="top" class="ep_row"><span class="ep_name_citation"><span class="person_name">Dr Helen E Phillips</span></span></td></tr><tr><th valign="top" class="ep_row">Deposited On:</th><td valign="top" class="ep_row">07 Mar 2007</td></tr><tr><th valign="top" class="ep_row">Last Modified:</th><td valign="top" class="ep_row">07 Feb 2008 12:24</td></tr><tr><th valign="top" class="ep_row">ePrint Statistics:</th><td valign="top" class="ep_row"><a target="ePrintStats" href="/es/index.php?action=show_detail_eprint;id=815;">View statistics for this ePrint</a></td></tr></table><p align="right">Repository Staff Only: <a href="http://eprints.utas.edu.au/cgi/users/home?screen=EPrint::View&amp;eprintid=815">item control page</a></p>
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