{"id":823,"date":"2010-09-06T03:09:04","date_gmt":"2010-09-06T07:09:04","guid":{"rendered":"http:\/\/mseas.net16.net\/?p=823"},"modified":"2021-07-30T16:43:32","modified_gmt":"2021-07-30T20:43:32","slug":"high-order-schemes-for-2d-unsteady-biogeochemical-ocean-models","status":"publish","type":"post","link":"https:\/\/mseas.mit.edu\/?p=823","title":{"rendered":"High Order Schemes for 2D Unsteady Biogeochemical Ocean Models"},"content":{"rendered":"Accurate numerical modeling of biogeochemical ocean dynamics is essential for numerous applications, including coastal ecosystem science, environmental management and energy, and climate dynamics. Evaluating computational requirements for such often highly nonlinear and multiscale dynamics is critical. To do so, we complete comprehensive numerical analyses, comparing low- to high-order discretization schemes, both in time and space, employing standard and hybrid discontinuous Galerkin finite element methods, on both straight and new curved elements. Our analyses and syntheses focus\r\non nutrient-phytoplankton-zooplankton dynamics under\r\nadvection and diffusion within an ocean strait or\r\nsill, in an idealized 2D geometry. For the dynamics,\r\nwe investigate three biological regimes, one with single\r\nstable points at all depths and two with stable\r\nlimit cycles. We also examine interactions that are\r\ndominated by the biology, by the advection, or that\r\nare balanced. For these regimes and interactions, we study the sensitivity to multiple numerical parameters\r\nincluding quadrature-free and quadrature-based\r\ndiscretizations of the source terms, order of the spatial\r\ndiscretizations of advection and diffusion operators,\r\norder of the temporal discretization in explicit\r\nschemes, and resolution of the spatial mesh, with and\r\nwithout curved elements. A first finding is that both\r\nquadrature-based and quadrature-free discretizations\r\ngive accurate results in well-resolved regions, but the\r\nquadrature-based scheme has smaller errors in underresolved\r\nregions. We show that low-order temporal\r\ndiscretizations allow rapidly growing numerical errors\r\nin biological fields. We find that if a spatial discretization\r\n(mesh resolution and polynomial degree) does not\r\nresolve the solution, oscillations due to discontinuities\r\nin tracer fields can be locally significant for both lowand\r\nhigh-order discretizations. When the solution is\r\nsufficiently resolved, higher-order schemes on coarser\r\ngrids perform better (higher accuracy, less dissipative)\r\nfor the same cost than lower-order scheme on finer\r\ngrids. This result applies to both passive and reactive\r\ntracers and is confirmed by quantitative analyses of\r\ntruncation errors and smoothness of solution fields. To\r\nreduce oscillations in un-resolved regions, we develop\r\na numerical filter that is active only when and where\r\nthe solution is not smooth locally. Finally, we consider\r\nidealized simulations of biological patchiness. Results\r\nreveal that higher-order numerical schemes can maintain\r\npatches for long-term integrations while lowerorder\r\nschemes are much too dissipative and cannot,\r\neven at very high resolutions. Implications for the use\r\nof simulations to better understand biological blooms,\r\npatchiness, and other nonlinear reactive dynamics in\r\ncoastal regions with complex bathymetric features are\r\nconsiderable.","protected":false},"excerpt":{"rendered":"<p>Accurate numerical modeling of biogeochemical ocean dynamics is essential for numerous applications, including coastal ecosystem science, environmental management and energy, and climate dynamics. Evaluating computational requirements for such often highly nonlinear and multiscale dynamics is critical. To do so, we complete comprehensive numerical analyses, comparing low- to high-order discretization schemes, both in time and space, [&hellip;]<\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"open","ping_status":"closed","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[32,37,28,39,5,58,54],"tags":[],"class_list":["post-823","post","type-post","status-publish","format-standard","hentry","category-numerical-ocean-modeling","category-applications-to-ocean-dynamics","category-multiscale-ocean-modeling","category-biogeochemical-physical-interactions","category-publications","category-papers-in-refereed-journals-biogeochemical-physical-interactions","category-papers-in-refereed-journals-multiscale-ocean-modeling"],"_links":{"self":[{"href":"https:\/\/mseas.mit.edu\/index.php?rest_route=\/wp\/v2\/posts\/823","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/mseas.mit.edu\/index.php?rest_route=\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/mseas.mit.edu\/index.php?rest_route=\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/mseas.mit.edu\/index.php?rest_route=\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/mseas.mit.edu\/index.php?rest_route=%2Fwp%2Fv2%2Fcomments&post=823"}],"version-history":[{"count":5,"href":"https:\/\/mseas.mit.edu\/index.php?rest_route=\/wp\/v2\/posts\/823\/revisions"}],"predecessor-version":[{"id":5669,"href":"https:\/\/mseas.mit.edu\/index.php?rest_route=\/wp\/v2\/posts\/823\/revisions\/5669"}],"wp:attachment":[{"href":"https:\/\/mseas.mit.edu\/index.php?rest_route=%2Fwp%2Fv2%2Fmedia&parent=823"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/mseas.mit.edu\/index.php?rest_route=%2Fwp%2Fv2%2Fcategories&post=823"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/mseas.mit.edu\/index.php?rest_route=%2Fwp%2Fv2%2Ftags&post=823"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}