{"id":3988,"date":"2014-08-21T22:41:54","date_gmt":"2014-08-22T02:41:54","guid":{"rendered":"http:\/\/mseas.mit.edu\/?p=3988"},"modified":"2022-11-22T15:01:37","modified_gmt":"2022-11-22T20:01:37","slug":"high-order-hybrid-discontinuous-galerkin-regional-ocean-modeling-2","status":"publish","type":"post","link":"https:\/\/mseas.mit.edu\/?p=3988","title":{"rendered":"High Order Hybrid Discontinuous Galerkin Regional Ocean Modeling"},"content":{"rendered":"Accurate modeling of physical and biogeochemical dynamics in coastal ocean regions\nis required for multiple scientific and societal applications, covering a wide range\nof time and space scales. However, in light of the strong nonlinearities observed in\ncoastal regions and in biological processes, such modeling is challenging. An important\nsubject that has been largely overlooked is the numerical requirements for\nregional ocean simulation studies. Major objectives of this thesis are to address such\ncomputational questions for non-hydrostatic multiscale flows and for biogeochemical\ninteractions, and to derive and develop numerical schemes that meet these requirements,\nutilizing the latest advances in computational fluid dynamics.\n\nWe are interested in studying nonlinear, transient, and multiscale ocean dynamics\nover complex geometries with steep bathymetry and intricate coastlines, from\nsub-mesoscales to basin-scales. These dynamical interests, when combined with our\nrequirements for accurate, efficient and flexible ocean modeling, led us to develop\nnew variable resolution, higher-order and non-hydrostatic ocean modeling schemes.\nSpecifically, we derived, developed and applied new numerical schemes based on the\nnovel hybrid discontinuous Galerkin (HDG) method in combination with projection\nmethods.\n\nThe new numerical schemes are first derived for the Navier-Stokes equations. To\nensure mass conservation, we define numerical fluxes that are consistent with the discrete\ndivergence equation. To improve stability and accuracy, we derive a consistent\nHDG stability parameter for the pressure-correction equation. We also apply a new\nboundary condition for the pressure-corrector, and show the form and origin of the\nprojection method&#8217;s time-splitting error for a case with implicit diffusion and explicit\nadvection. Our scheme is implemented for arbitrary, mixed-element unstructured\ngrids using a novel quadrature-free integration method for a nodal basis, which is\nconsistent with the HDG method. To prevent numerical oscillations, we design a selective\nhigh-order nodal limiter. We demonstrate the correctness of our new schemes\nusing a tracer advection benchmark, a manufactured solution for the steady diffusion\nand stokes equations, and the 2D lock-exchange problem.\n\nThese numerical schemes are then extended for non-hydrostatic, free-surface,\nvariable-density regional ocean dynamics. The time-splitting procedure using projection\nmethods is derived for non-hydrostatic or hydrostatic, and nonlinear free-surface\nor rigid-lid, versions of the model. We also derive consistent HDG stability parameters\nfor the free-surface and non-hydrostatic pressure-corrector equations to ensure\nstability and accuracy. New boundary conditions for the free-surface-corrector and\npressure-corrector are also introduced. We prove that these conditions lead to consistent\nboundary conditions for the free-surface and pressure proper. To ensure discrete\nmass conservation with a moving free-surface, we use an arbitrary LagrangianEulerian\n(ALE) moving mesh algorithm. These schemes are again verified, this time\nusing a tidal flow problem with analytical solutions and a 3D lock-exchange benchmark.\n\nWe apply our new numerical schemes to evaluate the numerical requirements of\nthe coupled biological-physical dynamics. We find that higher-order schemes are\nmore accurate at the same efficiency compared to lower-order (e.g. second-order)\naccurate schemes when modeling a biological patch. Due to decreased numerical\ndissipation, the higher-order schemes are capable of modeling biological patchiness\nover a sustained duration, while the lower-order schemes can lose significant biomass\nafter a few non-dimensional times and can thus solve erroneous nonlinear dynamics.\n\nFinally, inspired by Stellwagen Bank in Massachusetts Bay, we study the effect\nof non-hydrostatic physics on biological productivity and phytoplankton fields for\ntidally-driven flows over an idealized bank. We find that the non-hydrostatic pressure\nand flows are important for biological dynamics, especially when flows are supercritical.\nThat is, when the slope of the topography is larger than the slope of internal\nwave rays at the tidal frequency. The non-hydrostatic effects increase with increasing\nnonlinearity, both when the internal Froude number and criticality parameter\nincrease. Even in cases where the instantaneous biological productivity is not largely\nmodified, we find that the total biomass, spatial variability and patchiness of phytoplankton\ncan be significantly altered by non-hydrostatic processes.\n\nOur ultimate dynamics motivation is to allow quantitative simulation studies of\nfundamental nonlinear biological-physical dynamics in coastal regions with complex\nbathymetric features such as straits, sills, ridges and shelfbreaks. This thesis develops\nthe necessary numerical schemes that meet the stringent accuracy requirements for\nthese types of flows and dynamics.","protected":false},"excerpt":{"rendered":"<p>Accurate modeling of physical and biogeochemical dynamics in coastal ocean regions is required for multiple scientific and societal applications, covering a wide range of time and space scales. However, in light of the strong nonlinearities observed in coastal regions and in biological processes, such modeling is challenging. An important subject that has been largely overlooked [&hellip;]<\/p>\n","protected":false},"author":2,"featured_media":0,"comment_status":"open","ping_status":"closed","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[42,5,45],"tags":[236,227,235,229],"class_list":["post-3988","post","type-post","status-publish","format-standard","hentry","category-meche-theses","category-publications","category-ph-d-theses","tag-coastal-bank","tag-onr6-1","tag-philex","tag-shelf-it"],"_links":{"self":[{"href":"https:\/\/mseas.mit.edu\/index.php?rest_route=\/wp\/v2\/posts\/3988","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\/2"}],"replies":[{"embeddable":true,"href":"https:\/\/mseas.mit.edu\/index.php?rest_route=%2Fwp%2Fv2%2Fcomments&post=3988"}],"version-history":[{"count":2,"href":"https:\/\/mseas.mit.edu\/index.php?rest_route=\/wp\/v2\/posts\/3988\/revisions"}],"predecessor-version":[{"id":6268,"href":"https:\/\/mseas.mit.edu\/index.php?rest_route=\/wp\/v2\/posts\/3988\/revisions\/6268"}],"wp:attachment":[{"href":"https:\/\/mseas.mit.edu\/index.php?rest_route=%2Fwp%2Fv2%2Fmedia&parent=3988"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/mseas.mit.edu\/index.php?rest_route=%2Fwp%2Fv2%2Fcategories&post=3988"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/mseas.mit.edu\/index.php?rest_route=%2Fwp%2Fv2%2Ftags&post=3988"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}