In this thesis the finite and spectral element methods (FEM and SEM, respectively) applied to
problems in atmospheric simulations are explored through the common thread of Variational
Multiscale Stabilization (VMS). This effort is justified by three main reasons. (i) the recognized
need for new solvers that can efficiently execute on massively parallel architectures ¿a spreading
framework in most fields of computational physics in which numerical weather prediction
(NWP) occupies a prominent position. Element-based methods (e.g. FEM, SEM, discontinuous
Galerkin) have important advantages in parallel code development; (ii) the inherent flexibility of
these methods with respect to the geometry of the grid makes them a great candidate for dynamically
adaptive atmospheric codes; and (iii) the localized diffusion provided by VMS represents
an improvement in the accurate solution of multi-physics problems where artificial diffusion may
fail. Its application to atmospheric simulations is a novel approach within a field of research
that is still open. First, FEM and VMS are described and derived for the solution of stratified
low Mach number flows in the context of dry atmospheric dynamics. The validity of the method
to simulate stratified flows is assessed using standard two- and three-dimensional benchmarks
accepted by NWP practitioners. The problems include thermal and gravity driven simulations.
It will be shown that stability is retained in the regimes of interest and a numerical comparison
against results from the the literature will be discussed. Second, the ability of VMS to stabilize
the FEM solution of advection-dominated problems (i.e. Euler and transport equations) is taken
further by the implementation of VMS as a stabilizing tool for high-order spectral elements with
advection-diffusion problems. To the author¿s knowledge, this is an original contribution to the
literature of high order spectral elements involved with transport in the atmosphere. The problem
of monotonicity-preserving high order methods is addressed by combining VMS-stabilized
SEM with a discontinuity capturing technique. This is an alternative to classical filters to treat
the Gibbs oscillations that characterize high-order schemes. To conclude, a microphysics scheme
is implemented within the finite element Euler solver, as a first step toward realistic atmospheric
simulations. Kessler microphysics is used to simulate the formation of warm, precipitating clouds.
This last part combines the solution of the Euler equations for stratified flows with the solution
of a system of transport equations for three classes of water: water vapor, cloud water, and rain.
The method is verified using idealized two- and three-dimensional storm simulations.
| Identifer | oai:union.ndltd.org:TDX_UPC/oai:www.tdx.cat:10803/112755 |
| Date | 10 December 2012 |
| Creators | Marras, Simone |
| Contributors | Vázquez, Mariano, Jorba Casellas, Oriol |
| Source Sets | Universitat Politècnica de Catalunya |
| Language | English |
| Detected Language | English |
| Type | info:eu-repo/semantics/doctoralThesis, info:eu-repo/semantics/publishedVersion |
| Format | 210 p., application/pdf |
| Source | TDX (Tesis Doctorals en Xarxa) |
| Rights | info:eu-repo/semantics/openAccess, ADVERTIMENT. L'accés als continguts d'aquesta tesi doctoral i la seva utilització ha de respectar els drets de la persona autora. Pot ser utilitzada per a consulta o estudi personal, així com en activitats o materials d'investigació i docència en els termes establerts a l'art. 32 del Text Refós de la Llei de Propietat Intel·lectual (RDL 1/1996). Per altres utilitzacions es requereix l'autorització prèvia i expressa de la persona autora. En qualsevol cas, en la utilització dels seus continguts caldrà indicar de forma clara el nom i cognoms de la persona autora i el títol de la tesi doctoral. No s'autoritza la seva reproducció o altres formes d'explotació efectuades amb finalitats de lucre ni la seva comunicació pública des d'un lloc aliè al servei TDX. Tampoc s'autoritza la presentació del seu contingut en una finestra o marc aliè a TDX (framing). Aquesta reserva de drets afecta tant als continguts de la tesi com als seus resums i índexs. |
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