Hamiltonian discontinuous Galerkin FEM for linear, rotating incompressible Euler equations: inertial waves

A discontinuous Galerkin finite element method (DGFEM) has been developed and tested for linear, three-dimensional, rotating incompressible Euler equations. These equations admit complicated wave solutions. The numerical challenges concern: (i) discretisation of a divergence-free velocity field; (ii) discretisation of geostrophic boundary conditions combined with no-normal flow at solid walls; (iii) discretisation of the conserved, Hamiltonian dynamics of the inertial-waves; and, (iv) large-scale computational demands owing to the three-dimensional nature of inertial-wave dynamics and possibly its narrow zones of chaotic attraction. These issues have been resolved: (i) by employing Dirac’s method of constrained Hamiltonian dynamics to our DGFEM for linear, compressible flows, thus enforcing the incompressibility constraints; (ii) by enforcing no-normal flow at solid walls in a weak form and geostrophic tangential flow —along the wall; (iii) by applying a symplectic time discretisation; and, (iv) by combining PETSc’s linear algebra routines with our high-level software. We compared our simulations with exact solutions of three-dimensional compressible and incompressible flows, in (non)rotating periodic and partly periodic cuboids (Poincar´e waves). Additional verifications concerned semi-analytical eigenmode solutions in rotating cuboids with solid walls

Error analysis of a continuous-discontinuous Galerkin finite element method for generalized 2D vorticity dynamics

A detailed a priori error estimate is provided for a continuous-discontinuous Galerkin finite element method suitable for two-dimensional geophysical flows. Special attention is given to derive estimates which require only minimal smoothness in the vorticity field

Two fluid space-time discontinuous Galerkin finite element method. Part I: numerical algorithm

A novel numerical method for two fluid flow computations is presented, which combines the space-time discontinuous Galerkin finite element discretization with the level set method and cut-cell based interface tracking. The space-time discontinuous Galerkin (STDG) finite element method offers high accuracy, an inherent ability to handle discontinuities and a very local stencil, making it relatively easy to combine with local {\it hp}-refinement. The front tracking is incorporated via cut-cell mesh refinement to ensure a sharp interface between the fluids. To compute the interface dynamics the level set method (LSM) is used because of its ability to deal with merging and breakup. Also, the LSM is easy to extend to higher dimensions. Small cells arising from the cut-cell refinement are merged to improve the stability and performance. The interface conditions are incorporated in the numerical flux at the interface and the STDG discretization ensures that the scheme is conservative as long as the numerical fluxes are conservative

A space-time discontinuous Galerkin finite element method for two-fluid problems

A space-time discontinuous Galerkin finite element method for two fluid flow problems is presented. By using a combination of level set and cut-cell methods the interface between two fluids is tracked in space-time. The movement of the interface in space-time is calculated by solving the level set equation, where the interface geometry is identified with the 0-level set. To enhance the accuracy of the interface approximation the level set function is advected with the interface velocity, which for this purpose is extended into the domain. Close to the interface the mesh is locally refined in such a way that the 0-level set coincides with a set of faces in the mesh. The two fluid flow equations are solved on this refined mesh. The procedure is repeated until both the mesh and the flow solution have converged to a reasonable accuracy.\ud The method is tested on linear advection and Euler shock tube problems involving ideal gas and compressible bubbly magma. Oscillations around the interface are eliminated by choosing a suitable interface flux

Investigation of the surface structure and activity of molybdenum oxide-containing catalysts : I. An infrared study of the surface structure of molybdena-alumina catalysts

A comparison has been made of the infrared spectra of alumina with molybdenum oxide-alumina in both the oxidized and reduced forms. In the case of molybdena-alumina prepared via adsorption of gaseous MoO2(OH)2, the spectra show that a practically complete monolayer of Mo6+ oxide covers the alumina. After reduction with hydrogen the hydroxyls of the carrier appear. From the reversibility of reduction and oxidation under mild conditions it has been established that the reduced oxide is present as an interrupted monolayer

Sticks, balls or a ribbon? Results of a formative user study with bioinformaticians

User interfaces in modern bioinformatics tools are designed for experts. They are too complicated for\ud novice users such as bench biologists. This report presents the full results of a formative user study as part of a\ud domain and requirements analysis to enhance user interfaces and collaborative environments for\ud multidisciplinary teamwork. Contextual field observations, questionnaires and interviews with bioinformatics\ud researchers of different levels of expertise and various backgrounds were performed in order to gain insight into\ud their needs and working practices. The analysed results are presented as a user profile description and user\ud requirements for designing user interfaces that support the collaboration of multidisciplinary research teams in\ud scientific collaborative environments. Although the number of participants limits the generalisability of the\ud findings, the combination of recurrent observations with other user analysis techniques in real-life settings\ud makes the contribution of this user study novel

Situational Awareness Support to Enhance Teamwork in Collaborative Environments

Modern collaborative environments often provide an overwhelming amount of visual information on multiple displays. The multitude of personal and shared interaction devices leads to lack of awareness of team members on ongoing activities, and awareness of who is in control of shared artefacts. This research addresses the situational awareness (SA) support of multidisciplinary teams in co-located collaborative environments. This work aims at getting insights into design and evaluation of large displays systems that afford SA and effective teamwork

A singlet-triplet extension for the Higgs search at LEP and LHC

We describe a simple extension of the standard model, containing a scalar singlet and a triplet fermion. The model can explain the possible enhancement in the decay $H \rightarrow \gamma \gamma$ at the LHC together with the excess found in the Higgs boson search at LEP2. The structure of the model is motivated by a recent argument, that was used to explain the number of fermion generations. For the sake of completenes we also considered the contributions from higher multiplets.Comment: 12 pages, 2 figure

Harmonic generation of noble-gas atoms in the Near-IR regime using ab-initio time-dependent R-matrix theory

We demonstrate the capability of ab-initio time-dependent R-matrix theory to obtain accurate harmonic generation spectra of noble-gas atoms at Near-IR wavelengths between 1200 and 1800 nm and peak intensities up to 1.8 X 10(14) W/cm(2) . To accommodate the excursion length of the ejected electron, we use an angular-momentum expansion up to Lmax = 279. The harmonic spectra show evidence of atomic structure through the presence of a Cooper minimum in harmonic generation for Kr, and of multielectron interaction through the giant resonance for Xe. The theoretical spectra agree well with those obtained experimentally.Comment: 6 pages, 5 figure