Discontinuous Galerkin finite element approximation of quasilinear elliptic boundary value problems II: Strongly monotone quasi-Newtonian flows

In this article, we develop the a priori and a posteriori error analysis of hp-version interior penalty discontinuous Galerkin finite element methods for strongly monotone quasi-Newtonian fluid flows in a bounded Lipschitz domain Ω ⊂ ℝd, d = 2, 3. In the latter case, computable upper and lower bounds on the error are derived in terms of a natural energy norm, which are explicit in the local mesh size and local polynomial degree of the approximating finite element method. A series of numerical experiments illustrate the performance of the proposed a posteriori error indicators within an automatic hp-adaptive refinement algorithm.

Flow-R, a model for susceptibility mapping of debris flows and other gravitational hazards at a regional scale

The development of susceptibility maps for debris flows is of primary importance due to population pressure in hazardous zones. However, hazard assessment by process-based modelling at a regional scale is difficult due to the complex nature of the phenomenon, the variability of local controlling factors, and the uncertainty in modelling parameters. A regional assessment must consider a simplified approach that is not highly parameter dependant and that can provide zonation with minimum data requirements. A distributed empirical model has thus been developed for regional susceptibility assessments using essentially a digital elevation model (DEM). The model is called Flow-R for Flow path assessment of gravitational hazards at a Regional scale (available free of charge under http://www.flow-r.org) and has been successfully applied to different case studies in various countries with variable data quality. It provides a substantial basis for a preliminary susceptibility assessment at a regional scale. The model was also found relevant to assess other natural hazards such as rockfall, snow avalanches and floods. The model allows for automatic source area delineation, given user criteria, and for the assessment of the propagation extent based on various spreading algorithms and simple frictional laws. We developed a new spreading algorithm, an improved version of Holmgren's direction algorithm, that is less sensitive to small variations of the DEM and that is avoiding over-channelization, and so produces more realistic extents. The choices of the datasets and the algorithms are open to the user, which makes it compliant for various applications and dataset availability. Amongst the possible datasets, the DEM is the only one that is really needed for both the source area delineation and the propagation assessment; its quality is of major importance for the results accuracy. We consider a 10 m DEM resolution as a good compromise between processing time and quality of results. However, valuable results have still been obtained on the basis of lower quality DEMs with 25 m resolution.

Scheduling of continuous and discontinuous material flows with intermediate storage restrictions

This paper deals with scheduling batch (i.e., discontinuous), continuous, and semicontinuous production in process industries (e.g., chemical, pharmaceutical, or metal casting industries) where intermediate storage facilities and renewable resources (processing units and manpower) of limited capacity have to be observed. First, different storage configurations typical of process industries are discussed. Second, a basic scheduling problem covering the three above production modes is presented. Third, (exact and truncated) branch-and-bound methods for the basic scheduling problem and the special case of batch scheduling are proposed and subjected to an experimental performance analysis. The solution approach presented is flexible and in principle simple, and it can (approximately) solve relatively large problem instances with sufficient accuracy.

Laminar and turbulent nozzle-jet flows and their acoustic near-field

We investigate numerically the effects of nozzle-exit flow conditions on the jet-flow development and the near-field sound at a diameter-based Reynolds number of Re D = 18 100 and Mach number Ma = 0.9. Our computational setup features the inclusion of a cylindrical nozzle which allows to establish a physical nozzle-exit flow and therefore well-defined initial jet-flow conditions. Within the nozzle, the flow is modeled by a potential flow core and a laminar, transitional, or developing turbulent boundary layer. The goal is to document and to compare the effects of the different jet inflows on the jet flow development and the sound radiation. For laminar and transitional boundary layers, transition to turbulence in the jet shear layer is governed by the development of Kelvin-Helmholtz instabilities. With the turbulent nozzle boundary layer, the jet flow development is characterized by a rapid changeover to a turbulent free shear layer within about one nozzle diameter. Sound pressure levels are strongly enhanced for laminar and transitional exit conditions compared to the turbulent case. However, a frequency and frequency-wavenumber analysis of the near-field pressure indicates that the dominant sound radiation characteristics remain largely unaffected. By applying a recently developed scaling procedure, we obtain a close match of the scaled near-field sound spectra for all nozzle-exit turbulence levels and also a reasonable agreement with experimental far-field data.

Magnitude-frequency aspects of alpine debris flows

Based on historic documents the event history for 17 mountain torrents in the Swiss Alps was evaluated. Four classes could be determined for the recurrence interval of the debris flow events. The magnitude is not necessarily dependent on the recurrence interval. The characteristics of the catchment basin (disposition) are mainly controlling the magnitude. In order to evaluate the effects of climatic change on the debris flow activity, knowledge about the magnitude and the frequency are necessary.

The 1987 debris flows in Switzerland: documentation and analysis

A great number of debris flows occurred during the flood catastrophes of the summer of 1987 in the Swiss Alps. Aerial photography, field investigations and eyewitness accounts documented and analysed the events. As an example of the reconstructed major events, the large debris flow in the Varuna valley involved an estimated peak discharge between 400 and 800 m3/s and an event magnitude of 200,000 m3. Several single pulses were observed; the duration of each of them appeared to be not more than a few minutes. Apart from incision into weak bedrock, the maximum erosion depth seemed to depend on the channel gradient. Based on approximately 600 events, typical starting zones and rainfall conditions are discussed with regard to the triggering conditions. Existing and new empirical formulae are proposed to estimate the most important flow parameters. These values are compared to debris flow data from Canada and Japan.

An evaluation of the Cypress Creek watershed for inorganic chemical load as it flows into Lake Houston

Background. The Cypress Creek is one of the main tributaries of Lake Houston, which provides drinking water to 21.4 million customers. Furthermore, the watershed is being utilized for contact and non-contact recreation, such as canoeing, swimming, hiking trail, and picnics. Water along the creek is impacted by numerous wastewater outfalls from both point and non-point sources. As the creek flows into Lake Houston, it carries both organic and inorganic contaminants that may affect the drinking water quality of this important water source reservoir. Objective. This study was carried out to evaluate the inorganic chemical load of the water in Cypress Creek along its entire length, from the headwaters in Waller County and up to the drainage into Lake Houston. The purpose was to determine whether there are hazardous concentrations of metals in the water and what would be the likely sources. Method. Samples were collected at 29 sites along the creek and analyzed for 29 metals, 17 of which were on the Environmental Protection Agency priority pollution list. Public access sites primarily at bridges were used for sample collection. Samples were transported on ice to the University Of Texas School Of Public Health laboratory, spiked with 2 ml HNO3 kept overnight in the refrigerator, and the following day transported to the EPA laboratory for analysis. Analysis was done by EPA Method 200.7-ICP, Method 200.8ICP/MS and Method 245.1-CVAAS. Results. Metals were present above the detection limits at 65% of sites. Concentrations of aluminum, iron, sodium, potassium, magnesium, and calcium, were particularly high at all sites. Aluminum, sodium, and iron concentrations greatly exceeded the EPA secondary drinking water standards at all sites. ^ Conclusion. The recreational water along Cypress Creek is impacted by wastewater from both permitted and non-permitted outfalls, which deposit inorganic substances into the water. Although a number of inorganic contaminants were present in the water, toxic metals regulated by the EPA were mostly below the recommended limits. However, high concentrations of aluminum, sodium, and iron in the Cypress Creek bring forward the issue of unauthorized discharges of salt water from mining, as well as industrial and domestic wastewater.^

Geochemistry of Cretaceous sills and lava flows of ODP Holes 129-800A and 129-802A

On the basis of their respective eruptive environments and chemical characteristics, alkalic dolerite sills from the northern Pigafetta Basin (Site 800) and tholeiitic pillow lavas from the Mariana Basin (Site 802) sampled during Ocean Drilling Program Leg 129 are considered to represent examples of the widespread mid-Cretaceous volcanic event in the western Pacific. Both groups of basic rocks feature mild, low-grade, anoxic smectite-celadonite-carbonate-pyrite alteration; late-stage oxidation is very limited in extent, with the exception of the uppermost sill unit at Site 800. The aphyric and nonvesicular Site 800 alkalic dolerite sills are all well-evolved mineralogically and chemically, being mainly of hawaiite composition, and are similar to ocean island basalts. They are characterized by high contents of incompatible elements (for example, 300-400 ppm Zr), well-fractionated rare earth element patterns ([La/Yb]N 18-21) and HIMU isotopic characters. They probably represent deep-sea, lateral, intrusive off-shoots from nearby seamounts of similar age. The olivine-plagioclase +/- clinopyroxene phyric tholeiitic pillow lavas and thin flows of Site 802 are nonvesicular and quench-textured throughout. Relative to normal-type mid-ocean ridge basalt, they are enriched in large-ion-lithophile elements, exhibit flat (unfractionated) rare earth element patterns and have distinctive (lower) Zr/Nb, Zr/Ta, La/Ta, and Hf/Th ratios. Overall they are compositionally and isotopically similar to the mid-Cretaceous tholeiites of the Nauru basin and the Ontong-Java and Manihiki plateaus. The Site 802 tholeiites differ from the thickened crustal segments of the oceanic plateaus, however, in apparently representing only a thin veneer over the local basement in an off-axis environment.