Comparative Study of Inner-Outer Krylov Solvers for Linear Systems in Structured and High-Order Unstructured CFD Problems

Advanced Krylov subspace methods are investigated for the solution of linear systems arising from an adjoint-based aerodynamic shape optimization problem. A special attention is paid for the flexible inner-outer GMRES strategy combined with most relevant preconditioning strategies and deflation techniques. The choice of this specific class of Krylov solvers for solving challenging problems is based on its outstanding convergence properties. Moreover, parallel scalability is improved by globalizing the preconditioning phase through an additive domain decomposition technique. However, maintaining the performance of the preconditioner may be challenging since scalability and efficiency of a preconditioning technique are properties often antagonistic to each other. We demonstrate how flexible inner-outer Krylov methods are able to overcome this critical issue. A numerical comparative study is provided on the supercritical OAT15A airfoil in turbulent flow under transonic regime conditions using a Finite Volume method (FV) and a High-Order Discontinuous Galerkin (DG) one. Based on this representative problem a discussion of the recommended numerical practices is proposed

A cloritização na Mina Uruguai, Minas do Camaquã, RS, Brasil

The area of Camaquã Mines is part of the camaquã basin, which has NE-NW directions and is filled out by silliciclastics sediments interbedded with volcanic rocks. Chlorite is the most abundant clay mineral in the area and appears in high amount in the halos of hydrothermal alteration present in the host's mineralization rocks. This work consists on the chlorite's petrologic, chemical and structural characterization, supplying important information on different processes and formation conditions of the hydrothermal environment. The following procedures were made: optical petrography, X-ray diffraction, difractograms modeling through the Reynolds Newmod© program, and scanning electron microscopy ( secondary electrons and microanalysis - EDS) in representative samples of the different identified hydrothermal alteration zones. Chlorites are present under three different tendencies: Chlorite I takes place with a pervasive aspect over the matrix rocks located near the mineralized veins; it is classified as Fe-chlinoclore, presents fraction ˂1 µm predominance of plytype IIb and a Mg2+  enrichment in the fraction of  ˂10 µm predominance of polytype Ib (90°) and Fetotal enrichment. Chlorite II occurs as veins filling out small fractures; it is classified as Chamosite and presents structural polytype IIb. Chlorite III occurs altering detrital minerals; it is classified as Mg-chamosite. The variation on the amount of Fe of the chlorites generated over the hydrothermal processes ( Chlorite I ˂10 µm and Chlorite II) indicates the occurrence of at least two pulses in the process of the hydrothermal alteration: one is responsible for the great matrix and clasts alternation and the other one for the generation of the late veins. The variation in the amount of Fetotal of the two different responsible fluids for the crystallization of the chlorites is was quite more enriched in iron than the early fluid that crystallized Chlorite I ˂10 µm.A região das Minas do Camaquã é a parte constituinte da Bacia do Camaquã, a qual possui direção NE-NW e é preenchida por sedimentos siliciclásticos intercalados com rochas vulcânicas. A clorita é o argilomineral mais abundante da área, ocorrendo em grande quantidade nos halos de alteração hidrotermal presentes nas rochas encaixantes nas mineralizações na Mina Uruguai. Este trabalho consiste na caracterização petrológica, química e estrutural das cloritas, que fornece importante informações sobre diferentes processos e condições de formação do ambiente hidrotermal. Para isso se realizou petrografia óptica, difratometria de raios X, modelamento dos difratogramas através do programa Reynolds Newmod © e  microscopia eletrônica de varredura (elétrons secundários e micro-análises por EDS) em amostras representativas de diferentes zonas de alteração hidrotermal identificadas. As cloritas se apresentam com três diferentes tendências: a Clorita I ocorre com aspecto pervasivo sobre matriz das rochas localizadas próximos aos filões mineralizados; é classificada como Fe-clinocloro, apresenta na fração ˂1 µm predominância do politipo IIb e um enriquecimento em Mg2+  e na fração ˂10 µm predominância do politipo Ib (90°) e enriquecimento em Fetotal .  A Clorita II ocorre com veios preenchendo pequenas fraturas; é classificada como Chamosita e apresenta politipo estrutural IIb. A Clorita III ocorre alterando minerais detríticos sendo classificada como Mg-Chamosita. A variação na quantidade de ferro das cloritas geradas por processos hidrotermais ( Clorita I ˂10 µm e Clorita II) fornece indícios da ocorrência de pelo menos dois pulsos no processo de alteração hidrotermal: um responsável pela intensa alteração da matriz e dos clastos das rochas e outro responsável pela geração de veios tardios. A variação na quantidade Fetotal  dos dois diferentes fluidos responsáveis pela cristalização das cloritas fica evidenciada pela associação de co-genecidade da Clorita II com a hematita, mostrando que o fluido final foi muito mais enriquecido em ferro que o fluido precoce cristalizou a Clorita I ˂10 µm

Role of hydrodynamic factors in controlling the formation and location of unconformity-related uranium deposits: insights from reactive-flow modeling

The role of hydrodynamic factors in controlling the formation and location of unconformity-related uranium (URU) deposits in sedimentary basins during tectonically quiet periods is investigated. A number of reactive-flow modeling experiments at the deposit scale were carried out by assigning different dip angles and directions to a fault and various permeabilities to hydrostratigraphic units). The results show that the fault dip angle and direction, and permeability of the hydrostratigraphic units govern the convection pattern, temperature distribution, and uranium mineralization. Avertical fault results in uranium mineralization at the bottom of the fault within the basement, while a dipping fault leads to precipitation of uraninite below the unconformity either away from or along the plane of the fault, depending on the fault permeability. A more permeable fault causes uraninite precipitates along the fault plane,whereas a less permeable one gives rise to the precipitation of uraninite away from it. No economic ore mineralization can form when either very low or very high permeabilities are assigned to the sandstone or basement suggesting that these units seem to have an optimal window of permeability for the formation of uranium deposits. Physicochemical parameters also exert an additional control in both the location and grade of URU deposits. These results indicate that the difference in size and grade of different URU deposits may result from variation in fluid flow pattern and physicochemical conditions, caused by the change in structural features and hydraulic properties of the stratigraphic units involved

Construction of Modern Robust Nodal Discontinuous Galerkin Spectral Element Methods for the Compressible Navier-Stokes Equations

Discontinuous Galerkin (DG) methods have a long history in computational physics and engineering to approximate solutions of partial differential equations due to their high-order accuracy and geometric flexibility. However, DG is not perfect and there remain some issues. Concerning robustness, DG has undergone an extensive transformation over the past seven years into its modern form that provides statements on solution boundedness for linear and nonlinear problems. This chapter takes a constructive approach to introduce a modern incarnation of the DG spectral element method for the compressible Navier-Stokes equations in a three-dimensional curvilinear context. The groundwork of the numerical scheme comes from classic principles of spectral methods including polynomial approximations and Gauss-type quadratures. We identify aliasing as one underlying cause of the robustness issues for classical DG spectral methods. Removing said aliasing errors requires a particular differentiation matrix and careful discretization of the advective flux terms in the governing equations.Comment: 85 pages, 2 figures, book chapte

Gossan mineralogy, textures, and gold enrichment over the Au (As, Bi, Ag) deposit in the Buracão Area (Brasília Fold Belt, Brazil): Implications for gold prospecting in weathering profiles

International audienc

P–T–X conditions on the genesis of orogenic Au (As, Bi, Ag) deposit in metasedimentary rocks of the Buracão Area, Araí Group, Brasília Fold Belt, Brazil

International audienceThe orogenic Au (As, Bi, Ag) mineralization (up to 31 g/t) of the Buracão area is hosted in the metasedimentary Paleo–Mesoproterozoic Traíras Formation, Araí Group, Brasília Fold Belt, Brazil. In order to discuss the P–T–X conditions that generated this mineralization, we present mineralogical, geochemical and fluid inclusion data of veins, gold and wall rocks. Coupled with previous structural data these additional data allow us to link metamorphism and deformation with fluid migration and ore genesis. The integration of fluid inclusion microthermometry with mineral geothermobarometers and structures show that rocks of the study area evolved from: (i) syn–D1a metamorphic peak (400–560 °C, <6 kbar), through to the (ii) development of syn–D1b type I barren veins from low salinity H2O–NaCl fluids during syn– to late–metamorphic peak; and to the (iii) development of syn–D2a type II veins with the pyritic ore precipitation from low to high salinity H2O–CO2–CH4–NaCl ± HCO3 fluids during post–metamorphic peak (345–285 °C, 2.7–1.6 kbar).The high fineness gold nuggets accompanied by As, Bi and Ag within pyrite–arsenopyrite–bismuthinite association in the pyritic ore allows the Buracão area to be classified as “a gold-only orogenic ore deposit”. Fluid inclusion compounds and the enrichment of As, Bi, Pb, Cu, Te, Se and Ag in pyrite from the pyritic ore point out to metamorphism of carbonaceous phyllites and carbonate rocks of the Traíras Formation as a source for ore–forming fluids. We suggest that sulfur and gold in these fluids were derived by metamorphism of sedimentary rocks and conversion of pyrite into pyrrhotite in a metamorphic–hydrothermal system. The Au(HS)2−–bearing fluids percolated along intrabasinal D2a regional shear zones through the Traíras Formation towards the Buracão area, where they precipitated type II ore–bearing veins within local structures. The ore precipitation was induced by contrasting fO2–fS2 related to the interaction between the sulfur-bearing fluid and host magnetite–graphite phyllites. The lithological control is represented by a series of reactions such as 2FeO(in silicates/magnetite) + 4Au(HS)2−(aq) + 4H+(aq) ↔ 2FeS2(s) + 4Au(s) + 4H2S(aq) + 2H2O(l).The deposits of the Buracão area and other orogenic gold deposits hosted in metasedimentary rocks in the Brasília Fold Belt and worldwide confirm the potential of ore genesis in zones that do not show any relation with (meta)igneous rocks, thus, expanding the exploration possibilities in metasedimentary successions

Implication of 40Ar/39Ar–petrochronology in the Buracão orogenic gold deposit for tectonic and low-temperature evolution of the northern Brasília Fold Belt, Brazil

International audienceThe 40Ar/39Ar ages (muscovite and biotite) and P-T estimations presented here allow us to reconstruct the Pressure–Temperature–time (P–T–t) path from the metamorphic peak to the generation of the orogenic Au (As, Bi, Ag) mineralization in the Buracão area. The application of software-based pseudosections for bulk phyllite composition allows us to better recognize three main stages in the P-T-t path. Rocks from the study area evolved from (i) syn-D1a greenschist metamorphic peak (T = 480–550 °C and P < 4.0 kbar) attained at ca. 538–530 Ma during the W-E shortening related to local D1 deformational stage, which is regionally reported in the external domain of the northern Brasilia Fold Belt. These younger ages, compared to those of mafic and felsic granulites from the northernmost internal domain west of the study area (ca. 610–570 Ma), indicate that the metamorphic peak in the external domain was attained after the internal domain. The (ii) syn-D1b barren type I quartz vein formation (T = 510–260 °C and P < 4.0 kbar) at ca. 531–525 Ma; and (iii) syn-D2a ore-bearing type II quartz vein formation and gold mineralization (T = 345–285 °C and P = 2.7–1.6 kbar) at ca. 522–515 Ma suggest that low temperature may represent cooling P-T conditions of the peripheral supracrustal cover. Moreover, the diachronicity between the local metamorphic peak and the gold mineralization (22 M.y.) is consistent with the structural relationship between gold veins and post-metamorphic peak D2a high deformation zones, which may have acted as fluid corridors through the metasedimentary pile. These features are coherent with the time span observed in several orogenic gold deposits worldwide, especially those associated with high-angle transpressive shear zones developed in the late stages of orogeny. The combination of the Ar–Ar petrochronology with previous published fluid reconstruction and tectonic data suggests metal-rich fluid percolated along regional shear zones through the Traíras Formation under post-metamorphic peak conditions. This regional tectonic and chronology might be useful for geodynamical reconstruction and as a prospection guide in poorly studied orogenic gold of the area

Adaptive modeling and numerical approximation for a simple example of multiscale hyperbolic relaxation system

The present work considers the mathematical and numerical analysis of a new adaptive goal-oriented strategy based on local hpm discontinuous Galerkin (DG) method (h for grid, p for accuracy of shape function and m for model). In order to perform an exhaustive analysis, we consider steady-state solutions to the one-dimensional linear hyperbolic system with multiple relaxation times ε ( x ) : ∂t uε+∂x vε = 0, x ∈[ 0,L ] , t >0, ∂t v ε +a2 ∂x uε = −1/ε ( x ) (v ε−buε ) , (1) with L> 0 , a , b given constants satisfying 0<∣b∣< a and prescribed initial and boundary conditions [1]. The above system, for which the associated equilibrium equation reads ∂t u+ ∂x bu= 0, t > 0 (2), may be viewed as a simple model of a hierarchy of PDE systems arranged according to a cascade of relaxation mechanisms. For instance, such relaxation systems are involved in the study of multiphase flows or multiscale coupling problems. In regions where ε is small, the numerical approximation of the full system (1) may become very costly and a strategy to overcome this difficulty may consist in approximating the associated steady-state equilibrium equation. According to the main features of the flow and to the required accuracy of the description, the model, coarse (2) or fine (1), has to be locally adapted for computational efficiency. Then, these different models have to be appropriately coupled at some interfaces [2]. The automatic choice of the appropriate model requires model adaptation procedures [3] where the position of the interface has to be optimized in such a way that in the region where one computes the coarse model, the model error (expressed in term of output functionals) between the fine and coarse models does not exceed some given tolerance. Nevertheless, only an approximation of the adapted model is known in practice, thus the approximation involves both a model and a discretization error [4]. These two kinds of errors have to be localized for the model and numerical adaptation procedure. The main goal of this work is to understand how the error of our hpm DG method depends on the relaxation parameter, the boundary layer effects and the coupling interface layer effects in order to validate our approach. Special emphasis is given to the theoretical (PDE level) study of the modeling error. Numerical experiments will be considered to assess the performances of the present method

New data on mantle metasomatism beneath the Deves, France

1 page(s