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

Estudo da evolução dos processos de alteração supergênica de rocha granítica - Granito Independência - Morro do IPA, Porto Alegre, RS

The rocks of the earth's surface are constantly exposed to the action of natural agents such as water, temperature variations, atmospheric gases and the action of living beings. Among the action of living beings, in the urban centers highlight the anthropogenic, which often ends up by degrading natural resources. In this context, understanding the processes of transformation of the rocks, you can understand the genesis and evolution of soils, and improve methods for their recovery. This study was conducted in a profile altered granitic rock located in the urban area of Porto Alegre, where eight samples were collected representing different levels, from rock to soil. The samples were analyzed by X-ray diffraction, by the powder method on whole rock and in the fraction <4 micrometers. The composition was determined by X-ray fluorescence. Fragments of the samples were observed by scanning electron microscopy (secondary electrons). Petrographic and mineralogical studies showed that there is little variation in the mineralogical composition of the vertical profiles, mainly composed of quartz, feldspar, and kaolinite, identified in all horizons, and illite/biotite, identified in saprolitic horizons. Analyzes whit secondary electron images allowed to identify even the presence of halloysite. The exudation of the iron plates of biotite observed in the optical microscope marking the beginning of supergene alteration in granite. X-ray fluorescence data show that the choice of the reference element property to check whether or not the enrichment of elements along the profile is very important since this paper was verified that Aluminum has a movable behavior probably associated with conditions soil acidity.As rochas da superfície terrestre estão permanentemente expostas à ação de agentes naturais, como a água, as variações de temperatura, os gases atmosféricos e a ação dos seres vivos. Dentre a ação dos seres vivos, nos centros urbanos destaca-se a ação antrópica, que por vezes acaba por degradar os recursos naturais. Nesse contexto, entender os processos de transformação das rochas, para que se possa compreender a gênese e evolução dos solos, e assim, aperfeiçoar métodos para sua recuperação, torna-se imprescindível. Este estudo foi desenvolvido em um perfil de alteração de rocha granítica localizado na área urbana de Porto Alegre, onde foram coletadas oito amostras representativas dos diferentes níveis, da rocha ao solo. As amostras foram analisadas por difratometria de raios X (DRX), pelo método do pó na rocha total e na fração < 4 μm. A composição química foi determinada por fluorescência de raios X (FRX). Fragmentos das amostras foram observados no microscópio eletrônico de varredura (elétrons secundários) e no microscópio ótico. Os estudos mineralógicos e petrográficos mostraram a existência de pequena variação composicional vertical no perfil, essencialmente composto por quartzo, feldspato alcalino e caolinita, identificados em todos os horizontes, e ilita/biotita identificadas nos horizontes saprolíticos. As análises através de imagens de elétrons secundários permitiram identificar ainda a presença de haloisita. A exsudação de ferro pelas lamelas da biotita observada no microscópio óptico marca o início da alteração supergênica no granito. Os dados de FRX mostram que a escolha do elemento imóvel de referência para verificar a existência ou não de enriquecimento dos elementos ao longo do perfil é muito importante, pois neste trabalho verificou-se que o alumínio tem um comportamento móvel, provavelmente associado às condições de acidez do solo

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

formation of non-expandable 7 A halloysite during Eocene-Miocene continental weathering at Djebel Debbagh, Algeria: A geochemical and stable-isotope study

International audienc

Role of compressive tectonics on gas charging into the Ordovician sandstone reservoirs in the Sbaa, Algeria : constrained by fluid inclusions and mineralogical data

International audienceStructure- and tectonic-related gas migration into Ordovician sandstone reservoirs and its impact on diagenesis history were reconstructed in two fields in the Sbaa Basin, in SW Algeria. This was accomplished by petrographical observations, fluid inclusion microthermometry and stable isotope geochemistry on quartz, dickite and carbonate cements and veins. Two successive phases of quartz cementation (CQ1 and CQ2) occurred in the reservoirs. Two- phase aqueous inclusions show an increase in temperatures and salinities from the first CQ1 diagenetic phase toward CQ2 in both fields. Microthermometric data on gas inclusions in quartz veins reveal the presence of an average of 92 ± 5 mole% of CH4 considering a CH4-CO2 system, which is similar to the present-day gas composition in the reservoirs. The presence of primary methane inclusions in early quartz overgrowths and in quartz and calcite veins suggests that hydrocarbon migration into the reservoir occurred synchronically with early quartz cementation in the sandstones located near the contact with the Silurian gas source rock at 100-140°C during the Late Carboniferous period and the late Hercynian episode fracturing at temperatures between 117 and 185°C, which increased in the NW-direction of the basin. During the fracture filling, three main types of fluids were identified with different salinities and formation temperatures. A supplementary phase of higher fluid temperature (up to 226°C) recorded in late quartz, and calcite veins is related to a Jurassic thermal event. The occurrence of dickite cements close to the Silurian base near the main fault areas in both fields is mainly correlated with the sandstones where the early gas was charged. It implies that dickite precipitation is related to acidic influx. Late carbonate cements and veins (calcite - siderite - ankerite and strontianite) occurred at the same depths resulting from the same groundwater precipitation. The absence

Role of compressive tectonics on gas charging into the Ordovician sandstone reservoirs in the Sbaa, Algeria : constrained by fluid inclusions and mineralogical data

International audienceStructure- and tectonic-related gas migration into Ordovician sandstone reservoirs and its impact on diagenesis history were reconstructed in two fields in the Sbaa Basin, in SW Algeria. This was accomplished by petrographical observations, fluid inclusion microthermometry and stable isotope geochemistry on quartz, dickite and carbonate cements and veins. Two successive phases of quartz cementation (CQ1 and CQ2) occurred in the reservoirs. Two- phase aqueous inclusions show an increase in temperatures and salinities from the first CQ1 diagenetic phase toward CQ2 in both fields. Microthermometric data on gas inclusions in quartz veins reveal the presence of an average of 92 ± 5 mole% of CH4 considering a CH4-CO2 system, which is similar to the present-day gas composition in the reservoirs. The presence of primary methane inclusions in early quartz overgrowths and in quartz and calcite veins suggests that hydrocarbon migration into the reservoir occurred synchronically with early quartz cementation in the sandstones located near the contact with the Silurian gas source rock at 100-140°C during the Late Carboniferous period and the late Hercynian episode fracturing at temperatures between 117 and 185°C, which increased in the NW-direction of the basin. During the fracture filling, three main types of fluids were identified with different salinities and formation temperatures. A supplementary phase of higher fluid temperature (up to 226°C) recorded in late quartz, and calcite veins is related to a Jurassic thermal event. The occurrence of dickite cements close to the Silurian base near the main fault areas in both fields is mainly correlated with the sandstones where the early gas was charged. It implies that dickite precipitation is related to acidic influx. Late carbonate cements and veins (calcite - siderite - ankerite and strontianite) occurred at the same depths resulting from the same groundwater precipitation. The absence

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

Local and Global Search Methods for Design in Aeronautics.

International audienceOptimization is used at all stages of aircraft design. In the early phases (also called preliminary or conceptual design) multicriteria Pareto optimization [11] based on heuristic laws is carried out. Conversely, in the late design phases, accurate structural and aerodynamics predictions are required to steer small changes of a baseline shape through mono-objective optimization. This article is devoted to the local and global optimization methods actually used during this second part of the design process.Through discretization, parametrization, and numerical simulation, the design problem can be formulated mathematically as a finite-dimensional optimization. Hence a good knowledge of global and local optimization algorithms is important to aerodynamic design engineers. The classical algorithms which are currently used at Onera for shape design are presented. Besides, many local optimization algorithms require the gradient of the functions of interest with respect to the design parameters. The different ways tocompute those derivatives - often called “sensitivities” - are also described. Numerous 2D and 3D applications were dealt with at Onera using the methods described; they are presented in a companion article [14] and also briefly described in a course [1]

I/O Post- and Co-Processing for High-Order Methods

While the exascale computing era is approaching, the growing gap between computing resources and IO bandwidth for massively parallel simulations has already become a major bottleneck for the scientific discovery process. In this context, various strategies to enable and accelerate the analysis of data produced by massively parallel high-order methods are presented, with an emphasis on in-situ visualization and co-processing techniques. First, a library of parallel procedures is presented for an efficient collection of turbulence statistics within the framework of a modal discontinuous Galerkin method. Afterwards, an acoustic co-processing strategy is presented whereby sound radiation calculations are performed concurrently with CFD calculations in order to avoid the need to store prohibitive amount of data. Finally, an open-source and scalable post-hoc visualization and processing tool dedicated to the analysis of large data sets produced by high order methods is first presented. This post-hoc processing tool has then been extended to a co-processing interface which enables live in-situ visualization and analysis of high-order solutions produced by massively parallel simulations