Optimisation de la méthode des éléments finis mixtes hybrides pour la modélisation des écoulements variablement saturés

Parmi les méthodes de résolution numérique utilisées en mécanique, la méthode des éléments finis mixtes hybrides constitue une approche récente et performante. Certaines techniques, notamment la condensation de la masse et le raffinement fictif, permettent d’améliorer la précision et la rapidité de cette méthode. L’illustration est réalisée pour des problèmes d’écoulements en milieux poreux variablement saturés qui sont décrits selon une approche mécaniste par l’équation de Richards

Albiglutide and cardiovascular outcomes in patients with type 2 diabetes and cardiovascular disease (Harmony Outcomes): a double-blind, randomised placebo-controlled trial

Background: Glucagon-like peptide 1 receptor agonists differ in chemical structure, duration of action, and in their effects on clinical outcomes. The cardiovascular effects of once-weekly albiglutide in type 2 diabetes are unknown. We aimed to determine the safety and efficacy of albiglutide in preventing cardiovascular death, myocardial infarction, or stroke. Methods: We did a double-blind, randomised, placebo-controlled trial in 610 sites across 28 countries. We randomly assigned patients aged 40 years and older with type 2 diabetes and cardiovascular disease (at a 1:1 ratio) to groups that either received a subcutaneous injection of albiglutide (30–50 mg, based on glycaemic response and tolerability) or of a matched volume of placebo once a week, in addition to their standard care. Investigators used an interactive voice or web response system to obtain treatment assignment, and patients and all study investigators were masked to their treatment allocation. We hypothesised that albiglutide would be non-inferior to placebo for the primary outcome of the first occurrence of cardiovascular death, myocardial infarction, or stroke, which was assessed in the intention-to-treat population. If non-inferiority was confirmed by an upper limit of the 95% CI for a hazard ratio of less than 1·30, closed testing for superiority was prespecified. This study is registered with ClinicalTrials.gov, number NCT02465515. Findings: Patients were screened between July 1, 2015, and Nov 24, 2016. 10 793 patients were screened and 9463 participants were enrolled and randomly assigned to groups: 4731 patients were assigned to receive albiglutide and 4732 patients to receive placebo. On Nov 8, 2017, it was determined that 611 primary endpoints and a median follow-up of at least 1·5 years had accrued, and participants returned for a final visit and discontinuation from study treatment; the last patient visit was on March 12, 2018. These 9463 patients, the intention-to-treat population, were evaluated for a median duration of 1·6 years and were assessed for the primary outcome. The primary composite outcome occurred in 338 (7%) of 4731 patients at an incidence rate of 4·6 events per 100 person-years in the albiglutide group and in 428 (9%) of 4732 patients at an incidence rate of 5·9 events per 100 person-years in the placebo group (hazard ratio 0·78, 95% CI 0·68–0·90), which indicated that albiglutide was superior to placebo (p<0·0001 for non-inferiority; p=0·0006 for superiority). The incidence of acute pancreatitis (ten patients in the albiglutide group and seven patients in the placebo group), pancreatic cancer (six patients in the albiglutide group and five patients in the placebo group), medullary thyroid carcinoma (zero patients in both groups), and other serious adverse events did not differ between the two groups. There were three (<1%) deaths in the placebo group that were assessed by investigators, who were masked to study drug assignment, to be treatment-related and two (<1%) deaths in the albiglutide group. Interpretation: In patients with type 2 diabetes and cardiovascular disease, albiglutide was superior to placebo with respect to major adverse cardiovascular events. Evidence-based glucagon-like peptide 1 receptor agonists should therefore be considered as part of a comprehensive strategy to reduce the risk of cardiovascular events in patients with type 2 diabetes. Funding: GlaxoSmithKline

Modélisation des écoulements en milieux poreux non saturés par la méthode des éléments finis mixtes hybrides

Cette étude traite de la modélisation des écoulements d'eau en milieux poreux non saturés. Après avoir caractérisé le domaine d'étude, le modèle déterministe fondé sur l'équation non linéaire de Richards est décrit. Ses limites et d'autres alternatives de modélisation sont évoquées. La méthode des éléments finis mixtes hybrides est présentée et une technique originale de condensation de la masse est proposée pour éviter l'apparition d'oscillations non physiques, notamment lors de la simulation de fronts raides d'infiltration. L'estimation de la conductivité relative, à l'échelle de chaque maille du domaine discrétisé, est un aspect essentiel pour améliorer la précision des résultats. Différentes formulations sont décrites, et les comparaisons effectuées sur de nombreux cas tests conduisent à privilégier la moyenne pondérée. Une partie est également consacrée à la gestion des non linéarités. La forme mixte de l'équation de Richards est conservée, et les investigations aboutissent à un algorithme de sélection de la variable de résolution. Concernant la gestion du temps, les méthodes heuristiques traditionnelles peuvent être avantageusement remplacées par des méthodes a priori, qui relient le pas de temps à un calcul d'erreur temporelle. La méthode d'extrapolation sur l'ordre peut alors être efficacement combinée à un contrôleur intégral. Dans la dernière partie de ce mémoire, toutes les optimisations étudiées dans un contexte monodimensionnel sont généralisées dans un algorithme adapté aux écoulements bidimensionnels. Des cas tests sont proposés pour étudier son efficacité par rapport à des méthodes standards.This study deals with unsaturated water flow modeling. After characterizing the considered porous media, the deterministic model based on Richards equation is described. Its limits and alternative approaches are mentioned. The mixed hybrid finite element method is presented and an original mass lumping technique is proposed to avoid unphysical oscillations, that could appear when sharp infiltration fronts are simulated. Estimation of relative conductivity on each cell of the discretized domain is an essential aspect to improve the results accuracy. Various formulations are depicted. Comparisons performed on several test cases show that the weighted formulation should be preferred. Another part is also devoted to non linearities management. The mixed form of Richards equation is kept. According to our investigations, the variable switching algorithm is the most efficient technique. Concerning the time step control, heuristic techniques could valuably be replaced by a priori methods, which establish a link between the temporal error and the time step size. Order extrapolation method can be efficiently combined with an integral controller. In the last part of this manuscript, all 1D optimisations are generalized in a 2D algorithm. Test cases are proposed to estimate its efficiency compared to classical methods

Modélisation des écoulements en milieux poreux non saturés par la méthode des éléments finis mixtes hybrides

Cette étude traite de la modélisation des écoulements d'eau en milieux poreux non saturés. Après avoir caractérisé le domaine d'étude, le modèle déterministe fondé sur l'équation non linéaire de Richards est décrit. Ses limites et d'autres alternatives deThis study deals with unsaturated water flow modeling. After characterizing the considered porous media, the deterministic model based on Richards equation is described. Its limits and alternative approaches are mentioned. The mixed hybrid finite elemen

Modélisation des écoulements en milieux poreux non saturés par la méthode des éléments finis mixtes hybrides

Cette étude traite de la modélisation des écoulements d eau en milieux poreux non saturés. Après avoir caractérisé le domaine d étude, le modèle déterministe fondé sur l équation non linéaire de Richards est décrit. Ses limites et d autres alternatives de modélisation sont évoquées. La méthode des éléments finis mixtes hybrides est présentée et une technique originale de condensation de la masse est proposée pour éviter l apparition d oscillations non physiques, notamment lors de la simulation de fronts raides d infiltration. L estimation de la conductivité relative, à l échelle de chaque maille du domaine discrétisé, est un aspect essentiel pour améliorer la précision des résultats. Différentes formulations sont décrites, et les comparaisons effectuées sur de nombreux cas tests conduisent à privilégier la moyenne pondérée. Une partie est également consacrée à la gestion des non linéarités. La forme mixte de l équation de Richards est conservée, et les investigations aboutissent à un algorithme de sélection de la variable de résolution. Concernant la gestion du temps, les méthodes heuristiques traditionnelles peuvent être avantageusement remplacées par des méthodes a priori, qui relient le pas de temps à un calcul d erreur temporelle. La méthode d extrapolation sur l ordre peut alors être efficacement combinée à un contrôleur intégral. Dans la dernière partie de ce mémoire, toutes les optimisations étudiées dans un contexte monodimensionnel sont généralisées dans un algorithme adapté aux écoulements bidimensionnels. Des cas tests sont proposés pour étudier son efficacité par rapport à des méthodes standards.This study deals with unsaturated water flow modeling. After characterizing the considered porous media, the deterministic model based on Richards equation is described. Its limits and alternative approaches are mentioned. The mixed hybrid finite element method is presented and an original mass lumping technique is proposed to avoid unphysical oscillations, that could appear when sharp infiltration fronts are simulated. Estimation of relative conductivity on each cell of the discretized domain is an essential aspect to improve the results accuracy. Various formulations are depicted. Comparisons performed on several test cases show that the weighted formulation should be preferred. Another part is also devoted to non linearities management. The mixed form of Richards equation is kept. According to our investigations, the variable switching algorithm is the most efficient technique. Concerning the time step control, heuristic techniques could valuably be replaced by a priori methods, which establish a link between the temporal error and the time step size. Order extrapolation method can be efficiently combined with an integral controller. In the last part of this manuscript, all 1D optimisations are generalized in a 2D algorithm. Test cases are proposed to estimate its efficiency compared to classical methods.STRASBOURG-Sc. et Techniques (674822102) / SudocSudocFranceF

Comparison of Equivalent Conductivities for Numerical Simulation of One-Dimensional Unsaturated Flow

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Image analysis method for the measurement of water saturation in a two-dimensional experimental flow tank

International audienceA novel, non-invasive imaging technique is proposed that determines 2D maps of water content in unsaturated porous media. This method directly relates digitally measured intensities to the water content of the porous medium. This method requires the classical image analysis steps, i.e., normalization, filtering, background subtraction, scaling and calibration. The main advantages of this approach are that no calibration experiment is needed, because calibration curve relating water content and reflected light intensities is established during the main monitoring phase of each experiment and that no tracer or dye is injected into the flow tank. The procedure enables effective processing of a large number of photographs and thus produces 2D water content maps at high temporal resolution. A drainage/imbibition experiment in a 2D flow tank with inner dimensions of 40 cm × 14 cm × 6 cm (L × W × D) is carried out to validate the methodology. The accuracy of the proposed approach is assessed using a statistical framework to perform an error analysis and numerical simulations with a state-of-the-art computational code that solves the Richards’ equation. Comparison of the cumulative mass leaving and entering the flow tank and water content maps produced by the photographic measurement technique and the numerical simulations demonstrate the efficiency and high accuracy of the proposed method for investigating vadose zone flow processes. Finally, the photometric procedure has been developed expressly for its extension to heterogeneous media. Other processes may be investigated through different laboratory experiments which will serve as benchmark for numerical codes validation

Implementation of Richardson extrapolation in an efficient adaptive time stepping method: applications to reactive transport and unsaturated flow in porous media

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On equivalent hydraulic conductivity for oscillation–free solutions of Richard’s equation

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Laboratory Experiments of Drainage, Imbibition and Infiltration under Artificial Rainfall Characterized by Image Analysis Method and Numerical Simulations

International audienceTwo laboratory experiments consisting of drainage/imbibition and rainfall were carried out to study flow in variably saturated porous media and to test the ability of a new measurement method. 2D maps of water content are obtained through a non-invasive image analysis method based on photographs. This method requires classical image analysis steps, i.e., normalization, filtering, background subtraction, scaling and calibration. The procedure was applied and validated for a large experimental tank of internal dimensions 180 cm long, 120 cm wide and 4 cm deep that had been homogenously packed with monodisperse quartz sand. The calibration curve relating water content and reflected light intensities was established during the main monitoring phase of each experiment, making this procedure very advantageous. Direct measurements carried out during the water flow experiments correspond to water content, pressure head, temperature, and cumulative outflow. Additionally, a great advantage of the proposed method is that it does not require any tracer or dye to be injected into the flow tank. The accuracy and other benefits of our approach were also assessed using numerical simulations with state-of-the-art computational code that solves Richards' equation