Comparison of data-driven uncertainty quantification methods for a carbon dioxide storage benchmark scenario

A variety of methods is available to quantify uncertainties arising with\-in the modeling of flow and transport in carbon dioxide storage, but there is a lack of thorough comparisons. Usually, raw data from such storage sites can hardly be described by theoretical statistical distributions since only very limited data is available. Hence, exact information on distribution shapes for all uncertain parameters is very rare in realistic applications. We discuss and compare four different methods tested for data-driven uncertainty quantification based on a benchmark scenario of carbon dioxide storage. In the benchmark, for which we provide data and code, carbon dioxide is injected into a saline aquifer modeled by the nonlinear capillarity-free fractional flow formulation for two incompressible fluid phases, namely carbon dioxide and brine. To cover different aspects of uncertainty quantification, we incorporate various sources of uncertainty such as uncertainty of boundary conditions, of conceptual model definitions and of material properties. We consider recent versions of the following non-intrusive and intrusive uncertainty quantification methods: arbitary polynomial chaos, spatially adaptive sparse grids, kernel-based greedy interpolation and hybrid stochastic Galerkin. The performance of each approach is demonstrated assessing expectation value and standard deviation of the carbon dioxide saturation against a reference statistic based on Monte Carlo sampling. We compare the convergence of all methods reporting on accuracy with respect to the number of model runs and resolution. Finally we offer suggestions about the methods' advantages and disadvantages that can guide the modeler for uncertainty quantification in carbon dioxide storage and beyond

A Lagrange multiplier method for a discrete fracture model for flow in porous media

International audienceIn this work we present a novel discrete fracture model for single-phase Darcy flow in porous media with fractures of co-dimension one, which introduces an additional unknown at the fracture interface. Inspired by the fictitious domain method this Lagrange multiplier couples fracture and matrix domain and represents a local exchange of the fluid. The multipliers naturally impose the equality of the pressures at the fracture interface. The model is thus appropriate for domains with fractures of permeability higher than that in the surrounding bulk domain. In particular the novel approach allows for independent, regular meshing of fracture and matrix domain and therefore avoids the generation of small elements. We show existence and uniqueness of the weak solution of the continuous primal formulation. Moreover we discuss the discrete inf-sup condition of two different finite element formulations. Several numerical examples verify the accuracy and convergence of proposed method

A stabilized Lagrange multiplier finite-element method for flow in porous media with fractures

International audienceIn this work we introduce a stabilized, numerical method for a multi-dimensional, discrete-fracture model (DFM) for single-phase Darcy flow in fractured porous media. In the model, introduced in an earlier work, flow in the (n − 1)-dimensional fracture domain is coupled with that in the n-dimensional bulk or matrix domain by the use of Lagrange multipliers. Thus the model permits a finite element discretization in which the meshes in the fracture and matrix domains are independent so that irregular meshing and in particular the generation of small elements can be avoided. In this paper we introduce in the numerical formulation, which is a saddle-point problem based on a primal, variational formulation for flow in the matrix domain and in the fracture system, a consistent stabilizing term which penalizes discontinuities in the Lagrange multipliers. For this penalized scheme we show stability and prove convergence. With numerical experiments we analyze the performance of the method for various choices of the penalization parameter and compare with other numerical DFM's

Improvement of medical education using web-based lecture repetition and extension: e-learning experiences of the Department of Obstetrics and Gynecology, University of Tuebingen

In order to improve the education of its medical students, the Department of Obstetrics and Gynecology of the University of Tuebingen established e-learning in terms of web-based lecture repetition and extension. Subsequent to lectures, questions are provided online. The participation is voluntary, but requires registration. The results of the analysed period (winter term 2004/2005, summer term 2005 and winter term 2005/2006) including more than 380 e-learning users are encouraging. An average of 45% of the target group used the offered online questions. The students who completed at least 75% of all prepared question units achieved significantly better results than their traditional learning fellow students (p=0.002). Users got more frequent the marks "good" and "very good". Twice as much conventional learning students as e-learning users failed the examination. E-Learning and the technical implementation are repeatedly appreciated by the students. In the future, more medical courses will be supplemented with e-learning, according to the students request

TLR3-dependent immune regulatory functions of human mesangial cells

In glomerulonephritis, the migration of inflammatory cells into the glomerulus is an important step in disease initiation and progression. The viral receptor Toll-like receptor 3 (TLR3) is known to play a role in virus-associated glomerulonephritis. Based on this knowledge, this study aimed to define the effects of the TLR3 ligand polyriboinosinic:polyribocytidylic acid (poly(I:C)) on the expression of adhesion molecules and macrophage colony-stimulating factor (M-CSF) on resident glomerular cells. Experiments in MCs demonstrated that the activation of viral receptors by poly(I:C) leads to a time- and dose-dependent induction of intercellular adhesion molecule 1 (ICAM-1), vascular cell adhesion molecule 1 (VCAM-1) and M-CSF at both the mRNA and protein levels; these results were confirmed by incubating MCs with HCV RNA. As shown in knockdown experiments, this effect is specifically mediated by TLR3. The prestimulation of MCs with proinflammatory cytokines increases the effects of poly(I:C), except for its induction of VCAM-1. Tumor-necrosis factor (TNF)-α, likewise, induces ICAM-1, VCAM-1 and M-CSF, and amplifies the mesangial response to poly(I:C). These results were confirmed by incubating MCs with HCV RNA. We thus provide evidence that human MCs represent a potential target of the leukocytes and monocytes that infiltrate the glomerulus in viral disease-associated GN, highlighting the possibility that MCs may act as resident antigen-presenting cells