Analytical and Numerical Aspects of Porous Media Flow

The Brinkman equations model fluid flow through porous media and are particularly interesting in regimes where viscous shear effects cannot be neglected. Two model parameters in the momentum balance function as weights for the terms related to inter-particle friction and bulk resistance. If these are not in balance, then standard finite element methods might suffer from instabilities or error estimates might deteriorate. In particular the limit case, where the Brinkman problem reduces to a Darcy problem, demands for special attention. This thesis proposes a low-order finite element method which is uniformly stable with respect to the flow regimes captured by the Brinkman model, including the Darcy limit. To that end, linear equal-order approximations are combined with a pressure stabilization technique, a grad-div stabilization, and a penalty-free non-symmetric Nitsche method. The combination of these ingredients allows to develop a robust method, which is proven to be well-posed for the whole family of problems in two spatial dimensions, even if any Brinkman parameter vanishes. An a priori error analysis reveals optimal convergence in the considered norm. A convergence study based on problems with known analytic solutions confirms the robust first order convergence for reasonable ranges of numerical (stabilization) parameters. Further, numerical investigations that partly extend the theoretical framework are considered, revealing strengths and weaknesses of the approach. An application motivated by the optimization of geothermal energy production completes the thesis. Here, the proposed method is included in a multi-physics discrete model, appropriate to describe the thermo-hydraulics in hot, sedimentary, essentially horizontal aquifers. An immersed boundary method is adopted in order to allow a flexible, automatic optimization without regenerating the computational mesh. Utilizing the developed computational framework, the optimized multi-well arrangements with respect to the net energy gain are presented and discussed for different geothermal and hydrogeological setups. The results show that taking into account heterogeneous permeability structures and variable aquifer temperatures might drastically affect the optimal configuration of the wells

Modeling, simulation, and optimization of geothermal energy production from hot sedimentary aquifers

Geothermal district heating development has been gaining momentum in Europe with numerous deep geothermal installations and projects currently under development. With the increasing density of geothermal wells, questions related to the optimal and sustainable reservoir exploitation become more and more important. A quantitative understanding of the complex thermo-hydraulic interaction between tightly deployed geothermal wells in heterogeneous temperature and permeability fields is key for a maximum sustainable use of geothermal resources. Motivated by the geological settings of the Upper Jurassic aquifer in the Greater Munich region, we develop a computational model based on finite element analysis and gradient-free optimization to simulate groundwater flow and heat transport in hot sedimentary aquifers, and investigate numerically the optimal positioning and spacing of multi-well systems. Based on our numerical simulations, net energy production from deep geothermal reservoirs in sedimentary basins by smart geothermal multi-well arrangements provides significant amounts of energy to meet heat demand in highly urbanized regions. Our results show that taking into account heterogeneous permeability structures and variable reservoir temperature may drastically affect the results in the optimal configuration. We demonstrate that the proposed numerical framework is able to efficiently handle generic geometrical and geologocal configurations, and can be thus flexibly used in the context of multi-variable optimization problems. Hence, this numerical framework can be used to assess the extractable geothermal energy from heterogeneous deep geothermal reservoirs by the optimized deployment of smart multi-well systems

Modeling, simulation, and optimization of geothermal energy production from hot sedimentary aquifers

Geothermal district heating development has been gaining momentum in Europe with numerous deep geothermal installations and projects currently under development. With the increasing density of geothermal wells, questions related to the optimal and sustainable reservoir exploitation become more and more important. A quantitative understanding of the complex thermo-hydraulic interaction between tightly deployed geothermal wells in heterogeneous temperature and permeability fields is key for a maximum sustainable use of geothermal resources. Motivated by the geological settings of the Upper Jurassic aquifer in the Greater Munich region, we develop a computational model based on finite element analysis and gradient-free optimization to simulate groundwater flow and heat transport in hot sedimentary aquifers, and investigate numerically the optimal positioning and spacing of multi-well systems. Based on our numerical simulations, net energy production from deep geothermal reservoirs in sedimentary basins by smart geothermal multi-well arrangements provides significant amounts of energy to meet heat demand in highly urbanized regions. Our results show that taking into account heterogeneous permeability structures and variable reservoir temperature may drastically affect the results in the optimal configuration. We demonstrate that the proposed numerical framework is able to efficiently handle generic geometrical and geologocal configurations, and can be thus flexibly used in the context of multi-variable optimization problems. Hence, this numerical framework can be used to assess the extractable geothermal energy from heterogeneous deep geothermal reservoirs by the optimized deployment of smart multi-well systems

Analysis of a stabilized penalty-free Nitsche method for the Brinkman, Stokes, and Darcy problems

International audienceIn this paper we study the Brinkman model as a unified framework to allow the transition between the Darcy and the Stokes problems. We propose an unconditionally stable low-order finite element approach, which is robust with respect to the whole range of physical parameters, and is based on the combination of stabilized equal-order finite elements with a non-symmetric penalty-free Nitsche method for the weak imposition of essential boundary conditions. In particular, we study the properties of the penalty-free Nitsche formulation for the Brinkman setting, extending a recently reported analysis for the case of incompressible elasticity (Boiveau and Burman, IMA J. Numer. Anal. 36 (2016) 770-795). Focusing on the two-dimensional case, we obtain optimal a priori error estimates in a mesh-dependent norm, which, converging to natural norms in the cases of Stokes or Darcy ows, allows to extend the results also to these limits. Moreover, we show that, in order to obtain robust estimates also in the Darcy limit, the formulation shall be equipped with a Grad-Div stabilization and an additional stabilization to control the discontinuities of the normal velocity along the boundary. The conclusions of the analysis are supported by numerical simulations

ParMooN - a modernized program package based on mapped finite elements

{\sc ParMooN} is a program package for the numerical solution of elliptic and parabolic partial differential equations. It inherits the distinct features of its predecessor {\sc MooNMD} \cite{JM04}: strict decoupling of geometry and finite element spaces, implementation of mapped finite elements as their definition can be found in textbooks, and a geometric multigrid preconditioner with the option to use different finite element spaces on different levels of the multigrid hierarchy. After having presented some thoughts about in-house research codes, this paper focuses on aspects of the parallelization for a distributed memory environment, which is the main novelty of {\sc ParMooN}. Numerical studies, performed on compute servers, assess the efficiency of the parallelized geometric multigrid preconditioner in comparison with some parallel solvers that are available in the library {\sc PETSc}. The results of these studies give a first indication whether the cumbersome implementation of the parallelized geometric multigrid method was worthwhile or not.Comment: partly supported by European Union (EU), Horizon 2020, Marie Sk{\l}odowska-Curie Innovative Training Networks (ITN-EID), MIMESIS, grant number 67571

Mutation of Vav1 adaptor region reveals a new oncogenic activation

International audienceVav family members function as remarkable scaffold proteins that exhibit both GDP/GTP exchange activity for Rho/Rac GTPases and numerous protein-protein interactions via three adaptor Src-homology domains. The exchange activity is under the unique regulation by phosphorylation of tyrosine residues hidden by intra-molecular interactions. Deletion of the autoinhibitory N-terminal region results in an oncogenic protein, onco-Vav, leading to a potent activation of Rac GTPases whereas the proto-oncogene barely leads to transformation. Substitution of conserved residues of the SH2-SH3 adaptor region in onco-Vav reverses oncogenicity. While a unique substitution D797N did not affect transformation induced by onco-Vav, we demonstrate that this single substitution leads to transformation in the Vav1 proto-oncogene highlighting the pivotal role of the adaptor region. Moreover, we identified the cell junction protein β-catenin as a new Vav1 interacting partner. We show that the oncogenicity of activated Vav1 proto-oncogene is associated with a non-degradative phosphorylation of β-catenin at residues important for its functions and its redistribution along the cell membrane in fibroblasts. In addition, a similar interaction is evidenced in epithelial lung cancer cells expressing ectopically Vav1. In these cells, Vav1 is also involved in the modulation of β-catenin phosphorylation. Altogether, our data highlight that only a single mutation in the proto-oncogene Vav1 enhances tumorigenicity. INTRODUCTION The Vav1 proto-oncogene has a restricted hematopoietic expression and exhibits both GTP/GDP exchange activities (GEF) for Rho family GTPases and adaptor functions within signalling complexes [1, 2]. Two other genes, Vav2 and Vav3 belong to the same family of signalling effectors and share high structural similarities and properties with Vav1. Unlike Vav1, Vav2 and Vav3 have an ubiquitous expression [3, 4]. Vav proteins display a number of characteristic structural domains with homology for: Calponin (CH), Dbl (DH), Pleckstrin (PH) and Src (SH2 and SH3) altogether with acidic residues-rich (AcR) and cysteine-rich (CR) motives. These domains mediate interactions with membrane receptors

ParMooN - a modernized program package based on mapped finite elements

PARMOON is a program package for the numerical solution of elliptic and parabolic partial differential equations. It inherits the distinct features of its predecessor MOONMD [28]: strict decoupling of geometry and finite element spaces, implementation of mapped finite elements as their definition can be found in textbooks, and a geometric multigrid preconditioner with the option to use different finite element spaces on different levels of the multigrid hierarchy. After having presented some thoughts about in-house research codes, this paper focuses on aspects of the parallelization, which is the main novelty of PARMOON. Numerical studies, performed on compute servers, assess the efficiency of the parallelized geometric multigrid preconditioner in comparison with parallel solvers that are available in external libraries. The results of these studies give a first indication whether the cumbersome implementation of the parallelized geometric multigrid method was worthwhile or not