January 19th – Laurent Monasse: A 3D conservative coupling between a compressible flow and a fragmenting structure

Laurent Monasse: January 19 December at 3pm, A415 Inria Paris. We will present a conservative method for three-dimensional inviscid fluid-structure interaction problems. Body-fitted methods are not well-suited for large displacements or fragmentation of the structure, since they involve possibly costly remeshing of the fluid domain. We use instead an immersed boundary technique through the modification of the finite volume fluxes in the vicinity of the solid. The method is tailored to yield the exact conservation of mass, momentum and energy of the system and exhibits consistency properties. In the event of fragmentation, void can appear due to the velocity of crack opening. In order to ensure stability in the presence of void, we resort locally to the Lax-Friedrichs flux near cracks. Since both fluid and solid methods are explicit, the coupling scheme is designed to be explicit too. The computational cost of the fluid and solid methods lies mainly in the evaluation of fluxes on the fluid side and of forces and torques on the solid side. It should be noted that the coupling algorithm evaluates these only once every time step, ensuring the computational efficiency of the coupling. We also analyze a corner instability of the conservative explicit immersed boundary method in the case of a Roe flux, explain its origin and propose a way to fix the issue.

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January 5th – Agnieszka Miedlar: Moving eigenvalues and eigenvectors by simple perturbations

Agnieszka Miedlar: Thursday 8 December at 3pm, A415 Inria Paris. Abstract: In the context of iterative solvers moving the eigenvalue or the eigenpair may be of particular importance in several cases, e.g., deflation techniques, increasing the spectral gap or determining the set of linearly independent eigenvectors. It can also be used for reducing the imaginary parts of the eigenvalues without chainging the matrix exponential; this can enhance the computation of $\exp(A)$. Exploiting the classical perturbation analysis for eigenvalue problems [Golub and Van Loan 2012] we study the following problem.

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December 8th – Luca Formaggia: Hybrid dimensional Darcy flow in fractured porous media, some recent results on mimetic discretization

Luca Formaggia: Thursday 8 December at 3pm, A415 Inria Paris. Fractures can alter greatly the characteristics of porous media. Their diverse scale distribution makes it often impossible to resort to averaging or homogenisation techniques to account for their presence. Thus, different models have been devised to account for the presence of fractures in porous media explicitly. We here present the general problem, together with a recent result of well-posedness for an hybrid dimensional mixed formulation  of Darcy flow in fractured porous media, and an analysis of a mimetic finite difference scheme adopted for its numerical solution.

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Internal Seminar: Paola Antonietti

Thursday 22 September at 3pm, Jacques Louis Lions lecture hall, Inria Paris Paola ANTONIETTI: Fast solution techniques for high order Discontinuous Galerkin methods We present two-level and multigrid algorithms for the efficient solution of the linear system of equations arising from high-order discontinuous Galerkin discretizations of second-order elliptic problems. Starting from the classical framework in geometric multigrid analysis, we define a smoothing and an approximation property, which are used to prove uniform convergence of the resulting multigrid schemes with respect to the discretization parameters and the number of levels, provided the number of smoothing steps is chosen sufficienly large.  A discussion on the effects of employing inherited or noninherited sublevel solvers is also presented as well the extension of the proposed techniques to agglomeration-based multigrid solvers. Numerical experiments confirm the theoretical results.

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10 Dec. 2015 – Nabil Birgle: Composite Method on Polygonal Meshes

Internal seminar of the SERENA team, Thursday 10 December, 4pm-5pm in building 13: Nabil Birgle: Composite Method on Polygonal Meshes Abstract: We develop a reliable numerical method to approximate a flow in a porous media, modeled by an elliptic equation. The simulation is made difficult because of the strong heterogeneities of the medium, the size together with complex geometry of the domain. A regular hexahedral mesh does not allow to describe accurately the geological layers of the domain.  Consequently, this leads us to work with a mesh made of deformed cubes.  There exists several methods of type finite volumes or finite elements which solve this issue.  For our method, we wish to have only one degree of freedom per element for the pressure and one degree of freedom per face for the Darcy velocity, to stay as close to the habits of industrial software.  Since standard mixed finite element methods does not converge, our method is based on composite mixed finite element. In two dimensions, a polygonal mesh is split into triangles by adding a node to the vertices’s barycenter, and explicit formulation of the basis functions was obtained.  In dimension 3, the method extend naturally to the case of pyramidal mesh.  In the case of a hexahedron or a deformed cube, the element is divided into 24 tetrahedra by adding a node to the vertices’s barycenter and splitting the faces into 4 triangles.  The basis functions are then built by solving a discrete problem.  The proposed methods have been theoretically analyzed and completed by a posteriori estimators.  They have been tested on academical and realistic examples by using parallel computation.

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03 Dec. 2015 – François Clément: Safe and Correct Programming for Scientific Computing

Internal seminar of the SERENA team, Thursday 03 December, 4pm-5pm in building 13: Francois Clément: Safe and Correct Programming for Scientific Computing Abstract: The increasing complexity of algorithms for modern scientific computing  makes it a major challenge to implement them in the traditional imperative languages that are popular in the community. The idea is to  explore the usage of formal tools from computing science, and in particular from the functional programming school, to design and  implement generic tools that may ease the development of scientific computing software. In this lecture, we will focus on: Sklml, an easy coarse grain parallelization compiler system; Ref-indic, a generic inversion platform for adaptive parameter  estimation; a comprehensive mechanical proof of correctness of a C program as a  PDE solver. Basic examples of the use of OCaml, Sklml, and Coq will be given.

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26 Nov. 2015 – Jérôme Jaffré: Discrete reduced models for flow in porous media with fractures and barriers

Internal seminar of the SERENA team, Thursday 19 November, 4pm-5pm in building 13: Jérôme Jaffré: Discrete reduced models for flow in porous media with fractures  and barriers Abstract: Flow in porous media is strongly influenced by the presence of fractures which can have higher or lower permeabilities (barriers). Depending on the goal of the study there are many models which take into account this influence. In this lecture we will focus on discrete fracture models, that are models where each fracture can be described individually, and reduced fracture models, where a fracture is reduced to an $(n-1)$ surface in an $n$-dimensional model. We will begin with one-phase flow models and continue with two-phase flow taking into account the change of rock types between the matrix rock and the fractures.

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19 Nov. 2015 – Géraldine Pichot: Generation algorithms of stationary Gaussian random fields

Internal seminar of the SERENA team, Thursday 19 November, 4pm-5pm in building 13: Géraldine Pichot: Generation algorithms of stationary Gaussian random fields Abstract: Flow and transport equation in geological media involve physical coefficients like the permeability and the porosity. Those coefficients are classically modeled by Gaussian random fields. In order to study the impact of the variability of those coefficients on flow and transport phenomenon, a large number of those fields are simulated which requires an efficient simulation method. I will present different algorithms to simulate stationary Gaussian random fields over a regular grid and based on the classical circulant embedding approach. I will also discuss some parallel issues and present numerical results with different covariance functions. This is a joint work with Jocelyne Erhel and Mestapha Oumouni (INRIA, Rennes).

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12 Nov. 2015 – Elyes Ahmed: Space-time domain decomposition method for two-phase flow equations

Internal seminar of the SERENA team, Thursday 12 November, 3pm-4pm in building 13: Elyes Ahmed: Space-time domain decomposition method for two-phase flow equations Abstract: We consider a simplified model of two-phase flow model through a heterogeneous meduim. Focusing on the capillary forces motion, we consider the Optimized Schwarz method with non-linear Robin conditions in the context of non-linear degenerate parabolic problem which is approximated in a domain shared in two homogeneous parts, each of them being a different rock type, each rock is characterized by its relative permeability and capillary curves functions of the phase saturations. We then propose a hybridized finite volume scheme for the approximation of the multi-domain solution. It relies on the Optimized Robin-Schwarz algorithm with a finite volume discretization of the subdomain problems. The existence of a weak solution for the Robin subdomain problems involved in the OSWR method is proved using the convergence of a finite volume approximation. Numerical results for three-dimensional problems are presented to illustrate the performance of the method.

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