Thu, November 2, 2017
Public Access

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November 2017
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11:00am [11:00am] Reebhu Bhattacharya
Speaker: Reebhu Bhattacharya Topic: Universal Bundles and Classifying Spaces Abstract: We will talk about the classifying theorem of principal G-bundles for a topological group G. For every group G, there is a classifying space BG so that the homotopy classes of maps from a space X to BG are in bijective correspondence with the set of isomorphism classes of principal G-bundles over X. We will be outlining the construction, due to Milnor, of a classifying space for any group G.

4:00pm [4:00pm] Jerome Droniou, Monash university, Melbourne
Speaker: Jerome Droniou, Monash university, Melbourne. Title: ELLAM schemes for a model of miscible flow in porous medium: design and analysis. Abstract: Tertiary oil recovery is the process which consists in injecting a solvent through a well in an underground oil reservoir, that will mix with the oil and reduce its viscosity, thus enabling it to flow towards a second reservoir. Mathematically, this process is represented by a coupled system of an elliptic equation (for the pressure) and a parabolic equation (for the concentration). The parabolic equation is strongly convection-dominated, and discretising the convection term properly is therefore essential to obtain accurate numerical representations of the solution. One of the possible discretisation techniques for this term involves using characteristic methods, applied on the test functions. This is called the Eulerian-Lagrangian Localised Adjoint Method (ELLAM). In practice, due to the ground heterogeneities, the available grids can be non-conforming and have cells of various geometries, including generic polytopal cells. Along with the non-linear and heterogeneous/anisotropic diffusion tensors present in the model, this creates issues in the discretisation of the diffusion terms. In this talk, we will present a generic framework, agnostic to the specific discretisation of the diffusion terms, to design and analyse ELLAM schemes. Our convergence result applies to a range of possible schemes for the diffusion terms, such as finite elements, finite volumes, discontinuous Galerkin, etc. Numerical results will be presented on various grid geometries.