17,823 research outputs found

    A Force-Balanced Control Volume Finite Element Method for Multi-Phase Porous Media Flow Modelling

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    Dr D. Pavlidis would like to acknowledge the support from the following research grants: Innovate UK ‘Octopus’, EPSRC ‘Reactor Core-Structure Re-location Modelling for Severe Nuclear Accidents’) and Horizon 2020 ‘In-Vessel Melt Retention’. Funding for Dr P. Salinas from ExxonMobil is gratefully acknowledged. Dr Z. Xie is supported by EPSRC ‘Multi-Scale Exploration of Multi-phase Physics in Flows’. Part funding for Prof Jackson under the TOTAL Chairs programme at Imperial College is also acknowledged. The authors would also like to acknowledge Mr Y. Debbabi for supplying analytic solutions.Peer reviewedPublisher PD

    Finite element analysis of non-isothermal multiphase porous media in dynamics

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    This work presents a mathematical and a numerical model for the analysis of the thermo-hydro-mechanical (THM) behavior of multiphase deformable porous materials in dynamics. The fully coupled governing equations are developed within the Hybrid Mixture Theory. To analyze the THM behavior of soil structures in the low frequency domain, e.g. under earthquake excitation, the u-p-T formulation is advocated by neglecting the relative acceleration of the fluids and their convective terms. The standard Bubnov-Galerkin method is applied to the governing equations for the spatial discretization, whereas the generalized Newmark scheme is used for the time discretization. The final non-linear and coupled system of algebraic equations is solved by the Newton method within the monolithic approach. The formulation and the implemented solution procedure are validated through the comparison with other finite element solutions or analytical solutions

    Mixed and discontinuous finite volume element schemes for the optimal control of immiscible flow in porous media

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    We introduce a family of hybrid discretisations for the numerical approximation of optimal control problems governed by the equations of immiscible displacement in porous media. The proposed schemes are based on mixed and discontinuous finite volume element methods in combination with the optimise-then-discretise approach for the approximation of the optimal control problem, leading to nonsymmetric algebraic systems, and employing minimum regularity requirements. Estimates for the error (between a local reference solution of the infinite dimensional optimal control problem and its hybrid approximation) measured in suitable norms are derived, showing optimal orders of convergence

    Higher-order conservative interpolation between control-volume meshes: Application to advection and multiphase flow problems with dynamic mesh adaptivity

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    © 2016 .A general, higher-order, conservative and bounded interpolation for the dynamic and adaptive meshing of control-volume fields dual to continuous and discontinuous finite element representations is presented. Existing techniques such as node-wise interpolation are not conservative and do not readily generalise to discontinuous fields, whilst conservative methods such as Grandy interpolation are often too diffusive. The new method uses control-volume Galerkin projection to interpolate between control-volume fields. Bounded solutions are ensured by using a post-interpolation diffusive correction. Example applications of the method to interface capturing during advection and also to the modelling of multiphase porous media flow are presented to demonstrate the generality and robustness of the approach

    Fine Scale Simulation of Fractured Reservoirs: Applications and Comparison

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    Multiphase modelling of vascular tumour growth in two spatial dimensions

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    In this paper we present a continuum mathematical model of vascular tumour growth which is based on a multiphase framework in which the tissue is decomposed into four distinct phases and the principles of conservation of mass and momentum are applied to the normal/healthy cells, tumour cells, blood vessels and extracellular material. The inclusion of a diffusible nutrient, supplied by the blood vessels, allows the vasculature to have a nonlocal influence on the other phases. Two-dimensional computational simulations are carried out on unstructured, triangular meshes to allow a natural treatment of irregular geometries, and the tumour boundary is captured as a diffuse interface on this mesh, thereby obviating the need to explicitly track the (potentially highly irregular and ill-defined) tumour boundary. A hybrid finite volume/finite element algorithm is used to discretise the continuum model: the application of a conservative, upwind, finite volume scheme to the hyperbolic mass balance equations and a finite element scheme with a stable element pair to the generalised Stokes equations derived from momentum balance, leads to a robust algorithm which does not use any form of artificial stabilisation. The use of a matrix-free Newton iteration with a finite element scheme for the nutrient reaction-diffusion equations allows full nonlinearity in the source terms of the mathematical model. Numerical simulations reveal that this four-phase model reproduces the characteristic pattern of tumour growth in which a necrotic core forms behind an expanding rim of well-vascularised proliferating tumour cells. The simulations consistently predict linear tumour growth rates. The dependence of both the speed with which the tumour grows and the irregularity of the invading tumour front on the model parameters are investigated
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