Numerical solutions of the incompressible miscible displacement equations in heterogeneous media

Li, Jizhou; Rivière, Béatrice

doi:10.1016/j.cma.2014.10.048

Cited by 22 publications

(15 citation statements)

References 15 publications

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“…This work was one of the first to highlight the potential of higher-order DG discretizations in the context of viscous fingering simulations, and was the first to propose the idea of the discrete sum compatibility principle when solving coupled flow/transport problems. More recent work [281,282] featured higher-order DG methods for miscible displacement viscous fingering problems in heterogeneous porous media.…”

Section: Fully Coupled Discontinuous Galerkin Methodsmentioning

confidence: 99%

Analytical and variational numerical methods for unstable miscible displacement flows in porous media

Scovazzi

Wheeler

Mikelić

et al. 2017

Journal of Computational Physics

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International audienceThe miscible displacement of one fluid by another in a porous medium has received considerable attention in sub-surface, environmental and petroleum engineering applications. When a fluid of higher mobility displaces another of lower mobility, unstable patterns-referred to as viscous fingering-may arise. Their physical and mathematical study has been the object of numerous investigations over the past century. The objective of this paper is to present a review of these contributions with particular emphasis on variational methods. These algorithms are tailored to real field applications thanks to their advanced features: handling of general complex geometries, robustness in the presence of rough tensor coefficients, low sensitivity to mesh orientation in advection dominated scenarios, and provable convergence with fully unstructured grids. This paper is dedicated to the memory of Dr. Jim Douglas Jr., for his seminal contributions to miscible displacement and variational numerical methods

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Section: Fully Coupled Discontinuous Galerkin Methodsmentioning

confidence: 99%

Analytical and variational numerical methods for unstable miscible displacement flows in porous media

Scovazzi

Wheeler

Mikelić

et al. 2017

Journal of Computational Physics

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“…the monograph [17] and its abundant list of references). A few recent works analyzing schemes for the partitioned coupling of reaction-di↵usion systems and flow equations include, for instance, Runge-Kutta-DG splitting methods for miscible displacement in porous media [23] and conservative finite volume-element schemes for the coupling of flow and transport [9,32]. A similar structure of the coupled equations is shared by other classical systems as the Biot equations in poroelasticity, or thermoelasticity-based problems, for which a much richer, numerically-oriented literature is available (see e.g.…”

Section: Introductionmentioning

confidence: 99%

Partitioned coupling of advection–diffusion–reaction systems and Brinkman flows

Lenarda

Paggi

Ruiz–Baier

2017

Journal of Computational Physics

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We present a partitioned algorithm aimed at extending the capabilities of existing solvers for the simulation of coupled advection-di↵usion-reaction systems and incompressible, viscous flow. The space discretization of the governing equations is based on mixed finite element methods defined on unstructured meshes, whereas the time integration hinges on an operator splitting strategy that exploits the di↵er-ences in scales between the reaction, advection, and di↵usion processes, considering the global system as a number of sequentially linked sets of partial di↵erential, and algebraic equations. The flow solver presents the advantage that all unknowns in the system (here vorticity, velocity, and pressure) can be fully decoupled and thus turn the overall scheme very attractive from the computational perspective. The robustness of the proposed method is illustrated with a series of numerical tests in 2D and 3D, relevant in the modelling of bacterial bioconvection and Boussinesq systems.

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“…DG methods are popular in the CFD community due to their local mass conservation property and their ability to handle elliptic, parabolic, and hyperbolic problems [14]. DG methods have been used for the simulation of flows in porous media, e.g., in References [7,28,44] and for the Stokes and Navier-Stokes equations, e.g., in References [24,38,51]. There are many variants of the DG method.…”

Section: Introductionmentioning

confidence: 99%

Automatic Code Generation for High-performance Discontinuous Galerkin Methods on Modern Architectures

Kempf

Heß

Müthing

et al. 2020

ACM Trans. Math. Softw.

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SIMD vectorization has lately become a key challenge in high-performance computing. However, hand-written explicitly vectorized code often poses a threat to the software’s sustainability. In this publication, we solve this sustainability and performance portability issue by enriching the simulation framework dune-pdelab with a code generation approach. The approach is based on the well-known domain-specific language UFL but combines it with loopy, a more powerful intermediate representation for the computational kernel. Given this flexible tool, we present and implement a new class of vectorization strategies for the assembly of Discontinuous Galerkin methods on hexahedral meshes exploiting the finite element’s tensor product structure. The performance-optimal variant from this class is chosen by the code generator through an auto-tuning approach. The implementation is done within the open source PDE software framework Dune and the discretization module dune-pdelab. The strength of the proposed approach is illustrated with performance measurements for DG schemes for a scalar diffusion reaction equation and the Stokes equation. In our measurements, we utilize both the AVX2 and the AVX512 instruction set, achieving 30% to 40% of the machine’s theoretical peak performance for one matrix-free application of the operator.

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Numerical solutions of the incompressible miscible displacement equations in heterogeneous media

Cited by 22 publications

References 15 publications

Analytical and variational numerical methods for unstable miscible displacement flows in porous media

Analytical and variational numerical methods for unstable miscible displacement flows in porous media

Partitioned coupling of advection–diffusion–reaction systems and Brinkman flows

Automatic Code Generation for High-performance Discontinuous Galerkin Methods on Modern Architectures

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