Aspects of Solvers for Large-Scale Coupled Problems in Porous Media

Nägel, Arne; Logashenko, D.; Schroder, Jacob B.; Yang, Ulrike Meier

doi:10.1007/s11242-019-01323-w

Cited by 4 publications

(3 citation statements)

References 131 publications

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“…For a glossary of common terms and information on multiphysics simulations in general, the reader is referred to a respective review [32]. Moreover, a recent review on conjugate heat transfer simulations can be found in [33], and solvers for coupled porous media flow have recently been reviewed in [34].…”

Section: Introductionmentioning

confidence: 99%

Numerical Simulation of Ammonothermal Crystal Growth of GaN—Current State, Challenges, and Prospects

et al. 2021

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Numerical simulations are a valuable tool for the design and optimization of crystal growth processes because experimental investigations are expensive and access to internal parameters is limited. These technical limitations are particularly large for ammonothermal growth of bulk GaN, an important semiconductor material. This review presents an overview of the literature on simulations targeting ammonothermal growth of GaN. Approaches for validation are also reviewed, and an overview of available methods and data is given. Fluid flow is likely in the transitional range between laminar and turbulent; however, the time-averaged flow patterns likely tend to be stable. Thermal boundary conditions both in experimental and numerical research deserve more detailed evaluation, especially when designing numerical or physical models of the ammonothermal growth system. A key source of uncertainty for calculations is fluid properties under the specific conditions. This originates from their importance not only in numerical simulations but also in designing similar physical model systems and in guiding the selection of the flow model. Due to the various sources of uncertainty, a closer integration of numerical modeling, physical modeling, and the use of measurements under ammonothermal process conditions appear to be necessary for developing numerical models of defined accuracy.

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Section: Introductionmentioning

confidence: 99%

Numerical Simulation of Ammonothermal Crystal Growth of GaN—Current State, Challenges, and Prospects

et al. 2021

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“…In comparison to the more conventional time-stepping methods or tensorstructured space-time methods [18,19,28], this unstructured space-time approach provides us with more flexibility in constructing parallel space-time solvers such as parallel space-time algebraic multigrid preconditioners [24] or space-time balancing domain decomposition by constraints (BDDC) preconditioners [26]. Moreover, it becomes more convenient to realize simultaneous space-time adaptivity on unstructured space-time meshes [24,25,33] than the other methods.…”

Section: Introductionmentioning

confidence: 99%

Unstructured Space-Time Finite Element Methods for Optimal Sparse Control of Parabolic Equations

Langer¹,

Steinbach²,

Tröltzsch³

et al. 2020

Preprint

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We consider a space-time finite element method on fully unstructured simplicial meshes for optimal sparse control of semilinear parabolic equations. The objective is a combination of a standard quadratic trackingtype functional including a Tikhonov regularization term and of the L 1norm of the control that accounts for its spatio-temporal sparsity. We use a space-time Petrov-Galerkin finite element discretization for the firstorder necessary optimality system of the associated discrete optimal sparse control problem. The discretization is based on a variational formulation that employs piecewise linear finite elements simultaneously in space and time. Finally, the discrete nonlinear optimality system that consists of coupled forward-backward state and adjoint state equations is solved by a semismooth Newton method.

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“…Other articles address experimental issues-at the macroscale (Falzone et al 2018) and fluid displacement at the pore scale (Gerami et al 2018), while Armstrong et al (2018) demonstrates how one can go from X-ray microcomputed tomography to characterizing porous media for modeling. And two articles address computational issues: one about open-source software (Bilke et al 2019) and one about numerical algorithms for large-scale porous media problems (Nägel et al 2019). Unfortunately, there are some topics that are not addressed in this issue.…”

mentioning

confidence: 99%