Efficiency gains of a multi-scale integration method applied to a scale-separated model for rapidly rotating dynamos

Tretiak, Krasymyr; Plumley, Meredith; Calkins, Michael A.; Tobias, Steven M.

doi:10.1016/j.cpc.2021.108253

Cited by 5 publications

(4 citation statements)

References 30 publications

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“…Different strategies for the solution may be needed for the two different cases, since the fluctuations evolve on a much more rapid timescale than their correlation functions (which usually evolve on the same timescale as the mean flows for a QL theory). For QL DNS, strategies may be developed that make use of the separation of timescales, either by utilizing a hidden Markov model-like solver that combines a macrosolver with a large integration timestep for the slow (mean) dynamics and a microsolver for the fast dynamics (see, e.g., Tretiak et al 2022), or by exploiting the linearity of the equations for the fluctuations (Michel & Chini 2019). While the first method is a tool that works well for general situations where the timescales are well separated, even for the case where the fast dynamics is inherently nonlinear, the second method utilizes the linearity of the fast system and therefore the fact that the slow field must stay close to a state of near marginality to achieve additional efficiency.…”

Section: Methods Of Solution For Fast/slow Quasi-linear Equationsmentioning

confidence: 99%

Recent Developments in Theories of Inhomogeneous and Anisotropic Turbulence

Marston

Tobias

2023

Annu. Rev. Fluid Mech.

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Understanding inhomogeneous and anisotropic fluid flows require mathematical and computational tools that are tailored to such flows and distinct from methods used to understand the canonical problem of homogeneous and isotropic turbulence. We review some recent developments in the theory of inhomogeneous and anisotropic turbulence, placing special emphasis on several kinds of quasi-linear approximations and their corresponding statistical formulations. Aspects of quasi-linear theory that have received insufficient attention in the literature are discussed, and open questions are framed. Expected final online publication date for the Annual Review of Fluid Mechanics, Volume 55 is January 2023. Please see http://www.annualreviews.org/page/journal/pubdates for revised estimates.

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Section: Methods Of Solution For Fast/slow Quasi-linear Equationsmentioning

confidence: 99%

Recent Developments in Theories of Inhomogeneous and Anisotropic Turbulence

Marston

Tobias

2023

Annu. Rev. Fluid Mech.

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“…For QL DNS, strategies may be developed that make use of the separation of timescales, either by utilizing a HMM-like solver that combines a macrosolver with a large integration timestep for the slow (mean) dynamics and a microsolver for the fast dynamics (see e.g. Tretiak et al 2022) or by exploiting the linearity of the equations for the fluctuations (Michel & Chini 2019). Whilst the first method is a general tool that works well for general situations where the timescales are well separated, even for the case where the fast dynamics is inherently nonlinear, the second method utilizes the linearity of the fast system, and therefore the fact that the slow field must stay close to a state of near marginality to achieve additional efficiency.…”

Section: Methods Of Solution For Fast/slow Ql Equationsmentioning

confidence: 99%

Recent Developments in Theories of Inhomogeneous and Anisotropic Turbulence

Marston¹,

Tobias²

2022

Preprint

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Understanding inhomogeneous and anisotropic fluid flows require mathematical and computational tools that are tailored to such flows and distinct from methods used to understand the canonical problem of homogeneous and isotropic turbulence. We review some recent developments in the theory of inhomogeneous and anisotropic turbulence, placing special emphasis on several kinds of quasilinear approximations and their corresponding statistical formulations. Aspects of quasilinear theory that have received insufficient attention in the literature are discussed, and open questions are framed.

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“…Recently, a number of researchers addressed this issue through techniques such as model reduction, GPU programming, and replacement of lower-scale solutions with machine learning-based surrogate models (Fritzen and Hodapp 2016;Raschi et al 2021;Rocha et al 2021). HMM and EFM are similar approaches that employ a macro-scale model with large time steps, in which the primary variables evolve through the solution of a micro-scale model over smaller time steps (Tretiak et al 2022). In such models, the need for macroscopic constitutive equations is avoided, and in some cases (e.g.…”

Section: Introductionmentioning

confidence: 99%

“…In such models, the need for macroscopic constitutive equations is avoided, and in some cases (e.g. EFM) the macro-scale finite element equations also are not required (Tretiak et al 2022). As with the FE 2 approach, the main disadvantage is the computational cost (Vassaux et al 2019).…”

Section: Introductionmentioning

confidence: 99%

A Statistical Finite Element Method Integrating a Plurigaussian Random Field Generator for Multi-scale Modelling of Solute Transport in Concrete

et al. 2023

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A new model for the multi-scale simulation of solute transport in concrete is presented. The model employs plurigaussian simulations to generate stochastic representations of concrete micro- and meso-structures. These are idealised as two-phase medium comprising mortar matrix and pores for the micro-structure, and mortar and large aggregate particles for the meso-structure. The generated micro- and meso-structures are employed in a finite element analysis for the simulation of steady-state diffusion of solutes. The results of the simulations are used to calculate effective diffusion coefficients of the two-phase micro- and meso-structures, and in turn, the effective diffusion coefficient at the macro-scale at which the concrete material is considered homogenous. Multiple micro- and meso-structures are generated to account for uncertainty at the macro-scale. In addition, the level of uncertainty in the calculated effective diffusion coefficients is quantified through a statistical analysis. The numerical predictions are validated against experimental observations concerning the diffusion of chloride through a concrete specimen, suggesting that the generated structures are representative of the pore-space and coarse aggregate seen at the micro- and meso-scales, respectively. The method also has a clear advantage over many other structural generation methods, such as packing algorithms, due to its low computational expense. The stochastic generation method has the ability to represent many complex phenomena in particulate materials, the characteristics of which may be controlled through the careful choice of intrinsic field parameters and lithotype rules.

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Efficiency gains of a multi-scale integration method applied to a scale-separated model for rapidly rotating dynamos

Cited by 5 publications

References 30 publications

Recent Developments in Theories of Inhomogeneous and Anisotropic Turbulence

Recent Developments in Theories of Inhomogeneous and Anisotropic Turbulence

Recent Developments in Theories of Inhomogeneous and Anisotropic Turbulence

A Statistical Finite Element Method Integrating a Plurigaussian Random Field Generator for Multi-scale Modelling of Solute Transport in Concrete

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