Reduced Model-Error Source Terms for Fluid Flow

Edeling, Wouter; Crommelin, Daan

doi:10.7712/120219.6351.18769

Cited by 2 publications

(5 citation statements)

References 17 publications

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“…Finally, an interesting avenue of future research is the a-priori incorporation of constraints from mathematical physics. Initial work along these lines showed promising results [4], with no enstrophy bias. Another option involves rewriting the eddy forcing in tensor format, such that certain constraints on the tensor shape can be found [20].…”

Section: Discussionmentioning

confidence: 99%

Towards Data-Driven Dynamic Surrogate Models for Ocean Flow

Edeling

Crommelin

2019

Proceedings of the Platform for Advanced Scientific Computing Conference

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Coarse graining of (geophysical) flow problems is a necessity brought upon us by the wide range of spatial and temporal scales present in these problems, which cannot be all represented on a numerical grid without an inordinate amount of computational resources. Traditionally, the effect of the unresolved eddies is approximated by deterministic closure models, i.e. so-called parameterizations. The effect of the unresolved eddy field enters the resolved-scale equations as a forcing term, denoted as the 'eddy forcing'. Instead of creating a deterministic parameterization, our goal is to infer a stochastic, data-driven surrogate model for the eddy forcing from a (limited) set of reference data, with the goal of accurately capturing the long-term flow statistics. Our surrogate modelling approach essentially builds on a resampling strategy, where we create a probability density function of the reference data that is conditional on (time-lagged) resolved-scale variables. The choice of resolved-scale variables, as well as the employed time lag, is essential to the performance of the surrogate. We will demonstrate the effect of different modelling choices on a simplified ocean model of two-dimensional turbulence in a doubly periodic square domain. CCS CONCEPTS• Mathematics of computing → Stochastic processes; • Computing methodologies → Multiscale systems; • Applied computing → Environmental sciences.

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Section: Discussionmentioning

confidence: 99%

Towards Data-Driven Dynamic Surrogate Models for Ocean Flow

Edeling

Crommelin

2019

Proceedings of the Platform for Advanced Scientific Computing Conference

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“…We study the same model as in [3,15] , i.e. the forced-dissipative vorticity equations for two-dimensional incompressible flow.…”

Section: Governing Equationsmentioning

confidence: 99%

“…Initial results along these lines can be found in [15] . These results were specific to the energy E and enstrophy Z , and employed ad-hoc parameterizations in the reduced subgrid scale term.…”

Section: Has An Unclosed Component Which Is Of the Same Dimension Asmentioning

confidence: 99%

“…Let us now introduce the short-hand notation V i := ∂ q i / ∂ ω, such that ( V i , r ) is the subgrid scale term in the transport equations of our QoI. Thus, since we replace r by r (given by (15) ), and that we aim to track Q re f i via r , the only terms by which we can do so directly have the following form…”

Section: Has An Unclosed Component Which Is Of the Same Dimension Asmentioning

confidence: 99%

“…The physical insight we gained is that for Q i , our eddy-forcing parameterization (15) results in a Q i source term containing ( V i , P i ), which can act to either dissipate or produce Q i at any given time. Therefore, in light of our goal to track the reference value Q re f i during the training phase, the task of τ i must be to switch on dissipation or production conditional on the value of…”

Section: Has An Unclosed Component Which Is Of the Same Dimension Asmentioning

confidence: 99%

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Reducing data-driven dynamical subgrid scale models by physical constraints

Edeling¹,

Crommelin²

2020

Computers & Fluids

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a b s t r a c tRecent years have seen a growing interest in using data-driven (machine-learning) techniques for the construction of cheap surrogate models of turbulent subgrid scale stresses. These stresses display complex spatio-temporal structures, and constitute a difficult surrogate target. In this paper we propose a datapreprocessing step, in which we derive alternative subgrid scale models which are virtually exact for a user-specified set of spatially integrated quantities of interest. The unclosed component of these new subgrid scale models is of the same size as this set of integrated quantities of interest. As a result, the corresponding training data is massively reduced in size, decreasing the complexity of the subsequent surrogate construction.

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Reduced Model-Error Source Terms for Fluid Flow

Cited by 2 publications

References 17 publications

Towards Data-Driven Dynamic Surrogate Models for Ocean Flow

Towards Data-Driven Dynamic Surrogate Models for Ocean Flow

Reducing data-driven dynamical subgrid scale models by physical constraints

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