A preliminary study on multiscale ELLAM schemes for transient advection‐diffusion equations

Cheng, Aijie; Wang, Qing; Hong, Weiyi

doi:10.1002/num.20496

Cited by 9 publications

(3 citation statements)

References 13 publications

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“…A feasible objective is to develop a new set of computational methods that can fill in the large gap between these two model types, with a specific focus on more efficient models to solve the complex set of equations, hybrid models that combine both the simplified and the complex in a kind of multi-scale framework, and a more efficient treatment that will allow the probabilistic treatment of the leakage problem to be accomplished much more efficiently. Certain upscaling or multiscale techniques might also need to be applied [63][64][65][66]. (iv) We considered the critical leakage pathways like human-induced, abandoned wells and assumed that they are vertical.…”

Section: Discussionmentioning

confidence: 99%

A probabilistic collocation Eulerian–Lagrangian localized adjoint method on sparse grids for assessingCO2leakage through wells in randomly heterogeneous porous media

Wang

Ren

Jia

et al. 2015

Computer Methods in Applied Mechanics and Engineering

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We develop a probabilistic collocation Eulerian-Lagrangian localized adjoint method on sparse grids for assessing CO 2 leakage through wells in randomly heterogeneous porous media, by utilizing the intrinsic mathematical, numerical, and physical properties of the mathematical model. We model the process in which CO 2 is injected into a deep aquifer, spreads within the aquifer and, upon reaching a leaky well, rises up to a shallower aquifer, to quantify the leakage rate, which depends on the pressure build-up in the aquifer due to injection and the buoyancy of CO 2 . The underlying Eulerian-Lagrangian framework has high potential to improve the efficiency and accuracy for the numerical simulation of complex flow and transport processes in CO 2 sequestration. The sparse grid probabilistic collocation framework adds computationally efficient uncertainty quantification functionality onto pre-existing Eulerian-Lagrangian methods in a nonintrusive manner. It also provides a scalable framework to consider uncertainty in a straightforward parallel manner. Preliminary numerical experiments show the feasibility and potential of the method.

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Section: Discussionmentioning

confidence: 99%

A probabilistic collocation Eulerian–Lagrangian localized adjoint method on sparse grids for assessingCO2leakage through wells in randomly heterogeneous porous media

Wang

Ren

Jia

et al. 2015

Computer Methods in Applied Mechanics and Engineering

Self Cite

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“…One early attempt to use multiscale methods are Eulerian Lagrangian localized adjoint methods (ELLAM), which constitute a space-time finite element framework, see [9,18], and form the basis of the multiscale version MsELLAM [10,37]. Such methods rely on operator splitting and basis functions are required to satisfy an adjoint equation.…”

Section: Motivation and Overviewmentioning

confidence: 99%

Semi-Lagrangian Subgrid Reconstruction for Advection-Dominant Multiscale Problems with Rough Data

Simon

Behrens

2021

J Sci Comput

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We introduce a new framework of numerical multiscale methods for advection-dominated problems motivated by climate sciences. Current numerical multiscale methods (MsFEM) work well on stationary elliptic problems but have difficulties when the model involves dominant lower order terms. Our idea to overcome the associated difficulties is a semi-Lagrangian based reconstruction of subgrid variability into a multiscale basis by solving many local inverse problems. Globally the method looks like a Eulerian method with multiscale stabilized basis. We show example runs in one and two dimensions and a comparison to standard methods to support our ideas and discuss possible extensions to other types of Galerkin methods, higher dimensions and nonlinear problems.

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“…One early attempt to use multiscale methods are Eulerian Lagrangian localized adjoint methods (ELLAM), which constitute a space-time finite element framework, see [9,20], and form the basis of their multiscale version MsELLAM [36,10]. Such methods rely on operator splitting and basis functions are required to satisfy an adjoint equation.…”

Section: Introductionmentioning

confidence: 99%

Semi-Lagrangian Subgrid Reconstruction for Advection-Dominant Multiscale Problems

Simon¹,

Behrens²

2019

Preprint

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We introduce a new framework of numerical multiscale methods for advectiondominated problems motivated by climate sciences. Current numerical multiscale methods (MsFEM) work well on stationary elliptic problems but have difficulties when the model involves dominant lower order terms. Our idea to overcome the assocociated difficulties is a semi-Lagrangian based reconstruction of subgrid variablity into a multiscale basis by solving many local inverse problems. Globally the method looks like a Eulerian method with multiscale stabilized basis. We show example runs in one and two dimensions and a comparison to standard methods to support our ideas and discuss possible extensions to other types of Galerkin methods, higher dimensions and nonlinear problems.

show abstract

A preliminary study on multiscale ELLAM schemes for transient advection‐diffusion equations

Cited by 9 publications

References 13 publications

A probabilistic collocation Eulerian–Lagrangian localized adjoint method on sparse grids for assessingCO2leakage through wells in randomly heterogeneous porous media

A probabilistic collocation Eulerian–Lagrangian localized adjoint method on sparse grids for assessingCO2leakage through wells in randomly heterogeneous porous media

Semi-Lagrangian Subgrid Reconstruction for Advection-Dominant Multiscale Problems with Rough Data

Semi-Lagrangian Subgrid Reconstruction for Advection-Dominant Multiscale Problems

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