Homogenization of Nonlocal Navier--Stokes--Korteweg Equations for Compressible Liquid-Vapor Flow in Porous Media

Rohde, Christian; Wolff, Lars von

doi:10.1137/19m1242434

Cited by 6 publications

(3 citation statements)

References 18 publications

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“…Classical two-scale convergence and compactness result can be found in [30] and [2] ; see also [24]. The earliest result that we know regarding homogenization and dimension reduction for a thin layer including also a drift with a Navier-Stokes-type nonlinearity is [25]; see also [36] for a more recent account. The simultaneous homogenization and dimension reduction of reaction-diffusion equations with nonlinear reaction rates posed in a thin heterogeneous layer have been carefully studied in [29].…”

Section: Introductionmentioning

confidence: 96%

Scaling effects on the periodic homogenization of a reaction-diffusion-convection problem posed in homogeneous domains connected by a thin composite layer

Raveendran¹,

Cirillo²,

Bonis³

et al. 2021

Preprint

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We study the question of periodic homogenization of a variably scaled reaction-diffusion problem with non-linear drift posed for a domain crossed by a flat composite thin layer. The structure of the non-linearity in the drift was obtained in earlier works as hydrodynamic limit of a totally asymmetric simple exclusion process (TASEP) process for a population of interacting particles crossing a domain with obstacle.Using energy-type estimates as well as concepts like thin-layer convergence and two-scale convergence, we derive the homogenized evolution equation and the corresponding effective model parameters for a regularized problem. Special attention is paid to the derivation of the effective transmission conditions across the separating limit interface in essentially two different situations: (i) finitely thin layer and (ii) infinitely thin layer.This study should be seen as a preliminary step needed for the investigation of averaging fast non-linear drifts across material interfaces -a topic with direct applications in the design of thin composite materials meant to be impenetrable to high-velocity impacts.

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Section: Introductionmentioning

confidence: 96%

Scaling effects on the periodic homogenization of a reaction-diffusion-convection problem posed in homogeneous domains connected by a thin composite layer

Raveendran¹,

Cirillo²,

Bonis³

et al. 2021

Preprint

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“…Phase-field models for two-phase porous-media flow, including the derivation of macro-scale models are discussed in [5][6][7][8][9][10]. More precisely, in [5,6] phase-field pore-scale models are discussed, and the convergence to the corresponding sharp-interface model is proved when passing the diffuse-interface parameter to zero.…”

Section: Introductionmentioning

confidence: 99%

“…A macro-scale model is derived in [9] under certain scaling assumptions, but without accounting for variable surface-tension effects. A macro-scale phase-field model for compressible fluids is derived in [8]. Here we consider a two-scale phasefield model derived by formal homogenization techniques [11].…”

Section: Introductionmentioning

confidence: 99%

A numerical scheme for two-scale phase-field models in porous media

Bastidas

Sharmin

Bringedal

et al. 2021

Proceedings of the YIC 2021 - VI ECCOMAS Young Investigators Conference

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A porous medium is a highly complex domain, in which various processes can take place at different scales. Examples in this sense are the multi-phase flow and reactive transport. Here, due to processes like dissolution or precipitation, or chemical deposition, which are encountered at the scale of pores (the micro-scale), the local structure and geometry of the pores may change, impacting the fluid flow. Since these micro-scale processes depend on the model unknowns (e.g., the solute concentration), free boundaries are encountered, separating the space available for flow from the solid, impermeable part in the medium. Here we consider a phase-field approach to model the evolution of the evolving interfaces at the micro-scale. For mineral precipitation and dissolution, we have evolving fluid-solid interfaces. If considering multi-phase flow, evolving fluid-fluid interfaces are also present. After applying a formal homogenization procedure, a two-scale phase-field model is derived, describing the averaged behavior of the system at the Darcy scale (the macro-scale). In this two-scale model, the micro and the macro scale are coupled through the calculation of the effective parameters. Although the resulting two-scale model is less complex than the original, the numerical strategies based on the homogenization theory remain computationally expensive as they require the computation of several problems over different scales, and in each mesh element. Here, we propose an adaptive two-scale scheme involving different techniques to reduce the computational effort without affecting the accuracy of the simulations. These strategies include iterations between scales, an adaptive selection of the elements wherein effective parameters are computed, adaptive mesh refinement, and efficient non-linear solvers.

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A relaxation model for the non-isothermal Navier-Stokes-Korteweg equations in confined domains

Keim¹,

Munz²,

Rohde³

2023

Journal of Computational Physics

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Homogenization of Nonlocal Navier--Stokes--Korteweg Equations for Compressible Liquid-Vapor Flow in Porous Media

Cited by 6 publications

References 18 publications

Scaling effects on the periodic homogenization of a reaction-diffusion-convection problem posed in homogeneous domains connected by a thin composite layer

Scaling effects on the periodic homogenization of a reaction-diffusion-convection problem posed in homogeneous domains connected by a thin composite layer

A numerical scheme for two-scale phase-field models in porous media

A relaxation model for the non-isothermal Navier-Stokes-Korteweg equations in confined domains

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