Asymptotic analysis for Korteweg models

Dreyer, Wolfgang; Giesselmann, Jan; Kraus, Christiane; Rohde, Christiane

doi:10.4171/ifb/275

Cited by 19 publications

(27 citation statements)

References 19 publications

(20 reference statements)

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“…At a theoretical level, the sharp interface limit of the NavierStokes-Korteweg system has been analyzed using matched asymptotic expansions in the interface thickness [60,90]. From a physical perspective, should be chosen to match the actual vapor-liquid surface tension at a given temperature.…”

Section: A Scaling Of Effective Surface Tension With the Numerical Imentioning

confidence: 99%

Pore-scale modeling of phase change in porous media

Cueto‐Felgueroso

Juanes

2018

Phys. Rev. Fluids

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The combination of high-resolution visualization techniques and pore-scale flow modeling is a powerful tool used to understand multiphase flow mechanisms in porous media and their impact on reservoir-scale processes. One of the main open challenges in pore-scale modeling is the direct simulation of flows involving multicomponent mixtures with complex phase behavior. Reservoir fluid mixtures are often described through cubic equations of state, which makes diffuse-interface, or phase-field, theories particularly appealing as a modeling framework. What is still unclear is whether equation-of-state-driven diffuse-interface models can adequately describe processes where surface tension and wetting phenomena play important roles. Here we present a diffuse-interface model of single-component two-phase flow (a van der Waals fluid) in a porous medium under different wetting conditions. We propose a simplified Darcy-Korteweg model that is appropriate to describe flow in a Hele-Shaw cell or a micromodel, with a gap-averaged velocity. We study the ability of the diffuse-interface model to capture capillary pressure and the dynamics of vaporization-condensation fronts and show that the model reproduces pressure fluctuations that emerge from abrupt interface displacements (Haines jumps) and from the breakup of wetting films.

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Section: A Scaling Of Effective Surface Tension With the Numerical Imentioning

confidence: 99%

Pore-scale modeling of phase change in porous media

Cueto‐Felgueroso

Juanes

2018

Phys. Rev. Fluids

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“…The system (16) extends the classical NSK system by an additional screened Poisson equation for the new unknown c ;˛D c ;˛. x; t / 2 R. Before we discuss the relation between the relaxation system and the NSK system (10), let us present the following result on thermodynamical consistency for (16). (16), which satisfies the initial conditions…”

Section: A Relaxation For the Navier-stokes-korteweg Systemmentioning

confidence: 99%

“…For the last line, we used the density equation in (16). Multiplying the elliptic equation in (16) by c t .x; t / and using the second boundary condition in (18) yields…”

Section: Proofmentioning

confidence: 99%

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Relaxation of the Navier–Stokes–Korteweg equations for compressible two‐phase flow with phase transition

Neusser

Rohde

Schleper

2015

Numerical Methods in Fluids

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SUMMARYThe Navier-Stokes-Korteweg (NSK) system is a classical diffuse-interface model for compressible twophase flow. However, the direct numerical simulation based on the NSK system is quite expensive and in some cases even not possible. We propose a lower-order relaxation of the NSK system with hyperbolic firstorder part. This allows applying numerical methods for hyperbolic conservation laws and removing some of the difficulties of the original NSK system. To illustrate the new ansatz, we first present a local discontinuous Galerkin method in one and two spatial dimensions. It is shown that we can compute initial boundary value problems with realistic density ratios and perform stable computations for small interfacial widths. Second, we show that it is possible to construct a semi-discrete finite-volume scheme that satisfies a discrete entropy inequality.

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“…The issue of very small interfaces is especially important because the NSK model can only provide the correct amount of capillary forces if the interface is extremely small [17,25,27]. One idea to loosen the strict coupling between interfacial width and capillary forces is to introduce an additional Cahn-Hilliard or Allen-Cahn type equation for a new phase field variable.…”

Section: Introductionmentioning

confidence: 99%

An asymptotic-preserving method for a relaxation of the Navier–Stokes–Korteweg equations

Chertock

Degond

Neusser

2017

Journal of Computational Physics

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The Navier-Stokes-Korteweg (NSK) equations are a classical diffuse-interface model for compressible two-phase flow. As direct numerical simulations based on the NSK system are quite expensive and in some cases even impossible, we consider a relaxation of the NSK system, for which robust numerical methods can be designed. However, time steps for explicit numerical schemes depend on the relaxation parameter and therefore numerical simulations in the relaxation limit are very inefficient. To overcome this restriction, we propose an implicitexplicit asymptotic-preserving finite volume method. We prove that the new scheme provides a consistent discretization of the NSK system in the relaxation limit and demonstrate that it is capable of accurately and efficiently computing numerical solutions of problems with realistic density ratios and small interfacial widths.

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Asymptotic analysis for Korteweg models

Cited by 19 publications

References 19 publications

Pore-scale modeling of phase change in porous media

Pore-scale modeling of phase change in porous media

Relaxation of the Navier–Stokes–Korteweg equations for compressible two‐phase flow with phase transition

An asymptotic-preserving method for a relaxation of the Navier–Stokes–Korteweg equations

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