Travelling wave solutions for gravity fingering in porous media flows

Koondanibha Mitra; Andreas Rätz; Ben Schweizer

doi:10.1016/j.jde.2024.02.036

Travelling wave solutions for gravity fingering in porous media flows

Koondanibha Mitra, Andreas Rätz, Ben Schweizer (Corresponding author)

Computational Illumination Optics

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Abstract

We study an imbibition problem for porous media. When a wetted layer is above a dry medium, gravity leads to the propagation of the water downwards into the medium. In experiments, the occurrence of fingers was observed, a phenomenon that can be described with models that include hysteresis. In the present paper we describe a single finger in a moving frame and set up a free boundary problem to describe the shape and the motion of one finger that propagates with a constant speed. We show the existence of solutions to the travelling wave problem and investigate the system numerically.

Original language	English
Pages (from-to)	120-151
Number of pages	32
Journal	Journal of Differential Equations
Volume	394
DOIs	https://doi.org/10.1016/j.jde.2024.02.036
Publication status	Published - 15 Jun 2024

Keywords

Porous media
Higher dimensional travelling waves
Hysteresis
Free boundaries

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title = "Travelling wave solutions for gravity fingering in porous media flows",

abstract = "We study an imbibition problem for porous media. When a wetted layer is above a dry medium, gravity leads to the propagation of the water downwards into the medium. In experiments, the occurrence of fingers was observed, a phenomenon that can be described with models that include hysteresis. In the present paper we describe a single finger in a moving frame and set up a free boundary problem to describe the shape and the motion of one finger that propagates with a constant speed. We show the existence of solutions to the travelling wave problem and investigate the system numerically.",

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T1 - Travelling wave solutions for gravity fingering in porous media flows

AU - Mitra, Koondanibha

AU - Rätz, Andreas

AU - Schweizer, Ben

PY - 2024/6/15

Y1 - 2024/6/15

N2 - We study an imbibition problem for porous media. When a wetted layer is above a dry medium, gravity leads to the propagation of the water downwards into the medium. In experiments, the occurrence of fingers was observed, a phenomenon that can be described with models that include hysteresis. In the present paper we describe a single finger in a moving frame and set up a free boundary problem to describe the shape and the motion of one finger that propagates with a constant speed. We show the existence of solutions to the travelling wave problem and investigate the system numerically.

AB - We study an imbibition problem for porous media. When a wetted layer is above a dry medium, gravity leads to the propagation of the water downwards into the medium. In experiments, the occurrence of fingers was observed, a phenomenon that can be described with models that include hysteresis. In the present paper we describe a single finger in a moving frame and set up a free boundary problem to describe the shape and the motion of one finger that propagates with a constant speed. We show the existence of solutions to the travelling wave problem and investigate the system numerically.

KW - Porous media

KW - Higher dimensional travelling waves

KW - Hysteresis

KW - Free boundaries

U2 - 10.1016/j.jde.2024.02.036

DO - 10.1016/j.jde.2024.02.036

M3 - Article

SN - 0022-0396

VL - 394

SP - 120

EP - 151

JO - Journal of Differential Equations

JF - Journal of Differential Equations

ER -

Travelling wave solutions for gravity fingering in porous media flows

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Keywords

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