|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 occurence 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.|
|Subject Headings:||porous media|
|Subject Headings (RSWK):||Numerische Strömungssimulation|
|Appears in Collections:||Preprints der Fakultät für Mathematik|
Schweizer, Ben Prof. Dr.
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