Samenvatting
In this thesis we investigate pseudoparabolic equations modelling the twophase flow in porous media, where dynamic effects in the difference of the phase pressures are included. Specifically, the time derivative of saturation is taken into account.
The first chapter investigates the travelling wave (TW) solutions, the existence anduniqueness of smooth TW solutions are proved by ordinary differential equation techniques.
The existence depends on the parameters involved. There is a threshold value for one of the parameters, the damping coefficient. When the damping coefficient is beyond the threshold value, smooth TW solutions do not exist any more. Instead, nonsmooth (sharp) TW solutions are introduced and their existence is shown. The theoretical results for both smooth and nonsmooth TW solutions are confirmed by numerical computations.
In the next chapter, the analysis is extended to weak solutions. In a simplified case where the mixed (time and space) orderthree derivative term is linear, the existence and uniqueness of a weak solution are obtained. Next, the complex model involving nonlinear and possibly degenerate capillary induced diffusion function is considered. Then the existence is obtained by employing regularization techniques, compensated compactness and equiintegrability arguments.
Finally, inspired by the nature of the capillary pressure, different formulations of the equation are introduced and their equivalence is proved. The corresponding numerical scheme is implemented and numerical results are given, which agree well with the theoretical results.
Originele taal2  Engels 

Kwalificatie  Doctor in de Filosofie 
Toekennende instantie 

Begeleider(s)/adviseur 

Datum van toekenning  31 jan 2012 
Plaats van publicatie  Eindhoven 
Uitgever  
Gedrukte ISBN's  9789038630694 
DOI's  
Status  Gepubliceerd  2012 
Vingerafdruk Duik in de onderzoeksthema's van 'Dynamic capillarity in porous media : mathematical analysis'. Samen vormen ze een unieke vingerafdruk.
Citeer dit
Fan, Y. (2012). Dynamic capillarity in porous media : mathematical analysis. Technische Universiteit Eindhoven. https://doi.org/10.6100/IR721598