A Model Problem for Unsaturated Porous Media Flow with Dynamic Capillary Pressure
نویسندگان
چکیده
We consider a simplified model of vertical non-static groundwater flow, resulting in a Burgers’ diffusive equation extended with a third order term with mixed derivatives in space and time. This model is motivated by previous work on the existence of travelling wave solutions on a more general model. We investigate stability of travelling wave solutions of the simplified model, for which we first obtain well-posedness results. 2000 Mathematics Subject Classification: 35K70, 76S05,74H40.
منابع مشابه
Solvability of an Unsaturated Porous Media Flow Problem with Thermomechanical Interaction
Abstract. A PDE system consisting of the momentum balance, mass balance, and energy balance equations for displacement, capillary pressure, and temperature as a model for unsaturated fluid flow in a porous viscoelastoplastic solid is shown to admit a solution under appropriate assumptions on the constitutive behavior. The problem involves two hysteresis operators accounting for plastic and capi...
متن کاملCapillary Effects on Surface Enhancement in a Non-Homogeneous Fibrous Porous Medium
The evaluation of a free fluid surface in a porous medium has several mathematical applications that are important in industries using molds, particularly in the fluid injection process. The vacuum-assisted resin transfer molding (VARTM) process is a promising technology in the primary composite industry. An accurate computational simulation of the VARTM process would be a cost-effective tool i...
متن کاملAn analytical solution for transient radial flow through unsaturated fractured porous media
[1] This paper presents analytical solutions for one-dimensional radial transient flow through a horizontal, unsaturated fractured rock formation. In these solutions, unsaturated flow through fractured media is described by a linearized Richards’ equation, while fracture-matrix interaction is handled using the dual-continuum concept. Although linearizing Richards’ equation requires a specially ...
متن کاملA global existence result for the equations describing unsaturated flow in porous media with dynamic capillary pressure
In this paper we investigate the pseudoparabolic equation ∂tc = div { k (c) μ ( − P ′ C (c)∇c + τ∇∂tc + gρen )} , where τ is a positive constant, c is the moisture content, k is the hydraulic conductivity and PC is the static capillary pressure. This equation describes unsaturated flows in porous media with dynamic capillary pressure saturation relationship. In general, such models arise in a n...
متن کاملHysteresis models and gravity fingering in porous media
We study flow problems in unsaturated porous media. Our main interest is the gravity driven penetration of a dry material, a situation in which fingering effects can be observed experimentally and numerically. The flow is described by either a Richards or a two-phase model. The important modelling aspect regards the capillary pressure relation which can include static hysteresis and dynamic cor...
متن کامل