Sharif Digital Repository

In this thesis , we consider nonnegative (continuous) weak solutions of the porous medium equation with source , u_t-∆u^m=u^p, and p>m>1 .
Assume that, m>1 and 1< p/m u_t-∆u^m=u^p,xϵR^n ,tϵR
has no nontrivial, bounded radial solutions u≥0 .
In one space-dimensional, the conclusion of the result mentioned above remains true without the assumption of the radial symmetry. The proof is based on the intersection-comparison arguments , zero number argum- ents and a key step is to show the... 

Many natural and engineering materials have a heterogeneous structure at a certain level of observation. These materials are often referred to as composite materials or multi-phase materials or heterogeneous materials. It has been widely recognized that many macroscopic phenomena originate from the mechanics of the microstructural constituents, such as inclusions, cracks, voids, etc. The size, shape, spatial distribution, volume fraction and properties of the microstructural constituents have a significant impact on the behavior of the material observed at the macroscale. The nature of hydrocarbon reservoirs as multi-phase porous media are known for heterogeneous media at various multiple... 

Rapid preparation of a homogeneous mixture is essential for many chemical and biological applications, such as micro-scale biological-chemical agent detection, drug delivery, and DNA hybridization. Some mixing systems have a micro-scale geometry, which results in a very slow mixing process, mainly due to laminar flow in these systems. Mixing in a slow flow is performed only by molecular diffusion. In the absence of any disturbances, increased mixing is not possible simply by diffusion. Accordingly, a suitable and innovative method to improve mixing for such systems is required. Induced charge electro-osmosis is a new field of electro-osmotic flow, which performs better than conventional... 

The probability of crack appearance in soil structures and porous media is not avoidable, which could be the reason of structures collapse. According to the important affects, which they play in the vulnerability of the structures, they should be taking into account. The cracks have different effects on various materials. The most properties that cracks have, is their ability of conveying the fluid flow. For the most accurate analysis of discontinues domains, their governing equations should be taken and solved. Finite Element Method is one of the best solutions of differential governing equations. However, the appearance of some problems in the modeling of discontinues domain, was the... 

Shear band is more relevant in porous medias rather than continuum media. Shear band is a narrow region of solid experiencing intense shearing. After initiation of shear band, the sliding on two sides of the band occurs. The area inside the shear band undergoes extreme plastic deformation, while experiences elastic unloading outside of the band. In porous materials, the direction of slip and discontinuity in displacement field is not same, as a result of dilation. In fact dilation requires an increase in the volume of the shear band zone. The main difficulty in modeling the shear band is that the width of shear band in contrast to the dimension of the media, is too small. Consequently, the... 

Hydraulic fracture propagation occures in fractured saturated porous media due to fluid leakage from the crack faces and the consequent fluid pressure. In many cases, hydraulic fracturing may be considered as a detrimental phenomenon which endangers stability of human made structures like rock-fill dames. However, in recent decades the hydraulic fracturing has been an appealing method for increasing the production rate of low-permeability oil and gas reservoirs in petroleum industries.
In order to efficiently assess the behavior of saturated madia one needs to consider the coupling between the solid and fluid phases of the medium. To do so, the coupled formulation refered to as u-p... 

Modeling the water flow in cohesive fracture is a fundamental issue in the crack growth simulation of cracked concrete gravity dams and hydraulic fracture problems. Discontinuities in porous materials such as concrete, soil and rock have important role on the mechanical and hydraulic behavior of a multiphase system. The creation and propagation of discontinuities, such as cracks in a multi-physics system, lead to a complex non-linear coupled problem with continuous topological changes in the domain.In this study, a mathematical model is presented for for the analysis of dynamic fracture propagation in the saturated and semi-saturated porous media. The solid behavior incorporates a discrete... 

In this thesis, a fully coupled numerical model is developed for the modeling of dynamic cohesive crack propagation and hydraulic fracture in saturated porous media using extended finite element method. Many engineering structures like concrete or soil dams and buildings foundation are built with porous materials like concrete, rock and soil. Behavior of these materials in which void among the solid particles are filled with one or more fluids are so complicated rather than single solid phase. Dynamic analysis of porous mediums containing a discontinuity has many applications in various civil engineering fields including structure, earthquake, hydraulic structures, etc. For instance... 

In current study, we investigate crack propagation is saturated porous media by using the extended finite element method. The porous media is simulated by using well-known u-p formulation. In this regard the equilibrium equation of the bulk is employed together with momentum and mass balance equations of the fluid phase. The XFEM, known as one of the best methods in crack simulations, will be employed for numerical modelings. According to the method, crack propagation does not involve any changes in meshing, yet by using the concept of enrichment the elements are enabled to possess crack interfaces inside themselves. Thus by crack growth, only discritization alters and new DOFs are inserted... 

The main purpose of this study is computational modeling of saturated deformable porous media using multiscale finite element method and explicit modeling of discontinuities such as microcracks at the microscopic scale. The real engineering problems we deal with in the simulation of the phenomenas happening in nature or industrial applications, in contrast to the simplifications being assumed, occur in heterogeneous materials. Although most microscopic heterogeneities are not present in macroscopic scale, they do have their effects on material behavior. In the computational homogenization method, the problem is analyzed coupled in two scales, therefore, the macroscopic behavior of media is... 

Soil structures have important roles in civil engineering applications. The most important types of these structures are soil dams and foundations which their damages may cause huge loss. Thus, appropriate analysis of these structures under possible loading conditions is unavoidable. The real behavior of this media can be achieved from the solution of its coupled governing differential equations. In order to solve this set of equations in practical applications, appropriate numerical solutions should be used. The finite element method can be called as one of the most important numerical solutions of differential equations which have been used in analyzing different types of engineering... 

The main goal of this research is to investigate the effects of different types of heterogeneities on fluid flow and solute transport in saturated porous media. These heterogeneities are micro- and macro-fractures and cavities. For modeling micro- and macro-fractures we used an equivalent continuum model and extended finite element, respectively. Also, we modeled the problem by using mass conservation law for both components of the problem – fluid flow and the solute – and Darcy’s law. In modeling vuggy porous media, due to the high velocity of the fluid inside the free flow areas i.e. channels and cavities, we could not model the medium properly using Darcy’s law. Therefore, we had to use a... 

A considerable number of engineering applications deal with flow of fluid(s) through particulate porous media. For certain engineering problems, fluid flow may displace and even dislodge the solid particles from the mass where a fluid-particle flow occurs. The complexity of involving processes which should be studied at the scale of moving particles transforms the analyses of these problems towards a difficult engineering task. Characteristics of solid grains such as size and shape and properties of the flowing fluid(s) such as viscosity and surface tension play essential roles in the behavior of fluid-particle systems. Also, when fluid flows through porous media, secondary processes such as... 

Particulate porous mateials have always been of interest in terms of reducing shock waves effects in different protective applications. Therefore, the physics governing the flow in porous media is especially significant for which different models have been presented by the researchers. The complexities of these media have caused many existing models to be unable to properly predict the behavior of granular media under shock loadings. On the other hand, the complexity of the equations makes the numerical solution of them cumbersome and costly in a way that many researchers do not solve the whole coupled equations and reduce their number. In addition, current high-resolution TVD solutions of...