OPTIMAL ERROR ESTIMATES OF A DECOUPLED SCHEME BASED ON TWO-GRID FINITE ELEMENT FOR MIXED NAVIER-STOKES/DARCY MODEL

Although the two-grid finite element decoupled scheme for mixed Navier-Stokes/ Darcy model in literatures has given the numerical results of optimal convergence order, the theoretical analysis only obtain the optimal error order for the porous media flow and a non-optimal error order for the fluid flow. In this article, we give a more rigorous of the error analysis for the fluid flow and obtain the optimal error estimates of the velocity and the pressure.

Modified two-grid method for solving coupled Navier-Stokes/Darcy model based on Newton iteration

A new decoupled two-gird algorithm with the Newton iteration is proposed for solving the coupled Navier-Stokes/Darcy model which describes a fluid flow filtrating through porous media. Moreover the error estimate is given, which shows that the same order of accuracy can be achieved as solving the system directly in the fine mesh when h = H2. Both theoretical analysis and numerical experiments illustrate the efficiency of the algorithm for solving the coupled problem.

Model and method of permeability evaluation based on mud invasion effects

The evaluation of permeability in reservoir assessment is a complex problem. Thus, it is difficult to perform direct evaluation permeability with conventional well-logging methods. Considering that reservoir permeability significantly affects mud invasion during drilling, we derive a mathematical model to assess the reservoir permeability based on mud invasion. A numerical model is first used to simulate the process of mud invasion and mud cake growth. Then, based on Darcy＇s law, an approximation is derived to associate the depth of mud invasion with reservoir permeability. A mathematical model is constructed to evaluate the reservoir permeability as a function of the mud invasion depth in time-lapse logging. Sensitivity analyses of the reservoir porosity, permeability, and water saturation are performed, and the results suggest that the proposed model and method are well suited for oil layers or oil-water layers of low porosity and low permeability. Numerical simulations using field logging and coring data suggest that the evaluated and assumed permeability data agree, validating the proposed model and method.

Stokes'first problem for the fourth order fluid in a porous half space

In this study, the flow of a fourth order fluid in a porous half space is modeled. By using the modified Darcy＇s law, the flow over a suddenly moving flat plate is studied numerically. The influence of various parameters of interest on the velocity profile is revealed.

Linear instability of the electrified free interface between two cylindrical shells of viscoelastic fluids through porous media

In this paper, we have discussed the linear stabil- ity analysis of the electrified surface separating two coaxial Oldroyd-B fluid layers confined between two impermeable rigid cylinders in the presence of both interfacial insoluble surfactant and surface charge through porous media. The case of long waves interfacial stability has been studied. The dispersion relation is solved numerically and hence the ef- fects of various parameters are illustrated graphically. Our results reveal that the influence of the physicochemical pa- rameterβ is to shrink the instability region of the surface and reduce the growth rate of the unstable normal modes. Such important effects of the surfactant on the shape of in- terfacial structures are more sensitive to the variation of the βcorresponding to non-Newtonian fluids-model compared with the Newtonian fluids model. In the case of long wave limit, it is demonstrated that increasing r, has a dual role in- fluence （de-stabilizing effects） depending on the viscosity of the core fluid. It has a destabilizing effect at the large values of the core fluid viscosity coefficient, while this role is ex- changed to a regularly stabilizing influence at small values of such coefficient.

The Reflection of Normal Incident Waves by Absorbing-Type Breakwaters

This paper investigates the reflection of normal incident waves produced by absorbing-type breakwaters. The absorbing-type breakwaters in this study consist of a vertical porous plate, a submerged permeable caisson, and an impermeable back wall. The flow field is divided into four regions： a porous caisson region, and three pure water regions. Under the assumptions of linear wave theory, Darcy＇s law in the perforated wall, and the pore velocity potential theory of Sollitt and Cross （1972） in the porons caisson region, this study creates a 2-D BEM model to calculate the reflection coefficients of water waves using several breakwater properties. This numerical model is calibrated by previous numerical studies and limiting cases for a partially perforated-wall caisson breakwater and a vertical porous breakwater with an impermeable back wall. Generally speaking, the wave dissipation in absorbing-type breakwaters is bigger than that for a partially perforatedwall caisson breakwater. The reflection coefficient values imply the performance of wave absorbers in this study. Therefore, we examine the major factors that affect the reflection coefficient.

Theoretical and Experimental Analysis of Vortex Origin

Several investigations refer to the issue of creation and identification of vortices in flows with different regime and presence of obstacles. Reasons have to do with the crucial role that vortices play in nature and industrial processes （sediment transport, mixing, radiation, noise, etc.）. Despite the contributions, further work is needed in order to perform more analysis of the mathematical arguments used to explain this phenomenon. In this idea order, the paper presents some advances in mathematical analysis and experimental results. In the first section, we do a description of the fluid motion from a fractional view through a sequence of three steps： Darcy＇s law, Navier-Stokes equations and Reynolds equations. Next, a representation of the temporal change of kinetic energy is found, which allows the possibility of the two signs. We obtain a description of the process of vortex creation. A length that represents the transition between flow and vortex intensity is found; then a succession of lengths is established that allows scaling from micro to macro. In the second section, experimental results are present; we consider vortex creation and its detection upstream of a bed form similar to that found in rivers, installed in an open channel, equipped with a water circulation system. For vortex detection, a methodology based on the particle image velocimetry PIV technique is proposed. So, we fulfill two objectives： vortex identification and its passage frequencies behind the bed form installed in the channel. Such procedure allows a computer process time reduction in vortices identification task.

Experimental Study on Aero Conductivity of Porous Media

To study the variation pattern of aero conductivity of different porous media under low pressure conditions, three kinds of media are selected. These include sandy clay loam, fine sand, and medium sand, and air us fluid to conduct soil column ventilation tests. Pressure at both ends of the colruns is measured under different ventilation flow rates during testing. The test results show that the aero conductivity, solved by Darcy＇s law, is not a coustant. It is a variable, which increases first when air flow velocity is less than 0. 258 7 cm/s for sandy clay loam, 0. 637 3 cm/s for fine sand and then decreases when air flow velocity is bigger than that with the increase of the ventilation flow rate when the medium is determined. By analyzing various factors that influence the flow resistance, the reasons for variation in aero conductivity are found us follows： first, the change of pore structure results in better ventilation; second, the relatiouship hetwcen pressure head loss and air flow velocity is nonlinear, and it is beyond the condition of the Iminar flow domain to which Darcy＇ s law can he applied, when the air flow rate increases to a certain value and the flow velocity is in the transition range to turbulent flow.

Prediction of preferential fluid flow in porous structures based on topological network models: Algorithm and experimental validation

The understanding and prediction of preferential fluid flow in porous media have attracted considerable attention in various engineering fields because of the implications of such flows in leading to a non-equilibrium fluid flow in the subsurface. In this study, a novel algorithm is proposed to predict preferential flow paths based on the topologically equivalent network of a porous structure and the flow resistance of flow paths. The equivalent flow network was constructed using Poiseuille's law and the maximal inscribed sphere algorithm. The flow resistance of each path was then determined based on Darcy's law. It was determined that fluid tends to follow paths with lower flow resistance. A computer program was developed and applied to an actual porous structure. To validate the algorithm and program, we tested and recorded two-dimensional(2 D) water flow using an ablated Perspex sheet featuring the same porous structure investigated using the analytical calculations. The results show that the measured preferential flow paths are consistent with the predictions.