Numerical study of wave overtopping of a seawall supported by porous structures

This paper presents a VOF-based two-phase flow model for the simulation of wave interactions with seawall supported by a porous terrace. Firstly, the model was verified against laboratory data in a simple case for wave overtopping of a vertical wall. Comparison of computed and measured wave properties showed reasonably good agreement. The model was then applied to study the interactions of waves and a seawall protected by porous structures with a permeable terrace. The application results showed that the overtopping rate was strongly related to the energy dissipation through the drag force; the porous reef and terrace were very effective to produce a low crest type seawall. It is concluded that there exist two optimum values of porosity of the submerged reef, about of 0.25 and 0.7, that give minimum overtopping rates. Whereas, there is an effective range of porosity of the permeable terrace varying from 0.4 to 0.65 for significantly reducing the overtopping rate. The verification results confirm that the VOF-based two-phase flow model is sufficient robust to simulate the wave overtopping of coastal structures with reasonable accuracy.     

Homogenization results for a coupled system modelling immiscible compressible two-phase flow in porous media by the concept of global pressure

A model for immiscible compressible two-phase flow in heterogeneous porous media is considered. Such models appear in gas migration through engineered and geological barriers for a deep repository for radioactive waste. The main feature of this model is the introduction of a new global pressure and it is fully equivalent to the original equations. The resulting equations are written in a fractional flow formulation and lead to a coupled degenerate system which consists of a nonlinear parabolic (the global pressure) equation and a nonlinear diffusion–convection one (the saturation) equation with rapidly oscillating porosity function and absolute permeability tensor. The major difficulties related to this model are in the nonlinear degenerate structure of the equations, as well as in the coupling in the system. Under some realistic assumptions on the data, we obtain a nonlinear homogenized problem with effective coefficients which are computed via a cell problem and give a rigorous mathematical derivation of the upscaled model by means of two-scale convergence.     

Interaction of a Solitary Wave with a Porous Elliptical Cylinder

In this paper the diffraction of a plane first order solitary wave by a vertical permeable elliptical cylinder is investigated and the corresponding wave loading is computed. The analytical model presented here is employs Boussinesq equations to describe the diffraction. The solution procedure is based on the perturbation theory, where a perturbation parameter defined in terms of the surface geometry of the cylinder is used. The flow through the porous cylinder is assumed to obey Darcy's law. The effects of porosity, relative wave length and the incident wave angle are discussed. (© 2006 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim)     

基于三维CFD-DEM的多孔介质流场数值模拟

将多孔介质局部细观流动与基于Darcy定律的宏观物理模型相结合，应用三维CFD-DEM对多孔介质流场进行局部细观数值模拟，得到多孔介质的惯性阻力系数和粘性阻力系数.并将其作为参数提供给基于Darcy定律的CFD多孔介质模型，从而可用于更大规模的多孔介质流场计算.应用Voronoi多面体作为网格单元，解决了CFD DEM中网格孔隙率精确计算的困难.文中发展的多尺度结合应用的研究方法，在计算精度和计算效率的矛盾中找到了较好的平衡，对于工程应用而言，有节约实验成本、提高计算结果可靠性的功效.     

粉末注射成形坯孔隙度的分形模型

粉末注射成形坯是一种具有分形特性的典型的多孔介质,借助于多孔介质孔隙结构的分形理论,对粉末注射成形坯孔隙率的分形模型进行推导。首先分析了粉末注射成形坯孔隙结构的双重分形特性,介绍了粉末注射成形坯孔隙分布分形维数和孔隙迂曲分形维数,然后推导出粉末注射成形坯孔隙度的分形模型。     

The residual velocity method applied to a steady free boundary-value problem of vector Laplacian type

We consider a free boundary-value problem based on a simplifiedmodel of two-phase flow in porous media. The model has two independentvariables on each side of the free interface. At the interfaceat steady state, five mixed Dirichlet and Neumann conditionsare given. The movement of the interface in time-dependent situationscan be reduced to a normal motion proportional to the residualin one of the steady-state interface conditions (the ellipticinterior problems and the other interface conditions are satisfiedat each time). Following previous work, we consider the useof other residuals for the normal velocity that have superiornumerical properties. The well-posedness criteria for this vectorexample are particularly clear. The advantages of the correctlychosen, non-physical residual velocities are demonstrated innumerical computations. Although the finite-difference implementationin this work is not applicable to general problems, it has superiorperformance to previous implementations.     

Travelling wave solutions for degenerate pseudo-parabolic equations modelling two-phase flow in porous media

We discuss a pseudo-parabolic equation modelling two-phase flow in porous media, which includes dynamic effects in the capillary pressure. We extend the results obtained previously for linear higher order terms and investigate the existence of travelling wave solutions in the non-linear and degenerate case. This case leads to non-smooth travelling waves, as well as to a discontinuous capillary pressure.     

Simulation of uncompressible fluid flow through a porous media

Recently, a great interest has been focused for investigations about transport phenomena in disordered systems. One of the most treated topics is fluid flow through anisotropic materials due to the importance in many industrial processes like fluid flow in filters, membranes, walls, oil reservoirs, etc. In this work is described the formulation of a 2D mathematical model to simulate the fluid flow behavior through a porous media (PM) based on the solution of the continuity equation as a function of the Darcy’s law for a percolation system; which was reproduced using computational techniques reproduced using a random distribution of the porous media properties (porosity, permeability and saturation). The model displays the filling of a partially saturated porous media with a new injected fluid showing the non-defined advance front and dispersion of fluids phenomena.     

Calculation of shock compression of porous media in conical solid-state targets with an outlet hole

The Godunov-type method that was earlier developed for the hydrodynamic equations of compressible media on regular grids is extended to the case of shock wave flows in elastoplastic porous media. The results of numerical simulations of a hypothetical experimental plant for checking the effect of an increased intensity of converging shock waves in porous media with increasing degree of porosity are presented. This effect was earlier discovered by numerical simulations.     

An equivalent pipe network model for free surface flow in porous media

Free surface flow analysis in porous media is challenging in many practical applications with strong non-linearity. An equivalent pipe network model is proposed for the simulation and evaluation of free surface flow in porous media. On the basis of representative elementary volume with homogeneous pore-scale patterns, the pore space of the homogeneous isotropic porous media is conceptualized as a collection of capillary tubes. According to Hagen-Poiseulle's law and flux equivalence principle, equivalent hydraulic parameters and unified governing formulations for the pipe network model are deduced. The two-dimensional free surface flow problem is reduced to a one-dimensional problem of pipe networks and a one-dimensional procedure based on the finite element method is then developed by introducing a continuous penalized Heaviside function. The proposed equivalent pipe network model is verified with results from numerical solutions and laboratory-measured data available in the literature, and good agreements are obtained. The proposed equivalent pipe network model is shown to be effective in analyzing the free surface flow in porous media. The numerical results also indicate that the proposed equivalent pipe network model has weak sensitivity of the mesh size and penalty parameters.     

Viscous potential flow analysis of magnetohydrodynamic interfacial stability through porous media

In the view of viscous potential flow theory, the hydromagnetic stability of the interface between two infinitely conducting, incompressible plasmas, streaming parallel to the interface and subjected to a constant magnetic field parallel to the streaming direction will be considered. The plasmas are flowing through porous media between two rigid planes and surface tension is taken into account. A general dispersion relation is obtained analytically and solved numerically. For Kelvin-Helmholtz instability problem, the stability criterion is given by a critical value of the relative velocity. On the other hand, a comparison between inviscid and viscous potential flow solutions has been made and it has noticed that viscosity plays a dual role, destabilizing for Rayleigh-Taylor problem and stabilizing for Kelvin-Helmholtz. For Rayleigh-Taylor instability, a new dispersion relation has been obtained in terms of a critical wave number. It has been found that magnetic field, surface tension, and rigid planes have stabilizing effects, whereas critical wave number and porous media have destabilizing effects.     

Numerical investigation into a liquid displacing a gas in thin porous layers

To examine the filling process in a lithium-ion battery, a numerical model to characterize the displacing flow of a liquid in air-filled pores of thin heterogeneous porous materials is elaborated. The investigation is based on the volume-averaged Navier-Stokes equations for small Reynolds numbers, using a volume-of-fluid method to cover the multiphase flow. The flow is investigated with respect to the wall effect and to capillary action within the porous matrix. On the one hand, model experiments with similar particle-size distributions as in the battery layers are conducted to extract the porosity as function of the wall distance. On the other hand, experiments with the three different porous layers of the battery are performed to receive mean values for the most important properties related to the two-phase flow. Results for the displacement flow in parts of the battery are presented and discussed, showing a considerable influence of the modeled effects onto the flow characteristics. (© 2016 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Some Self-Similar Two-Phase Flows of Non-Newtonian Fluids Through a Porous Medium

Pascal This paper addresses the question of the rheological effects of non-Newtonian fluids in a flow system, in which a two-phase flow zone is coupled to a single-phase flow zone by a moving fluid interface. This flow system is involved in a technique for oil displacement in a porous medium, where a non-Newtonian displacing fluid (a polymer solution) is used to displace a non-Newtonian heavy oil. The self-similar solutions of the equations governing the dynamics of the moving interface, separating the displacing and displaced fluids, are obtained for the one-dimensional and plane radial flows. The effects associated with the presence of a two-phase flow zone, behind the moving interface, on the interface movement are analyzed. The existence of a pressure front ahead of the moving interface, moving with a finite velocity, is also shown. The relevance of this result to the propagation of pressure disturbances in a non-Newtonian fluid flowing through a porous medium is discussed with regard to interpretation of the transient pressure response in an injection well for polymer-solution floods.     

A multiscale Darcy–Brinkman model for fluid flow in fractured porous media

The aim of this work is to present a reduced mathematical model for describing fluid flow in porous media featuring open channels or fractures. The Darcy’s law is assumed in the porous domain while the Stokes–Brinkman equations are considered in the fractures. We address the case of fractures whose thickness is very small compared to the characteristic diameter of the computational domain, and describe the fracture as if it were an interface between porous regions. We derive the corresponding interface model governing the fluid flow in the fracture and in the porous media, and establish the well-posedness of the coupled problem. Further, we introduce a finite element scheme for the approximation of the coupled problem, and discuss solution strategies. We conclude by showing the numerical results related to several test cases and compare the accuracy of the reduced model compared with the non-reduced one.     

Two-phase flow equations with outflow boundary conditions in the hydrophobic-hydrophilic case

We introduce an approximation procedure and provide existence results for two-phase flow equations in porous media. The medium can have hydrophobic and hydrophilic components such that the capillary pressure function is degenerate for extreme saturations. Our main interest is the outflow boundary condition which models an interface with open space. The approximate system introduces standard boundary conditions and can be used in numerical schemes. It allows the derivation of maximum principles. This is the basis for the derivation of the limiting system in the form of a variational inequality.     

Stability of reflection and refraction of shocks on interface

In this paper we study the stability of the nonlinear wave structure caused by the attack of an incident shock on an interface of two different kinds of media. The attack will produce a reflected wave and a refracted wave, and also let the interface deflected. In this paper we will mainly study the case, when the reflected wave is a shock, and the flow between the reflected wave and the refracted shock is relatively subsonic. Our result indicates that the wave structure and the flow field for the reflection-refraction problem in this case is conditionally stable.To describe the motion of the fluid we use the inviscid Euler system as the mathematical model. The reflection-refraction problem can be reduced to a free boundary value problem, where the unknown reflected shock and refracted shock are free boundaries, and the deflected interface is also to be determined. In the proof of the existence and the stability of the corresponding wave structure we apply the Lagrange transformation to fix the interface and the decoupling technique to decouple the elliptic-hyperbolic composite system in its principal part. Meanwhile, some efficient weighted Sobolev estimates are established to derive the existence for corresponding nonlinear problems.     

能源数值模拟计算方法的理论和应用

１引言石油是国民经济和社会发展的重要支柱,油田的勘探和开发是发展石油工业的关键．我国开发的油田均进入了二次采油期,大多数已进入注水开发中后期,特别是大庆油田和胜利油田,若继续单纯采用注水开采,产量每年将减少数百万吨．稳定石油产量的唯一方法是采用三次采油新技术,开发尚滞留在地下约５０％以上已探明的储量．若能平均提高３０％的采收率,即相当于再生了同等规模的油田．所谓油藏数值模拟,就是用电子计算机模拟地下油藏十分复杂的化学、物理及流体流动的真实过程,以便选出最佳的开采方案,监控措施．对于三次采油新技术…     

Contamination and remediation waves in a filtration model

We propose a model for the filtration of suspended particles in porous media and we examine some of its mathematical properties. The model includes a variable porosity that depends on the volume of particles retained through filtration and a kinetics law that allows both a positive and negative rate of particle accretion. We characterize the properties of accretion rates that lead to contamination and remediation wave fronts in the model.     

Modeling of water surface profile in subterranean channel by differential quadrature method (DQM)

This study, investigates the hydraulic of flow in a subterranean channel headspring. The continuity and momentum equations of flow in porous media considering real conditions were used and the basic equation of flow in a subterranean channel was resulted. This equation is very similar to the spatially varied flow with increasing discharge. An equation, defining the hydraulic parameters of a subterranean channel section was adopted. Then differential quadrature method (DQM), was applied to the equation of flow in subterranean channel, consequently the water surface profile was resulted. To illustrate the rightness of model, the hydraulic parameters of flow in the Gavgard branch of the Joopar Goharriz Qanat were measured and the water surface profile was determined. This water surface profile was compared to the water surface profile computed by the model, which are in good agreement.