Vulnerability for systems described by cellular automata: Application to flood phenomena

In this paper, we introduce the vulnerability and vulnerability index for systems described by cellular automata. A zone will be vulnerable to the space-time expansion of a given property during a time horizon if the property trajectory reaches the zone at a certain time. The space-time expansion of the property known as spreadability depends closely on the property definition, the cells properties and the transition function which governs the cellular automata evolution. These constraints exhibit two types of spreadability (inclusion sense and area sense) which affect vulnerable zones. When multiple zones are vulnerable during a given time horizon, we need criteria which describe whose are the most vulnerable. Then we consider iterative, average and global vulnerability index whose use depends on the considered phenomena. As an application we consider the flood phenomena. For this we use the two scale cellular automaton for flow dynamics modeling (2CAFDYM) over a given terrain. This application requires an adaptation of the general vulnerability index in order to take into account the both horizontal and vertical distributions of surface water. As practice application, we consider simulation for a basin in northern Morocco using a simulation software we have designed in Java Object Oriented Programming. Digital terrain model, geological maps and satellite image are used for input data.     

Numerical Solution of Newtonian and Non-Newtonian Flows

This paper deals with the numerical solution of Newtonian and non-Newtonian flows. The flows are supposed to be laminar, viscous, incompressible and steady. The model used for non-Newtonian fluids is some variant of power-law. Governing equations in this model are incompressible Navier-Stokes equations. For numerical solution one could use artificial compressibility method with three stage Runge-Kutta finite volume method in cell centered formulation for discretization of space derivatives. Following cases of flows are solwed: flow through a bypass connected to main channel in 2D and 3D and non-Newtonian flow through branching channels in 2D. These results are presented for 2D and 3D case. This problem could have an application in the area of biomedicine. (© 2006 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Assessment of subgrid-scale models for the incompressible Navier-Stokes equations

In this paper, we assess two kinds of subgrid finite element methods for the two-dimensional (2D) incompressible Naver-Stokes equations (NSEs). These methods introduce subgrid-scale (SGS) eddy viscosity terms which do not act on the large flow structures. The eddy viscous terms consist of the fluid flow fluctuation strain rate stress tensors. The fluctuation tensor can be calculated by a elliptic projection or a simple L² projection (projective filter) in finite element spaces. The finite element pair P₂/P₁ is adopted to numerically implement analysis and computation. We give a complete error analysis based on the assumptions of some regularity conditions. On the part of numerical tests, the numerical computations for the stationary flows show that the numerical results agree with some benchmark solutions and theoretical analysis very well. Furthermore, the given SGS models are applied to the non-stationary fluid flows.     

Two‐phase flows in karstic geometry

Multiphase flow phenomena are ubiquitous. Common examples include coupled atmosphere and ocean system (air and water), oil reservoir (water, oil, and gas), and cloud and fog (water vapor, water, and air). Multiphase flows also play an important role in many engineering and environmental science applications. In some applications such as flows in unconfined karst aquifers, karst oil reservoir, proton membrane exchange fuel cell, multiphase flows in conduits, and in porous media must be considered together. Geometric configurations that contain both conduit (or vug) and porous media are termed karstic geometry. Despite the importance of the subject, little work has been performed on multiphase flows in karstic geometry. In this paper, we present a family of phase–field (diffusive interface) models for two‐phase flow in karstic geometry. These models together with the associated interface boundary conditions are derived utilizing Onsager's extremum principle. The models derived enjoy physically important energy laws. A uniquely solvable numerical scheme that preserves the associated energy law is presented as well. Copyright © 2013 John Wiley & Sons, Ltd.     

A new integrated surface and subsurface flows model and its verification

A new coupled model for simulating surface and subsurface flows in a fully integrated way is presented. This model contains two sub-models; one is the 2D kinematic wave approximation of the Saint Venant’s equations used to model runoff, and another is Richards’ equation for variably saturated subsurface flow. In this model, boundary conditions (the conditions describing groundwater discharge at the land surface or surface water infiltration into the subsurface) could be eliminated through mathematic transformations of the governing equation of surface and subsurface flows. The solution of surface and subsurface flows could be simultaneous. And the surface domain and subsurface domain could be considered as a fully integrated domain. This approach naturally provides pressure and fluxes continuity along land surface. In order to assess this modelling approach, several classical validations, verification and application test cases are presented. For overland flow solely, the model is compared to an analytical solution and to commonly use hydrological models. The integrated model is then validated with a sandbox laboratory experiment and a soil column test. Finally, the effects of rainfall intensity, hydraulic conductivity of soils and initial bulk water content of soils to runoff and infiltration of a homogeneous soil slope are studied under different conditions.     

A kinetic formulation for a model coupling free surface and pressurised flows in closed pipes

The aim of this paper is to present a kinetic formulation of a model for the coupling of transient free surface and pressurised flows. Firstly, we revisit the system of Saint-Venant equations for free surface flow: we state some properties of Saint-Venant equations, we propose a kinetic formulation and we verify that this kinetic formulation leads to a Gibbs equilibrium that minimises (in some general case) an energy and preserves the still water steady state. Secondly, we propose a model for pressurised flows in a Saint-Venant-like conservative formulation. We then propose a kinetic formulation and we verify that this kinetic formulation leads to a Gibbs equilibrium that minimises in any case an energy and preserves the still water steady state. Finally, we propose a dual model that couples these two types of flow.     

Self-organizing map of soil properties in the context of hydrological modeling

One of the most relevant inputs for hydrological modeling is the soil map. The soil sources and scales for the soil properties are diverse, and the quality of soil mapping is increasing, but soil surveying is time-consuming and large area campaigns are expensive. The taxonomic unit approach for soil mapping is common and limited to one layer of data. This limitation causes errors in simulated water fluxes through the soil when taxonomic units approach is implemented during hydrological modeling analysis. Some strategies using geostatistics and machine learning algorithms such as Kriging and Self-Organizing maps (SOM) are improving the taxonomic units’ approach and could serve as an alternative for soil mapping for hydrological purposes. The aim of this work is to study the influence of different soil maps and resolutions on the main hydrological components of a sub-arid watershed in central Spain. For this, the Soil Water and Assessment Tool (SWAT) was parameterized with three different soil maps. A first one was based on Harmonized World Soil database from FAO, at scale 1:1,000,000 (HWSD). The other two were based on a Kriging interpolation at 100 × 100 m from soil samples. To obtain soil properties map from it, two strategies were applied: one was to average the soil properties following the official taxonomic soil units at 1:400,000 scale (Agricultural Technological Institute of Castilla and Leon - ITACyL) and the other was to applied Self-organizing map (SOM) to create the soil units (SOMM).The results suggest that scale and soil properties mapping influence HRU definition, which in turn affects water flow through the soils. Statistical metrics of model performance were improved from R² =0.62 and NSE=0.46 with HWSD soil map to R² =0.86 and NSE=0.84 with SOM and similar values were achieved during validation. Thus, the SOM is presented as an innovative algorithm applied for hydrological modeling with SWAT, significantly increasing the level of model accuracy to stream flow in sub-arid watersheds.     

Large time behavior for the incompressible Navier–Stokes flows in 2D exterior domains

The incompressible Navier–Stokes flows in a 2D exterior domain are considered, for which the associated total net force to the boundary may not vanish. The decay properties are shown for the first and second derivatives of the Navier–Stokes flows in L ¹ and weighted spaces, respectively, which improve Theorem 1.2 in Bae and Jin (J Funct Anal 240:508–529, 2006).     

Coupling of the Reynolds Fluid-Film Equation with the 2D Navier-Stokes Equations

The pressure field in thin fluid films can quite precisely be calculated by Reynolds fluid-film equation. In some problems, it may be useful to couple thin fluid-films with general 2D or 3D fluid flows. In the current work, we analyze the fluid flow, pressure and temperature field in a hydrodynamic journal bearing with a rectangular oil groove. Pressure and temperature in the fluid gap are calculated by means of the Reynolds equation and the 2D energy equation. Cavitation effects are taken into account by incorporating a 2-phase cavitation approach. In order to calculate the velocity and pressure field in the oil groove, the 2D Navier-Stokes equations are used; the temperature distribution in the oil groove is computed by means of the 2D energy equation. Appropriate coupling conditions for velocity, pressure and temperature are formulated in order to couple the flow in the fluid gap with the flow in the oil groove. Thermal expansion of journal shaft and bearing housing are also taken into account, since the bearing clearance changes with increasing temperature. (© 2011 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Proximal-isometric (P J) flows

We develop some new tools for the study of minimal transformation groups (flows) and apply these tools to extend the classification theory of minimal flows to a larger class than has previously been classified. The tools we develop arise from a simplification and unification of the techniques used by Furstenberg, Ellis, and Veech in their proofs of structure theorems about distal and point distal flows. This simplification is made possible largely through the use of recent results of Glasner on the structure of 2^X (whose points consist of closed subsets of the phase space X of a given flow).     

The Bernoulli Integral for a Certain Class of Non‐Stationary Viscous Vortical Flows of Incompressible Fluid

It has been shown in our paper [1] that there is a wide class of 3D motions of incompressible viscous fluid which can be described by one scalar function dabbed the quasi‐potential. This class of fluid flows is characterized by three‐component velocity field having two‐component vorticity field; both these fields can depend of all three spatial variables and time, in general. Governing equations for the quasi‐potential have been derived and simple illustrative example of 3D flow has been presented. Here, we derive the Bernoulli integral for that class of flows and compare it against the known Bernoulli integrals for the potential flows or 2D stationary vortical flows of inviscid fluid. We show that the Bernoulli integral for this class of fluid motion possesses unusual features: it is valid for the vortical nonstationary motions of a viscous incompressible fluid. We present a new very nontrivial analytical example of 3D flow with two‐component vorticity which hardly can be obtained by any of known methods. In the last section, we suggest a generalization of the developed concept which allows one to describe a certain class of 3D flows with the 3D vorticity.     

Loss of Smoothness and Inherent Instability of 2D Inviscid Fluid Flows

The paper is focused on the loss of smoothness hypothesis which claims that vorticity (or vorticity gradients in the 2D case) grows unboundedly for the substantial part of the inviscid incompressible flows. At least, every steady flow is supposed to belong to the closure of this set (relative to a reasonably strong topology). We approach the problem involving both direct Lyapunov method and some sort of the linearization. We present new (and rather wide) classes of 2D flows in a generic domains which admit the loss of smoothness and related phenomena.     

三维海洋水动力计算σ坐标转换存在的问题及改进方法

三维水动力模型在准确模拟海洋物理特性中起着重要的作用,传统的σ坐标转换由于当时计算机能力所限,舍去了复杂的高阶项,在实际复杂地形（或水深变化）环境下,会带来一定的误差或计算失真等问题.由此,为了适应高精度计算结果的需求,对原有σ坐标三维水动力模型进行了重新修正.在改进后的模型中,综合考虑了经σ坐标变换引入的与流速、水位、地形相关的复杂高阶项,选用特定的插值函数,利用有限元和差分相结合的方法,进行求解σ坐标下的完整三维浅水模式方程.相比原模型,改进的模型对底坡、水深、潮汐振幅等变化适用范围更为广泛,能更好地模拟出复杂水深变化下的垂向流动分布特征,计算结果具有更高的精确度;改进的模型针对一些极端水位条件（潮汐振幅与水深比大于0.15）,其计算误差同样可保持在一个较低的范围内;同时,改进的模型只需更短的时间就可运行至稳定状态.     

Heat Transfer in Rotor/Rotor and Rotor/Stator Cavity: Physics,Correlations and Numerical Modeling

The transitional and turbulent flow in the near wall sublayer is now mostly modeled based on the existing knowledge of simple 2D flows. To determine the effect of three dimensionality on the turbulent flow structures and turbulent heat transfer in the near wall areas the authors investigate numerically (SVV) turbulent flow in rotor/stator and rotor/rotor flows (with and without axial throughflow). These simple model flows contain most of the phenomena that are needed to understand more complex, 3D transitional and turbulent flows. Attention is focused on the turbulent characteristics which should have more universal character. To stabilize calculations for high Reynolds numbers (up to Re=800 000) the SVV operator is introduced into the Navier-Stokes and energy equations solver for cylindrical coordinate system without using complex numbers. Code optimization and parallelization have speeded up computations 20 times. (© 2013 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Environmental flow requirements for integrated water resources allocation in the Yellow River Basin,China

Based on the classification and regionalization of the ecosystem, multiple ecological management objectives and the spatial variability of the environmental flow requirements of the Yellow River Basin were analyzed in this study. The summation rule was used to calculate water consumption requirements and the compatibility rule, i.e., “maximum” principle, was also adopted to estimate the non-consumptive use of water in the river basin. The environmental flow requirements for integrated water resources allocation were determined by identifying the natural and artificial water consumption in the Yellow River Basin. The results indicated that the annual minimum environmental flow requirements amounted to 317.62 × 10⁸ m³, which represented 54.76% of the natural river flows, while for the environmental flow requirements for the integrated water resources allocation were 262.47 × 10⁸ m³, which represented 45.25% of the natural river flows. The highest percentage of environmental flow requirements was 93.64% for the river ecosystem. It can be concluded that the primary concerns should be put on the downstream river water requirements to determine the environmental flows for integrated water resources allocation in a river basin.     

An adaptive grid technique for the vertical structure of shallow water models

The efficient resolution of the boundary layers occurring in geophysical flows has motivated the search for criteria to optimize the vertical nodal placement in three-dimensional (3D) shallow water models. This paper describes the implementation and testing of an adaptive grid technique for the internal mode of shallow water models. The technique uses an r-method in which the nodes are moved vertically based on the velocity gradients between consecutive nodes. One-dimensional (1D) tests show that the method behaves well in tidal- and wind-driven flows, both in well-mixed and stratified conditions. Average accuracy improvements of 50% were obtained relative to uniform grids, with a 15% CPU time increase. The adaptive technique accounts accurately for the space and time variability of the flow, thus being attractive for any type of problem. Furthermore, the technique does not require an a priori knowledge of the flow conditions, thus simplifying greatly the modeling procedure.     

Soil moisture movement and groundwater recharge by tritium tracer tagging technique

The paper deals with the study of rate of soil moisture movement and recharge to groundwater system at Indian Agricultural Research Institute (IARI) farm for the years 1973, 1974 and 1975. The utility of artificially injected tritium, experimental techniques adopted and a quantitative determination of recharge and moisture movement rates are discussed. Corrections for upward movement of moisture after the end of monsoon have been used to calculate the average rates of water movement below the injection level and groundwater recharge. Average rates of soil moisture movement and recharge are 9.4 mm/d and 27.4% (193 mm) of monsoon precipitation for three years respectively. Under favourable conditions the diffusion coefficients for soil water system are calculated assuming Gaussian distribution of tritium concentrations in the soil profiles. The average value of diffusion coefficient is 2.5 × 10^?5 cm²/s for the sandy loam soils. The variation in recharge is mainly due to inherent variability in soil physical properties and vegetative cover. The technique is not found reliable for higher water table conditions on account of lateral flow.     

3D‐Flow structures behind a circular cylinder with hemispherical head geometry

An experimental investigation of the flow around a finite circular cylinder mounted on a flat plate, see fig. 1, is reported. The aspect ratio L/D (with length L and diameter D) of the cylinder model is 2.0. The focus of this study is toward examining the complex separated flow structures and wake properties. Velocity and turbulence measurements have been carried out with a three component Laser Doppler anemometer (LDA) at the Reynolds number Re_D = 2.0 · 10⁵. The experimental results show complex 3D fluid motions in the separated flow region. They are induced by the superposition of three main vortical flows.     

Long Eddies in Sheared Flows

The characteristic feature of the wide variety of hydraulic shear flows analyzed in this study is that they all contain a critical level where some of the fluid is turned relative to the ambient flow. One example is the flow produced in a thin layer of fluid, contained between lateral boundaries, during the passage of a long eddy. The boundaries of the layer may be rigid, or flexible, or free; the fluid may be either compressible or incompressible. A further example is the flow produced when a shear layer separates from a rigid boundary producing a region of recirculating flow. The equations used in this study are those governing inviscid hydraulic shear flows. They are similar in form to the classical boundary layer equations with the viscous term omitted. The main result of the study is to show that when the hydraulic flow is steady and contained between lateral boundaries, the variation of vorticity ω(ψ) cannot be prescribed at any streamline which crosses the critical level. This variation is, in fact, determined by (1) the vorticity distribution at all streamlines which do not cross the critical level, by (2) the auxiliary conditions which must be satisfied at the boundaries of the fluid layer, and by (3) the dimensions of the region containing the turned flow. If at some instant the vorticity distribution is specified arbitrarily at all streamlines, generally the subsequent flow will be unsteady. In order to emphasize this point, a class of exact solutions describing unsteady hydraulic flows are derived. These are used to describe the flow produced by the passage of a long eddy which distorts as it is convected with the ambient flow. They are also used to describe the unsteady flow that is produced when a shear layer separates from a boundary. Examples are given both of flows in which the shear layer reattaches after separation and of flows in which the shear layer does not reattach. When the shear layer vorticity distribution has the form ωαyⁿ, where y is a distance measure across the layer, the steady flows are of Falkner-Skan type inside, and adjacent to, the separation region. The unsteady flows described in this paper are natural generalizations of these Falkner-Skan flows. One important result of the analysis is to show that if the unsteady flow inside the separation region is strongly sheared, then the boundary of the separation region moves upstream towards the point of separation, forming large transverse currents. Generally, the assumption of hydraulic flow becomes invalid in a finite time. On the other hand, if the flow inside the separation region is weakly sheared, this region is swept downstream and the flow becomes self-similar.