Modeling full-tensor anisotropy in groundwater flow via an iterative scheme for mixed finite elements

This paper presents an iterative scheme for the efficient simulation of groundwater flow in a two-dimensional, heterogeneous aquifer in which the hydraulic conductivity is anisotropic. The scheme is applicable to matrix equations arising from both mixed finite-element and cell-centered finite-difference approximations to the flow equations, and it extends readily to three space dimensions. The scheme, which generalizes an earlier technique for isotropic aquifer, admits a fast multigrid solver for hydraulic heads. Numerical experiments illustrate both the effectiveness of the scheme and the importance of accurately treating anisotropy: Small changes in the off-diagonal terms in the conductivity tensor cause relatively large changes in both the predicted heads and the Darcy velocities.     

Two‐dimensional modeling for stability analysis of two‐phase stratified flow

The effect of wavelength and relative velocity on the disturbed interface of two‐phase stratified regime is modeled and discussed. To analyze the stability, a small perturbation is imposed on the interface. Growth or decline of the disturbed wave, relative velocity, and surface tension with respect to time will be discussed numerically. Newly developed scheme applied to a two‐dimensional flow field and the governing Navier–Stokes equations in laminar regime are solved. Finite volume method together with non‐staggered curvilinear grid is a very effective approach to capture interface shape with time. Because of the interface shape, for any time advancement, a new grid is performed separately on each stratified field, liquid, and gas regime. The results are compared with the analytical characteristics method and one‐dimensional modeling. This comparison shows that solving the momentum equation including viscosity term leads to physically more realistic results. In addition, the newly developed method is capable of predicting two‐phase stratified flow behavior more precisely than one‐dimensional modeling. It was perceived that the surface tension has an inevitable role in dissipation of interface instability and convergence of the two‐phase flow model. Copyright © 2009 John Wiley & Sons, Ltd.     

Modified asymptotic Adomian decomposition method for solving Boussinesq equation of groundwater flow

The Adomian decomposition method （ADM） is an approximate analytic method for solving nonlinear equations. Generally, an approximate solution can be ob- tained by using only a few terms. However, in applications, we need to use it flexibly according to the real problem. In this paper, based on the ADM, we give a modified asymptotic Adomian decomposition method and use it to solve the nonlinear Boussinesq equation describing groundwater flows. The example shows effectiveness of the modified asymptotic Adomian decomposition method.     

Numerical diffusion for flow‐aligned unstructured grids with application to estuarine modeling

The benefits of unstructured grids in hydrodynamic models are well understood but in many cases lead to greater numerical diffusion compared with methods available on structured grids. The flexible nature of unstructured grids, however, allows for the orientation of the grid to align locally with the dominant flow direction and thus decrease numerical diffusion. We investigate the relationship between grid alignment and diffusive errors in the context of scalar transport in a triangular, unstructured, 3‐D hydrodynamic code. Analytical results are presented for the 2‐D anisotropic numerical diffusion tensor and verified against idealized simulations. Results from two physically realistic estuarine simulations, differing only in grid alignment, show significant changes in gradients of salinity. Changes in scalar gradients are reflective of reduced numerical diffusion interacting with the complex 3‐D structure of the transporting flow. We also describe a method for utilizing flow fields from an unaligned grid to generate a flow‐aligned grid with minimal supervision. Copyright © 2013 John Wiley & Sons, Ltd.     

Steam condensing flow modeling in turbine channels

The numerical method for modeling of the transonic steam flows with homogeneous and/or heterogeneous condensation has been presented. The experiments carried out for the Laval nozzles, for 2-D turbine cascades and for a 3-D flow in real turbine were selected to validate an in-house CFD code adjusted to the calculations of the steam condensing flows in complicated geometries. The sensitivity of the condensation model and difficulties in the validation process of the CFD code have been discussed. These difficulties limit the possibilities of verification and improvement of the condensation theory based on the existing experimental data.     

大气绕山体的运动及其输移特性的研究

对分层大气山体绕流的流动模式及扩散输移特性进行了数值模拟。采用隐式时间离散方法在贴体网格系统下求解雷诺平均的N-S方程,计算结果描述出大气流动的特征,证实了分层(以Froude数为特征参数,定义为F=U/NH,U为来流风速,N为Brunt-Vaisala频率,H为山体高度)变化对山体绕流流态的影响。数值结果表明:当Froude数大于4.0时,山体绕流的流动不再依赖于大气分层的变化。当Froude数介于4.0和1.0之间时,流场中出现了Lee波,并随着Froude数的进一步减小,流动分离发生及Lee波破碎现象。同时模型也预测了在各种流动模式下大气中夹杂着的污染物绕山体的传输特性,表明大气的分层现象对污染物的分布有着非常重要的影响。     

地下水流并行有限层方法及同伦反演研究

根据有限层求解格式存在的解耦性,实现了地下水三维流问题的高效并行化计算。在此基础上,结合非线性同伦方法,提出了地下水参数反演分析的并行同伦算法,利用MATLAB编译了相应的正反演计算程序。与已有解析解和有限差分解的对比以及数值算例,验证了并行化正反演方法及程序的正确性,探讨了并行算法的计算效率。研究表明,并行方法可以有效提高计算速度,较串行方法具有明显优势,同时同伦反演方法具有大范围收敛的特点,不依赖于参数值的初始选取。     

Modeling Three-Dimensional Groundwater Flows by the Body-Fitted Coordinate (BFC) Method: I. Stationary Boundary Problems

Based on the body-fitted coordinate (BFC) method, a three-dimensional finite difference computer code, BFC3DGW, was developed to simulate groundwater flow problems. Methodology and solution procedures of the BFC method for simulating groundwater flows, particularly when the flow domain is stationary as in the case of confined aquifers, are described. The code was verified by comparing numerical results with analytical solutions for well-flow problems in an isosceles right-triangular aquifer. An example simulation is made to demonstrate capability of the code for solving flow problems in anisotropic aquifers where directions of anisotropy change continuously. The method differs from the conventional finite difference method (FDM) in the ability to use a flexible, nonorthogonal, and body-fitted grid. The main advantages of the method are the convenience of grid generation, the simplified implementation of boundary conditions, and the capability to construct a generalized computer code which can be consistently applied to problem domains of any shape.     

Finite volume solution to integrated shallow surface–saturated groundwater flow

This paper describes development of an integrated shallow surface and saturated groundwater model (GSHAW5). The surface flow motion is described by the 2‐D shallow water equations and groundwater movement is described by the 2‐D groundwater equations. The numerical solution of these equations is based on the finite volume method where the surface water fluxes are estimated using the Roe shock‐capturing scheme, and the groundwater fluxes are computed by application of Darcy's law. Use of a shock‐capturing scheme ensures ability to simulate steady and unsteady, continuous and discontinuous, subcritical and supercritical surface water flow conditions. Ground and surface water interaction is achieved by the introduction of source‐sink terms into the continuity equations. Two solutions are tightly coupled in a single code. The numerical solutions and coupling algorithms are explained. The model has been applied to 1‐D and 2‐D test scenarios. The results have shown that the model can produce very accurate results and can be used for simulation of situations involving interaction between shallow surface and saturated groundwater flows. Copyright © 2005 John Wiley & Sons, Ltd.     

Modeling Three-Dimensional Groundwater Flows by the Body-Fitted Coordinate (BFC) Method: II. Free and Moving Boundary Problems

This paper presents a methodology and solution procedure of the time-dependent body-fitted coordinate (BFC) method for the analysis of transient, three-dimensional groundwater flow problems characterized by free and moving boundaries. The technique consists of numerical grid generation, time-dependent body-fitted coordinate transformation, and application of the finite difference method (FDM) to the transformed partial differential equations. Based on the time-dependent BFC method, a three-dimensional finite-difference computer code, BFC3DGW, was developed and used to solve two unconfined flow problems. The code was verified by comparing numerical results with analytical solutions for a steady-state seepage problem. In order to demonstrate capability of the method in dealing with flow problems with irregular and moving boundary surfaces, an unconfined well-flow problem was solved by the developed code. Difficulties associated with the free and moving irregular boundary have been successfully overcome by employing this method.     

Nonsteady flow of groundwater in aquifer system with viscoelastic properties

The transient flow behavior of groundwater in aquifer-aquitard system with viscoelastic properties is studied. On the basis of previous works (Hantush, Neuman, Brutsaert, Corapcioglu), the new partial differential-integral equations are derived. The well-known equations (Hantush, Brutsaert) are the special cases of the new equations. The new equations describe the flow of a slightly compressible groundwater in layers with viscoelastic properties.Analytical solutions of the partial differential-integral equations are obtained by using the method of Laplace transform. The viscoelastic properties enhance the heterogeneities of elastic aquifer system which have delay and feed qualities. The agreements between the numericl inversion results of Laplace transform and the analytical solutions are good. The formulae predict the transient flow behavior of groundwater in this heterogeneous layers.     

Numerical study of turbulent in-cylinder flow during motoring utilizing a general curvilinear coordinate system

A finite-volume numerical calculation method is presented to predict the flow field at unsteady, turbulent levels in a motoring reciprocating engine. An algebraic grid generation technique is used to map the complex fluid domain, on which the cylinder head is a deformed boundary, onto a rectangle for every time step. Hence the metric of the coordinate transformation can be determined by direct analytic differentiation. The model gives a good account of the axial, radial, and swirl velocity components and engine turbulence by means of a two-equation model of turbulence and wall functions. Effects of the shapes of both cylinder head and grid distribution on in-cylinder air motion are investigated.     

Analytical modeling of constricted channel flow

Analytical flow models are frequently applied when describing constricted channel flow at low and moderate Reynolds numbers. A common assumption underlying such flow models is two-dimensional or axi-symmetrical flow. In this work, two analytical model approaches are formulated in order to overcome this assumption in the case of naturally occurring channel flows for which the assumption might be critiqued. Advantages and flaws of both model approaches are discussed and their outcome is compared with experimental data.     

Numerical modeling of fluid flow and heat transfer in a narrow Taylor-Couette-Poiseuille system

We consider turbulent flows in a differentially heated Taylor-Couette system with an axial Poiseuille flow. The numerical approach is based on the Reynolds Stress Modeling (RSM) of [Elena and Schiestel, 1996] and [Schiestel and Elena, 1997] widely validated in various rotor-stator cavities with throughflow ( [Poncet, 2005], [Poncet et al., 2005] and [Haddadi and Poncet, 2008]) and heat transfer (Poncet and Schiestel, 2007). To show the capability of the present code, our numerical predictions are compared very favorably to the velocity measurements of Escudier and Gouldson (1995) in the isothermal case, for both the mean and turbulent fields. The RSM model improves, in particular, the predictions of the k-ε model of Naser (1997). Then, the second order model is applied for a large range of rotational Reynolds (3744 ? Re_i ? 37,443) and Prandtl numbers (0.01 ? Pr ? 12), flow rate coefficient (0 ? C_w ? 30,000) in a very narrow cavity of radius ratio s = R_i/R_o = 0.961 and aspect ratio L = (R_o − R_i)/h = 0.013, where R_i and R_o are the radii of the inner and outer cylinders respectively and h is the cavity height. Temperature gradients are imposed between the incoming fluid and the inner and outer cylinders. The mean hydrodynamic and thermal fields reveal three distinct regions across the radial gap with a central region of almost constant axial and tangential mean velocities and constant mean temperature. Turbulence, which is weakly anisotropic, is mainly concentrated in that region and vanishes towards the cylinders. The mean velocity distributions are not clearly affected by the rotational Reynolds number and the flow rate coefficient. The effects of the flow parameters on the thermal field are more noticeable and considered in details. Correlations for the averaged Nusselt numbers along both cylinders are finally provided according to the flow control parameters Re_i, C_w, and Pr.     

Numerical modeling of a turbulent flow behind a heated grid

A numerical model of the dynamics of turbulence and temperature fluctuations behind a heated grid located in a wind tunnel is constructed on the basis of closed Kármán-Howarth and Corrsin equations. Results calculated by this model are in reasonable agreement with available experimental data. __________ Translated from Prikladnaya Mekhanika i Tekhnicheskaya Fizika, Vol. 50, No. 3, pp. 118–126, May–June, 2009.     

Two approaches to modeling unstable flow and mixing of variable density fluids in porous media

Density variation of aqueous phase fluids flowing in a porous medium, resulting from spatial and temporal variation of solute concentration, often gives rise to unstable flow, and therefore has a significant effect on solute transport. Studies on simulating unstable flow and mixing of variable density fluids in seemingly homogeneous porous media are rare. In this study, a three-dimensional (3-D) and a one-dimensional (1-D) model were developed to simulate unstable flow and mixing in a vertical, nominally 1-D system. In the 3-D model, the fluid flow and solute transport equations were solved numerically with a very fine spatial discretization. The 1-D numerical model was derived from a theoretical model to simulate the flow and mixing of fluids with variable density and viscosity at the field scale. To evaluate the models, simulated results were compared with experimental data from displacement experiments in a vertical sand column. The results show that the 1-D model provides fairly good prediction of breakthrough curves and that the 3-D model is able to qualitatively simulate breakthrough curves for highly unstable flow and mixing.Contribution from the Alabama Agric. Exp. Sta. as AAES Journal No. 3-955037.     

Algebraic turbulence modeling in adiabatic and evaporating annular two-phase flow

The study considers algebraic turbulence modeling in adiabatic and evaporating annular two-phase flow, focusing in particular on momentum and heat transfer (so-called ‘convective boiling’) through the annular liquid film. In contrast with single-phase wall-bounded flow theory, shear-driven annular liquid films are assumed here to behave as fluid-bounded flows, mostly interacting with the shearing gas-entrained droplets core flow. Besides providing velocity and temperature profiles through the liquid film, the turbulence model proposed here predicts key parameters such as the average liquid film thickness, the void fraction and the convective boiling heat transfer coefficient with accuracies comparable or better than those of leading design correlations. This turbulence model is part of a unified annular flow modeling suite that includes methods to predict the entrained liquid fraction and the axial frictional pressure gradient. The underlying heat transfer database covers nine fluids (water, two hydrocarbons and six refrigerants) for vertical and horizontal tubes of 1.03-14.4 mm diameter and pressures of 0.1-7.2 MPa. Importantly, this study shows that there appears to be no macro-to-microscale transition when it comes to annular flow. Simply better physical modeling is required to span this range.     

Adaptive grid computation of three-dimensional natural convection in horizontal high-pressure mercury lamps

A three-dimensional model has been developed to compute the thermofluid transport within a discharge arctube. The model has proved very useful for guiding the choice of design parameters to optimize the lamp performance. However, uncertainties exist with respect to quantitative aspects of the physical model, especially those related to radiation heat transfer. In the present work a grid refinement procedure and an adaptive grid method are used to improve the quantitative accuracy of the model and to help improve the physical modelling. The adaptive grid method, based on the multiple one-dimensional equidistribution concept, can responsively redistribute the grids to optimize the grid resolutions. Adaptive grid solutions modify the predicted maximum gas temperature, the buoyancy-induced convection strength, the location of the high-temperature core, and the wall temperature profiles. The adaptive grid solutions show more consistent trends when compared to the measurements. On the basis of the quantitatively more definite information, adjustments can be made with regard to the uncertainties of the physical model.