analysis of hydraulic tomography using temporal moments of drawdown recovery data received 2 june 2005 revised 30 september 2005 accepted 21 october 2005 published 1 february 2006 1 transient hydraulic tomography tht is a potentially cost effective and highresolution technique for mapping spatial distributions of the hydraulic conductivity and specific storage in aquifers interpretation of abundant well hydrographs of a tht survey however is a computational challenge we take on this challenge by developing an estimation approach that utilizes the zeroth and first temporal moments of well hydrographs instead of drawdown itself the governing equations for the temporal moments are poisson s equations these equations demand less computational resources as opposed to the parabolic equation that governs drawdown evolution likewise the adjoint equations for evaluating sensitivities of the moments for parameter estimation also take the same forms therefore a temporal moment approach is expected to expedite the interpretation of tht surveys on the basis of this premise we extend our sequential successive linear estimator to use the zeroth moment and characteristic time of the drawdown recovery data generated by tht surveys we subsequently investigate computational efficiency and accuracy of the moment approach results of the investigation show that the temporal moment approach yields results similar to those from the approach that uses transient heads but at significantly less computational costs limitations using temporal moments are discussed subsequently

traditional analysis of aquifer tests comparing apples to oranges 1 traditional analysis of aquifer tests uses the observed drawdown at one well induced by pumping at another well for estimating the transmissivity t and storage coefficient s of an aquifer the analysis relies on theis solution or jacob s approximate solution which assumes aquifer homogeneity aquifers are inherently heterogeneous at different scales if the observation well is screened in a low permeability zone while the pumping well is located in a high permeability zone the resulting situation contradicts the homogeneity assumption in the traditional analysis as a result what does the traditional interpretation of the aquifer test tell us using numerical experiments and a first order correlation analysis we investigate this question results of the investigation suggest that the effective t and s for an equivalent homogeneous aquifer of gaussian random t and s fields vary with time as well as the principal directions of the effective t the effective t and s converge to the geometric and arithmetic means respectively at large times analysis of the estimated t and s using drawdown from a single observation well shows that at early time both estimates vary with time the estimated s stabilizes rapidly to the value dominated by the storage coefficient heterogeneity in between the pumping and the observation wells at late time the estimated t approaches but does not equal the effective t it represents an average value over the cone of depression but influenced by the location size and degree of heterogeneity as the cone of depression evolves

sensitivity analysis for steady state groundwater flow using adjoint operators adjoint sensitivity theory is currently being considered as a potential method for calculating the sensitivity of nuclear waste repository performance measures to the parameters of the system for groundwater flow systems performance measures of interest include piezometric heads in the vicinity of a waste site velocities or travel time in aquifers and mass discharge to biosphere points the parameters include recharge discharge rates prescribed boundary heads or fluxes formation thicknesses and hydraulic conductivities the derivative of a performance measure with respect to the system parameters is usually taken as a measure of sensitivity to calculate sensitivities adjoint sensitivity equations are formulated from the equations describing the primary problem the solution of the primary problem and the adjoint sensitivity problem enables the determination of all of the required derivatives and hence related sensitivity coefficients in this study adjoint sensitivity theory is developed for equations of two dimensional steady state flow in a confined aquifer both the primary flow equation and the adjoint sensitivity equation are solved using the galerkin finite element method the developed computer code is used to investigate the regional flow parameters of the leadville formation of the paradox basin in utah the results illustrate the sensitivity of calculated local heads to the boundary conditions alternatively local velocity related performance measures are more sensitive to hydraulic conductivities

temporal moments revisited why there is no better way for physically based model reduction in time 1 many hydro geo logical problems are highly complex in space and time coupled with scale issues variability and uncertainty especially time dependent models often consume enormous computational resources but model reduction techniques can alleviate this problem temporal moments tm offer an approach to reduce the time demands of transient hydro geo logical simulations tm reduce transient governing equations to steady state and directly simulate the temporal characteristics of the system if the equations are linear and coefficients are time independent this is achieved by an integral transform projecting the dynamic system response onto monomials in time in comparison to classical approaches of model reduction that involve orthogonal base functions however the monomials for tm are nonorthogonal which might impair the quality and efficiency of model reduction thus we raise the question of whether there are more suitable temporal base functions than the monomials that lead to tm in this work we will derive theoretically that there is only a limited class of temporal base functions that can reduce hydro geo logical models by comparing those to tm we conclude that in terms of gained efficiency versus maintained accuracy tm are the best possible choice while our theoretical results hold for all systems of linear partial or ordinary differential equations pdes odes with any order of space and time derivatives we illustrate our study with an example of pumping tests in a confined aquifer for that case we demonstrate that two four tm are sufficient to represent more than 80 90 of the dynamic behavior and that the information content strictly increases with increasing tm order

a parallel oseen linearized algorithm for the stationary navier stokes equations abstract based on two grid discretizations and domain decomposition a parallel oseen linearized finite element algorithm for the stationary navier stokes equations with moderate or large viscosity parameter is proposed and analyzed the key idea of the algorithm is to first solve a nonlinear problem by picard iterative method on a coarse grid and then to solve an oseen problem in parallel on a fine grid to correct the coarse grid solution by using local a priori error estimate for the finite element solution and under the uniqueness condition error bounds of the corresponding finite element solution are analyzed numerical results are also given to demonstrate the high efficiency of the algorithm

hydraulic tomography using temporal moments of drawdown recovery data a laboratory sandbox study 1 hydraulic tomography ht is a new technology that images the hydraulic heterogeneity of the subsurface unlike steady state hydraulic tomography ssht which provides a hydraulic conductivity k tomogram transient hydraulic tomography tht provides reliable tomograms of both k and specific storage ss effective as it may be tht is a computationally demanding technique to ease the computational burden a ht which utilizes zeroth and first temporal moments of transient drawdown recovery data ht m has been developed by zhu and yeh 2006 this procedure simplifies the governing equation from a single parabolic equation to two poisson s equations for the zeroth moment and characteristic time defined as the ratio between the first and zeroth moments the approach was previously tested using synthetic simulations the numerical experiments tested the feasibility of ht m under ideal conditions where measurements and model are assumed to be free of error in this paper we further evaluate the performance of ht m using cross hole pumping tests conducted in a heterogeneous synthetic aquifer constructed in a laboratory sandbox in more realistic situations where the data used in the inversion are not free of experimental errors unlike field tests the laboratory tests were conducted in a synthetic aquifer created with a prescribed heterogeneity pattern and all forcing functions initial and boundary conditions and source sink terms controlled results from the ht m approach were compared to those from tht previously conducted by liu et al 2007 our results show that the estimation of the k tomogram using the ht m approach is reasonable but the estimation of the ss tomogram is unreliable in comparison to the tht approach

a stochastic inverse solution for transient groundwater flow parameter identification and reliability analysis in this paper a stochastic approach is developed for solving the inverse problem of parameter identification for transient groundwater flow adjoint state equations are derived for the stochastic partial differential equation spde relating transient head and log hydraulic conductivity perturbations the derived equations can be used to calculate the covariance matrix of head observations and the cross covariance matrix between head observations and log hydraulic conductivity measurements for each observation time as well as the covariance and cross covariance matrices between different observation times the number of simulation runs required for obtaining these matrices is equal to the number of head observations the reliability of model prediction is evaluated through the variance estimate method using adjoint sensitivity analysis and the cokriging estimate the reliability evaluation of model prediction can be used as an aid in the optimization of experimental design for sampling strategies a numerical example is given to illustrate the stochastic inverse procedure for a general transient flow problem the example shows that using head observations of all observation times simultaneously produces much better results than using them sequentially commonly known as the quasi steady approach the example also shows that it is possible to obtain a reliable stochastic inverse solution for meeting a given prediction objective based on a limited number of observations

fast iterative implementation of large scale nonlinear geostatistical inverse modeling 1 in nonlinear geostatistical inverse problems it often takes a significant amount of computational cost to form linear geostatistical inversion systems by linearizing the forward model more specifically the storage cost associated with the sensitivity matrix h m n where m and n are the numbers of measurements and unknowns respectively is high especially when both m and n are large in for instance 3 d tomography problems in this research instead of explicitly forming and directly solving the linear geostatistical inversion system we use minres a krylov subspace method to solve it iteratively during each iteration in minres we only compute the products hx and htx for any appropriately sized vectors x for which we solve the forward problem twice as a result we reduce the memory requirement from o mn to o m o n this iterative methodology is combined with the bayesian inverse method in kitanidis 1996 to solve large scale inversion problems the computational advantages of our methodology are demonstrated using a large scale 3 d numerical hydraulic tomography problem with transient pressure measurements 250 000 unknowns and 100 000 measurements in this case 200 gb of memory would otherwise be required to fully compute and store the sensitivity matrix h at each newton step during optimization the cpu cost can also be significantly reduced in terms of the total number of forward simulations in the end we discuss potential extension of the methodology to other geostatistical methods such as the successive linear estimator

a new local stabilized nonconforming finite element method for solving stationary navier stokes equations in this paper we study a new local stabilized nonconforming finite element method based on two local gauss integrals for solving the stationary navier stokes equations this nonconforming method utilizes the lowest equal order pair of mixed finite elements i e ncp 1 p 1 error estimates of optimal order are obtained and numerical results agreeing with these estimates are demonstrated numerical comparisons with other mixed finite element methods for solving the navier stokes equations are also presented to show the better performance of the present method

a two level newton finite element algorithm for approximating electrically conducting incompressible fluid flows we consider the approximation of stationary electrically conducting incompressible fluid flow problems at small magnetic reynolds number the finite element discretization of these systems leads to a very large system of nonlinear equations we consider a solution algorithm which involves solving a much smaller number of nonlinear equations on a coarse mesh then one large linear system on a fine mesh under a uniqueness condition this one step two level newton fem procedure is shown to produce an optimally accurate solution this result extends both the two level method of xu 1 2 from elliptic boundary value problems to mhd problems and the energy norm error analysis of peterson 3 see also 4 of mhd problems at a small magnetic reynolds number to l2 error estimates and multilevel discretization and solution procedures

second order sufficient optimality conditions for some state constrained control problems of semilinear elliptic equations this paper deals with a class of optimal control problems governed by elliptic equations with nonlinear boundary condition the case of boundary control is studied pointwise constraints on the control and certain equality and set constraints on the state are considered second order sufficient conditions for local optimality of controls are established

two dimensional characterization of hydraulic heterogeneity by multiple pumping tests 1 the conventional analysis of pumping tests by type curve methods is based on the assumption of a homogeneous aquifer applying these techniques to pumping test data from real heterogeneous aquifers leads to estimates of the hydraulic parameters that depend on the choice of the pumping and observation well positions in this paper we test whether these values may be viewed as pseudo local values of transmissivity and storativity which can be interpolated by kriging we compare such estimates to those obtained by geostatistical inverse modeling where heterogeneity is assumed in all stages of estimation we use drawdown data from multiple pumping tests conducted at the test site in krauthausen germany the geometric mean values of transmissivity and storativity determined by type curve analysis are very close to those obtained by geostatistical inversion but the conventional approach failed to resolve the spatial variability of transmissivity in contrast the estimate from geostatistical inversion reveals more structure this indicates that the estimates of the type curve approaches can not be treated as pseudo local values concerning storativity both analysis methods show strong fluctuations because the variability of all terms making up the storativity is small we believe that the estimated variability of storativity is biased we examine the influence of measurement error on estimating structural parameters of covariance functions in the inversion we obtain larger correlation lengths and smaller prior variances if we trust the measured data less

preconditioning for the steady state navier stokes equations with low viscosity we introduce a preconditioner for the linearized navier stokes equations that is effective when either the discretization mesh size or the viscosity approaches zero for constant coefficient problems with periodic boundary conditions we show that the preconditioning yields a system with a single eigenvalue equal to 1 so that performance is independent of both viscosity and mesh size for other boundary conditions we demonstrate empirically that convergence depends only mildly on these parameters and we give a partial analysis of this phenomenon we also show that some expensive subsidiary computations required by the new method can be replaced by inexpensive approximate versions of these tasks based on iteration with virtually no degradation of performance

predictor and steplength selection in continuation methods for the navier stokes equations abstract continuation methods are in common use for solving the nonlinear equations resulting from discretizations of the navier stokes equations an imoportant ingrediet in these algorithms is the selection of the step size in the continuation parameter for certain values of the reynolds number it is shown that the step size in the reynolds number may be chosen independently of the particular predictor step used within the continuation algorithm estimates for the path derivatives are derived and used to show that the allowable step sizes are substantially greater than would be predicted by theories that apply to general nonlinear mappings

an inverse model for three dimensional flow in variably saturated porous media geostatistical theory has shown promise in dealing with issues of stability uniqueness and identity of estimates inherent in inverse problems of subsurface flow here the geostatistical method is extended to three dimensional unsteady flow in variably saturated porous geological media the vadose zone that are modeled using the richards equation and the van genuchten mualem constitutive equations the saturated hydraulic conductivity and n parameters of this relationship are treated as spatially correlated statistically independent stochastic processes for representing heterogeneity of porous media for given covariance functions of the parameters the adjoint state sensitivity method is used to calculate first order approximations for covariances of capillary pressure and moisture content and cross covariances between capillary pressure moisture content and the hydraulic properties these covariances and cross covariances are then used in a successive linear estimator sle to estimate the conditional means of the heterogeneous hydraulic property fields based on measurements of pressure and moisture content data a sequential conditioning approach for our sle was also applied to data sets collected at different sampling times during a transient infiltration event this approach has the benefit of reducing the size of the matrices and so helps avoid numerical stability problems on the basis of our study pressure and moisture content data sets collected at later times of an infiltration event or during steady state flow were found to provide better estimates smaller mean square error compared to the true field of the hydrological parameters of the vadose zone than data from very early times

a two grid method based on newton iteration for the navier stokes equations in this paper we consider a two grid method for resolving the nonlinearity in finite element approximations of the equilibrium navier stokes equations we prove the convergence rate of the approximation obtained by this method the two grid method involves solving one small nonlinear coarse mesh system and two linear problems on the fine mesh which have the same stiffness matrix with only different right hand side the algorithm we study produces an approximate solution with the optimal asymptotic in h and accuracy for any reynolds number numerical example is given to show the convergence of the method

trivariate spline approximations of 3d navier stokes equations we present numerical approximations of the 3d steady state navier stokes equations in velocity pressure formulation using trivariate splines of arbitrary degree d and arbitrary smoothness r with r d using functional arguments we derive the discrete navier stokes equations in terms of b coefficients of trivariate splines over a tetrahedral partition of any given polygonal domain smoothness conditions boundary conditions and the divergence free condition are enforced through lagrange multipliers the pressure is computed by solving a poisson equation with neumann boundary conditions we have implemented this approach in matlab and present numerical evidence of the convergence rate as well as experiments on the lid driven cavity flow problem

on a galerkin lagrange multiplier method for the stationary navier stokes equations a galerkin lagrange multiplier formulation is used for the numerical solution of the stationary navier stokes equations in order to avoid the construction of zero divergence elements the formulation is based on different approximating spaces for the velocity field and the pressure optimal rate of convergence estimates are derived moreover a galerkin newton scheme for the solution of the nonlinear equations is shown to be quadratically locally convergent another scheme is shown to be linearly globally convergent

an iterative geostatistical inverse method for steady flow in the vadose zone an iterative geostatistical inverse approach is developed to estimate conditional effective unsaturated hydraulic conductivity parameters soil water pressure head and degree of saturation in heterogeneous vadose zones this approach is similar to the classical cokriging technique and it uses a linear estimator that depends on covariances and cross covariances of unsaturated hydraulic parameters soil water pressure head and degree of saturation the linear estimator is however improved successively by solving the governing flow equation and by updating the residual covariance and cross covariance functions in an iterative manner as a result the nonlinear relationship between unsaturated hydraulic conductivity parameters and head is incorporated in the estimation and the estimated fields are approximate conditional means the ability of the iterative approach is demonstrated through some numerical examples

large scale inverse model analyses employing fast randomized data reduction when the number of observations is large it is computationally challenging to apply classical inverse modeling techniques we have developed a new computationally efficient technique for solving inverse problems with a large number of observations e g on the order of 107 or greater our method which we call the randomized geostatistical approach rga is built upon the principal component geostatistical approach pcga we employ a data reduction technique combined with the pcga to improve the computational efficiency and reduce the memory usage specifically we employ a randomized numerical linear algebra technique based on a so called sketching matrix to effectively reduce the dimension of the observations without losing the information content needed for the inverse analysis in this way the computational and memory costs for rga scale with the information content rather than the size of the calibration data our algorithm is coded in julia and implemented in the mads open source high performance computational framework http mads lanl gov we apply our new inverse modeling method to invert for a synthetic transmissivity field compared to a standard geostatistical approach ga our method is more efficient when the number of observations is large most importantly our method is capable of solving larger inverse problems than the standard ga and pcga approaches therefore our new model inversion method is a powerful tool for solving large scale inverse problems the method can be applied in any field and is not limited to hydrogeological applications such as the characterization of aquifer heterogeneity

parameter estimation by ensemble kalman filters with transformed data approach and application to hydraulic tomography 1 ensemble kalman filters enkfs are a successful tool for estimating state variables in atmospheric and oceanic sciences recent research has prepared the enkf for parameter estimation in groundwater applications enkfs are optimal in the sense of bayesian updating only if all involved variables are multivariate gaussian subsurface flow and transport state variables however generally do not show gaussian dependence on hydraulic log conductivity and among each other even if log conductivity is multi gaussian to improve enkfs in this context we apply nonlinear monotonic transformations to the observed states rendering them gaussian gaussian anamorphosis ga similar ideas have recently been presented by beal et al 2010 in the context of state estimation our work transfers and adapts this methodology to parameter estimation additionally we address the treatment of measurement errors in the transformation and provide several multivariate analysis tools to evaluate the expected usefulness of ga beforehand for illustration we present a first time application of an enkf to parameter estimation from 3 d hydraulic tomography in multi gaussian log conductivity fields results show that 1 ga achieves an implicit pseudolinearization of drawdown data as a function of log conductivity and 2 this makes both parameter identification and prediction of flow and transport more accurate combining enkfs with ga yields a computationally efficient tool for nonlinear inversion of data with improved accuracy this is an attractive benefit given that linearization free methods such as particle filters are computationally extremely demanding

a bayesian approach for inverse modeling data assimilation and conditional simulation of spatial random fields 1 this paper addresses the inverse problem in spatially variable fields such as hydraulic conductivity in groundwater aquifers or rainfall intensity in hydrology common to all these problems is the existence of a complex pattern of spatial variability of the target variables and observations the multiple sources of data available for characterizing the fields the complex relations between the observed and target variables and the multiple scales and frequencies of the observations the method of anchored distributions mad that we propose here is a general bayesian method of inverse modeling of spatial random fields that addresses this complexity the central elements of mad are a modular classification of all relevant data and a new concept called anchors data types are classified by the way they relate to the target variable as either local or nonlocal and as either direct or indirect anchors are devices for localization of data they are used to convert nonlocal indirect data into local distributions of the target variables the target of the inversion is the derivation of the joint distribution of the anchors and structural parameters conditional to all measurements regardless of scale or frequency of measurement the structural parameters describe large scale trends of the target variable fields whereas the anchors capture local inhomogeneities following inversion the joint distribution of anchors and structural parameters is used for generating random fields of the target variable s that are conditioned on the nonlocal indirect data through their anchor representation we demonstrate mad through a detailed case study that assimilates point measurements of the conductivity with head measurements from natural gradient flow the resulting statistical distributions of the parameters are non gaussian similarly the moments of the estimates of the hydraulic head are non gaussian we provide an extended discussion of mad vis a vis other inversion methods including maximum likelihood and maximum a posteriori with an emphasis on the differences between mad and the pilot points method

an efficient solver for the incompressible navier stokes equations in rotation form we consider preconditioned iterative methods applied to discretizations of the linearized navier stokes equations in two and three dimensional bounded domains both unsteady and steady flows are considered the equations are linearized by picard iteration we make use of the rotation form of the momentum equations which has several advantages from the linear algebra point of view we focus on a preconditioning technique based on the hermitian skew hermitian splitting of the resulting nonsymmetric saddle point matrix we show that this technique can be implemented efficiently when the rotation form is used we study the performance of the solvers as a function of mesh size reynolds number time step and algorithm parameters our results indicate that fast convergence independent of problem parameters is achieved in many cases the preconditioner appears to be especially attractive in the case of low viscosity and for unsteady problems

an iterative stochastic inverse method conditional effective transmissivity and hydraulic head fields an iterative stochastic approach is developed to estimate transmissivity and head distributions in heterogeneous aquifers this approach is similar to the classical cokriging technique it uses a linear estimator that depends on the covariances of transmissivity and hydraulic head and their cross covariance the linear estimator is however improved successively by solving the governing flow equation and by updating the covariances and cross covariance function of transmissivity and hydraulic head fields in an iterative manner as a result the nonlinear relationship between transmissivity and head is incorporated in the estimation and the estimated fields are approximate conditional means the ability of the iterative approach is tested with some deterministic and stochastic inverse problems the results show that the estimated transmissivity and hydraulic head fields have smaller mean square errors than those obtained by classical cokriging even in the aquifer with variance of transmissivity up to 3

on the existence uniqueness and finite element approximation of solutions of the equations of stationary incompressible magnetohydrodynamics the authors consider the equations of stationary incompressible magneto hydrodynamics posed in a bounded domain in three dimensions and treat the full coupled system of equations with inhomogeneous boundary conditions under certain conditions on the data they show that the existence and uniqueness of the solution of a weak formulation of the equations can be guaranteed they discuss a finite element discretization of the equations and prove an optimal estimate for the error of the approximate solution

numerical solution to a mixed navier stokes darcy model by the two grid approach we study numerical methods for a coupled navier stokes darcy model which describes a fluid flow filtrating through porous media a decoupled and linearized two grid algorithm is proposed numerical analysis and experiments are presented to show the efficiency and effectiveness of the decoupled and linearized algorithm

cokriging estimation of the conductivity field under variably saturated flow conditions a linear estimator cokriging was applied to estimate hydraulic conductivity using pressure head solute concentration and solute arrival time measurements in a hypothetical heterogeneous vadose zone under steady state infiltrations at different degrees of saturation covariances and cross covariances required by the estimator were determined by a first order approximation in which sensitivity matrices were calculated using an adjoint state method the effectiveness of the pressure concentration and arrival time measurements for the estimator were then evaluated using two statistical criteria l1 and l2 norms i e the average absolute error and the mean square error of the estimated conductivity field results of our analysis showed that pressure head measurements at steady state flow provided the best estimation of hydraulic conductivity among the three types of measurements in addition head measurements of flow near saturation were found more useful for estimating conductivity than those at low saturations the arrival time measurements do not have any significant advantage over concentration factors such as variability linearity and ergodicity were discussed to explain advantage and limitation of each type of data set finally to take advantage of different types of data set e g head and concentration a computationally efficient estimation approach was developed to combine them sequentially to estimate the hydraulic conductivity field the conductivity field estimated by using this sequential approach proves to be better than all the previous estimates using one type of data set alone

geostatistical inverse modeling of transient pumping tests using temporal moments of drawdown 1 pumping tests belong to the most common techniques of hydrogeological site assessment while the steady state drawdown is determined by the distribution of transmissivity alone the transient behavior is also influenced by the storativity field in geostatistical inverse modeling the spatial distributions of both transmissivity and storativity are inferred from the drawdown curves and prior information on the spatial correlation of the parameter fields so far however transient data have hardly been analyzed by geostatistical inverse methods because the computational effort is rather high in the present study we characterize the drawdown by its temporal moments we present moment generating equations and corresponding equations to compute the sensitivity of the temporal moments of drawdown with respect to the distributions of transmissivity and storativity we utilize these equations to infer the transmissivity and storativity fields from transient pumping tests using the quasi linear geostatistical approach of inverse modeling considering temporal moments rather than full drawdown curves drastically reduces the computational effort of the estimation procedure in test cases we show that the first two temporal moments are sufficient to characterize the drawdown curves we investigate how erroneous assumptions regarding the spatial variability of storativity affect the estimate of the transmissivity field and we analyze the effect of truncating the measured drawdown curves

solute transport in low heterogeneity sandboxes the role of correlation length and permeability variance this work examines how heterogeneity structure in particular correlation length controls flow and solute transport we used two dimensional 2d sandboxes 21 9 cm 20 6 cm and four modeling approaches including 2d advection dispersion equation ade with explicit heterogeneity structure 1d ade with average properties and nonlocal continuous time random walk ctrw and fractional ade fade the goal is to answer two questions 1 how and to what extent does correlation length control effective permeability and breakthrough curves btc 2 which model can best reproduce data under what conditions sandboxes were packed with the same 20 v v fine and 80 v v coarse sands in three patterns that differ in correlation length the mixed cases contain uniformly distributed fine and coarse grains the four zone and one zone cases have four and one square fine zones respectively a total of seven experiments were carried out with permeability variance of 0 10 lc 0 22 mc and 0 43 hc experimental data show that the btc curves depend strongly on correlation length especially in the hc cases the hc one zone hco case shows distinct breakthrough steps arising from fast advection in the coarse zone slow advection in the fine zone and slow diffusion while the lco and mco btcs do not exhibit such behavior with explicit representation of heterogeneity structure 2d ade reproduces btcs well in all cases ctrw reproduces temporal moments with smaller deviation from data than fade in all cases except hco where fade has the lowest deviation

on conforming finite element methods for the inhomogeneous stationary navier stokes equations we consider the stationary navier stokes equations written in terms of the primitive variables in the case where both the partial differential equations and boundary conditions are inhomogeneous under certain conditions on the data the existence and uniqueness of the solution of a weak formulation of the equations can be guaranteed a conforming finite element method is presented and optimal estimates for the error of the approximate solution are proved in addition the convergence properties of iterative methods for the solution of the discrete nonlinear algebraic systems resulting from the finite element algorithm are given numerical examples using an efficient choice of finite element spaces are also provided

type curve interpretation of late time pumping test data in randomly heterogeneous aquifers 1 the properties of heterogeneous media vary spatially in a manner that can seldom be described with certainty it may however be possible to describe the spatial variability of these properties in terms of geostatistical parameters such as mean integral spatial correlation scale and variance neuman et al 2004 proposed a graphical method to estimate the geostatistical parameters of natural log transmissivity on the basis of quasi steady state head data when a randomly heterogeneous confined aquifer is pumped at a constant rate from a fully penetrating well they conjectured that a quasi steady state during which heads vary in space time while gradients vary only in space develops in a statistically homogeneous and horizontally isotropic aquifer as it does in a uniform aquifer we confirm their conjecture numerically for gaussian log transmissivities show that time drawdown data from randomly heterogeneous aquifers are difficult to interpret graphically and demonstrate that quasi steady state distance drawdown data are amenable to such interpretation by the type curve method of neuman et al the method yields acceptable estimates of statistical log transmissivity parameters for fields having either an exponential or a gaussian spatial correlation function these estimates are more robust than those obtained using the graphical time drawdown method of copty and findikakis 2003 2004a we apply the method of neuman et al 2004 simultaneously to data from a sequence of pumping tests conducted in four wells in an aquifer near tubingen germany and compare our transmissivity estimate with estimates obtained from 312 flowmeter measurements of hydraulic conductivity in these and eight additional wells at the site we find that 1 four wells are enough to provide reasonable estimates of lead log transmissivity statistics for the tubingen site using this method and 2 the time drawdown method of cooper and jacob 1946 underestimates the geometric mean transmissivity at the site by 30 40

what does a slug test measure an investigation of instrument response and the effects of heterogeneity 1 we consider parameters determined by the inversion of slug test head recovery data with the homogeneous parameter model of cooper et al 1967 to be weighted spatial averages of transmissivity and storage defined at a smaller scale we quantify the spatial averaging using a power average spatial filter expression we determine the form of the filter function and the power exponent using numerically simulated slug test data the filter function that describes how smaller scale transmissivity is weighted by slug tests displays an approximate 1 r2 behavior with r the radial distance from the well the radius of the cylinderical volume that is averaged by the slug test is inversely proportional to the square root of the storage coefficient larger averaging volume with smaller storage the power exponent grows from 0 19 to 0 345 as the ratio of the characteristic scale of the heterogeneity to the characteristic scale of the averaging volume grows although a power exponent of zero corresponding to geometric averaging provides good results for most simulations our results show that while slug tests are useful to estimate transmissivity they have dubious value for estimating storage coefficients we find that the transmissivity estimate is unbiased and does not appear to be strongly influenced by storage properties the storage coefficient estimate is however strongly influenced by the transmissivity and is biased we investigate the interaction between storage coefficient and transmissivity by examining an analytical slug test model that contains two annular zones each with distinct transmissivity and storage coefficient

performance and analysis of saddle point preconditioners for the discrete steady state navier stokes equations we examine the convergence characteristics of iterative methods based on a new preconditioning operator for solving the linear systems arising from discretization and linearization of the steady state navier stokes equations with a combination of analytic and empirical results we study the effects of fundamental parameters on convergence we demonstrate that the preconditioned problem has an eigenvalue distribution consisting of a tightly clustered set together with a small number of outliers the structure of these distributions is independent of the discretization mesh size but the cardinality of the set of outliers increases slowly as the viscosity becomes smaller these characteristics are directly correlated with the convergence properties of iterative solvers