variational properties and orbital stability of standing waves for nls equation on a star graph we study standing waves for a model of nonlinear schr odinger equation on a graph the graph is obtained joining n halflines at a vertex i e it is a star graph at the vertex an interaction occurs due to a boundary condition of delta type with strength alpha leqslant 0 which includes the free or kirchhoff case alpha 0 there imposed the nonlinearity is of focusing power type the dynamics is given by an equation of the form i frac d dt psi t h psi t psi t 2 mu psi t where h is the s a operator which generates the linear schr odinger dynamics on the graph in the hilbert space l 2 gg we show the existence of several families of standing waves solutions of the form phi t e i omega t psi omega where psi omega is a vector amplitude parametrized by a frequency omega they exist for every sign of the coupling at the vertex attractive alpha 0 and for every omega frac alpha 2 n 2 the number of the families depends on the number n of the edges of the graph we moreover determine the ground state which is the standing wave the amplitude of which minimizes the action on the natural nehari constraint and order the various families of standing waves according to their increasing action thus determining a nonlinear spectrum of the problem finally we show that the ground state is orbitally stable for every allowed omega if the nonlinearity is subcritical or critical for supercritical nonlinearities there exists an omega frac alpha 2 n 2 such that the ground state is orbitally stable for frac alpha 2 n 2 omega omega action minimization requires technical subtleties in particular an adaptation of decreasing rearrangements on a star graph is developed with a generalization of the p olya szeg h o inequality

estimation of aquifer parameters under transient and steady state conditions 2 uniqueness stability and solution algorithms paper 2 of this three part series starts with a discussion of the question under what conditions is the aquifer inverse problem well posed after defining the terms uniqueness identifiability and stability theoretical considerations and synthetic examples are used to demonstrate that ill posedness can be mitigated by including prior information about the parameters in the estimation criterion to be minimized at the same time the inclusion of such information is shown to be insufficient to guarantee uniqueness and stability in all cases several test problems in the recent literature which have resulted in pessimistic conclusions about the solvability of the aquifer inverse problem are shown to be ill posed a question is thus raised about the validity of these conclusions in the general case various conjugate gradient algorithms coupled with the adjoint state finite element method for computing the gradient of the estimation criterion and with newton s method for determining the optimum step size downgradient are compared a marked improvement in the rate at which these algorithms converge is shown to be achieved by switching from one method to another when the former slows down or fails to converge

a stable and efficient method for treating surface tension in incompressible two phase flow a new approach based on volume preserving motion by mean curvature for treating surface tension in two phase flows is introduced many numerical tests and a theoretical justification are included which provide evidence regarding the efficacy of the new approach for many flows which exhibit stiff surface tension effects the new approach gives a factor of at least three and sometimes five or more speed up for a given accuracy the new method is easy to implement in the context of 1 level set methods or coupled level set and volume of fluid methods 2 complicated interfaces separating gas from liquid and 3 three dimensional axisymmetric or fully three dimensional adaptive mesh refinement

nonlinear schrodinger equation with growing potential on infinite metric graphs abstract the paper deals with nonlinear schrodinger equations on infinite metric graphs we assume that the linear potential is infinitely growing we prove an existence and multiplicity result that covers both self focusing and defocusing cases furthermore under some additional assumptions we show that solutions obtained bifurcate from trivial ones we prove that these solutions are superexponentially localized our approach is variational and based on generalized nehari manifold

a quadratic spline based interface quasi reconstruction algorithm for accurate tracking of two phase flows a new quadratic spline based interface quasi reconstruction algorithm is presented which provides an accurate and continuous representation of the interface in a multiphase domain and facilitates the direct estimation of local interfacial curvature the fluid interface in each of the mixed cells is represented by piecewise parabolic curves and an initial discontinuous plic approximation of the interface is progressively converted into a smooth quadratic spline made of these parabolic curves the conversion is achieved by a sequence of predictor corrector operations enforcing function c 0 and derivative c 1 continuity at the cell boundaries using simple analytical expressions for the continuity requirements the efficacy and accuracy of the current algorithm has been demonstrated using standard test cases involving reconstruction of known static interface shapes and dynamically evolving interfaces in prescribed flow situations these benchmark studies illustrate that the present algorithm performs excellently as compared to the other interface reconstruction methods available in literature quadratic rate of error reduction with respect to grid size has been observed in all the cases with curved interface shapes only in situations where the interface geometry is primarily flat the rate of convergence becomes linear with the mesh size the flow algorithm implemented in the current work is designed to accurately balance the pressure gradients with the surface tension force at any location as a consequence it is able to minimize spurious flow currents arising from imperfect normal stress balance at the interface this has been demonstrated through the standard test problem of an inviscid droplet placed in a quiescent medium finally the direct curvature estimation ability of the current algorithm is illustrated through the coupled multiphase flow problem of a deformable air bubble rising through a column of water

a general mass conservative numerical solution for the unsaturated flow equation numerical approximations based on different forms of the governing partial differential equation can lead to significantly different results for unsaturated flow problems numerical solution based on the standard h based form of richards equation generally yields poor results characterized by large mass balance errors and erroneous estimates of infiltration depth conversely numerical solutions based on the mixed form of richards equation can be shown to possess the conservative property so that mass is perfectly conserved this leads to significant improvement in numerical solution performance while requiring no additional computational effort however use of the mass conservative method does not guarantee good solutions accurate solution of the unsaturated flow equation also requires use of a diagonal time or mass matrix only when diagonal time matrices are used can the solution be shown to obey a maximum principle which guarantees smooth nonoscillatory infiltration profiles this highlights the fact that proper treatment of the time derivative is critical in the numerical solution of unsaturated flow

behavior of sensitivities in the one dimensional advection dispersion equation implications for parameter estimation and sampling design the spatial and temporal variability of sensitivities has a significant impact on parameter estimation and sampling design for studies of solute transport in porous media physical insight into the behavior of sensitivities is offered through an analysis of analytically derived sensitivities for the one dimensional form of the advection dispersion equation when parameters are estimated in regression models of one dimensional transport the spatial and temporal variability in sensitivities influences variance and covariance of parameter estimates several principles account for the observed influence of sensitivities on parameter uncertainty 1 information about a physical parameter may be most accurately gained at points in space and time with a high sensitivity to the parameter 2 as the distance of observation points from the upstream boundary increases maximum sensitivity to velocity during passage of the solute front increases and the consequent estimate of velocity tends to have lower variance 3 the frequency of sampling must be in phase with the s shape of the dispersion sensitivity curve to yield the most information on dispersion 4 the sensitivity to the dispersion coefficient is usually at least an order of magnitude less than the sensitivity to velocity 5 the assumed probability distribution of random error in observations of solute concentration determines the form of the sensitivities 6 if variance in random error in observations is large trends in sensitivities of observation points may be obscured by noise and thus have limited value in predicting variance in parameter estimates among designs 7 designs that minimize the variance of one parameter may not necessarily minimize the variance of other parameters 8 the time and space interval over which an observation point is sensitive to a given parameter depends on the actual values of the parameters in the underlying physical system

an interface capturing method with a continuous function the thinc method with multi dimensional reconstruction an interface capturing method with a continuous function is proposed within the framework of the volume of fluid vof method being different from the traditional vof methods that require a geometrical reconstruction and identify the interface by a discontinuous heaviside function the present method makes use of the hyperbolic tangent function known as one of the sigmoid type functions in the tangent of hyperbola interface capturing thinc method f xiao y honma k kono a simple algebraic interface capturing scheme using hyperbolic tangent function int j numer methods fluids 48 2005 1023 1040 to retrieve the interface in an algebraic way from the volume fraction data of multi component materials instead of the 1d reconstruction in the original thinc method a multi dimensional hyperbolic tangent function is employed in the present new approach the present scheme resolves moving interface with geometric faithfulness and compact thickness and has at least the following advantages 1 the geometric reconstruction is not required in constructing piecewise approximate functions 2 besides a piecewise linear interface curved quadratic surface can be easily constructed as well and 3 the continuous multi dimensional hyperbolic tangent function allows the direct calculations of derivatives and normal vectors numerical benchmark tests including transport of moving interface and incompressible interfacial flows are presented to validate the numerical accuracy for interface capturing and to show the capability for practical problems such as a stationary circular droplet a drop oscillation a shear induced drop deformation and a rising bubble

estimating unsaturated soil hydraulic properties from tension disc infiltrometer data by numerical inversion tension disc infiltrometers are becoming increasingly popular devices for in situ measurement of the unsaturated hydraulic properties of soil tension infiltration data are generally used to evaluate the parametersks and ain gardner s exponential model of the unsaturated hydraulic conductivity either two measurements using different disc diameters or measurements with a single disc but using multiple pressure heads are then used in this paper we describe a parameter estimation procedure which combines the levenberg marquardt nonlinear parameter optimization method involving weighted least squares with a quasi three dimensional numerical model which solves the variably saturatedflow equation by numerical inversion of richards equation the unknown parameters in van genuchten s model of the unsaturated soil hydraulic properties are estimated from observed cumulative infiltration data during transient waterflow additional measurements of the pressure head or water content as well as a penalty function for constraining the unknown parameters to remain in some feasible region bayesian estimation can be optionally included into the parameter estimation procedure the problem of optimal sampling design that is selecting the best points in space and time for making measurements is addressed by studying the sensitivity of the objective function to changes in the optimized hydraulic parameters we calculate objective functions based on available cumulative infiltration pressure head and water content measurements and also on several combinations of these data the behavior of the objective function in three dimensional parameter space is evaluated by means of a series of two dimensional response surfaces the utility of the parameter estimation procedure is demonstrated using numerically generated data the sensitivity of the procedure to different initial estimates of the model parameters is also discussed

estimation of root water uptake parameters by inverse modeling with soil water content data 1 in this paper we have tested the feasibility of the inverse modeling approach to derive root water uptake parameters rwup from soil water content data using numerical experiments for three differently textured soils and for an optimal drying period the rwup of interest are the rooting depth and the bottom root length density in a first step a thorough sensitivity analysis was performed this showed that soil water content dynamics is relatively insensitive to rwup and that the sensitivity depends on the texture of the considered soil for medium fine textured soil the sensitivity is particularly low due to relatively high unsaturated hydraulic conductivity values these ones allow a compensating effect to occur i e vertical unsaturated water fluxes overshadowing in some way the root water uptake in a second step we analyzed the well posedness of the solution stability and nonuniqueness when only rwup are optimized for this case the inverse problem is clearly ill posed except for the estimation of the rooting depth parameter for coarse and the very fine textured soils in a third step we addressed the case where rwup are estimated simultaneously with additional parameters of the system i e with soil hydraulic parameters for this case our study showed that the inverse problem is well posed for the coarse and very fine textured soils allowing for the estimation of both rwup of interest provided that a powerful global optimization algorithm is used on the contrary the estimation of rwup is unfeasible for medium fine textured soil due to the compensating effect of the vertical unsaturated water flows in conclusion we can state that the inverse modeling approach can be applied to derive rwup for some soils coarse and very fine textured and that the feasibility is strongly improved if the rwup are simultaneously optimized with additional parameters nevertheless more detailed research is needed to apply the inverse modeling approach to real cases for which additional issues are likely to be encountered such as soil heterogeneity and root dynamics

short note analytical and geometrical tools for 3d volume of fluid methods in general grids it is well known that volume of fluid vof methods in three dimensions especially those based on unsplit advection schemes involve highly complex geometrical operations the objective of this work is to propose for general grids and three dimensional cartesian geometry simple and efficient geometrical tools for volume truncation operations that typically arise in vof methods and an analytical method for local volume enforcement the results obtained for different tests and grid types show that the proposed analytical method may be as much as three times faster than brent s iterative method advection tests were carried out using hexahedral grids obtained from deformation of a cubic grid to assess the accuracy of the proposed tools in combination with a recently proposed unsplit plic vof method

quantum graphs ii some spectral properties of quantum and combinatorial graphs the paper deals with some spectral properties of mostly infinite quantum and combinatorial graphs quantum graphs have been intensively studied lately due to their numerous applications to mesoscopic physics nanotechnology optics and other areas a schnol type theorem is proven that allows one to detect that a point belongs to the spectrum when a generalized eigenfunction with an sub exponential growth integral estimate is available a theorem on spectral gap opening for decorated quantum graphs is established its analogue is known for the combinatorial case it is also shown that if a periodic combinatorial or quantum graph has a point spectrum it is generated by compactly supported eigenfunctions scars

estimation of spatial covariance structures by adjoint state maximum likelihood cross validation 1 theory this series of three papers describes a cross validation method to estimate the spatial covariance structure of intrinsic or nonintrinsic random functions from point or spatially averaged data that may be corrupted by noise any number of relevant parameters including nugget effect can be estimated the theory described in this paper is based on a maximum likelihood approach which treats the cross validation errors as gaussian various a posteriori statistical tests are used to verify this hypothesis and to show that in many cases correlation between these errors is weak the log likelihood criterion is optimized through a combination of conjugate gradient algorithms an adjoint state theory is used to efficiently calculate the gradient of the estimation criterion optimize the step size downgradient and compute a lower bound for the covariance matrix of the estimation errors issues related to the identifiability stability and uniqueness of the resulting adjoint state maximum likelihood cross validation asmlcv method are discussed this paper also describes the manner in which asmlcv allows one to use model structure identification criteria to select the best covariance model among a given set of alternatives practical aspects of asmlcv and its application to synthetic data are presented in paper 2 samper and neuman this issue a applications to real hydrogeological data transmissivities and groundwater levels have been presented elsewhere while hydrochemical and isotopic data are analyzed by asmlcv in paper 3 samper and neuman this issue b

uniqueness and observability of conceptual rainfall runoff model parameters the percolation process examined many researchers have expressed concerns regarding the uniqueness of parameter estimates for conceptual rainfall runoff r r models obtained through calibration recent studies sorooshian et al this issue sorooshian and gupta this issue have revealed that even though stochastic parameter estimation techniques can help the problems are not all due to inefficiencies in the calibration techniques used but are caused by the manner in which the model is structurally formulated thus even when calibrated under ideal conditions simulation studies it is often impossible to obtain unique estimates for the parameters it is possible to resolve this problem at least in part by appropriate reparameterizations of the pertinent model equations in this paper the percolation equation of the soil moisture accounting model of the national weather service river forecast system sma nwsrfs will be discussed it is shown that a logical reparameterization of this equation can result in conditions that improve the chances of obtaining unique parameter estimates it is believed that these results have implications for other conceptual r r models in which similar approaches are used in the representation of the percolation infiltration process

an improved height function technique for computing interface curvature from volume fractions an improved height function technique for calculating the interface curvature from volume fractions in three dimensions is presented a detailed analysis of the performance of the height function technique shows that depending on the interface orientation relative to the computational mesh appropriate discretization of the partial derivatives of the height function may considerably reduce the computed interface curvature errors and thus the spurious currents induced in flows with surface tension effects the accuracy and efficiency of the improved height function technique for 3d problems is compared with those of a convolution technique

effective and efficient global optimization for conceptual rainfall runoff models the successful application of a conceptual rainfall runoff crr model depends on how well it is calibrated despite the popularity of crr models reports in the literature indicate that it is typically difficult if not impossible to obtain unique optimal values for their parameters using automatic calibration methods unless the best set of parameters associated with a given calibration data set can be found it is difficult to determine how sensitive the parameter estimates and hence the model forecasts are to factors such as input and output data error model error quantity and quality of data objective function used and so on results are presented that establish clearly the nature of the multiple optima problem for the research crr model sixpar these results suggest that the crr model optimization problem is more difficult than had been previously thought and that currently used local search procedures have a very low probability of successfully finding the optimal parameter sets next the performance of three existing global search procedures are evaluated on the model sixpar finally a powerful new global optimization procedure is presented entitled the shuffled complex evolution sce ua method which was able to consistently locate the global optimum of the sixpar model and appears to be capable of efficiently and effectively solving the crr model optimization problem

negative energy ground states for the l2 critical nlse on metric graphs we investigate the existence of ground states with prescribed mass for the focusing nonlinear schrodinger equation with l2 critical power nonlinearity on noncompact quantum graphs we prove that unlike the case of the real line for certain classes of graphs there exist ground states with negative energy for a whole interval of masses a key role is played by a thorough analysis of gagliardo nirenberg inequalities and by estimates of the optimal constants most of the techniques are new and suited to the investigation of variational problems on metric graphs

short note on reducing interface curvature computation errors in the height function technique a detailed analysis of the errors involved in computing the interface curvature from volume fraction distributions using a height function technique is presented an improved version of the height function technique is proposed based on introducing a correction of the height function discretization error estimated from the local osculating spheres at interface points by using this error correction and an appropriate discretization of the partial derivatives of the height function a substantial improvement in the accuracy of the interface curvature computation can be efficiently achieved

interface curvature via volume fractions heights and mean values on nonuniform rectangular grids estimating the local curvature of an interface involves the local determination of normals to the interface and the rates that they turn along the interface this is challenging in volume of fluid type methods since the interface between materials is specified by the relative amount it cuts off from the computational cells that it crosses also referred to as volume fraction data rather than by a discrete set of points lying on the interface itself in this work we generalize the height function method to nonuniform rectangular grids we demonstrate analytically and numerically that using three successive adjacent integral mean values or column heights interface curvature can be estimated to second order accuracy the first derivative interface normal to third order accuracy and the curve location to fourth order accuracy each at its own special points we also show that there are special points where the curvature can be estimated to fourth order accuracy when using five successive mean values instead underlying all this is a result about the accuracy of the jth derivative of the kth degree polynomial that interpolates a function f at k 1 stencil points placed irregularly in an interval of width h namely for all smooth enough functions f and for k fixed and h getting small there are k 1 j special points in the interval at which the error in the jth derivative is of order o h k 2 j this is one order higher than the usual o h k 1 j error holding over the whole interval for that derivative the special points in the interval are the k 1 j real zeroes of certain f independent polynomials of degree k 1 j with coefficients depending on the interval s stencil points in our case let f x be an indefinite integral of the unknown interfacial curve f x then f x i at k 1 successive stencil points x i is calculated using cumulative sums of the k successive integral mean values of f weighted by the successive interval sizes the k 1 points x i f x i are now interpolated by a kth degree polynomial pf x it s first derivative pf 1 approximates the unknown curve f while pf 2 and pf 3 respectively approximate f 1 and f 2 thus the results above using three successive mean values correspond to k 3 and j 3 2 1 the curvature result using five successive mean values correspond to k 5 and j 3 for this last case since the curvature k f 2 1 f 1 2 3 2 we use the facts that f 1 f 2 pf 2 o h 4 on the whole stencil interval not just at the three special points having o h 4 accuracy for f 2

computational experience with confidence regions and confidence intervals for nonlinear least squares we present the results of a monte carlo study of the leading methods for constructing approximate confidence regions and confidence intervals for parameters estimated by nonlinear least squares we examine three variants of the linearization method the likelihood method and the lack of fit method the linearization method is computationally inexpensive produces easily understandable results and is widely used in practice the likelihood and lack of fit methods are much more expensive and more difficult to report in our tests both the likelihood and lack of fit methods perform very reliably all three variants of the linearization method however often grossly underestimate confidence regions and sometimes significantly underestimate confidence intervals the linearization method variant based solely on the jacobian matrix appears preferable to the two variants that use the full hessian matrix because it is less expensive more numerically stable and at least as accurate the bates and watts curvat

improving the shuffled complex evolution scheme for optimization of complex nonlinear hydrological systems application to the calibration of the sacramento soil moisture accounting model 1 an innovative algorithm shuffled complexes with principal components analysis sp uci is developed to overcome a critical deficiency of the shuffled complex evolution scheme population degeneration population degeneration means that during the evolutionary search process the population of search particles may degenerate into a subspace of the full parameter space thereby missing the capacity of fully exploring the parameter space being confined in a subspace may even lead the particle population to converge to nonstationary points which is a fatal malfunction to overcome this problem sp uci employs the principal components analysis to detect the occurrence of population degeneration and remedy the adverse effects the ensemble of calibrations of the sacramento soil moisture accounting model with the sp uci method over the leaf river basin mississippi retrieves the optimal parameter values with the lowest recorded root mean squared error of simulated daily runoff against the observation moreover the result also provides consistent narrow ranges model parameter distribution which results in a better understanding of the model s behavior given the watershed s hydrologic features

evaluation of maximum likelihood parameter estimation techniques for conceptual rainfall runoff models influence of calibration data variability and length on model credibility the success of an automatic calibration procedure is highly dependent on the choice of the objective function and the nature quantity and quality of the data used the objective function should be selected on the basis of the stochastic properties of the errors present in the data and in the model also the data should be chosen so as to contain as much valuable information about the process as possible in this paper we compare the performance of two maximum likelihood estimators the amle which assumes the presence of first lag autocorrelated homogeneous variance errors and the hmle which assumes the presence of uncorrelated inhomogeneous variance errors to the commonly used simple least squares criterion sls the model calibrated was the soil moisture accounting model of the u s national weather service s river forecast system sma nwsrfs the results indicate that a properly chosen objective function can enhance the possibility of obtaining unique and conceptually realistic parameter estimates furthermore the sensitivity of the estimation results to various characteristics of the calibration data such as hydrologic variability and length are substantially reduced

practical identifiability analysis of large environmental simulation models large environmental simulation models are usually overparameterized with respect to given sets of observations this results in poorly identifiable or nonidentifiable model parameters for small models plots of sensitivity functions have proven to be useful for the analysis of parameter identifiability for models with many parameters however near linear dependence of sensitivity functions can no longer be assessed graphically in this paper a systematic approach for tackling the parameter identifiability problem of large models based on local sensitivity analysis is presented the calculation of two identifiability measures that are easy to handle and interpret is suggested the first accounts for the sensitivity of model results to single parameters and the second accounts for the degree of near linear dependence of sensitivity functions of parameter subsets it is shown how these measures provide identifiability diagnosis for parameter subsets how they are able to guide the selection of identifiable parameter subsets for parameter estimation and how they facilitate the interpretation of the correlation matrix of the parameter estimate with respect to parameter identifiability in addition we show how potential bias of the parameter estimates due to a priori fixing of some of the parameters can be analyzed finally two case studies are presented in order to illustrate the suggested approach

determining soil hydraulic functions from evaporation experiments by a parameter estimation approach experimental verifications and numerical studies a parameter estimation method is developed for the determination of unsaturated soil hydraulic properties from evaporation experiments under laboratory conditions variables used in the inversion procedure are soil water pressure heads at various positions and total soil weights both measured as a function of time during the experiment unknown parameters of different analytical expressions used to describe the soil hydraulic properties are estimated by coupling a finite difference solution of the richards equation with a nonlinear optimization problem this problem is formulated by minimizing the deviations between the numerical solution of the transient flow process and the real system response measured during the experiment minimization of the objective function is performed using a version of the levenberg marquardt s method the procedure also provides information about the uncertainty in parameter estimates the performance of the selected parametric relationships is evaluated and the applicability and accuracy of the proposed inverse method are shown by comparing estimated water retention and hydraulic conductivity functions with experimental results obtained via the instantaneous profile method parameter sensitivity analyses and stability of the inverse solutions are discussed with reference to the originally designed evaporation experiment and to an evaporation method that is developed with a view to reducing experimental efforts further insights into the properties of existence and uniqueness of inverse solutions are gained by examining contour plots of the objective functions under varying experimental conditions the results confirm the reliability and flexibility of the proposed method and suggest that the evaporation flux imposed at the upper soil surface may determine the well posedness of the optimization problem

water quality modeling a review of the analysis of uncertainty this paper reviews the role of uncertainty in the identification of mathematical models of water quality and in the application of these models to problems of prediction more specifically four problem areas are examined in detail uncertainty about model structure uncertainty in the estimated model parameter values the propagation of prediction errors and the design of experiments in order to reduce the critical uncertainties associated with a model the review is rather lengthy and it has therefore been prepared in effect as two papers there is a shorter largely nontechnical version which gives a quick impression of the current and future issues in the analysis of uncertainty in water quality modeling enclosed by this shorter discussion is the main body of the review dealing in turn with 1 identifiability and experimental design 2 the generation of preliminary model hypotheses under conditions of sparse grossly uncertain field data 3 the selection and evaluation of model structure 4 parameter estimation model calibration 5 checks and balances on the identified model i e model verification and model discrimination and 6 prediction error propagation much time is spent in discussing the algorithms of system identification in particular the methods of recursive estimation and in relating these algorithms and the subject of identification to the problems of prediction uncertainty and first order error analysis there are two obvious omissions from the review it is not concerned primarily with either the development and solution of stochastic differential equations or the issue of decision making under uncertainty although clearly some reference must be made to these topics in brief the review concludes not surprisingly that much work has been done on the analysis of uncertainty in the development of mathematical models of water quality and much remains to be done a lack of model identifiability has been an outstanding difficulty in the interpretation and explanation of past observed system behavior and there is ample evidence to show that the larger more comprehensive models are easily capable of generating highly uncertain predictions of future behavior for the future of the subject it is speculated that there is the possibility of progress in the development of novel algorithms for model structure identification a need for new questions to be posed in the problem of prediction and a distinct challenge to the conventional views of this review in the new forms of knowledge representation and manipulation now emerging from the field of artificial intelligence

ground state solutions for some indefinite variational problems abstract we consider the nonlinear stationary schrodinger equation u v x u f x u in r n here f is a superlinear subcritical nonlinearity and we mainly study the case where both v and f are periodic in x and 0 belongs to a spectral gap of v inspired by previous work of li et al 2006 11 and pankov 2005 13 we develop an approach to find ground state solutions i e nontrivial solutions with least possible energy the approach is based on a direct and simple reduction of the indefinite variational problem to a definite one and gives rise to a new minimax characterization of the corresponding critical value our method works for merely continuous nonlinearities f which are allowed to have weaker asymptotic growth than usually assumed for odd f we obtain infinitely many geometrically distinct solutions the approach also yields new existence and multiplicity results for the dirichlet problem for the same type of equations in a bounded domain

a volume of fluid method based on multidimensional advection and spline interface reconstruction a new volume of fluid method for tracking two dimensional interfaces is presented the method involves a multidimensional advection algorithm based on the use of edge matched flux polygons to integrate the volume fraction evolution equation and a spline based reconstruction algorithm the accuracy and efficiency of the proposed method are analyzed using different tests and the results are compared with those obtained recently by other authors despite its simplicity the proposed method represents a significant improvement and compares favorably with other volume of fluid methods as regards the accuracy and efficiency of both the advection and reconstruction steps

estimation of aquifer parameters under transient and steady state conditions 1 maximum likelihood method incorporating prior information in this series of three papers a method is presented to estimate the parameters of groundwater flow models under steady and nonsteady state conditions the parameters include values and directions of principal hydraulic conductivities or transmissivities in anisotropic media specific storage or storativity interior and boundary recharge or leakage rates coefficients of head dependent interior and boundary sources and boundary heads in transient situations the initial head distribution can also be estimated if the system is originally at a steady state paper 1 of the series discusses some of the advantage in treating the inverse problem statistically and in regularizing its solution by means of penalty criteria based on prior estimates of the parameters the inverse problem is posed in the framework of maximum likelihood theory cast in a manner that accounts for prior information about the parameters since not all the factors which contribute to the prior errors can be quantified statistically at the outset the covariance matrices of these errors are expressed in terms of several parameters which if unknown can be estimated jointly with the hydraulic parameters by a stagewise optimization process when transient head data are separated by a fixed time interval the temporal structure of these data is approximated by a lag one autoregressive model with a correlation coefficient that can be treated as another unknown parameter estimation errors are analyzed by examining the lower bound of their covariance matrix in the eigenspace paper 1 concludes by suggesting that certain model identification criteria developed in the time series literature all of which are based on the maximum likelihood concept might be useful for selecting the best groundwater model or the best method of parameterizing a particular model among a number of given alternatives

experimental evidence of randomness and nonuniqueness in unsaturated outflow experiments designed for hydraulic parameter estimation single transient outflow experiments are commonly conducted for inverse estimation of unsaturated hydraulic parameters we assess the validity of this procedure through several repeated experiments on the same sample a medium sand contained in a pressure cell outflow was induced by one or multiple step changes in bottom boundary suction such that there were replicates for each of several step levels in suction we observed that experiments with small initial step changes were poorly reproducible even though our setup allowed reproduction of almost identical initial saturation for each run experiments with large step changes were well reproducible but the outflow response was virtually the same for different step levels neither type of observation was predicted by a theoretical sensitivity analysis of the richards equation given the minimal inaccuracy in our experiments inverse estimation yielded incompatible apparent hydraulic parameters for different flow conditions our results imply experimental limitations of the inversion procedure

prost a parabolic reconstruction of surface tension for the volume of fluid method volume of fluid vof methods are popular for the direct numerical simulation of time dependent viscous incompressible flow of multiple liquids as in any numerical method however it has its weaknesses namely for flows in which the capillary force is the dominant physical mechanism the lack of convergence with spatial refinement or convergence to a solution that is slightly different from the exact solution has been documented in the literature a well known limiting case for this is the existence of spurious currents for the simulation of a spherical drop with zero initial velocity these currents are present in all previous versions of vof algorithms in this paper we develop an accurate representation of the body force due to surface tension which effectively eliminates spurious currents we call this algorithm prost parabolic reconstruction of surface tension there are several components to this procedure including the new body force algorithm improvements in the projection method for the navier stokes solver and a higher order interface advection scheme the curvature to the interface is calculated from an optimal fit for a quadratic approximation to the interface over groups of cells

harnack s inequality and green s functions on locally finite graphs abstract in this paper we study the gradient estimate for positive solutions of schrodinger equations on locally finite and connected graphs then we derive harnack s inequality for positive solutions of the schrodinger equations on such graphs we also set up some existence results about green s functions of the laplacian equations on locally finite graphs we derive a lower bound for the principal eigenvalue of the laplace operator in terms of the upper bound of total integral of green s function interesting existence results for positive solutions of schrodinger equations are derived via the use of related principal eigenvalues

calibration of rainfall runoff models application of global optimization to the sacramento soil moisture accounting model conceptual rainfall runoff models are difficult to calibrate by means of automatic methods one major reason for this is the inability of conventional procedures to locate the globally optimal set of parameters this paper investigates the consistency with which two global optimization methods the shuffled complex evolution sce ua method developed by the authors and the multistart simplex msx method are able to find the optimal parameter set during calibration of the sacramento soil moisture accounting model sac sma of the national weather service river forecast system nwsrfs in the first phase of this study error free synthetic data are used to conduct a comparative evaluation of the algorithms under ideal conditions in 10 independent trials of each algorithm in which 13 parameters of the sac sma model were optimized simultaneously the sce ua method achieved a 100 success rate in locating the precise global optimum i e the true parameter values while the msx method failed in all trials even with more than twice the number of function evaluations in the second phase historical data from the leaf river watershed are used to conduct a comparative evaluation of the algorithms under real conditions using two different estimation criteria drms and hmle the sce ua algorithm obtained consistently lower function values and more closely grouped parameter estimates while using one third fewer function evaluations than the msx algorithm

parameter estimation for coupled unsaturated flow and transport this paper deals with the estimation of soil hydraulic and transport parameters from transient unsaturated flow and tracer experiments using a combined simulations optimization approach hydraulic properties are defined by a modified form of van genuchten s 1980 parametric model for two phase permeability saturation pressure relations and transport properties are defined by an empirical parametric dispersion model a nonlinear weighted least squares algorithm is used to estimate unknown model parameters by minimizing deviations between concentrations water contents and pressure heads obtained from hypothetical infiltration redistribution evaporation experiments and those predicted by solving a numerical model of coupled unsaturated flow and transport simultaneous estimation of hydraulic and transport properties is found to yield smaller estimation errors for model parameters than sequential inversion of hydraulic properties from water content and pressure head data followed by inversion for transport properties from concentration data effects of random noise in data measurements soil layering and choice of improper parametric model on the parameter estimation process are discussed

convergence properties of the nelder mead simplex method in low dimensions the nelder mead simplex algorithm first published in 1965 is an enormously popular direct search method for multidimensional unconstrained minimization despite its widespread use essentially no theoretical results have been proved explicitly for the nelder mead algorithm this paper presents convergence properties of the nelder mead algorithm applied to strictly convex functions in dimensions 1 and 2 we prove convergence to a minimizer for dimension 1 and various limited convergence results for dimension 2 a counterexample of mckinnon gives a family of strictly convex functions in two dimensions and a set of initial conditions for which the nelder mead algorithm converges to a nonminimizer it is not yet known whether the nelder mead method can be proved to converge to a minimizer for a more specialized class of convex functions in two dimensions

on the identification of macroscopic root water uptake parameters from soil water content observations 1 in this paper we analyze the identification problem of macroscopic root water uptake parameters from soil water content observations for this study the macroscopic root water uptake is considered to be linearly decreasing with depth with a and b parameters conditioning respectively the maximum root water uptake at the surface and the decreasing rate with depth for identification of parameter a and b two different identification approaches are tested using a detailed soil moisture data set consisting of vertical profiles measured with time domain reflectometry tdr and neutron probe on 28 locations within a small maize cropped field during a dry period of 26 days the first approach is based on a simplified water balance while the second one uses an integrated soil vegetation atmosphere transfer svat model in an inverse mode results of the simplified water balance show first that the root water uptake measured within the field is quite variable with cv ranging from 22 to 34 for the root uptake parameters a and b respectively furthermore positive correlation between a and b suggests that low superficial root water uptake could be compensated by high deep root water uptake second numerical simulations used to test the validity of this simplified approach show that the method is quite robust at least for a certain range of a parameter values 0 008 a 0 013 for b and for all investigated differently textured soils except the coarse sand to investigate the feasibility and the robustness of the second approach we address the problems of insensitivity instability and nonuniqueness by means of numerical simulations results show for soils with different textures that the soil water content and to a lesser extent the time derivative of soil water content are quite insensitive to root water uptake parameters at least compared to soil hydraulic parameters furthermore instability analysis clearly illustrates that root water uptake parameters are quite and even very instable with respect to small uncertainties on the apparently known parameters e g soil parameters finally results show that if root water uptake plus additional other parameters e g soil parameters are simultaneously optimized nonuniqueness of parameter sets must be expected therefore a robust identification of root water uptake parameters by means of a full svat inversion is unlikely to be achieved during a dry period with soil water content observations at least when some other parameters driving the system like soil hydraulic properties are not error free in this context further in depth research is needed to investigate if the use of longer periods characterized by both drying and redistribution events may increase the success of a full svat inversion finally to extend the results of this study we recommend applying a similar analysis to other macroscopic conceptual root water uptake models

a global multilevel coordinate search procedure for estimating the unsaturated soil hydraulic properties we present a new inverse modeling procedure to characterize the hydraulic properties of partially saturated soils from soil moisture measurements during a natural transient flow experiment the inversion of the governing one dimensional richards equation is carried out using the global multilevel coordinate search optimization algorithm in sequential combination with the local nelder mead simplex algorithm gmcs nms we introduce this optimization method in the area of unsaturated zone hydrology since it is adapted for solving accurately and efficiently complex nonlinear problems several numerical experiments have been conducted to evaluate the proposed inversion method using synthetic error free and error contaminated data for different textured soils inversion of the simulated error free data and examination of the related response surfaces demonstrated the uniqueness of the inverse solution and the suitability of the gmcs nms strategy when identifying four key parameters of the hydraulic functions described by the mualem van genuchten model inversion of the error contaminated data proved further the good stability of the inverse solution that is consistent with the needs required by real experiments

threshold phenomena and existence results for nls ground states on metric graphs abstract we investigate the existence of ground states of prescribed mass for the nonlinear schrodinger energy on a noncompact metric graph g while in some cases the topology of g may rule out or on the contrary guarantee the existence of ground states of any given mass in general also some metric properties of g and their quantitative relation with the actual value of the prescribed mass are relevant as concerns the existence of ground states this may give rise to interesting phase transitions from nonexistence to existence of ground states when a certain quantity reaches a critical threshold

on hydrological model complexity its geometrical interpretations and prediction uncertainty knowledge of hydrological model complexity can aid selection of an optimal prediction model out of a set of available models optimal model selection is formalized as selection of the least complex model out of a subset of models that have lower empirical risk this may be considered equivalent to minimizing an upper bound on prediction error defined here as the mathematical expectation of empirical risk in this paper we derive an upper bound that is free from assumptions on data and underlying process distribution as well as on independence of model predictions over time we demonstrate that hydrological model complexity as defined in the presented theoretical framework plays an important role in determining the upper bound the model complexity also acts as a stabilizer to a hydrological model selection problem if it is deemed ill posed we provide an algorithm for computing complexity of any arbitrary hydrological model we also demonstrate that hydrological model complexity has a geometric interpretation as the size of model output space the presented theory is applied to quantify complexities of two hydrological model structures sac sma and sixpar it detects that sac sma is indeed more complex than sixpar we also develop an algorithm to estimate the upper bound on prediction error which is applied on five different rainfall runoff model structures that vary in complexity we show that a model selection problem is stabilized by regularizing it with model complexity complexity regularized model selection yields models that are robust in predicting future but yet unseen data

yamabe type equations on graphs abstract let g v e be a locally finite graph v be a bounded domain be the usual graph laplacian and 1 be the first eigenvalue of with respect to dirichlet boundary condition using the mountain pass theorem due to ambrosetti rabinowitz we prove that if 1 then for any p 2 there exists a positive solution to u u u p 2 u in u 0 on where and denote the interior and the boundary of respectively also we consider similar problems involving the p laplacian and poly laplacian by the same method such problems can be viewed as discrete versions of the yamabe type equations on euclidean space or compact riemannian manifolds

one two and three dimensional root water uptake functions for transient modeling although solutions of multidimensional transient water flow can be obtained by numerical modeling their application may be limited as root water uptake is generally considered to be one or two dimensional only this is especially the case for trees the first objective of this paper is to test the suitability of a three dimensional root water uptake model for the simultaneous simulation of transient soil water flow around an almond tree the soil hydraulic and root water uptake parameters were optimized by minimizing the residuals between measured and simulated water content data water content was measured in a three dimensional grid around a sprinkler irrigated almond tree for a 16 day period following irrigation a second objective was to compare the performance and results of the three dimensional flow model with one and two dimensional root water uptake models for this purpose measured water contents were aggregated in the x and y direction in the one dimensional case and in the radial direction for the two dimensional uptake model for the estimation of root water uptake model parameters a genetic algorithm was used to estimate the approximate global minimum of the parameter space whereas final parameters were determined using the simplex optimization algorithm with the optimized root water uptake parameters simulated and measured water contents during the 16 day period were in excellent agreement for all root water uptake models most significantly the spatial variation in flux density below the rooting zone decreased when reducing multidimensional root water uptake to fewer dimensions thereby justifying the proposed multidimensional approach

two phase flows on interface refined grids modeled with vof staggered finite volumes and spline interpolants abstract a two phase 2d model that combines the volume of fluid vof method with implicit staggered finite volumes discretization of the navier stokes equation is presented staggered finite volumes are developed on the basis of nonconforming crouzeix raviart finite elements where all components of the velocity lie in the middle of the element edges and the pressure degrees of freedom are found in the centers of mass of the elements staggered finite volumes extend marker and cell mac regular staggered grids to unstructured mesh a linear saddle point problem resulting from either the discretization or the newton method is solved for all unknown pressures and velocities interface is represented with spline interpolants which follow the vof distribution adaptive mesh refinement is used to obtain a high level of uniform refining at the domain of dependence of the interface the aligned grid is obtained by irregular refining of the cells which are intersected by a curve the boundaries of its elements coincide with the slope segments going through the intersections of the curve with the underlying regular elements boundary the deformable computational grids are used only to discretize the navier stokes equation the advection of volume fractions is done on the advection mesh which corresponds to highest regular refining on the computational grid approximation of the surface tension on spline interpolants offers a straightforward way to describe correctly the pressure jumps on interface fitted staggered grids this allows deletion of the anomalous currents around a statical bubble and their effective reduction in real simulations on the aligned grid the continuity of the viscous stress is modeled exactly due to the finite volume approach using the proposed numerical techniques single bubble rise is analyzed

analyses of infiltration events in relation to determining soil hydraulic properties by inverse problem methodology at the field scale because of the relatively large number of observation points required to estimate the spatial distributions of hydraulic properties application of inversion procedures must be based on a characteristic of the flow that for a given point in the field can be measured with relative ease and can be used as input for the inversion procedure suggesting the use of infiltration data for this purpose and recognizing the fact that a basic requirement for the design of a transient flow experiment is that the resulting inverse problem be sufficiently well posed to allow solution this paper addresses the question under which circumstances the resulting inverse problem is well posed utilizing the concepts of identifiability uniqueness and stability for this purpose three different models of the soil hydraulic properties were analyzed the main conclusion of this study is that when infiltration data measured at the darcy scale are used as input for the inversion procedure the inclusion of prior information on a single measurable parameter the saturated conductivity ks in the estimation criterion will enhance the likelihood of uniqueness and stability of the inverse solution provided that the structure of the hydraulic model is sufficiently simple however since for a particular situation it is impossible to determine a priori whether the resultant inverse problem is well posed or not this must be carried out only a posteriori by solving the problem several times with different initial parameter estimates accompanied by an analysis of the associated estimation errors

determining soil hydraulic properties by parameter estimation on the selection of a model for the hydraulic properties parameter estimation procedures involving solution of the inverse flow problem pertinent to a transient experiment constitute a powerful method of determining the soil hydraulic properties one of the problems associated with these procedures is the selection of an appropriate model to describe the soil hydraulic properties three different models were considered those of van genuchten vg and brooks and corey bc model and the exponential model of gardner for the hydraulic conductivity soil water pressure relationships coupled with a new expression for the soil water content soil water pressure relationship gr model for a given model the soil hydraulic properties were determined from simulated and measured outflow experiments supplemented with water content at a soil water pressure head of 15 000 cm h2o using the parameter estimation procedure of kool et al 1985a and data from two soils a hypothetical sandy loam soil assumed to be described by the vg model and a silt loam soil model validation tests were performed and the most appropriate model was selected from the candidate models by discrimination tests using the akaike information criterion aic in the case of the hypothetical sandy loam the vg model was found to be the most accurate and most consistent with the data the performance of both the bc and the gr models in terms of the aic was less good but very similar to each other in the case of the silt loam soil the vg model with additional parameter m which accounts for the correlation between pores and for the flow path tortuosity m 2 02 rather than a constant m 0 5 was found to be most accurate and most consistent with the data the performance of the bc and the gr models was similar when m was considered as an unknown parameter instead of a constant

a reassessment of the groundwater inverse problem this paper presents a functional formulation of the groundwaterflow inverse problem that is sufficiently general to accommodate most commonly used inverse algorithms unknown hydrogeological properties are assumed to be spatial functions that can be represented in terms of a possibly infinite basis function expansion with random coefficients the unknown parameter function is related to the measurements used for estimation by a forward operator which describes the measurement process in the particular case considered here the parameter of interest is the large scale log hydraulic conductivity the measurements are point values of log conductivity and piezometric head and the forward operator is derived from an upscaled groundwaterflow equation the inverse algorithm seeks the most probable or maximum a posteriori estimate of the unknown parameter function when the measurement errors and parameter function are gaussian and independent the maximum a posteriori estimate may be obtained by minimizing a least squares performance index which can be partitioned into goodness of fit and prior terms when the parameter is a stationary random function the prior portion of the performance index is equivalent to a regularization term which imposes a smoothness constraint on the estimate this constraint tends to make the problem well posed by limiting the range of admissible solutions the gaussian maximum a posteriori problem may be solved with variational methods using functional generalizations of gauss newton or gradient based search techniques several popular groundwater inverse algorithms are either special cases of or variants on the functional maximum a posteriori algorithm these algorithms differ primarily with respect to the way they describe spatial variability and the type of search technique they use linear versus nonlinear the accuracy of estimates produced by both linear and nonlinear inverse algorithms may be measured in terms of a bayesian extension of the cramer rao lower bound on the estimation error covariance this bound suggests how parameter identifiability can be improved by modifying the problem structure and adding new measurements

solving the estimation identification problem in two phase flow modeling in this paper a procedure is presented to solve the estimation identification problem in two phase flow modeling given discrete observations made on the system response an optimum parameter set is derived for an appropriate conceptual model by solving the inverse problem using standard optimization techniques subsequently a detailed error analysis is performed and nonlinearity effects are considered we discuss the iterative process of model identification and parameter estimation for a ventilation test performed at the grimsel rock laboratory switzerland a numerical model of the ventilation drift and the surrounding crystalline rock matrix is developed evaporation of moisture at the drift surface and the propagation of the unsaturated zone into the formation are simulated a sensitivity analysis is performed to identify the parameters to be estimated absolute permeability and two parameters of van genuchten s characteristic curves are subsequently determined based on measurements of negative water potentials evaporation rates and gas pressure data the performance of the minimization algorithm and the system behavior for the optimum parameter set are discussed the study shows that a field experiment conducted under two phase flow conditions can be successfully reproduced by taking into account a variety of physical processes and that it is possible to reliably determinemore the two phase hydraulic properties that are related to the given conceptual model 32 refs 8 figs 7 tabs less

a novel representation of the surface tension force for two phase flow with reduced spurious currents abstract a new numerical model for the solution of the single fluid formulation of the incompressible navier stokes equations for two phase flows is presented the model couples an interface front tracking algorithm to a solver of the navier stokes equations based on the finite element method the interface line is described by an ordered set of markers which are advected along the flow streamlines and from the knowledge of their position the local normal and mean curvature are calculated the local mean curvature has been extended to the whole computational domain and the singular surface tension force has been transformed within the framework of the variational formulation into a regular volume force isoparametric taylor hood elements have been used to discretize the navier stokes equations the resulting system has been solved with a fully multigrid method coupled with a vanka like smoother the model has been tested with a dynamical system characterized by a droplet surrounded by another fluid equilibrium solutions described by the laplace s law are reproduced with great accuracy with a very low level of spurious currents which disappear completely if the exact value of the curvature is used damped oscillations are investigated in terms of the oscillation period the damping coefficient and the critical reynolds number for the transition from periodic to aperiodic regimes good agreement with theoretical solutions and the results of other numerical models has been found when the comparison is applicable

on nonexistence of global solutions for a semilinear heat equation on graphs abstract let g v e be a simple finite connected weighted graph satisfying curvature condition c d e n 0 and polynomial volume growth v x r c 0 r m be the normalized laplacian in this paper we prove that the semilinear heat equation u t u u 1 on g has no non negative global solutions for any bounded non negative and non trivial initial value in the case of m 2 the obtained result provides a significant complement to the work that was done recently by lin and wu 2017 concerning the existence and nonexistence of global solutions for the semilinear heat equation on graphs

parameter estimation of hydraulic properties from one step outflow data the one step outflow method was presented by kool et al 1985a b as a fast procedure to estimate unsaturated soil hydraulic properties many investigators however encountered difficulties obtaining a unique solution to the problem the purpose of this paper is to evaluate some of the problems related to this method by looking at response surfaces and to make recommendations for improvements in the methodology the one step outflow procedure was investigated using synthetic data sets generated for 7 6 cm diameter by 7 6 cm high soil cores a finite difference solution of richards equation was used to generate the synthetic data sets response surfaces were calculated for the van genuchten parameters n and ks for various combinations of matric potential water content and outflow data from initially saturated soil cores subjected to a step change in pressure at one of its boundaries the results clearly show that with outflow data alone the parameter estimation procedure will have difficulty converging however if matric potential data are available for a point in the core at some distance from the outflow boundary parameter estimation sensitivity is greatly improved the procedure used was found to be most helpful for determining which auxiliary variables should be measured for parameter estimation from outflow experiments

a balanced force algorithm for continuous and sharp interfacial surface tension models within a volume tracking framework a new balanced force algorithm is presented for modeling interfacial flow with surface tension the algorithm is characterized by a pressure correction method with the interfaces represented by volume fractions within this flow algorithm we devise a continuous e g continuum surface tension model and a sharp e g a ghost fluid method interface representation of the surface tension induced interfacial pressure jump condition the sharp interface representation is achieved by temporarily reconstructing distance functions from volume fractions we demonstrate that a flow algorithm designed to legislate force balance retains an exact balance between surface tension forces and the resulting pressure gradients this balance holds for both continuous and sharp representations of interfacial surface tension the algorithm design eliminates one of the elusive impediments to more accurate models of surface tension driven flow the remaining of which is accurate curvature estimation to validate our formulation we present results for an equilibrium static drop in two and three dimensions having an arbitrary density jump across the interface we find that the sharp surface tension method yields an abrupt pressure jump across the interface whereas the continuous surface tension method results in a smoother transition both methods however yield spurious velocities of the same order the origin of which is due solely to errors in curvature dynamic results are also presented to illustrate the versatility of the method

the analysis of structural identifiability theory and application to conceptual rainfall runoff models the identification of a conceptual hydrologic model involves two stages selection of a suitable model structure and parameter estimation these two stages cannot be treated as distinct and it is important that the limitations of available parameter estimation methodologies be given serious consideration during the procedure of model structure selection this paper focuses on the concepts and tools necessary for the evaluation of whether the structure of a hydrologic model is such that its parameters can be successfully identified a definition of structural identifiability is advanced that is based purely on model properties and is independent of the stochastic nature of the output observation errors the approach is used to develop a measure of local structural identifiability which is useful in the analysis of parameter sensitivity a measure called the sensitivity ratio is introduced which is suitable for studying parameter interactions in the multidimensional parameter space also the use of allowable reparameterizations to improve identifiability is discussed the utility of the concepts discussed in this paper are demonstrated by a simulation example using a conceptual rainfall runoff model

a coupled level set and volume of fluid method for computing 3d and axisymmetric incompressible two phase flows we present a coupled level set volume of fluid clsvof method for computing 3d and axisymmetric incompressible two phase flows this method combines some of the advantages of the volume of fluid method with the level set method to obtain a method which is generally superior to either method alone we present direct comparisons between computations made with the clsvof method and computations made with the level set method the volume of fluid method and the boundary integral method we also compare our computations to the exact solution for an oscillating ellipse due to lamb and experimental results obtained for a rising gas bubble in liquid obtained by hnat and buckmaster our computational examples focus on flows in which surface tension forces and changes in topology are dominant features of the flow

accurate interface normal and curvature estimates on three dimensional unstructured non convex polyhedral meshes this paper presents a framework for extending the height function technique for the calculation of interface normals and curvatures to unstructured non convex polyhedral meshes with application to the piecewise linear interface calculation volume of fluid method the methodology is developed with reference to a collocated node based finite volume two phase flow solver that utilizes the median dual mesh requiring a set of data structures and algorithms for non convex polyhedral operations truncation of a polyhedron by a plane intersection of two polyhedra joining of two convex polyhedra volume enforcement of a polyhedron by a plane and volume fraction initialization by a signed distance function by leveraging these geometric tools a geometric interpolation strategy for embedding structured height function stencils in unstructured meshes is developed the embedded height function technique is tested on surfaces with known interface normals and curvatures namely cylinder sphere and ellipsoid tests are performed on the median duals of a uniform cartesian mesh a wedge mesh and a tetrahedral mesh and comparisons are made with conventional methods across the tests the embedded height function technique outperforms contemporary methods and its accuracy approaches the accuracy that the traditional height function technique exemplifies on uniform cartesian meshes