fully implicit mixed hybrid finite element discretization for general purpose subsurface reservoir simulation abstract we present a new fully implicit mixed hybrid finite element mhfe discretization scheme for general purpose compositional reservoir simulation the locally conservative scheme solves the coupled momentum and mass balance equations simultaneously and the fluid system is modeled using a cubic equation of state we introduce a new conservative flux approach for the mass balance equations for this fully implicit approach we discuss the nonlinear solution procedure for the proposed approach and we present extensive numerical tests to demonstrate the convergence and accuracy of the mhfe method using tetrahedral elements we also compare the method to other advanced discretization schemes for unstructured meshes and tensor permeability finally we illustrate the applicability and robustness of the method for highly heterogeneous reservoirs with unstructured grids

trust region based solver for nonlinear transport in heterogeneous porous media we describe a new nonlinear solver for immiscible two phase transport in porous media where viscous buoyancy and capillary forces are significant the flux fractional flow function f is a nonlinear function of saturation and typically has inflection points and can be non monotonic the non convexity and non monotonicity of f are major sources of difficulty for nonlinear solvers of coupled multiphase flow and transport in natural porous media we describe a modified newton algorithm that employs trust regions of the flux function to guide the newton iterations the flux function is divided into saturation trust regions delineated by the inflection unit flux and end points the updates are performed such that two successive iterations cannot cross any trust region boundary if a crossing is detected the saturation value is chopped back to the appropriate trust region boundary the proposed trust region newton solver which is demonstrated across the parameter space of viscous buoyancy and capillary effects is a significant extension of the inflection point strategy of jenny et al jcp 2009 5 for viscous dominated flows we analyze the discrete nonlinear transport equation obtained using finite volume discretization with phase based upstream weighting then we prove convergence of the trust region newton method irrespective of the timestep size for single cell problems numerical results across the full range of the parameter space of viscous gravity and capillary forces indicate that our trust region scheme is unconditionally convergent for 1d transport that is for a given choice of timestep size the unique discrete solution is found independently of the initial guess for problems dominated by buoyancy and capillarity the trust region newton solver overcomes the often severe limits on timestep size associated with existing methods to validate the effectiveness of the new nonlinear solver for large reservoir models with strong heterogeneity we compare it with state of the art nonlinear solvers for two phase flow and transport using the spe 10 model compared with existing nonlinear solvers our trust region solver results in superior convergence performance and achieves reduction in the total newton iterations by more than an order of magnitude together with a corresponding reduction in the overall computational cost

geometry of pdes i integral bordism groups in pdes we improve some our previous theorems on the calculation of integral bordism groups of formally integrable and completely integrable pdes emphasizing the role played by singular solutions and weak solutions some applications to interesting pdes defined on finite dimensional manifolds are also considered

surgery and bordism groups in quantum partial differential equations i the quantum poincare conjecture abstract in this work in two parts we continue to develop the geometric theory of quantum pde s introduced by us starting from 1996 the second part is quoted in prastaro a prastaro surgery and bordism groups in quantum partial differential equations ii variational quantum pde s nonlinear anal tma in press 10 1016 j na 2008 10 063 this theory has the purpose to build a rigorous mathematical theory of pde s in the category d s of noncommutative manifolds quantum super manifolds necessary to encode physical phenomena at microscopic level i e quantum level aim of the present paper is to report on some new issues in this direction emphasizing an interplaying between surgery integral bordism groups and conservations laws in particular a proof of the poincare conjecture generalized to the category d s is given by using our geometric theory of pde s just in such a category

implicit hybrid upwinding for two phase flow in heterogeneous porous media with buoyancy and capillarity abstract we consider the numerical solution of the partial differential equations governing multiphase flow in porous media for highly nonlinear problems the temporal discretization of choice is often the unconditionally stable fully implicit method however the nonlinear systems often solved with newton s method are difficult to solve thus the computational cost is strongly dependent on the nonlinear convergence rate and enhancing this convergence property is key to speed up subsurface flow simulation we focus on the case of spatially discontinuous capillary pressure between rock regions to efficiently and accurately simulate the flow dynamics in heterogeneous porous media the flux computation combines implicit hybrid upwinding with transmission conditions between different rock regions this leads to a scheme that correctly represents the trapping mechanisms while improving the nonlinear convergence we extend our previous results hamon et al 2016 18 by generalizing the scheme to fully implicit coupled flow and transport to address realistic problems in multiple dimensions the generalized scheme is supported by an analysis of its mathematical properties our multidimensional numerical examples which range from buoyancy driven flow with capillary barriers to viscous dominated flow demonstrate that the implicit hybrid upwinding scheme improves the accuracy compared to the standard phase based upwinding scheme while leading to significant reductions in the number of nonlinear iterations in multiple dimensions

local polynomial kernel regression for generalized linear models and quasi likelihood functions abstract we investigate the extension of the nonparametric regression technique of local polynomial fitting with a kernel weight to generalized linear models and quasi likelihood contexts in the ordinary regression case local polynomial fitting has been seen to have several appealing features in terms of intuitive and mathematical simplicity one noteworthy feature is the better performance near the boundaries compared to the traditional kernel regression estimators these properties are shown to carry over to generalized linear model and quasi likelihood settings we also derive the asymptotic distributions of the proposed class of estimators that allow for straightforward interpretation and extensions of state of the art bandwidth selection methods

kernel methods in machine learning we review machine learning methods employing positive definite kernels these methods formulate learning and estimation problems in a reproducing kernel hilbert space rkhs of functions defined on the data domain expanded in terms of a kernel working in linear spaces of function has the benefit of facilitating the construction and analysis of learning algorithms while at the same time allowing large classes of functions the latter include nonlinear functions as well as functions defined on nonvectorial data we cover a wide range of methods ranging from binary classifiers to sophisticated methods for estimation with structured data

an effective semiparametric estimation approach for the sufficient dimension reduction model abstractin the exploratory data analysis the sufficient dimension reduction model has been widely used to characterize the conditional distribution of interest different from the existing approaches our main achievement is to simultaneously estimate two essential elements basis and structural dimension of the central subspace and the bandwidth of a kernel distribution estimator through a single estimation criterion with an appropriate order of kernel function the proposed estimation procedure can be effectively carried out by starting with a dimension of zero until the first local minimum is reached meanwhile the optimal bandwidth selector is ensured to be a valid tuning parameter for the central subspace estimator an important advantage of this estimation technique is its flexibility to allow a response to be discrete and some of covariates to be discrete or categorical providing that a certain continuity condition holds under very mild assumptions we further derive the uniform consistency of

a semiparametric approach to canonical analysis summary classical canonical correlation analysis is one of the fundamental tools in statistics to investigate the linear association between two sets of variables we propose a method called semiparametric canonical analysis to generalize canonical correlation analysis to incorporate the important non linear association semiparametric canonical analysis is easy to implement and interpret statistical properties are proved a consistent estimation method is developed selection of significant semiparametric canonical analysis components is discussed simulations suggest that the methods proposed have satisfactory performance in finite samples one environmental data set and one data set in social science are investigated in which non linear canonical associations are observed and interpreted

geometry of pde s ii variational pde s and integral bordism groups in the framework of the geometry of pde s we classify variational equations of any order with respect to their formal properties following our previous results a prastaro quantized partial differential equations world scientific singapore 2004 we relate constrained variational pde s to their integral bordism groups in this way we are able to characterize global solutions of constrained variational pde s and to relate them to the structure of global solutions for the corresponding constraint equations some applications are also considered

dimension reduction for the conditional kth moment in regression the idea of dimension reduction without loss of information can be quite helpful for guiding the construction of summary plots in regression without requiring a prespecified model central subspaces are designed to capture all the information for the regression and to provide a population structure for dimension reduction here we introduce the central kth moment subspace to capture information from the mean variance and so on up to the kth conditional moment of the regression new methods are studied for estimating these subspaces connections with sliced inverse regression are established and examples illustrating the theory are presented

global sensitivity analysis for repeated measures studies with informative drop out a semi parametric approach in practice both testable and untestable assumptions are generally required to draw inference about the mean outcome measured at the final scheduled visit in a repeated measures study with drop out scharfstein et al 2014 proposed a sensitivity analysis methodology to determine the robustness of conclusions within a class of untestable assumptions in their approach the untestable and testable assumptions were guaranteed to be compatible their testable assumptions were based on a fully parametric model for the distribution of the observable data while convenient these parametric assumptions have proven especially restrictive in empirical research here we relax their distributional assumptions and provide a more flexible semi parametric approach we illustrate our proposal in the context of a randomized trial for evaluating a treatment of schizoaffective disorder

geometry of pde s iv navier stokes equation and integral bordism groups abstract following our previous results on this subject r p agarwal a prastaro geometry of pde s iii i webs on pde s and integral bordism groups the general theory adv math sci appl 17 2007 239 266 r p agarwal a prastaro geometry of pde s iii ii webs on pde s and integral bordism groups applications to riemannian geometry pde s adv math sci appl 17 2007 267 285 a prastaro geometry of pde s and mechanics world scientific singapore 1996 a prastaro quantum and integral co bordism in partial differential equations acta appl math 5 3 1998 243 302 a prastaro co bordism groups in pde s acta appl math 59 2 1999 111 201 a prastaro quantized partial differential equations world scientific publishing co singapore 2004 500 pp a prastaro geometry of pde s i integral bordism groups in pde s j math anal appl 319 2006 547 566 a prastaro geometry of pde s ii variational pde s and integral bordism groups j math anal appl 321 2006 930 948 a prastaro th m rassias ulam stability in geometry of pde s nonlinear funct anal appl 8 2 2003 259 278 i stakgold boundary value problems of mathematical physics i the macmillan company new york 1967 i stakgold boundary value problems of mathematical physics ii collier macmillan canada ltd toronto ontario 1968 integral bordism groups of the navier stokes equation are calculated for smooth singular and weak solutions respectively then a characterization of global solutions is made on this ground enough conditions to assure existence of global smooth solutions are given and related to nullity of integral characteristic numbers of the boundaries stability of global solutions are related to some characteristic numbers of the space like cauchy data global solutions of variational problems constrained by ns are classified by means of suitable integral bordism groups too

projection pursuit density estimation abstract the projection pursuit methodology is applied to the multivariate density estimation problem the resulting nonparametric procedure is often less biased than the kernel and near neighbor methods in addition graphical information is produced that can be used to help gain geometric insight into the multivariate data distribution

potential based reduced newton algorithm for nonlinear multiphase flow in porous media we present a phase based potential ordering that is an extension of the cascade ordering introduced by appleyard and cheshire john r appleyard ian m cheshire the cascade method for accelerated convergence in implicit simulators in european petroleum conference 1982 pp 113 122 the proposed ordering is valid for both two phase and three phase flow and it can handle countercurrent flow due to gravity and or capillarity we show how this ordering can be used to reduce the nonlinear algebraic system that arises from the fully implicit method fim into one with only pressure dependence the potential based reduced newton algorithm is then obtained by applying newton s method to this reduced order system numerical evidence shows that our potential based reduced newton solver is able to converge for time steps that are much larger than what the standard newton s method can handle in addition whenever standard newton converges so does the reduced newton algorithm and the number of global nonlinear iterations required for convergence is significantly reduced compared with the standard newton s method

approximating conditional distribution functions using dimension reduction motivated by applications to prediction and forecasting we sug gest methods for approximating the conditional distribution function of a random variable y given a dependent random d vector x the idea is to estimate not the distribution of y x but that of y t x where the unit vectoris selected so that the approximation is opti mal under a least squares criterion we show thatmay be estimated root n consistently furthermore estimation of the conditional distri bution function of y givent x has the same first order asymptotic properties that it would enjoy ifwere known the proposed method is illustrated using both simulated and real data examples showing its effectiveness for both independent datasets and data from time series numerical work corroborates the theoretical result thatcan be estimated particularly accurately

kernel quantile estimators abstract for an estimator of quantiles the efficiency of the sample quantile can be improved by considering linear combinations of order statistics that is l estimators a variety of such methods have appeared in the literature an important aspect of this article is that asymptotically several of these are shown to be kernel estimators with a guassian kernel and the bandwidths are identified it is seen that some implicit choices of the smoothing parameter are asymptotically suboptimal in addition the theory of this article suggests a method for choosing the smoothing parameter how much reliance should be placed on the theoretical results is investigated through a simulation study over a variety of distributions little consistent difference is found between various estimators an important conclusion made during the theoretical analysis is that all of these estimators usually provide only modest improvement over the sample quantile the results indicate that even if one knew the best estimator

goodness of fit tests for conditional models under censoring and truncation the problem of specification tests for conditional models is studied when the data are subject to left truncation and right censoring a general method is applied to derive tests for the polynomial regression the proportional hazards the additive risks and the proportional odds models bootstrap versions to approximate the critical values of the test are introduced and proved to work both from a theoretical viewpoint as well as in a small simulation study

dimension reduction and adaptation in conditional density estimation an orthogonal series estimator of the conditional density of a response given a vector of continuous and ordinal nominal categorical predictors is suggested the estimator is based on writing a conditional density as a sum of orthogonal projections on all possible subspaces of reduced dimensionality and then estimating each projection via a shrinkage procedure the shrinkage procedure uses a universal thresholding and a dyadic blockwise shrinkage for low and high frequencies respectively the estimator is data driven is adaptive to underlying smoothness of a conditional density and attains a minimax rate of the mean integrated squared error convergence furthermore if a conditional density depends only on a subgroup of predictors then the estimator seizes the opportunity and attains a corresponding minimax rate of convergence the latter property relaxes the notorious curse of dimensionality moreover the estimator is fast because neither projections nor shrinkages are computation intensive a nu

mann whitney test with adjustments to pretreatment variables for missing values and observational study the conventional wilcoxon mann whitney test can be invalid for comparing treatment effects in the presence of missing values or in observational studies this is because the missingness of the outcomes or the participation in the treatments may depend on certain pre treatment variables we propose an approach to adjust the mann whitney test by correcting the potential bias via consistently estimating the conditional distributions of the outcomes given the pre treatment variables we also propose semiparametric extensions of the adjusted mann whitney test which leads to dimension reduction for high dimensional covariate a novel bootstrap procedure is devised to approximate the null distribution of the test statistics for practical implementations results from simulation studies and an economic observational study data analysis are presented to demonstrate the performance of the proposed approach

unconditionally convergent nonlinear solver for hyperbolic conservation laws with s shaped flux functions this paper addresses the convergence properties of implicit numerical solution algorithms for nonlinear hyperbolic transport problems it is shown that the newton raphson nr method converges for any time step size if the flux function is convex concave or linear which is in general the case for cfd problems in some problems e g multiphase flow in porous media the nonlinear flux function is s shaped not uniformly convex or concave as a result a standard nr iteration can diverge for large time steps even if an implicit discretization scheme is used to solve the nonlinear system of equations in practice when such convergence difficulties are encountered the current time step is cut previous iterations are discarded a smaller time step size is tried and the nr process is repeated the criteria for time step cutting and selection are usually based on heuristics that limit the allowable change in the solution over a time step and or nr iteration here we propose a simple modification to the nr iteration scheme for conservation laws with s shaped flux functions that converges for any time step size the new scheme allows one to choose the time step size based on accuracy consideration only without worrying about the convergence behavior of the nonlinear solver the proposed method can be implemented in an existing simulator e g for co 2 sequestration or reservoir flow modeling quite easily the numerical analysis is confirmed with simulation studies using various test cases of nonlinear multiphase transport in porous media the analysis and numerical experiments demonstrate that the modified scheme allows for the use of arbitrarily large time steps for this class of problems

optimal smoothing in single index models single index models generalize linear regression they have applications to a variety of fields such as discrete choice analysis in econometrics and dose response models in biometrics where high dimensional regression models are often employed single index models are similar to the first step of projection pursuit regression a dimension reduction method in both cases the orientation vector can be estimated root n consistently even if the unknown univariate function or nonparametric link function is assumed to come from a large smoothness class however as we show in the present paper the similarities end there in particular the amount of smoothing necessary for root n consistent orientation estimation is very different in the two cases we suggest a simple empirical rule for selecting the bandwidth appropriate to single index models this rule is studied in a small simulation study and an application in binary response models

nonlinear analysis of multiphase transport in porous media in the presence of viscous buoyancy and capillary forces nonlinear convergence problems in numerical reservoir simulation can lead to unacceptably large computational time and are often the main impediment to performing simulation studies of large scale problems we analyze the nonlinearity of the discrete transport mass conservation equation for immiscible incompressible two phase flow in porous media in the presence of viscous buoyancy and capillary forces although simulation problems are multi dimensional with large numbers of cells and variables we find that the essence of the nonlinear behavior can be understood by studying the discretized numerical flux function for the interface between two cells the numerical flux is expressed in terms of the saturations of the two cells discontinuities in the first order derivative of the flux function referred to as kinks and inflection lines are identified as the cause of convergence difficulty these critical features kinks and inflections change the curvature of the numerical flux function abruptly and can lead to overshoots oscillations or divergence in newton iterations based on our understanding of the nonlinearity a nonlinear solver is developed referred to as the numerical trust region ntr solver the solver is able to guide the newton iterations safely and efficiently through the different saturation trust regions delineated by the kinks and inflections specifically overshoots and oscillations that often lead to convergence failure are avoided numerical examples demonstrate that our ntr solver has superior convergence performance compared with existing methods in particular convergence is achieved for a wide range of timestep sizes and courant friedrichs lewy cfl numbers spanning several orders of magnitude in addition a discretization scheme is proposed for handling heterogeneities in capillary pressure saturation relationship the scheme has less degree of nonlinearity compared with the standard single point phase based upstream weighting scheme leading to an improved nonlinear convergence performance especially when used together with our ntr solver our proposed numerical solution strategy that is based on the numerical flux and handles capillarity extends the previous work by jenny et al 2009 6 and wang and tchelepi 2013 7 significantly the nonlinearity of multiphase transport in porous media is analyzed the analysis considers viscous buoyancy and capillary forces the critical features that cause nonlinear convergence failures are identified a nonlinear solver that converges without oscillations and divergence is developed the solver converges faster than existing methods and allows large timesteps

exploratory projection pursuit abstract a new projection pursuit algorithm for exploring multivariate data is presented that has both statistical and computational advantages over previous methods a number of practical issues concerning its application are addressed a connection to multivariate density estimation is established and its properties are investigated through simulation studies and application to real data the goal of exploratory projection pursuit is to use the data to find low one two or three dimensional projections that provide the most revealing views of the full dimensional data with these views the human gift for pattern recognition can be applied to help discover effects that may not have been anticipated in advance since linear effects are directly captured by the covariance structure of the variable pairs which are straightforward to estimate the emphasis here is on the discovery of nonlinear effects such as clustering or other general nonlinear associations among the variables although arbitrary

surgery and bordism groups in quantum partial differential equations ii variational quantum pdes abstract this is the second part of a work devoted to the interplay between surgery integral bordism groups and conservation laws in order to characterize the geometry of pdes in the category q s of quantum super manifolds part i is quoted in ref a prastaro surgery and bordism groups in quantum partial differential equations i the quantum poincare conjecture nonlinear anal tma in press doi 10 1016 j na 2008 11 077 in this paper we will consider variational problems in the category q s constrained by partial differential equations we get theorems of existence for local and global solutions the characterization of global solutions is made by means of integral bordism groups applications to some important examples of mathematical physics as quantum super black hole solutions of quantum super yang mills equations are discussed in some detail quantum supermanifolds allow us to unify at the quantum level the four fundamental forces gravitational electromagnetic weak nuclear strong nuclear in an unique geometric structure the geometric theory of pdes built in the category q s of quantum supermanifolds gives us the right mathematic tool to describe quantum phenomena also at very high energy levels where quantum gravity becomes dominant

operator based linearization approach for modeling of multiphase multi component flow in porous media a new approach for the linearization of governing equations that describe flow and transport in porous media is proposed in this work it is based on an approximate representation of the exact physics of the problem which is similar to an approximate representation of space and time discretization performed in conventional simulation the governing equations are introduced as a combination of operators dependent on spatially altered properties and operators fully controlled by nonlinear properties of fluid and rock next a parametrization in the physics space of the problem is introduced the property based operators are approximated using direct interpolation in the space of nonlinear unknowns the discrete version of the governing equations is constructed as a combination of operators that approximate both nonlinear physics and discretization in time and space this approach is applied to the reservoir simulation of miscible and immiscible displacement processes the performance of the method demonstrates a convergence of simulation results by resolution in physical space with the improved performance

conditional density estimation in a regression setting regression problems are traditionally analyzed via univariate characteristics like the regression function scale function and marginal density of regression errors these characteristics are useful and informative whenever the association between the predictor and the response is relatively simple more detailed information about the association can be provided by the conditional density of the response given the predictor for the first time in the literature this article develops the theory of minimax estimation of the conditional density for regression settings with fixed and random designs of predictors bounded and unbounded responses and a vast set of anisotropic classes of conditional densities the study of fixed design regression is of special interest and novelty because the known literature is devoted to the case of random predictors for the aforementioned models the paper suggests a universal adaptive estimator which i matches performance of an oracle that knows both an underlying model and an estimated conditional density ii is sharp minimax over a vast class of anisotropic conditional densities iii is at least rate minimax when the response is independent of the predictor and thus a bivariate conditional density becomes a univariate density iv is adaptive to an underlying design fixed or random of predictors

upstream differencing for multiphase flow in reservoir simulation upstream weighting for multiphase flow in reservoir simulation is analyzed the associated numerical flux is shown to be well defined monotone lipschitz continuous and consistent in the case of a two phase flow the corresponding numerical flux is compared to that of godunov and engquist and osher finally simple way to obtain a higher order scheme is outlined

analysis of hybrid upwinding for fully implicit simulation of three phase flow with gravity the systems of algebraic equations arising from implicit backward euler finite volume discretization of the conservation laws governing multiphase flow in porous media are quite challenging for nonlinear solvers in the presence of countercurrent flow due to buoyancy the numerical flux obtained with single point phase potential upwinding ppu is not differentiable which causes convergence difficulties for nonlinear solvers recently lee efendiev and tchelepi adv water resour 82 2015 pp 27 38 proposed a hybrid upwinding strategy for two phase flow that gives rise to a differentiable numerical flux across the entire viscous gravity parameter space here we first present an implicit hybrid upwinding ihu scheme for hyperbolic conservation laws extending the work of lee efendiev and tchelepi to an arbitrary number of fluid phases we show that the numerical flux obtained with the ihu is consistent and a monotone function of its own saturation it is also a differentiable function of t

blind source separation by sparse decomposition in a signal dictionary the blind source separation problem is to extract the underlying source signals from a set of linear mixtures where the mixing matrix is unknown this situation is common in acoustics radio medical signal and image processing hyperspectral imaging and other areas we suggest a two stage separation process a priori selection of a possibly overcomplete signal dictionary for instance a wavelet frame or a learned dictionary in which the sources are assumed to be sparsely representable followed by unmixing the sources by exploiting the their sparse representability we consider the general case of more sources than mixtures but also derive a more efficient algorithm in the case of a nonovercomplete dictionary and an equal numbers of sources and mixtures experiments with artificial signals and musical sounds demonstrate significantly better separation than other known techniques

robust estimation of dispersion matrices and principal components abstract this paper uses monte carlo methods to compare the performances of several robust procedures for estimating a correlation matrix and its principal components the estimators are formed either from separate bivariate analyses or by simultaneous manipulation of all variables by using techniques such as multivariate trimming and m estimation the m estimators stand up exceptionally well they and the multivariate trimming procedure are especially effective at estimating the principal components including a near singularity however the m estimators can break down relatively easily when the dimensionality is large and the outliers are asymmetric with missing data the element wise approach becomes more attractive

methods for estimating a conditional distribution function abstract motivated by the problem of setting prediction intervals in time series analysis we suggest two new methods for conditional distribution estimation the first method is based on locally fitting a logistic model and is in the spirit of recent work on locally parametric techniques in density estimation it produces distribution estimators that may be of arbitrarily high order but nevertheless always lie between 0 and 1 the second method involves an adjusted form of the nadaraya watson estimator it preserves the bias and variance properties of a class of second order estimators introduced by yu and jones but has the added advantage of always being a distribution itself our methods also have application outside the time series setting for example to quantile estimation for independent data this problem motivated the work of yu and jones

convergence of implicit monotone schemes with applications in multiphase flow in porous media phase based upstreaming which is a commonly used spatial discretization for multiphase flow in reservoir simulation naturally gives rise to implicit monotone schemes when implicit time stepping is used the nonlinear gauss seidel and jacobi algorithms are shown to converge to a unique bounded solution when applied to the resulting system of equations thus for one dimensional problems we obtain an alternate constructive proof that such schemes are well defined and converge to the entropy solution of the conservation law for arbitrary cfl numbers the accuracy of phase based upstream solutions is studied for various spatial and temporal grids revealing the importance of unconditional stability when nonuniform grids and or variable porosity is involved

implicit hybrid upwind scheme for coupled multiphase flow and transport with buoyancy abstract numerical simulation of coupled multiphase flow and transport in porous media is used in many scientific and industrial applications such as groundwater management and oil recovery to solve the governing partial differential equations we focus on the fully implicit backward euler finite volume method fim in this numerical scheme large algebraic systems must be solved at each time step using newton s method this can be quite expensive especially for highly nonlinear problems with buoyancy in this work we present a new first order approximation of the flux in the fim leading to improved nonlinear convergence rate and radius this approximation is based on implicit hybrid upwinding and relies on separate treatments of the viscous and buoyancy parts of the numerical flux moreover in the viscous part the total velocity discretization is key as it controls the coupling between the elliptic flow problem and the hyperbolic multiphase transport problem to achieve robustness and efficiency we propose a differentiable total velocity discretization that adapts to the balance of forces at each interface we analyze the theoretical properties of the resulting numerical scheme and prove that saturations remain between physical bounds challenging two and three phase test cases illustrate that our numerical scheme brings a significant reduction in the number of nonlinear iterations compared to a finite volume discretization relying on the widely used phase per phase upstream weighting our numerical scheme therefore reduces the simulation cost while providing similar accuracy