formulations and numerical methods of the black oil model in porous media the black oil model for describing the hydrocarbon equilibrium in porous media is considered in this paper various formulations of the governing equations that describe this model including phase weighted fluid global and pseudoglobal pressure saturation formulations with the total velocity and flux are first constructed these formulations are more suitable for their mathematical and numerical analysis finite element approximate procedures are then analyzed these procedures are based on the use of mixed finite element methods for the pressure equations and galerkin finite element methods for the saturation equations error estimates are stated first for the case where capillary diffusion coefficients are assumed to be uniformly positive then an error analysis is carried out in detail for a degenerate case where these coefficients can be zero

analysis of a semidiscrete discontinuous galerkin scheme for compressible miscible displacement problem numerical approximation of the coupled system of compressible miscible displacement problem in porous media is considered in this paper a continuous in time discontinuous galerkin scheme is developed the symmetric interior penalty discontinuous galerkin method is used to solve both the flow and transport equations upwind technique is used to treat the convection term in the transport equation the hp a priori error bounds are derived

on a nonlinear parabolic system modelling miscible compressible displacement in porous media abstract we give an existence result for a nonlinear parabolic system modelling the single phase miscible displacement of one slightly compressible fluid by another in a porous medium to this aim we study the asymptotic behaviour of a flow at low dispersion coefficients we use suitable test functions to establish a priori estimates and then compactness arguments to pass to the limit in a perturbated problem we also state the existence and the uniqueness of a strong solution

an unsplit higher order godunov method for scalar conservation laws in multiple dimensions abstract in this paper we develop an unsplit higher order godunov method for scalar conservation laws in two dimensions the method represents an extension for the special case being considered of methods developed by colella and by van leer in our method we begin with a piecewise bilinear representation of the solution on each grid cell a new piecewise bilinear representation at the next time level is then obtained from a two step procedure in the first step a conservative predictor corrector scheme derived from the integral form of the differential equation and characteristic considerations is used to obtain average values of the solution over grid cells at the new time level next these new average values are then used to construct a limited piecewise bilinear profile for each cell at the new time level the resulting method is shown to satisfy a maximum principle for constant coefficient linear advection computational results are presented comparing the new method to colella s method for linear advection the method is also applied to two model problems from porous media flow miscible and immiscible displacement the new scheme provides accurate resolution of sharp fronts without any significant distortion

why nonconservative schemes converge to wrong solutions error analysis this paper attempts to give a qualitative and quailtitative description of the numerical error introduced by using finite difference schemes in nonconservative form for scalar conservation laws we show that these schemes converge strongly in li norm to the solution of an inhomogeneous conservation law containing a borel measure source term moreover we analyze the properties of this borel measure and derive a sharp estimate for the l1 error between the limit function given by the scheme and the correct solution in general the measure source term is of the order of the entropy dissipation measure associated with the scheme in certain cases the error can be small for short times which makes it difficult to detect numerically but generically such an error will grow in time and this would lead to a large error for large time calculations finally we show that a local correction of any high order accurate scheme in nonconservative form is sufficient to ensure its convergence to the correct solution

a new discontinuous galerkin mixed finite element method for compressible miscible displacement problem abstract a new combined discontinuous galerkin method is proposed for compressible miscible displacement problem in porous media here a splitting positive definite mixed finite element method is used for the pressure and darcy velocity while an interior penalty discontinuous galerkin ipdg method is used for the transport equation the stability and convergence of this algorithm are considered and the optimal a priori error estimate in l l 2 for velocity pressure and concentration are given finally we provide some numerical results to confirm our theoretical analysis and simulate compressible fluid flows through homogeneous and isotropic porous media

the classification of 2 2 systems of non strictly hyperbolic conservation laws with application to oil recovery on considere un systeme 2 2 a une variable d espace u f u x 0 0 ou u u x t r 2 et f r 2 r 2 on montre que pour des equations hyperboliques des points ombilicaux sont typiquement isoles et que en un point ombilical isole df est typiquement diagonalisable on donne une classification des equations hyperboliques a points ombilicaux isoles

higher order godunov methods for general systems of hyperbolic conservation laws abstract we describe an extension of higher order godunov methods to general systems of hyperbolic conservation laws this extension allow the method to be applied to problems that are not strictly hyperbolic and exhibit local linear degeneracies in the wave fields the method constructs an approximation of the riemann problem from local wave information a generalization of the engquist osher flux for systems is then used to compute a numerical flux based on this approximation this numerical flux replaces the godunov numerical flux in the algorithm thereby eliminating the need for a global riemann problem solution the additional modifications to the godunov methodology that are needed to treat loss of strict hyperbolicity are described in detail the method is applied to some simple model problems for which the global analytic structure is known the method is also applied to the black oil model for multiphase flow in petroleum reservoirs

front tracking for shear bands in an antiplane shear model in this paper we describe a numerical algorithm for the study of shear band formation and growth in two dimensional antiplane shear the constitutive model uses a non associative flow rule the numerical scheme is based on a godunov method for updating the velocity while the stress is updated via integration along particle paths the scheme is coupled with a front tracking algorithm for careful evolution of the shear bands the main challenges are the non hyperbolicity of the shear band formation and growth front tracking avoids the catastrophic effects of the loss of hyperbolicity in the godunov type numerical scheme the existence of endpoints for the shear band the tracked front does not separate the computational domain into disconnected regions and the non hyperbolic rate of growth of the shear band we give examples of the success of the algorithm and show convergence tests

a discussion of stress rates in finite deformation problems abstract it has recently been shown that the finite elastic plastic solution of the simple shear problem exhibits an oscillatory stress response when kinematic hardening is employed while the solution for isotropic hardening gives a monotonically increasing stress this paper analyzes this response on the basis of continuum mechanical descriptions of the problem three objective stress rates are recalled and spatial descriptions of plasticity at finite deformation are reviewed for the usual generalization of the infinitesimal theory as well as a theory based on an invariant measure of true stress in light of the equations for the evolution of the yield surface the hypoelastic solution to the simple shear problem for each of the three stress rates is presented it is shown that the use of the jaumann rate in the generalization of the infinitesimal theory leads to an oscillation in the evolution of the yield surface in simple shear which is explained on the basis of the hypoelastic solution an alternative theory which makes use of the polar decomposition predicts a monotonically increasing shear stress

a free lagrange augmented godunov method for the simulation of elastic plastic solids a lagrangian finite volume godunov scheme is extended to simulate two dimensional solids in planar geometry the scheme employs an elastic perfectly plastic material model implemented using the method of radial return and either the stiffened gas or osborne equation of state to describe the material the problem of mesh entanglement common to conventional two dimensional lagrangian schemes is avoided by utilising the free lagrange method the lagrangian formulation enables features convecting at the local velocity such as material interfaces to be resolved with minimal numerical dissipation the governing equations are split into separate subproblems and solved sequentially in time using a time operator split procedure local riemann problems are solved using a two shock approximate riemann solver and piecewise linear data reconstruction is employed using a muscl based approach to improve spatial accuracy to illustrate the effectiveness of the technique numerical simulations are presented and compared with results from commercial fixed connectivity lagrangian and smooth particle hydrodynamics solvers autodyn 2d the simulations comprise the low velocity impact of an aluminium projectile on a semi infinite target the collapse of a thick walled beryllium cylinder and the high velocity impact of cylindrical aluminium and steel projectiles on a thin aluminium target the analytical solution for the collapse of a thick walled cylinder is also presented for comparison

error analysis of the semi discrete local discontinuous galerkin method for compressible miscible displacement problem in porous media in this paper local discontinuous galerkin method for flow and transport is introduced for the coupled system of compressible miscible displacement problem optimal error estimates in l 0 t l 2 norm not only for the solution itself but also for the auxiliary variables are derived the main technical difficulties in the analysis include the nonlinearity the coupling of the models and the treatment of the inter element jump terms which arise from the discontinuous nature of the numerical method the numerical results illustrate the accuracy and capability of the method

on the riemann problem for a prototype of a mixed type conservation law we study the system of conservation laws given by with initial value the system is elliptic when u2 v2 2 and hyperbolic when u2 v2 2 following liu s construction it is found that the system always has a weak solution which however is not necessarily unique

a fourier based method for approximating the joint detection probability in mimo communications we propose a numerically efficient technique to approximate the joint detection probability of a coherent multiple input multiple output mimo receiver in the presence of inter symbol interference isi and additive white gaussian noise awgn this technique approximates the probability of detection by numerically integrating the product of the characteristic function cf of the received filtered signal with the fourier transform of the multi dimension decision region naturally the accuracy of the approximation is dependent on the number of points in the numerical integration the proposed method selects the number of points to integrate over by deriving bounds on the approximation error as such a reduction of up to 1 100th of the number points can be achieved when comparing with existing single input single output siso techniques simulation results demonstrate that the proposed method is highly accurate with the calculated errors being well within the bounded approximation error in addition the results are closely matched with those obtained using the monte carlo simulations with a typical error less than 10 4 while requiring only a fraction of the computation time

finite element approximation of an evolution problem modeling shear band formation abstract an error analysis is provided for the spatial approximation by the finite element method of a nonlinear time dependent problem which models the antiplane shear deformations of a thermoplastic material this problem consists of a system of two coupled partial differential equations with velocity and temperature unknowns optimal order error estimates in the l 2 norm are given for each of these

error rate evaluation of linear equalization and decision feedback equalization with error propagation we propose applying an approximate fourier series to evaluate efficiently the bit error rate ber performance of finite length linear equalization le and decision feedback equalization dfe by extending the fourier series we enable ber calculations for quadrature phase shift keying qpsk transmission on complex channels with in phase and crosstalk intersymbol interference isi the ber calculation is based on determining the residual isi samples and background gaussian noise variance at the equalizer output for static channels or for realizations of quasi static fading channels a simple bound on the series error magnitude in terms of the fourier series parameters ensures the required accuracy and precision improved state transition probability estimates are derived and verified by simulation for an approximate markov model of the dfe error propagation for the case in which residual isi exists even when the previous decisions stored in the feedback filter fbf are correct we demonstrate the ease and widespread applicability of our approach by producing results which elucidate a variety of equalization tradeoffs our analysis includes symbol spaced and fractionally spaced minimum mean square error mmse le zero forcing zf le and mmse dfe with and without error propagation on static isi channels and multipath channels with quasi static rayleigh fading a comparison between suboptimum and optimum receiver filtering in conjunction with equalization and an assessment of the accuracy of some widely used equalization ber approximations and bounds

a method for reducing numerical dispersion in two phase black oil reservoir simulation abstract in this paper a new sequential method for 1 dimensional two phase black oil reservior simulation is presented the model includes compressibility and mass transfer between phases the method decouples the system of equations into a parabolic equation and a hyperbolic system one dimensional numerical examples are presented using both first and second order godunov discretizations for the hyperbolic part of the system the results are compared to a fully implicit method using upwind differences the second order godunov method shows dramatic improvement over those obtained with the more dispersive first order methods

efficient solution algorithms for the riemann problem for real gases a procedure for constructing solutions to the riemann problem for gas dynamics with a general convex equation of state is given approximate procedures involving a local parametrization of the equation of state are introduced in order to calculate numerical fluxes in conservative finite difference schemes this leads to difference schemes which are as accurate and almost as fast as the analogous schemes for polytropic gases numerical results in one and two space variables are presented

inequalities between kappa and kappa like statistics for k k tables the paper presents inequalities between four descriptive statistics that can be expressed in the form p e p 1 e p where p is the observed proportion of agreement of a k k table with identical categories and e p is a function of the marginal probabilities scott s is an upper bound of goodman and kruskal s and a lower bound of both bennett et al s and cohen s we introduce a concept for the marginal probabilities of the k k table called weak marginal symmetry using the rearrangement inequality it is shown that bennett et al s is an upper bound of cohen s if the k k table is weakly marginal symmetric

accurate evaluation of multiple access performance in th ppm and th bpsk uwb systems a characteristic function method is proposed for precisely calculating the bit error probability of time hopping th ultra wideband uwb systems with multiple access interference in an additive white gaussian noise environment the analytical expressions are validated by simulation and used to assess the accuracy of the gaussian approximation the gaussian approximation is shown to be inaccurate for predicting bit error rates bers for medium and large signal to noise ratio snr values the performances of th pulse position modulation ppm and binary phase shift keying bpsk modulation schemes are accurately compared in terms of the ber it is shown that the bpsk system outperforms the binary ppm system for all values of snr the sensitivity of the performance of the modulation schemes to the system parameters is also addressed through numerical examples

numerically efficient fourier based technique for calculating error probabilities with intersymbol interference we propose a numerically efficient technique for calculating the probability of symbol error for arbitrary coherent modulation schemes in the presence of intersymbol interference isi and additive noise the probability of error is formulated in terms of an inverse fourier transform of the windowed characteristic function of the random variable representing the interfering symbols and the noise process the integral is evaluated numerically using the sampling theorem

an a posteriori error analysis of mixed finite element galerkin approximations to second order linear parabolic problems in this article a posteriori error estimates are derived for mixed finite element galerkin approximations to second order linear parabolic initial and boundary value problems using mixed elliptic reconstructions a posteriori error estimates in l infty l 2 and l 2 l 2 norms for the solution as well as its flux are proved for the semidiscrete scheme finally based on a backward euler method a completely discrete scheme is analyzed and a posteriori error bounds are derived which improves upon earlier results on a posteriori estimates of mixed finite element approximations to parabolic problems results of numerical experiments verifying the efficiency of the estimators have also been provided

a combined mixed and discontinuous galerkin method for compressible miscible displacement problem in porous media in this paper we present a numerical scheme for solving the coupled system of compressible miscible displacement problem in porous media the flow equation is solved by the mixed finite element method and the transport equation is approximated by a discontinuous galerkin method the scheme is continuous in time and a priori hp error estimates is presented

a numerical model for trickle bed reactors trickle bed reactors are governed by equations of flow in porous media such as darcy s law and the conservation of mass our numerical method for solving these equations is based on a total velocity splitting sequential formulation which leads to an implicit pressure equation and a semi implicit mass conservation equation we use high resolution finite difference methods to discretize these equations our solution scheme extends previous work in modeling porous media flows in two ways first we incorporate physical effects due to capillary pressure a nonlinear inlet boundary condition spatial porosity variations and inertial effects on phase mobilities in particular capillary forces introduce a parabolic component into the recast evolution equation and the inertial effects give rise to hyperbolic nonconvexity second we introduce a modification of the slope limiting algorithm to prevent our numerical method from producing spurious shocks we present a numerical algorithm for accommodating these difficulties show the algorithm is second order accurate and demonstrate its performance on a number of simplified problems relevant to trickle bed reactor modeling c 2000 academic press

characteristic block centered finite difference method for compressible miscible displacement in porous media in this paper the characteristic block centered finite difference method is introduced and analyzed to solve compressible miscible displacement in porous media error estimates for the pressure velocity concentration and its flux in different discrete norms are established rigorously and carefully on non uniform grids finally some numerical experiments are presented to show that the convergence rates are in agreement with the theoretical analysis

mixed finite volume element upwind mixed volume element of compressible two phase displacement and its numerical analysis abstract a fundamental topic in numerical simulation of two phase displacement is discussed in this paper the mathematical model for the compressible problem is defined mainly by two nonlinear partial differential equations a parabolic equation for the pressure and a convection diffusion equation for the saturation the darcy velocity is determined by the pressure and affects the whole physical process the system is solved by a composite numerical scheme the conservative mixed volume element is used for the first equation the computational accuracy is improved for the darcy velocity the second equation is solved by a conservative upwind mixed volume element where the mixed volume element and upwind approximation treat the diffusion and convection respectively the upwind method preserves the high computational accuracy and numerical dispersion and nonphysical oscillation are eliminated the saturation and its adjoint vector function are obtained simultaneously an important feature in numerical scheme the conservation of mass is proved by the traditional theoretical work of numerical analysis such as a priori estimates of differential equations the optimal order error estimate is obtained finally numerical tests show the effectiveness and practicability then the present method possibly solves the challenging problems as a powerful tool

bound preserving discontinuous galerkin method for compressible miscible displacement in porous media in this paper we develop bound preserving discontinuous galerkin dg methods for the coupled system of compressible miscible displacement problems we consider the problem with two components and the volumetric concentration of the i th component of the fluid mixture c i should be between 0 and 1 however c i does not satisfy the maximum principle therefore the numerical techniques introduced in x zhang and c w shu j comput phys 229 2010 pp 3091 3120 cannot be applied directly the main idea is to apply the positivity preserving techniques to both c 1 and c 2 respectively and enforce c 1 c 2 1 simultaneously to obtain physically relevant approximations by doing so we have to treat the time derivative of the pressure dp dt as a source in the concentration equation moreover c i s are not the conservative variables as a result the classical bound preserving limiter in x zhang and c w shu j comput phys 229 2010 pp 3091 3120 cannot be applied there

timestepping along characteristics for amixed finite element approximation for compressible flow of contamination from nuclear waste in porous media a nonlinear parabolic system describing compressible nuclear waste disposal contamination in porous media is presented a finite element procedure is introduced to approximate the transport of brin

a mcc finite element approximation of incompressible miscible displacement in porous media in this paper we analyze an efficient numerical scheme for the coupled system of incompressible miscible displacement in porous media mass conservative characteristic finite element is used for concentration equation which continuous velocities are needed therefore we solve flow equation by mixed finite element method with continuous flux approximation then we show this scheme preserves the mass balance identity and optimal l l 2 error estimate of the concentration numerical experiments are given to confirm the convergence and the property of mass balance

a higher order godunov method for modeling finite deformation in elastic plastic solids in this paper we develop a first order system of conservation laws for finite deformation in solids describe its characteristic structure and use this analysis to develop a second order numerical method for problems involving finite deformation and plasticity the equations of mass momentum and energy conservation in lagrangian and eulerian frames of reference are combined with kinetic equations of state for the stress and with caloric equations of state for the internal energy as well as with auxiliary equations representing equality of mixed partial derivatives of the deformation gradient particular attention is paid to the influence of a curl constraint on the deformation gradient so that the characteristic speeds transform properly between the two frames of reference next we consider models in rate form for isotropic elastic plastic materials with work hardening and examine the circumstances under which these models lead to hyperbolic systems for the equations of motion in spite of the fact that these models violate thermodynamic principles in such a way that the acoustic tensor becomes nonsymmetric we still find that the characteristic speeds are always real for elastic behavior and essentially always real for plastic response these results allow us to construct a second order godunov method for the computation of three dimensional displacement in a one dimensional material viewed in the lagrangian frame of reference we also describe a technique for the approximate solution of riemann problems in order to determine numerical fluxes in this algorithm finally we present numerical examples of the results of the algorithm

mixed finite element and finite volume discretization for heavy brine simulations in groundwater recently a new theory of high concentration brine transport in groundwater has been developed this approach is based on two nonlinear mass conservation equations one for the fluid flow equation and one for the salt transport equation both having nonlinear diffusion terms in this paper we present and analyze a numerical technique for the solution of such a model the approach is based on the mixed hybrid finite element method for the discretization of the diffusion terms in both the flow and transport equations and a high resolution tvd finite volume scheme for the convective term this latter technique is coupled to the discretized diffusive flux by means of a time splitting approach a commonly used benchmark test elder problem is used to verify the robustness and nonoscillatory behavior of the proposed scheme and to test the validity of two different formulations one based on using pressure head and concentration c as dependent variables and one using pressure p and mass fraction as dependent variables it is found that the latter formulation gives more accurate and reliable results in particular at large times the numerical model is then compared against a semi analytical solution and the results of a laboratory test these tests are used to verify numerically the performance and robustness of the proposed numerical scheme when high concentration gradients i e the double nonlinearity are present

numerical resolution for a compressible two phase flow model based on the theory of thermodynamically compatible systems this paper is concerned with the numerical solution of the equations governing two phase gas solid mixture in the framework of thermodynamically compatible systems theory the equations constitute a non homogeneous system of nonlinear hyperbolic conservation laws a total variation diminishing tvd slope limiter centre slic numerical scheme based on the splitting approach is presented and applied for the solution of the initial boundary value problem for the equations the model equations and the numerical methods are systematically assessed through a series of numerical test cases strong numerical evidence shows that the model and the methods are accurate robust and conservative the model correctly describes the formations of shocks and rarefactions in two phase gas solid flow

on association coefficients for 2 2 tables and properties that do not depend on the marginal distributions we discuss properties that association coefficients may have in general e g zero value under statistical independence and we examine coefficients for 2 2 tables with respect to these properties furthermore we study a family of coefficients that are linear transformations of the observed proportion of agreement given the marginal probabilities this family includes the phi coefficient and cohen s kappa the main result is that the linear transformations that set the value under independence at zero and the maximum value at unity transform all coefficients in this family into the same underlying coefficient this coefficient happens to be loevinger s h

optimal sequences for channel estimation using discrete fourier transform techniques this paper addresses the problem of selecting the optimum training sequence for channel estimation in communication systems over time dispersive channels by processing in the frequency domain a new explicit form of search criterion is found the gain loss factor glf which minimizes the variance of the estimation error and is easy to compute theoretical upper and lower bounds on the glf are derived an efficient directed search strategy and optimal sequences up to length 42 are given these sequences are optimal only for frequency domain estimation not for time domain estimation

numerical methods for a model for compressible miscible displacement in porous media a nonlinear parabolic system is derived to describe compressible miscible displace ment in a porous medium the system is consistent with the usual model for incompressible miscible displacement two finite element procedures are introduced to approximate the concentration of one of the fluids and the pressure of the mixture the concentration is treated by a galerkin method in both procedures while the pressure is treated by either a lalerkin method or by a parabolic mixed finite element method optimal order estimates in l2 and essentially optimal order estimates in lx are derived for the errors in the approximate solutions for both methods introduction we shall consider the single phase miscible displacement of one compressible fluid by another in a porous medium under the assumptions that no volume change results from the mixing of the components and that a pressure den sity relation exists for each component in a form that is independent of the mixing these equations of state will imply that the fluids are in the liquid state our model will represent a direct generalization of the model 3 4 7 that has been treated extensively for incompressible miscible displacement the reservoir s will be taken to be of unit thickness and will be identified with a bounded domain in r2 we shall omit gravitational terms for simplicity of exposi tion no significant mathematical questions arise when the lower order terms are included

modified chernoff bounds for pam systems with noise and interference corresp by using principles of analytic continuation upper and lower bounds on the error probability of a canonical binary system corrupted by additive interference and independent zero mean gaussian noise are derived the bounds which are simple functions require only the evaluation or bounding of the moment generating function of the interference for large signal to noise ratios snr and even for moderately large interference the bounds are shown to be tight and useful

efficient computation of erfc x for large arguments a new infinite series representation for the error function is developed it is especially suitable for computing erfc x for large x for instance for any x spl ges 4 the error function can be evaluated with a relative error less than 10 sup 10 by using only eight terms similarly the error function can be evaluated with a relative error less than 8 spl times 10 sup 7 for any x spl ges 2 using just six terms an analytical bound is derived to show that the total error due to series truncation and undersampling rapidly decreases as x increases comparisons with two other series are provided

global weak solutions for a parabolic system modeling a one dimensional miscible flow in porous media abstract we consider an initial boundary value problem for a nonlinear differential system of two equations such a system is formed by the equations of compressible miscible flow in a one dimensional porous medium no assumption about the mobility ratio is involved under some reasonable assumptions on the data we prove the existence of a global weak solution our basic approach is the semi galerkin method we use the technique of renormalized solutions for parabolic equations in the derivation of a priori estimates

a gram charlier series method for calculating general signal constellation error probabilities we develop a method for calculating the probability of symbol error via a multivariate gram charlier series for arbitrary coherent modulation schemes with statistically independent source symbols and subject to intersymbol interference isi and additive white gaussian noise awgn the resulting error probability approximations have closed form solutions and yield very accurate results with very little computational expense

mixed finite element methods for compressible miscible displacement in porous media a differential system describing compressible miscible displacement in a porous medium is given the concentration equation is treated by a galerkin method and the pressure equation is treated by a parabolic mixed fi nite element method optimal order estimates in l and almost optimal order estimates in l are obtained for the errors in the approximate solutions under the condition that h logh 2 0 this condition is much weaker than one given earlier by douglas and roberts for the same model furthermore we obtain the l l i2 estimates for the time derivatives of the concentration and the pressure which were not given by the above authors in addition we also consider newer mixed spaces in two or three dimensions

fully discrete finite element analysis of multiphase flow in groundwater hydrology this paper deals with the development and analysis of a fully discrete finite element method for a nonlinear differential system for describing an air water system in groundwater hydrology the nonlinear system is written in a fractional flow formulation i e in terms of a saturation and a global pressure the saturation equation is approximated by a finite element method while the pressure equation is treated by a mixed finite element method the analysis is carried out first for the case where the capillary diffusion coefficient is assumed to be uniformly positive and is then extended to a degenerate case where the diffusion coefficient can be zero it is shown that error estimates of optimal order in the l 2 norm and almost optimal order in the l infty norm can be obtained in the nondegenerate case in the degenerate case we consider a regularization of the saturation equation by perturbing the diffusion coefficient the norm of error estimates depends on the severity of the degeneracy in diffusivity with almost optimal order convergence for nonsevere degeneracy implementation of the fractional flow formulation with various nonhomogeneous boundary conditions is also discussed results of numerical experiments using the present approach for modeling groundwater flow in porous media are reported

a mixed element method for darcy forchheimer incompressible miscible displacement problem abstract a numerical scheme for incompressible miscible displacement problem in porous media is considered in which the velocity pressure relation is described by the darcy forchheimer equation mixed element such as raviart thomas element brezzi douglas marini element is used to handle the darcy forchheimer equation and standard finite element is used to approximate concentration error estimates for velocity pressure and concentration in different norms are established numerical experiments are given to verify the efficiency of the presented scheme

high order bound preserving discontinuous galerkin methods for compressible miscible displacements in porous media on triangular meshes abstract in this paper we develop high order bound preserving bp discontinuous galerkin dg methods for the coupled system of compressible miscible displacements on triangular meshes we consider the problem with multi component fluid mixture and the volumetric concentration of the jth component c j should be between 0 and 1 there are three main difficulties firstly c j does not satisfy a maximum principle therefore the numerical techniques introduced in zhang and shu 2010 44 cannot be applied directly the main idea is to apply the positivity preserving techniques to all c j s and enforce j c j 1 simultaneously to obtain physically relevant approximations by doing so we have to treat the time derivative of the pressure d p d t as a source in the concentration equation and choose suitable fluxes in the pressure and concentration equations secondly it is not easy to construct first order numerical fluxes for interior penalty dg methods on triangular meshes one of the key points in the high order bp technique applied in this paper is the combination of high order and lower order numerical fluxes we will construct second order bp schemes and use the second order numerical fluxes as the lower order one finally the classical slope limiter cannot be applied to c j to construct the bp technique we will not approximate c j directly therefore a new limiter will be introduced numerical experiments will be given to demonstrate the high order accuracy and good performance of the numerical technique

modelling wave dynamics of compressible elastic materials an eulerian conservative hyperbolic model of isotropic elastic materials subjected to finite deformation is addressed it was developed by godunov s k godunov elements of continuum mechanics nauka moscow 1978 in russian and g h miller p colella a high order eulerian godunov method for elastic plastic flow in solids j comput phys 167 2001 131 176 some modifications are made concerning a more suitable form of governing equations they form a set of evolution equations for a local cobasis which is naturally related to the almansi deformation tensor another novelty is that the equation of state is given in terms of invariants of the almansi tensor in a form which separates hydrodynamic and shear effects this model is compared with another hyperbolic non conservative model which is widely used in engineering sciences for this model we develop a riemann solver and determine some reference solutions which are compared with the conservative model the numerical results for different tests show good agreement of both models for waves of very small and very large amplitude however for waves of intermediate amplitude important discrepancies between results are clearly visible

on a fully coupled nonlinear parabolic problem modelling miscible compressible displacement in porous media we study a model describing a compressible and miscible displacement in a porous medium it consists of a coupled system of nonlinear parabolic partial differential equations using nonclassical estimates and renormalization tools we prove the existence of relevant weak solutions for the problem this is the first existence result obtained for a transport model containing both the coupling due to the compressibility assumption and the coupling due to the concentration dependent viscosity

an efficient shock capturing scheme for multicomponent multiphase thermal flow in porous media this paper is concerned with multicomponent two phase thermal fluid flow in porous media the fluid model consists of component conservation equations darcy s law for volumetric flow rates and a

comparison of cp based single carrier and ofdm with power allocation existing performance comparisons of single carrier sc and multicarrier transmission are mainly based on simulations in this letter we present a framework to compare the performance of cyclic prefix cp based sc block transmission and orthogonal frequency division multiplexing ofdm in frequency selective fading channels minimum mean squared error equal gain and approximate minimum bit error rate power allocation schemes for cp ofdm are considered performance of these methods is compared analytically and verified by simulations

analytical distribution of linearly modulated cochannel interferers the closed form expressions of the probability density function pdf the cumulative distribution function cdf and the characteristic function of the disturbance due to a multilevel cochannel interferer are obtained the analysis assumes l level amplitude shift keying l ask modulated signals nonreturn to zero nrz pulses transmission over a distortion free channel and matched filter reception the distribution for the multiple cochannel interferers case can then be obtained by means of the characteristic function method as an application example the closed form expression of the error floor for an l ask system in the presence of one cochannel interferer is given the comparison with respect to the gaussian approximation is also discussed

finite element methods for nonlinear flows in porous media abstract a model problem is presented for fluid flow in porous media which has numerical difficulties common with many other areas of nonlinear mechanics special finite element techniques are described which have proved useful in alleviating many of these difficulties a modified method of characteristics mixed finite element methods for fluid velocities singularity removal and self adaptive local grid refinement techniques are presented both theoretical and computational results are described together with an indication of the present and future uses of finite element methods in large scale reservoir simulation

mathematical problems in error calculations for interference several treatments of interference problems are examined with a view to determine whether doubtful mathematical assumptions about the existence of probability density functions affect the conclusions most derivations can be recast so that the existence of a density function is not necessary for the conclusions to be valid

a comparison of dct based ofdm and dft based ofdm in frequency offset and fading channels a precise method for calculating the bit error probability bep of a discrete cosine transform dct based orthogonal frequency division multiplexing ofdm system on additive white gaussian noise awgn channels in the presence of frequency offset is derived these accurate results are used to examine and compare the bep performance of a dct ofdm system and the conventional discrete fourier transform dft based ofdm system in an awgn environment several signaling formats such as binary phase shift keying quaternary phase shift keying and 16 ary quadrature amplitude modulation are considered the performance of a dct ofdm with a zero padding guard interval scheme is then compared with a zero padded dft ofdm with the employment of minimum mean square error mmse detection and mmse decision feedback detection with ordering scheme over frequency selective fast rayleigh fading channels analysis and simulation results show that the dct ofdm system outperforms the dft ofdm system in the presence of frequency offset and in frequency selective fast fading environments

a useful technique for interference analysis in nakagami fading this paper presents a unified analytical method for computing the average e g x sigmak 1 k yk b of some arbitrary function g when x is a gamma random variable and independent of the arbitrary random variables y1 y2 yk this leads to new explicit expressions for the averages of some specific functions including erfc radicz exp z zn and in 1 z in terms of the moment generating functions of y1 y2 yk

a kraemer type rescaling that transforms the odds ratio into the weighted kappa coefficient this paper presents a simple rescaling of the odds ratio that transforms the association measure into the weighted kappa statistic for a 2 2 table

characteristic finite element methods for nonlinear sobolev equations1this work is supported by the doctoral fundation of the educational committee of china 1 in this paper the time stepping along characteristic finite element methods for the nonlinear sobolev equation is considered optimal convergence rates in h 1 and l 2 are demonstrated for this scheme numerical results published elsewhere have confirmed that larger time steps are appropriate with these scheme and that the approximations exhibit improved qualitative behavior

two grid method for compressible miscible displacement problem by cfem mfem abstract this paper is concerned about the error analysis of two grid method for compressible miscible displacement in porous medium a characteristics finite element method cfem is presented for the concentration equation to handle the convection part and standard mixed finite element method mfem is used for the pressure equation moreover we linearize the equations based on the newton iteration method then two grid method is considered in this full discrete scheme problem we prove the l p error estimates for the pressure darcy velocity concentration variables in the two grid method it is shown that coarse space can be extremely coarse and we achieve asymptotically optimal approximation finally numerical experiment indicates that two grid method is a very effective method for solving miscible displacement problem

split least squares finite element methods for linear and nonlinear parabolic problems in this paper we propose some least squares finite element procedures for linear and nonlinear parabolic equations based on first order systems by selecting the least squares functional properly each proposed procedure can be split into two independent symmetric positive definite sub procedures one of which is for the primary unknown variable u and the other is for the expanded flux unknown variable s optimal order error estimates are developed finally we give some numerical examples which are in good agreement with the theoretical analysis

probability of error calculation of ofdm systems with frequency offset orthogonal frequency division multiplexing ofdm is sensitive to the carrier frequency offset cfo which destroys orthogonality and causes intercarrier interference ici previously two methods were available for the analysis of the resultant degradation in performance firstly the statistical average of the ici could be used as a performance measure secondly the bit error rate ber caused by cfo could be approximated by assuming the ici to be gaussian however a more precise analysis of the performance i e ber or ser degradation is desirable in this letter we propose a precise numerical technique for calculating the effect of the cfo on the ber or symbol error in an ofdm system the subcarriers can be modulated with binary phase shift keying bpsk quaternary phase shift keying qpsk or 16 ary quadrature amplitude modulation 16 qam used in many ofdm applications the bpsk case is solved using a series due to beaulieu 1990 for the qpsk and 16 qam cases we use an infinite series expression for the error function in order to express the average probability of error in terms of the two dimensional characteristic function of the ici

parametric construction of nyquist i pulses a novel parametric approach for constructing families of intersymbol interference isi free pulses is presented and examined some new pulses so constructed have smaller maximum distortion a more open receiver eye and a smaller probability of error in the presence of symbol timing error than the nyquist raised cosine pulse for the same excess bandwidth the parametric approach gives more degrees of freedom in the design of isi free pulses and subsumes previous isi free pulses as special cases a number of theorems that relate time domain behaviors of a pulse to the pulse s frequency spectrum are proved a previously known result relating pulse tail time decay to discontinuity of the pulse frequency spectrum is corrected and clarified

the evaluation of error probabilities for intersymbol and cochannel interference an efficient series that can be used to calculate the probability of error in a binary symmetric channel with intersymbol interference and additive noise is derived the series is derived by representing the noise complementary probability distribution function by an exact or approximate fourier series bounds on the accuracy of the estimate are derived for gaussian noise examples show that only a small numerical effort may be required to compute error probabilities of interest using the series applications to both finite and infinite intersymbol interference systems are discussed a similar technique is used to derive series representations for the probability of error of additive noise channels with cochannel interference or with combined intersymbol and cochannel interferences the accuracy of the results is bounded for gaussian noise

further results on the beaulieu series a frequent problem in digital communications is the computation of the probability density function pdf and cumulative distribution function cdf given the characteristic function chf of a random variable rv this problem arises in signal detection equalizer performance equal gain diversity combining intersymbol interference and elsewhere often it is impossible to analytically invert the chf to get the pdf and cdf in closed form beaulieu 1990 1991 has derived an infinite series for the cdf of a sum of rvs that has been widely used we rederive his series using the gil pelaez 1951 inversion formula and the poisson sum formula this derivation has several advantages including both the bridging of the well known sampling theorem with beaulieu s series and yielding a simple expression for calculating the truncation error term it is also shown that the pdf and cdf can be computed directly using a discrete fourier transform

calculating error probabilities for intersymbol and cochannel interference the probability of error in a binary symmetric channel with intersymbol interference and additive noise is efficiently calculated by numerical quadrature of a laplace inversion integral along a contour in the complex plane passing through a saddlepoint of the integrand for gaussian noise a bound is set on the truncation error incurred by necessarily restricting the integration to a finite interval the probability of error resulting from cochannel interference is calculated by a similar technique

a new jameson schmidt turkel smooth particle hydrodynamics algorithm for large strain explicit fast dynamics this paper presents a new smooth particle hydrodynamics sph computational framework for large strain explicit solid dynamics a mixed based set of total lagrangian conservation laws bonet et al 2015 gil et al 2016 is presented in terms of the linear momentum and an extended set of geometric strain measures comprised of the deformation gradient its co factor and the jacobian taking advantage of this representation the main aim of this paper is the adaptation of the very efficient jameson schmidt turkel jst algorithm jameson et al 1981 extensively used in computational fluid dynamics to a sph based discretisation of the mixed based set of conservation laws with three key distinct novelties first a conservative jst based sph computational framework is presented with emphasis in nearly incompressible materials second the suppression of numerical instabilities associated with the non physical zero energy modes is addressed through a well established stabilisation procedure third the use of a discrete angular momentum projection algorithm is presented in conjunction with a monolithic total variation diminishing runge kutta time integrator in order to guarantee the global conservation of angular momentum for completeness exact enforcement of essential boundary conditions is incorporated through the use of a lagrange multiplier projection technique a series of challenging numerical examples e g in the near incompressibility regime are examined in order to assess the robustness and accuracy of the proposed algorithm the obtained results are benchmarked against a wide spectrum of alternative numerical strategies

fully discrete mixed finite element approximations for non darcy flows in porous media a numerical approximation procedure is proposed to solve equations describing non darcy flow of a single phase fluid in a porous medium in two or three spacial dimensions including the generalized forchheimer equation fully discrete mixed finite element methods are considered and analyzed for the approximation existence and uniqueness of the approximation are discussed and optimal order error estimates in l2 are derived for the three relevant functions

a priori error estimates of a combined mixed finite element and local discontinuous galerkin method for an incompressible miscible displacement problem abstract a numerical approximation for a kind of incompressible miscible displacement problems in high dimension in porous media is studied mixed finite element method is applied to the flow equation and the transport one is solved by the local discontinuous galerkin method ldg based on interpolation projection properties and the induction hypothesis a priori hp error estimates are obtained numerical results are presented which verify the theoretical results

a new mcc mfe method for compressible miscible displacement in porous media this paper presents a new mass conservative finite element method for solving the compressible miscible displacement problem in porous media this new method combines characteristic tracking with the mixed finite element method specifically the mass conservative characteristic finite element method is applied to the concentration equation whereas the mixed finite element method with continuous flux approximation is used for the flow equation this procedure conserves mass globally convergence of the fully discrete scheme is analyzed and optimal l 2 norm and h 1 norm error estimates for the concentration are obtained numerical experiments are presented to illustrate the theoretical analysis

a simple and accurate method of probability of bit error analysis for asynchronous band limited ds cdma systems this paper considers probability of bit error p sub e analysis in asynchronous band limited direct sequence code division multiple access ds cdma systems it presents a simple and accurate method of p sub e analysis the proposed method can serve as an attractive alternative to the only two techniques currently available for band limited systems the standard gaussian approximation sga and the characteristic function method the former is prone to inaccuracy while the latter large computational complexity the method generalizes the simplified improved gaussian approximation siga derived previously for rectangular pulses this paper also outlines a generalization of another method referred to as the improved gaussian approximation iga numerical examples demonstrate the far greater accuracy of the generalized siga with respect to the sga the examples consider the is 95 and square root raised cosine sqrt rc pulses as well as uniform and nonuniform received power conditions

numerical integration of rate constitutive equations in finite deformation analysis abstract in analysis of finite deformation problems the use of constitutive equations in rate form is often required in a spatial setting these equations may express a relationship between some objective rate of spatial stress tensor and the rate of deformation constitutive equations of this type characterize a variety of material models including hyperelasticity hypoelasticity and elastoplasticity employing geometrical concepts a family of unconditionally stable and incrementally objective algorithms is proposed for the integration of such rate constitutive equations these algorithms which are appropriate for finite deformation analysis are applicable to any choice of stress rate and in most cases employ quantities that arise naturally in the context of finite element analysis examples illustrate the objectivity and accuracy of the algorithms

mathematical structure of the black oil model for petroleum reservoir simulation this model incorporates compressibility and general mass transfer between phases it consists of the conditions of thermodynamic equilibrium an equation of state for the volume balance between the fluidand the rock void darcy s law for the volumetric flow rates and component conservation equations these relations are manipulated to form a pressure equation and a modified system of component conservation equations it is shown that the pressure equation is parabolic and that in the absence of diffusive forces such as capillary pressure and mixing the component conservation equations are hyperbolic subject to technical conditions on the relative permeabilities this sequential formulation of the flow equations forms types of wave structures that occur for the system

error probabilities for qam systems on partially coherent channels with intersymbol interference and crosstalk we describe an efficient procedure to calculate the probability of error p sub e for a quadrature amplitude modulation qam communications system operating over a channel that introduces distortion interference and noise the method is an extension of the saddlepoint integration technique introduced by helstrom 1986 to efficiently evaluate p sub e for one dimensional pulse amplitude modulation pam systems with intersymbol interference isi and crosstalk we consider the effects of noise random carrier phase offset isi and crosstalk between the i and q channels the error probability is written as a double laplace inversion integral and can be easily applied to any rectangular constellation this integral is calculated by extending the saddlepoint integration technique to two complex dimensions results are presented for qam systems with 16 64 and 256 symbols the technique can be directly extended to environments with cochannel interference consisting of other qam signals

approximating the tetrachoric correlation coefficient samples x y taken from a bivariate normal distribution with correlation p can be allocated to one of the cells of a 2 x 2 contingency table according to whether x t xo or x xo and whether y yo where xo and yo are cut off values such a contingency table is shown in table 1 where a is the number of samples for which x xo and y yo and si is the proportion of samples for which x xo the tetrachoric correlation coefficient r is obtained from a 2 x 2 contingency table and provides an estimate of the underlying correlation p everitt 1910 tabulated the parameters of a kth order polynomial in r for k 6 and gave details of the parameters for 7 24 to obviate this additional tables for use when r 2 0 8 were given by everitt 1912 these tables are also given in the compilation by pearson 1914 where they cover 16 pages clearly this method of calculating r is cumbersome and brown 1977 has given an algorithm for finding the tetrachoric correlation thus the original laborious method is replaced by a computer program

analytical and variational numerical methods for unstable miscible displacement flows in porous media the miscible displacement of one fluid by another in a porous medium has received considerable attention in sub surface environmental and petroleum engineering applications when a fluid of higher mobility displaces another of lower mobility unstable patterns referred to as viscous fingering may arise their physical and mathematical study has been the object of numerous investigations over the past century the objective of this paper is to present a review of these contributions with particular emphasis on variational methods these algorithms are tailored to real field applications thanks to their advanced features handling of general complex geometries robustness in the presence of rough tensor coefficients low sensitivity to mesh orientation in advection dominated scenarios and provable convergence with fully unstructured grids this paper is dedicated to the memory of dr jim douglas jr for his seminal contributions to miscible displacement and variational numerical methods

a new low order least squares nonconforming characteristics mixed finite element method for burgers equation in this paper a new low order least squares nonconforming characteristics mixed finite element method mfem is considered for two dimensional burgers equation by use of two typical characters of the elements for approximating the velocity and flux variables a the consistency errors of the elements can be estimated as order o h 2 with respect to the mesh size h in the broken h 1 norm one order higher than their interpolation errors b the elements interpolation operators satisfy certain orthogonalities which lead to o h 2 order error estimates in l 2 norm and some superclose results the accuracy of corresponding variables in l 2 norm is improved by one order compared with other mfems in the existing literature it seems that the results provided herein have never been derived before