coupling fluid flow with porous media flow the transport of substances back and forth between surface water and groundwater is a very serious problem we study herein the mathematical model of this setting consisting of the stokes equations in the fluid region coupled with the darcy equations in the porous medium coupled across the interface by the beavers joseph saffman conditions we prove existence of weak solutions and give a complete analysis of a finite element scheme which allows a simulation of the coupled problem to be uncoupled into steps involving porous media and fluid flow subproblems this is important because there are many legacy codes available which have been optimized for uncoupled porous media and fluid flow

canonical representations of complex vibratory subsystems time domain dirichlet to neumann maps large scale dynamic simulations can often be simplified by appropriately replacing large portions of the domain by a dirichlet to neumann or dtn map givoli 1992 numerical methods for problems on infinite domains 1st ed elsevier amsterdam here we consider the problem of representing a linear dynamical subsystem by such a map the exact dtn map is computed as a modal summation and its properties are studied bounds on the symbol of the dtn map in the laplace domain are obtained the exact map is then approximated in particular in the high modal density regime in the high modal density limit we obtain the result that a subsystem can be accurately represented with just three parameters within such an approximation we obtain representations based on a maximum entropy representation self similar or fractal representation and a rational function representation the rational function representation leads to the interesting result that any complicated dynamical subsystem with a large number of degrees of freedom is asymptotically equivalent in the limit of infinite modal density to a single mass dashpot spring system we end with numerical examples showing the efficiency of the rational function approximation

time stepping schemes for systems of volterra integro differential equations linear volterra type systems of integro differential equations sides with kernels in the form of sums of complex exponentials are considered such systems arise for example in the semi discrete finite element model of dynamic viscoelasticity and of some dispersive wave equations and in the representation of dynamic subsystems on interfaces several new families of time stepping schemes are proposed here for the solution of this class of sides the accuracy stability and efficiency properties of these schemes are demonstrated via both theoretical analysis using a scalar model problem and numerical experiments applied to first and second order sides

existence of a weak solution for the fully coupled navier stokes darcy transport problem abstract this paper analyzes the surface subsurface flow coupled with transport the flow is modeled by the coupling of navier stokes and darcy equations the transport of a species is modeled by a convection dominated parabolic equation the two way coupling between flow and transport is nonlinear and it is done via the velocity field and the viscosity this problem arises from a variety of natural phenomena such as the contamination of the groundwater through rivers the main result is existence and stability bounds of a weak solution

high modal density approximations for equipment in the time domain this article considers modeling the effect of complex subsystems on the dynamics of the main structure to which they are attached it is proposed that the substructure say a piece of equipment be replaced by an equivalent set of forces which react back on the main structure these forces are given as time convolutions of the displacements at the equipment attachment points the convolution integral which represents a time domain dtn dirichlet to neumann map is approximated in the high modal density limit with determined error bounds this approximation leads to a family of equipment representations the simplest requires few measured equipment properties though more information can lead to greater accuracy our approximate dtns are demonstrated numerically in finite element simulations

on existence and uniqueness results for a coupled system modeling miscible displacement in porous media initial boundary value problems for a nonlinear differential system of two equations are considered in this paper this system of equations one of elliptic form for the pressure and the other of parabolic form for the concentration of one fluid governs the miscible displacement of one incompressible fluid by another in a porous medium under some reasonable assumptions on the data it is proved that the system possesses a weak solution and uniqueness is also established for the semiclassical solution of the system

existence and uniqueness of global weak solutions to a cahn hilliard stokes darcy system for two phase incompressible flows in karstic geometry abstract we study the well posedness of a coupled cahn hilliard stokes darcy system which is a diffuse interface model for essentially immiscible two phase incompressible flows with matched density in a karstic geometry existence of finite energy weak solution that is global in time is established in both 2d and 3d weak strong uniqueness property of the weak solutions is provided as well

which are the important modes of a subsystem a linearly behaving vibrational substructure or more generally a linear dynamic subsystem attached to a main structure or a main dynamic system is considered after discretization the substructure is represented by afinite typically large number of degrees of freedom n and hence also by n s eigenmodes in order to reduce the computational effort it is common to apply modal reduction to the subsystem such that only n r modes out of the total number of n modes are retained where n r n s the following question then arises which n r modes should be retained in structural dynamics it is traditional to retain those modes associated with the lowest frequencies in this paper the question is answered by solving an appropriate optimization problem the most important modes of the subsystem are shown to be those whose coupling matrices which are defined in a particular way have the highest norm this leads to a simple and effective algorithm for optimal modal reduction the new criterion for modal importance is explained both mathematically and physically and is demonstrated by numerical examples

a combined analytic finite element method for elastic shells abstract a method is devised for the numerical analysis of structures that include semi infinite circular cylindrical shells the so called edge stiffness coefficients of the cylinder are used to eliminate the semi infinite domain only a small region is thus left for discretization in this computational domain a finite element scheme is used which incorporates transverse shear deformation numerical examples demonstrate the superiority of the suggested method to the standard one

the solutions to a smooth pde can be dense in c i abstract the solutions to a partial differential equation that arises in the physical sciences are expected to be restricted in nature since they are intended to represent some physically significant behavior in particular they can approximate the general continuous function on a compact set k only if k is thin e g nowhere dense in rsuperscript n the purpose of this note is to show that this does not hold for all smooth partial differential equations specifically for any n or 2 there exist partial differential equations of polynomial type on rsuperscript n whose cat infinity solutions are uniformly dense in the space c i of all continuous functions on the n cube i author

optimal modal reduction of vibrating substructures optimal modal reduction of vibrating substructures a structure which consists of a main part and a number of attached substructures is considered a model reduction scheme is developed and applied to each of the discrete substructures linear undamped transient vibrational motion of the structure is assumed with general external forcing and initial conditions the goal is to replace each discrete substructure by another substructure with a much smaller number of degrees of freedom while minimizing the effect this reduction has on the dynamic behaviour of the main structure the approach taken here involves ritz reduction and the dirichlet to neumann map as analysis tools the resulting scheme is based on a special form of modal reduction and is shown to be optimal in a certain sense for long simulation times the performance of the scheme is demonstrated via numerical examples and is compared to that of standard modal reduction copyright c 2003 john wiley sons ltd

coupled generalized nonlinear stokes flow with flow through a porous medium in this article we analyze the flow of a fluid through a coupled stokes darcy domain the fluid in each domain is non newtonian modeled by the generalized nonlinear stokes equation in the free flow region and the generalized nonlinear darcy equation in the porous medium a flow rate is specified along the inflow portion of the free flow boundary we show existence and uniqueness of a variational solution to the problem we propose and analyze an approximation algorithm and establish a priori error estimates for the approximation

generalized newtonian fluid flow through a porous medium abstract we present a model for generalized newtonian fluid flow through a porous medium in the model the dependence of the fluid viscosity on the velocity is replaced by a dependence on a smoothed locally averaged velocity with appropriate assumptions on the smoothed velocity existence of a solution to the model is shown two examples of smoothing operators are presented in the appendices a numerical approximation scheme is presented and an a priori error estimate derived a numerical example is given illustrating the approximation scheme and the a priori error estimate

on a universal differential equation for the analytic terms of c superpositions on the real line it is proved that every continuous function on the real line can be approximated uniformly in the sense of a specific norm by superpositions of analytic functions which are solutions of a single universal differential equation every superposition is some function belonging to c r this improves a former result of the author from which the superpositions are known to be continuous

trax an approach for the time rational analysis of complex dynamic systems this paper introduces a theoretical and algorithmic reduced model approach to efficiently evaluate time responses of complex dynamic systems the proposed approach combines four main components analytical expressions of the average of the system s transfer functions in the frequency domain precise and convergent rational approximations of these exact expressions exact evaluation of these approximations through model reduction in rational krylov subspaces and semi analytical interpolation at just a few frequency points the resulting algorithmic principles to evaluate the time response of a particular system are relatively straightforward one first evaluates the response of the system with slight additional damping at a few frequencies and one then projects or reduces the system in the subspace spanned by these responses the time response of the reduced model implicitly provides a precise evaluation of that of the original system the properties of the reduced models and the precision of the proposed approach are studied and applications on complex matrix systems are presented and discussed while the theory and numerical algorithms are presented in a matrix context they are also transposable in a continuous functional context

discontinuous galerkin finite element convergence for incompressible miscible displacement problems of low regularity in this article we analyze the numerical approximation of incompressible miscible displacement problems with a combined mixed finite element and discontinuous galerkin method under minimal regularity assumptions the main result is that sequences of discrete solutions weakly accumulate at weak solutions of the continuous problem in order to deal with the nonconformity of the method and to avoid overpenalization of jumps across interelement boundaries the careful construction of a reflexive subspace of the space of bounded variation which compactly embeds into l 2 omega and of a lifting operator which is compatible with the nonlinear diffusion coefficient are required an equivalent skew symmetric formulation of the convection and reaction terms of the nonlinear partial differential equation allows us to avoid flux limitation and nonetheless leads to an unconditionally stable and convergent numerical method numerical experiments underline the robustness of the proposed algorithm

mean and mean square responses of a prototypical master fuzzy structure analytical estimates are made for mean and mean square transient responses of a single degree of freedom master oscillator attached to an undamped n degree of freedom random substructure the ensemble averaged response is found to be asymptotically for a large number of substructural degrees of freedom in accord with the predictions of the pierce sparrow russell theory in particular the mean response of the master oscillator manifests an apparent damping corrections to this behavior are also predicted but are found to lie well below the root mean square level of the fluctuations the corrections are therefore for practical purposes unimportant the ensemble average of the square of the response is also investigated and found to take a value at later times that is in accord with simple equipartition arguments advanced in an earlier paper the power spectral density of the late time behavior is shown to be proportional to the square of the power spectrum of the early time response and thus to be a n

convergence of a discontinuous galerkin method for the miscible displacement equation under low regularity discontinuous galerkin time discretizations are combined with the mixed finite element and continuous finite element methods to solve the miscible displacement problem stable schemes of arbitrary order in space and time are obtained under low regularity assumptions on the data convergence of the scheme is proved by using compactness results for functions that may be discontinuous in time

mixed stabilized finite element method for the stationary stokes dual permeability fluid flow model abstract this article proposes a stabilized mixed finite element method to investigate the stationary stokes dual permeability fluid flow model which couples the free flow region modeled by the stokes equations and dual porous medium modeled by the dual permeability equations the robust mixed finite element method developed here does not require any lagrange multiplier but a mesh dependent stabilization term with a relaxation parameter is introduced essentially to ensure the numerical stability of the algorithm the well posedness and the optimal error estimate of the finite element scheme are derived furthermore an iterative scheme is developed based on the traditional coupled algorithm we prove that the iterative scheme converges to the coupled scheme and the rate of convergence is estimated the feature of the model is illustrated by considering five numerical examples which reveal the applicability of the fluid flow model as well as the accuracy of the numerical method

a deposition model coupling stokes and darcy s equations with nonlinear deposition abstract in this work we investigate a filtration process whereby particulate is deposited in the flow domain causing the porosity of the region to decrease the fluid flow is modeled as a coupled stokes darcy flow problem and the deposition in the darcy domain is modeled using a nonlinear equation for the porosity existence and uniqueness of a solution to the governing equations is established additionally the nonnegativity and boundedness of the porosity is shown a finite element approximation scheme that preserves the nonnegativity and boundedness of the porosity is investigated accompanying numerical experiments support the analytical findings

a finite element method for domains with corners a new finite element method is devised for the numerical solution of elliptic boundary value problems with geometrical singularities in it the singularity is eliminated form the computational domain in an exact fashion this is in contrast to other common methods such as those which use a refined mesh in the singularity region or those which use special singular finite elements in them the singularity is treated as a part of the numerical scheme the new method is illustrated on an elliptic differential equation in a domain containing a re entrant corner numerical experiments show that the new method yields result which are generally much more accurate than those obtained by using the standard finite element method with mesh refinement in the singularity region both methods require about the same computing time

a multilevel decoupling method for the navier stokes darcy model abstract this paper considers a multilevel decoupling method for the coupled navier stokes darcy model describing a free flowing fluid over a porous medium the method utilizes a sequence of meshes on which a low dimensional fully coupled nonlinear problem is solved only on a very coarse initial mesh on subsequent finer meshes the approximate solution in each flow region is obtained by solving a linear decoupled problem and performing a correction step the correction step in each domain is achieved by solving a linear system that differs from the original decoupled system only in the right hand side we prove optimal error estimates and demonstrate that for a sequence of meshes with spacing h j h j 1 2 the decoupling method is computationally efficient and achieves the same order of approximation as the fully coupled method

a dual porosity stokes model and finite element method for coupling dual porosity flow and free flow in this paper we propose and numerically solve a new model considering confined flow in dual porosity media coupled with free flow in embedded macrofractures and conduits such situation arises for example for fluid flows in hydraulic fractured tight shale oil gas reservoirs the flow in dual porosity media which consists of both matrix and microfractures is described by a dual porosity model and the flow in the macrofractures and conduits is governed by the stokes equation then the two models are coupled through four physically valid interface conditions on the interface between dual porosity media and macrofractures conduits which play a key role in a physically faithful simulation with high accuracy all the four interface conditions are constructed based on fundamental properties of the traditional dual porosity model and the well known stokes darcy model the weak formulation is derived for the proposed model and the well posedness of the model is analyzed a finite element semidiscretizati