physalis a new method for particle simulation part ii two dimensional navier stokes flow around cylinders this paper presents a new approach to the direct numerical simulation of particle flows the basic idea is to use a local analytic representation valid near the particle to transfer the no slip condition from the particle surface to the adjacent grid nodes in this way the geometric complexity arising from the irregular relation between the particle boundary and the underlying mesh is avoided and fast solvers can be used the results suggest that the computational effort increases very slowly with the number of particles so that the method is efficient for large scale simulations the focus here is on the two dimensional case cylindrical particles but the same procedure to be developed in forthcoming papers applies to three dimensions spherical particles several extensions are briefly discussed

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

time stepping along characteristics with incomplete iteration for a galerkin approximation of miscible displacement in porous media miscible displacement of one incompressible fluid by another in a porous medium is modeled by a nonlinear coupled system of two partial differential equations the pressure equation is elliptic while the concentration equation is parabolic but normally convection dominated a sequential backward difference time stepping scheme is defined it approximates the pressure by a standard galerkin procedure and the concentration by a combination of a galerkin method and the method of characteristics optimal convergence rates in l 2 and h 1 are demonstrated for this scheme and for a modified version in which the algebraic equations at each time step are solved approximately by a limited number of preconditioned conjugate gradient iterations time stepping along the characteristics of the hyperbolic part of the concentration equation is shown to result in smaller time truncation errors than those of standard methods numerical results published elsewhere have confirmed that larger time steps are appropriate

strange attractors of infinitesimal widths in the bifurcation diagram with an unusual mechanism of onset nonlinear dynamics in coupled fuzzy control systems ii abstract a new type of onset of chaos in a multidimensional dissipative system is reported that has been observed under a circumstance in which a delicate balance of order formation and chaos is materialized two limit cycles are connected directly to a sequence of strange attractors the widths in the bifurcation feigenbaum diagram of which converge to zero in a range close to the onset the measures of the extent of chaos are also zero there and the trajectories behave regularly in a macroscopic scale the chaos zones appear alternately with the windows of resonance frequency locking in the bifurcation diagram whose number of periodicity decreases as a system parameter is increased from an infinity in the manner of arithmetical progression 28 n 2 with n being integers down to unity concomitantly the extent of chaos develops and thereby grows measurable also the ranges of both the chaos and resonance zones in the bifurcation diagram become wider two lorenz plots of quantum numbers n and n 1 are always necessary to characterize the n th chaos zone for a chaotic state they appear in such a manner as to sandwich the identity map y x this chaos is readily interrupted by a limit cycle since one of the lorenz maps is crossed with y x by a small change of the control parameter moreover the tangential parts of the individual lorenz plots to y x have as many folds as their quantum numbers they form clusters each of which consists of many stable points being located densely at the limit of onset n both the intervals between these stable points and the folds lying between two neighboring stable points converge to zero this is the origin of the unmeasurable degree of chaos

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

resonance regions for mathieu type dynamical systems on a torus abstract mathieu type dynamical systems on a torus are torus maps or differential equations whose right hand side components are trigonometric polynomials the asymptotic behaviour of resonance regions for mathieu type dynamical systems close to the integrable ones is drastically different from the behaviour of generic systems because the scaling law of resonance regions depends on the degree of the trigonometric polynomial or its newton polyhedron we prove this scaling law and compare our results with numerical experiments

on the transport diffusion algorithm and its applications to the navier stokes equations this paper deals with an algorithm for the solution of diffusion and or convection equations where we mixed the method of characteristics and the finite element method globally it looks like one does one step of transport plus one step of diffusion or projection but the mathematics show that it is also an implicit time discretization of thepde in lagrangian form we give an error bound h t h h t in the interesting case that holds also for the navier stokes equations even when the reynolds number is infinite euler equation

a hybrid mixed finite element method for miscible displacement problem with mcc procedure abstract a new combined method is developed for solving incompressible miscible displacement in porous media in this method a hybrid mixed element method is constructed for the pressure and velocity equation while a mass conservative characteristic mcc finite element method is presented for concentration equation the introduction of these two numerical algorithms not only makes the coefficient matrixes symmetric positive definite but also keeps the mass balance the stability and consistence of this method are analyzed and the optimal error estimates in l2 norm for velocity concentration and pressure are derived finally some numerical results are presented

spatio temporal dimensionality in the overall complex dynamics of an experimental cable mass system an experimental model of an elastic cable mass hanging at in phase or out of phase vertically moving supports is considered system parameters are adjusted to produce two different conditions of multiple internal resonance nonregular dynamics are analyzed in various frequency ranges including meaningful external resonance conditions attention is devoted to characterization of system dimensionality in terms of both time and spatial complexity the aims of this paper are i to give a general overview of the richness and robustness of different quasiperiodic and homoclinic bifurcation scenarios to chaos in various regions of the control parameter space ii to characterize steady nonregular response through delay embedding technique for attractor reconstruction and proper orthogonal decomposition of spatio temporal flow and iii to identify spatial configuration variables experimental eigenfunctions contributing mostly to nonregular dynamics thus obtaining hints about possible reduced models for reproducing complex regimes system dimensionality will be evaluated both by relating the dimension of attractors to the dimension of the linear phase space and from the dominating proper orthogonal modes

behavior of a three torus in truncated navier stokes equations abstract the presence of a three torus in a seven mode truncation of the three dimensional navier stokes equations is investigated numerically by means of cross section and power spectra furthermore by taking advantage of particular features of the model rotation vectors circle maps and torus maps can be computed with high accuracy and used to study the dynamics in particular some interesting phenomena of partial phase locking are described in deep detail the three torus which arises via a hopf bifurcation and persists in a wide parameter range is found to break and originate a strange attractor the onset of chaos and the associated bifurcation point can be defined quite precisely

efficient time stepping methods for miscible displacement problems in porous media efficient procedures for time stepping galerkin methods for approximating the solution of a coupled system for c c x t and p p x t with nonlinear neumann boundary conditions of the form begin gathered nabla cdot a x c nabla p y x c nabla g equiv nabla cdot u f 1 x t quad x in omega quad t in 0 t hfill nabla cdot b x c nabla p nabla c u cdot nabla c phi x frac partial c partial t f 2 x t c quad x in omega quad t in 0 t hfill u cdot v q 1 x t quad x in partial omega quad t in 0 t hfill b frac partial c partial v q x t c quad x in partial omega quad t in 0 t hfill c x 0 c 0 x quad x in omega hfill end gathered where omega subset mathbb r d 2 leqq d leqq 3 are presented and analyzed this system is a possible model system for describing the miscible displacement of one incompressible fluid by another in a porous medium when flow conditions a

numerical methods for convection dominated diffusion problems based on combining the method of characteristics with finite element or finite difference procedures finite element and finite difference methods are combined with the method of characteristics to treat a parabolic problem of the form cu t bu x au x x f optimal order error estimates in l 2 and w 1 2 are derived for the finite element procedure various error estimates are presented for a variety of finite difference methods the estimates show that for convection dominated problems b gg a these schemes have much smaller time truncation errors than those of standard methods extensions to n space variables and time dependent or nonlinear coefficients are indicated along with applications of the concepts to certain problems described by systems of differential equations

superconvergence in the pressure in the simulation of miscible displacement a modification of a finite element method of douglas ewing and wheeler for approximating the solution of the equations describing miscible displacement in porous media is proposed and analyzed in a periodic setting the pressure is approximated by a mixed finite element procedure using a raviart thomas space of index k over a uniform grid the resulting darcy velocity field is post processed by convolution with a bramble schatz kernel and this enhanced velocity is used in the evaluation of the coefficients in the galerkin procedure for the concentration if the concentration space is of local degree l then the error as measured in l 2 omega in the concentration is o h c l 1 h p 2k 2 i e an optimal reflection of the superconvergent velocity approximation

renormalization in a circle map with two inflection points abstract an extended version of the sine circle map becomes non invertible by developing simultaneously two critical points in part of parameter space universality in the corresponding transition from quasiperiodicity to chaos manifests itself in the organisation of doubly superstable orbits four operators are needed to generate all such orbits the existence of non trivial equivalence relations for operation sequences makes the present theory different from other multi operator renormalisation approaches possible implications of the theory in higher dimensional systems are discussed

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

global estimates for mixed methods for second order elliptic equations global error estimates in l2 92 l 9 and h s q 2 in r2 or a re derived for a mixed finite element method for the dirichlet problem for the elliptic operator lp div a grad p bp cp based on the raviart thomas nedelec space vh x wh c h div 92 x l2 g2 optimal order estimates are obtained for the approximation of p and the associated velocity field u a grad p bp in l2 g2 and h s 92 0 6 s k 1 and if q c r2 forp in lv2

mixed volume element combined with characteristic mixed finite volume element method for oil water two phase displacement problem abstract as the basic of numerical simulation of energy science the displacement of three dimensional oil water two phase in porous media is discussed in this paper for incompressible miscible displacement the pressure is described by a flow equation in an elliptic mathematical formulation and the saturation is defined by a convection diffusion equation the pressure exists in the saturation equation by darcy velocity and controls the whole flow we develop and improve substantially the work of arbogast and wheeler then put forward a mixed volume element combined with characteristic mixed finite volume element method for two phase displacement problem the flow equation is discretized by the conservative mixed volume element method which could improve the accuracy of an order for computing darcy velocity the saturation equation is solved by a characteristic mixed volume element method where mixed volume element method is used to compute the diffusion term and the method of characteristics is adopted to discretize the convection term the method of characteristics can confirm high stability of numerical simulation at the fronts avoid numerical dispersion and nonphysical oscillation and can adopt large time steps obtain smaller time truncation error and improve the computation accuracy mixed volume element can solve the convection term confirm conservation of mass at each element and approximate the saturation and the adjoint vector meanwhile it is most important in numerical computation of seepage mechanics optimal second order estimates in l 2 norm are derived by theory and special techniques of priori estimates finally numerical experiments are shown to illustrate the efficiency and practicability and to solve the international problem successfully

characterizing bifurcations and classes of motion in the transition to chaos through 3d tori of a continuous experimental system in solid mechanics abstract the dynamics of a continuous experimental system exhibiting quasiperiodic transition to chaos has been investigated an elastic cable mass system hanging at in phase vertically moving supports is considered with vibrational parameters in the neighbourhood of external and internal resonance conditions adjusted to be able to introduce three torus dynamics measurements of the nonregular response are made in frequency ranges including primary resonance of the first symmetric in plane mode of the cable quantitative characterisation of regular and nonregular attractors and of the configuration variables involved in the motion is made by means of delay embedding technique and proper orthogonal decomposition of spatio temporal flow attention is devoted to analyse in depth the scenario of transition to chaos exhibited by the model steady quasiperiodic motions on three tori partial and full phase locking of the flow and chaotic attractors are observed in spite of the dynamics variedness the systematic characterisation of the response allows us to set the bifurcation behaviour of the experimental system in the framework of theoretic numeric transition to chaos through three dimensional tori

physalis a new method for particle flow simulation part iii convergence analysis of two dimensional flows in this paper we study the convergence property of physalis when it is applied to incompressible particle flows in two dimensional space physalis is a recently proposed iterative method which computes the solution without imposing the boundary conditions on the particle surfaces directly instead a consistency equation based on the local near particle representation of the solution is used as the boundary conditions one of the important issues needs to be addressed is the convergence properties of the iterative procedure in this paper we present the convergence analysis using laplace and biharmonic equations as two model problems it is shown that convergence of the method can be achieved but the rate of convergence depends on the relative locations of the cages the results are directly related to potential and stokes flows however they are also relevant to navier stokes flows heat conduction in composite media and other problems

torus maps and the problem of a one dimensional optical resonator with a quasiperiodically moving wall abstract we study the problem of the asymptotic behavior of the electromagnetic field in an optical resonator one of whose walls is at rest and the other is moving quasiperiodically with d 2 incommensurate frequencies we show that this problem can be reduced to a problem about the behavior of the iterates of a map of the d dimensional torus that preserves a foliation by irrational straight lines in particular the jacobian of this map has d 1 eigenvalues equal to 1 we present rigorous and numerical results about several dynamical features of such maps we also show how these dynamical features translate into properties for the field in the cavity in particular we show that when the torus map satisfies a kam theorem which happens for a cantor set of positive measure of parameters the energy of the electromagnetic field remains bounded when the torus map is in a resonant region which happens in open sets of parameters inside the gaps of the previous cantor set the energy grows exponentially

chaotic motion on hamiltonian tori kam tori are well known to be that finite part of phase space in which the motion of a weakly perturbed classical hamiltonian system remains integrable moreover they are barriers in the phase space of systems with two degrees of freedom the authors show that certain hamiltonian systems contain invariant non regular tori with compressible flow using as an example an electron moving in electromagnetic fields which are periodic in space they demonstrate i that strange attractors and repellers of well known autonomous or quasi periodically time driven systems may occur on such strange tori ii that one may find barriers consisting of non regular hamiltonian tori in systems with any number of degrees of freedom the flow on such barriers is non chaotic though and iii that certain kam tori transform into non regular tori rather than breaking up when the perturbation becomes strong

a turbulence model with stochastic soliton motion a dissipative benjamin ono equation is used to study fluid and plasma turbulence the system is studied by an exact nonlinear mode truncation method in which a finite number of poles are used to present the solution the justification of the pole expansion approach is discussed with the proof of a completeness theorem the stability and spectrum analysis show that asymptotic behavior of the system is completely represented by a finite number of nonlinear modes the behavior of those nonlinear modes resembles solitons and exhibits a wide range of bifurcation phenomena and routes to turbulence

an approximation of incompressible miscible displacement in porous media by mixed finite element method and characteristics mixed finite element method an approximation scheme is defined for incompressible miscible displacement in porous media this scheme is constructed by using two methods standard mixed finite element is used for the darcy velocity equation a characteristics mixed finite element method is presented for the concentration equation characteristic approximation is applied to handle the convection part of the concentration equation and a lowest order mixed finite element spatial approximation is adopted to deal with the diffusion part thus the scalar unknown concentration and the diffusive flux can be approximated simultaneously in order to derive the optimal l 2 norm error estimates a post processing step is included in the approximation to the scalar unknown concentration this scheme conserves mass globally in fact on the discrete level fluid is transported along the approximate characteristics numerical experiments are presented finally to validate the theoretical analysis

an approximation of semiconductor device by mixed finite element method and characteristics mixed finite element method the mathematical model of a semiconductor device is described by a system of three quasi linear partial differential equations for initial boundary value problem the electric potential is governed by an elliptic equation the electron and hole concentrations are governed by two equations of convection dominated diffusion type standard mixed finite element is used for the electric potential equation a characteristics mixed finite element method is presented for the concentration equations this scheme conserves mass locally in order to derive the optimal l 2 norm error estimates a post processing step is included in the approximation to the scalar concentration numerical experiment is presented finally to validate the theoretical analysis

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

strange attractors that are not chaotic abstract it is shown that in certain types of dynamical systems it is possible to have attractors which are strange but not chaotic here we use the word strange to refer to the geometry or shape of the attracting set while the word chaotic refers to the dynamics of orbits on the attractor in particular the exponential divergence of nearby trajectories we first give examples for which it can be demonstrated that there is a strange nonchaotic attractor these examples apply to a class of maps which model nonlinear oscillators continuous time which are externally driven at two incommensurate frequencies it is then shown that such attractore are persistent under perturbations which preserve the original system type i e there are two incommensurate external driving frequencies this suggests that for systems of the typw which we have considered nonchaotic strange attractors may be expected to occur for a finite interval of parameter values on the other hand when small perturbations which do not preserve the system type are numerically introduced the strange nonchaotic attractor is observed to be converted to a periodic or chaotic orbit thus we conjecture that in general continuous time systems flows which are not externally driven at two incommensurate frequencies should not be expected to have strange nonchaotic attractors except possibly on a set of measure zero in the parameter space

chaotic attractors on a 3 torus and torus break up abstract two coupled driven van der pol oscillators can have three frequency quasiperiodic attractors which lie on a 3 torus the evidence presented in this paper indicates that the torus is destroyed when the stable and unstable manifolds of an unstable orbit become tangent furthermore no chaotic orbits lying on a torus were observed suggesting that in most cases at least in the case of this system orbits do not become chaotic before their tori are destroyed to expedite the calculations a method was developed which can be used to determine if an orbit is on a torus without actually displaying that orbit the method also described in this paper was designed specifically for our system the basic idea however could be used for studying attractors of other systems very few modifications of the method if any would be necessary when studying systems with the number of degrees of freedom equal to that of our van der pol system

physalis a new o n method for the numerical simulation of disperse systems potential flow of spheres this paper presents a new approach to the direct numerical simulation of potential problems with many spherical internal boundaries e g many spheres in potential flow the basic idea is to use a local analytic representation valid near the particle and to match it to an external field calculated by a standard finite difference or finite element method in this way the geometric complexity arising from the irregular relation between the particle boundary and the underlying mesh is avoided and fast solvers can be used the results suggest that the computational effort increases less than proportionally to the number of particles and additionally that meshes that would be excessively coarse as measured in terms of particle radius in a conventional calculation can be used without significant loss of accuracy in separate if preliminary work the same approach has been extended to the simulation of viscous flow about spheres and cylinders at finite reynolds numbers

three coupled oscillators mode locking global bifurcations and toroidal chaos abstract many systems exhibit behaviour which can be described by three coupled oscillators provided the coupling is not too strong such systems can be modelled by maps of the two torus to itself in this paper we describe and explain those aspects of the bifurcation diagram for two parameter families of torus maps that involve change of mode locking type we introduce the concepts of partial and full mode locking for the coupled oscillators these notions correspond to the presence of one or two rational relations between the frequencies respectively numerical investigation of a particular family of torus maps reveals an intricate web of global bifurcations in order to explain the results we first show that we can approximate maps in the neighbourhood of a rational translation to arbitrary order by the time 1 map of a flow on the torus then we analyse those condimension 1 and 2 bifurcations for flows on the torus which change the set of frequency ratios we find a large variety of bifurcation diagrams in particular many involving homotopically non trivial saddle connections next we ask how the picture changes when the time 1 maps of a family of flows are perturbed to a general family of diffeomorphisms we find toroidal chaos in the neighbourhood of all these bifurcations meaning that there exist orbits which perform a pseudo random sequence of rotations in different directions around the torus the corresponding behaviour for the coupled oscillators is that the frequency ratios perform a random walk finally we show how all these ingredients can be put together to give global scenarios for bifurcation for families of torus maps which we believe to be of general applicability to physical systems with three weakly coupled modes of oscillation

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

analysis of least squares mixed finite element methods for nonlinear nonstationary convection diffusion problems some least squares mixed finite element methods for convection diffusion problems steady or nonstationary are formulated and convergence of these schemes is analyzed the main results are that a new optimal a priori l 2 error estimate of a least squares mixed finite element method for a steady convection diffusion problem is developed and that four fully discrete least squares mixed finite element schemes for an initial boundary value problem of a nonlinear nonstationary convection diffusion equation are formulated also some systematic theories on convergence of these schemes are established

unconditional convergence and optimal error estimates of a galerkin mixed fem for incompressible miscible flow in porous media in this paper we study the unconditional convergence and error estimates of a galerkin mixed fem with the linearized semi implicit euler scheme for the equations of incompressible miscible flow in porous media we prove that the optimal l 2 error estimates hold without any time step convergence conditions while all previous works require certain time step restrictions our theoretical results provide a new understanding on commonly used linearized schemes the proof is based on a splitting of the error into two parts the error from the time discretization of the pdes and the error from the finite element discretization of corresponding time discrete pdes the approach used in this paper can be applied to more general nonlinear parabolic systems and many other linearized semi implicit time discretizations

analysis on block centered finite differences of numerical simulation of semiconductor device detector abstract a finite difference scheme on block centered method is presented on nonuniform partition to simulate numerically three dimensional transient problems of semiconductor detector of photoconduction applying the method of mixed finite element the principle of duality the induction hypothesis the prior error theory of differential equations and other special techniques we give error estimates of second order accuracy in l2 norm the numerical simulation is super convergent for the electric field intensity really important in actual applications

attractors on an n torus quasiperiodicity versus chaos the occurrence of quasiperiodic motions in nonconservative dynamical systems is of great fundamental importance however current understanding concerning the question of how prevalent such motions should be is incomplete with this in mind the types of attractors which can exist for flows on an n torus are studied numerically for n 3 and 4 specifically nonlinear perturbations are applied to maps representing n frequency quasiperiodic attractors these perturbations can cause the original n frequency quasiperiodic attractors to bifurcate to other types of attractors our results show that for small and moderate nonlinearity the frequency of occurrence of quasiperiodic motions is as follows n frequency quasiperiodic attractors are the most common followed by n 1 frequency quasiperiodic attractors followed by periodic attractors however as the nonlinearity is further increased n frequency quasiperiodicity becomes less common ceasing to occur when the map becomes noninvertible chaotic attractors are very rare for n 3 for small to moderate nonlinearity but are somewhat more common for n 4 examination of the types of chaotic attractors that occur for n 3 reveals a rich variety of structure and dynamics in particular we see that there are chaotic attractors which apparently fill the entire n torus i e limit sets of orbits on these attractors are the entire torus furthermore these are the most common types of chaotic attractors at moderate nonlinearities

a characteristics mixed finite element method for advection dominated transport problems we define a new finite element method called the characteristics mixed method for approximating the solution to an advection dominated transport problem the method is based on a space time variational form of the advection diffusion equation our test functions are piecewise constant in space and in time they approximately follow the characteristics of the advective i e hyperbolic part of the equation thus the scheme uses a characteristic approximation to handle advection in time this is combined with a low order mixed finite element spatial approximation of the equation boundary conditions are incorporated in a natural and mass conservative fashion the scheme is completely locally conservative in fact on the discrete level fluid is transported along the approximate characteristics a postprocessing step is included in the scheme in which the approximation to the scalar unknown is improved by utilizing the approximate vector flux this has the effect of improving the rate of convergence of

the nonlinear dynamics of the damped and driven toda chain ii fourier and lyapunov analysis of tori abstract the dynamics of a periodically damped and driven toda chain with periodic boundary conditions is investigated with the help of spectral energy bifurcation diagrams and lyapunov diagrams it can be shown that quasiperiodic motions on tori tk of dimension k 3 exist the technical problems concerning the fourier and lyapunov analysis of the motions on tori tk k 2 are addressed

an efficient two grid method for miscible displacement problem approximated by mixed finite element methods abstract in the paper we present an efficient two grid method for the miscible displacement problem which discretized by mixed finite element methods for the pressure equation and concentration equation at the same time and then analyzed the error estimate of the two gird algorithm at last the numerical experiment presented confirmed the theoretical results compared with the standard mixed finite element methods this two grid scheme based on the mixed methods can keep the same convergence order and cost much less work

finite difference methods for two phase incompressible flow in porous media two phase incompressible flow in porous media is governed by a system of nonlinear partial differential equations convection physically dominates diffusion and the object of this paper is to develop a finite difference procedure that reflects this dominance the pressure equation which is elliptic in appearance is discretized by a standard five point difference method the concentration equation is treated by an implicit finite difference method that applies a form of the method of characteristics to the transport terms a convergence analysis is given for the method

smoothed profile method for particulate flows error analysis and simulations abstract we re formulate and analyze a new method for particulate flows the so called smoothed profile method spm first proposed in y nakayama r yamamoto simulation method to resolve hydrodynamic interactions in colloidal dispersions phys rev e 71 2005 036707 which uses a fixed computational mesh without conformation to the geometry of the particles the method represents the particles by certain smoothed profiles to construct a body force term added into the navier stokes equations spm imposes accurately and efficiently the proper conditions at the particle fluid interface in particular while the original method employs a fully explicit time integration scheme we develop a high order semi implicit splitting scheme which we implement in the context of spectral hp element discretization first we show that the modeling error of spm has a non monotonic dependence on the time step size t it is a function of t where is the kinematic viscosity of fluid and is the interface thickness of the smoothed profile subsequently we present several steady and unsteady simulations including flow past 3d complex shaped particles and compare against direct numerical simulations and the force coupling method fcm

a second order method for three dimensional particle simulation this paper describes a numerical method for the direct numerical simulation of navier stokes flows with one or more solid spheres the particles may be fixed or mobile and they may have different radii the basic idea of the method stems from the observation that due to the no slip condition in the reference frame of each particle the velocity near the particle boundary is very small so that the stokes equations constitute an excellent approximation to the full navier stokes problem the general analytic solution of the stokes equations can then be used to transfer the no slip condition from the particle surface to the adjacent grid nodes in this way the geometric complexity arising from the irregular relation between the particle boundary and the underlying mesh is avoided and fast solvers can be used the method is validated by a detailed comparison with spectral solutions for the flow past a sphere at reynolds numbers of 50 and 100 the existence in these situations of a stokes region near the particle is explicitly demonstrated other numerical experiments to show the performance of the code are also described to illustrate the power and efficiency of the method a simulation of decaying homogeneous turbulence in a cell containing 100 moveable spheres is described as implemented here the method can only be applied to simple body shapes such as spheres and cylinders extensions to more general situations are mentioned in the last section

global bifurcation destroying the experimental torus t 2 we show experimentally the scenario of a two frequency torus t 2 breakdown in which a global bifurcation occurs due to the collision of a torus with an unstable periodic orbit creating a heteroclinic saddle connection followed by an intermittent behavior

convergence analysis of an approximation of miscible displacement in porous media by mixed finite elements and a modified method of characteristics abstract a nonlinear system of two coupled partial differential equations models miscible displacement of one incompressible fluid by another in a porous medium conservation of mass for the mixture leads to an elliptic equation for pressure and conservation for the displacing fluid yields a convectiondominated parabolic equation for the concentration of that fluid a sequential implicit time stepping procedure is defined in which the pressure and darcy velocity of the mixture are approximated simultaneously by a mixed finite element method and the concentration is approximated by a combination of a galerkin finite element method and the method of characteristics optimal order convergence in l2 is proved time truncation errors of standard procedures are reduced by time stepping along the characteristics of the hyperbolic part of the concentration equation temporal and spatial errors are lessened by direct computation of the velocity in the mixed method as opposed to differentiation of the pressure several extensions of these results are outlined

some improved error estimates for the modified method of characteristics improved error estimates are derived for a finite element modified method of characteristics for a coupled system of partial differential equations modeling flow in porous media these results impro