stabilized finite element schemes with lbb stable elements for incompressible flows we study stabilized fe approximations of supg type to the incompressible navier stokes problem revisiting the analysis for the linearized model we show that for conforming lbb stable elements the design of the stabilization parameters for many practical flows differs from that commonly suggested in literature and initially designed for the case of equal order approximation then we analyze a reduced supg scheme often used in practice for lbb stable elements to provide the reduced scheme with appropriate stability estimates we introduce a modified lbb condition which is proved for a family of fe approximations the analysis is given for the linearized equations numerical experiments for some linear and nonlinear benchmark problems support the theoretical results

active control and drag optimization for flow past a circular cylinder the main objective of this article is to investigate computational methods for the active control and drag optimization of incompressible viscous flow past cylinders using the two dimensional navier stokes equations as the flow model the computational methodology relies on the following ingredients space discretization of the navier stokes equations by finite element approximations time discretization by a second order accurate two step implicit explicit finite difference scheme calculation of the cost function gradient by the adjoint equation approach and minimization of the cost function by a quasi newton method a la bfgs the above methods have been applied to boundary control by rotation of the flow around a circular cylinder and show 30 to 60 drag reduction compared to the fixed cylinder configuration for reynolds numbers in the range from 200 to 1000

a generalized finite difference gfd ale scheme for incompressible flows around moving solid bodies on hybrid meshfree cartesian grids a scheme using the mesh free generalized finite differencing gfd on flows past moving bodies is proposed the aim is to devise a method to simulate flow past an immersed moving body that avoids the intensive remeshing of the computational domain and minimizes data interpolation associated with the established computational fluid methodologies as such procedures are time consuming and are a significant source of error in flow simulation in the present scheme the moving body is embedded and enveloped by a cloud of mesh free nodes which convects with the motion of the body against a background of cartesian nodes the generalized finite difference gfd method with weighted least squares wls approximation is used to discretize the two dimensional viscous incompressible navier stokes equations at the mesh free nodes while standard finite difference approximations are applied elsewhere the convecting motion of the mesh free nodes is treated by the arbitrary lagrangian eulerian ale formulation of the flow equations which are solved by a second order crank nicolson based projection method the proposed numerical scheme was tested on a number of problems including the decaying vortex flow external flows past moving bodies and body driven flows in enclosures

high order compact computation and nonuniform grids for streamfunction vorticity equations abstract fourth order compact difference schemes for steady streamfunction vorticity formulation of 2d incompressible navier stokes equations on nonuniform grids are derived using maple software package especially we deduce fourth order compact difference scheme of the first partial derivative terms in order to resolve boundary layers grid transformation techniques are used which maps a nonuniform grid onto a uniform one for use with the fourth order compact difference scheme a krylov subspace iterative method with an ilut preconditioning technique is employed to solve the resulting linear system the proposed high accuracy computation method is applied to two model problems computational results are compared with results computed by other schemes in the literature

a numerical investigation into the steady flow past a rotating circular cylinder at low and intermediate reynolds numbers abstract numerical solutions have been obtained for steady uniform flow past a rotating circular cylinder results are presented for reynolds numbers based on the diameter of the cylinder 5 and 20 and the rotational parameters in the range of 0 3 to avoid the difficulties in satisfying the boundary conditions at large distances from the cylinder a new numerical technique is introduced further series expansion solutions are obtained which are valid at small values of but the results are found to be applicable over a wide range of values of the calculated values of the drag and lift coefficients and the general nature of the streamline patterns are in good agreement with the most recent time dependent calculations performed by badr and dennis

developing numerical techniques for solving low mach number fluid acoustic problems conservation equations applicable to this regime are derived by applying four simplifying assumptions to the fully compressible form of the navier stokes and energy equations isentropic state changes adiabatic flow negligible density variation inertial terms and stokes hypothesis the resulting equations termed acoustic compressible are similar to the traditional pseudocompressible equations except for two distinctions pseudocompressible solutions use artificially high mach numbers for computational convenience and neglect the pressure convection term in the mass conservation equation

moffatt eddies in the driven cavity a quantification study by an hoc approach abstract in this paper we establish moffatt likeness of the corner vortices in the lid driven square cavity for stokes flow and flow for moderate reynolds numbers in the pre asymptotic regime the flow is computed by using an efficient transient navier stokes n s solver on compact non uniform space grids the quantification of the corner vortices in succession as moffatt vortices follows from them following a fixed geometric ratio in sizes and intensities in the process we also provide more detailed benchmarking results for the corner vortices in the cavity flow the accuracy of the scale resolution of the vortices has been verified by a novel approach to grid independence analysis this approach utilizes the concept of adverse pressure gradients as a tool to validate that the separation zones in the neighborhood of the corners are consistent with the vortices obtained from our computed solution of the n s equations

a new family of 5 5 cc 4oc schemes applicable for unsteady navier stokes equations in this paper a new family of implicit compact finite difference schemes for computation of unsteady convection diffusion equation with variable convection coefficient is proposed the schemes which are fourth order accurate in space and second or lower order accurate in time depending on the choice of weighted time average parameter are then applied to unsteady navier stokes system the proposed schemes where transport variable and its first derivatives are carried as the unknowns combine virtues of compact discretization and pade scheme for spatial derivative these schemes which are based on a five point stencil with constant coefficients named as 5 5 constant coefficient 4th order compact 5 5 cc 4oc give rise to a diagonally dominant system of equations and shows higher accuracy and better phase and amplitude error characteristics than some of the standard methods these schemes are capable of using a grid aspect ratio other than unity and are unconditionally stable they efficiently capture both transient and steady solutions of linear and nonlinear convection diffusion equations with dirichlet as well as neumann boundary conditions subsequently the proposed schemes are applied to problems governed by the incompressible navier stokes equations the results obtained are in excellent agreement with analytical and available numerical results in all cases establishing efficiency and accuracy of the proposed schemes

a hybrid cartesian grid and gridless method for compressible flows a hybrid cartesian grid and gridless method is presented to compute unsteady compressible flows for complex geometries in this method a cartesian grid is used as baseline mesh to cover the computational domain while the boundary surfaces are addressed using a gridless method this hybrid method combines the efficiency of a cartesian grid method and the flexibility of a gridless method for the complex geometries the developed method is used to compute a number of test cases to validate the accuracy and efficiency of the method the numerical results obtained indicate that the use of this hybrid method leads to a significant improvement in performance over its unstructured grid counterpart for the time accurate solution of the compressible euler equations an overall speed up factor of about eight and a saving in storage requirements about one order of magnitude for a typical three dimensional problem in comparison with the unstructured grid method are demonstrated

modified scaling relation for the random field ising model abstract we investigate the low temperature critical behavior of the three dimensional random field ising ferromagnet by a scaling analysis we find that in the limit of temperature t 0 the usual scaling relations have to be modified as far as the exponent of the specific heat is concerned at zero temperature the rushbrooke equation is modified to 2 1 an equation which we expect to be valid also for other systems with similar critical behavior we test the scaling theory numerically for the three dimensional random field ising system with gaussian probability distribution of the random fields by a combination of calculations of exact ground states with an integer optimization algorithm and monte carlo methods by a finite size scaling analysis we calculate the critical exponents 1 0 0 05 2 9 1 5 and 0 55

the random field ising model with an asymmetric trimodal probability distribution the ising model in the presence of a random field is investigated within the mean field approximation based on landau expansion the random field is drawn from the trimodal probability distribution p hi p hi h0 q hi h0 r hi where the probabilities p q r take on values within the interval 0 1 consistent with the constraint p q r 1 asymmetric distribution hi is the random field variable and h0 the respective strength this probability distribution is an extension of the bimodal one allowing for the existence in the lattice of non magnetic particles or vacant sites the current random field ising system displays second order phase transitions which for some values of p q and h0 are followed by first order phase transitions thus confirming the existence of a tricritical point and in some cases two tricritical points also reentrance can be seen for appropriate ranges of the aforementioned variables using the variational principle we determine the equilibrium equation for magnetization solve it for both transitions and at the tricritical point in order to determine the magnetization profile with respect to h0

monte carlo analysis of the critical properties of the two dimensional randomly bond diluted ising model via wang landau algorithm abstract the influence of random bond dilution on the critical properties of the two dimensional ising model on a square lattice with periodic boundary conditions is presented using the monte carlo process with wang landau sampling the lattice linear size is l 20 140 and the concentration of the diluted bonds spans a wide range from weak to strong dilution namely q 0 05 0 1 0 2 0 3 0 4 the respective percolation limit for the square lattice is q c p e r c 0 5 its pure version q 0 has a second order phase transition with vanishing specific heat critical exponent an example of inapplicability of the harris criterion the main effort is focused on the temperature dependence of the specific heat and magnetic susceptibility to estimate the respective maximum values and subsequent pseudocritical temperatures for extracting the relative critical exponents we have also looked at the probability distribution of the susceptibility pseudocritical temperature and specific heat for assessing self averaging the study is carried out in the appropriately restricted but dominant energy subspaces by applying the finite size scaling analysis the critical exponents are estimated the specific heat exponent vanishes the correlation length exponent is equal to one and the critical exponents ratio retains its pure ising model value thus supporting the strong universality hypothesis

a staggered space time discontinuous galerkin method for the three dimensional incompressible navier stokes equations on unstructured tetrahedral meshes in this paper we propose a novel arbitrary high order accurate semi implicit space time discontinuous galerkin method for the solution of the three dimensional incompressible navier stokes equations on staggered unstructured curved tetrahedral meshes as is typical for space time dg schemes the discrete solution is represented in terms of space time basis functions this allows to achieve very high order of accuracy also in time which is not easy to obtain for the incompressible navier stokes equations similarly to staggered finite difference schemes in our approach the discrete pressure is defined on the primary tetrahedral grid while the discrete velocity is defined on a face based staggered dual grid while staggered meshes are state of the art in classical finite difference schemes for the incompressible navier stokes equations their use in high order dg schemes is still quite rare a very simple and efficient picard iteration is used in order to derive a space time pressure correction algorithm that achieves also high order of accuracy in time and that avoids the direct solution of global nonlinear systems formal substitution of the discrete momentum equation on the dual grid into the discrete continuity equation on the primary grid yields a very sparse five point block system for the scalar pressure which is conveniently solved with a matrix free gmres algorithm from numerical experiments we find that the linear system seems to be reasonably well conditioned since all simulations shown in this paper could be run without the use of any preconditioner even up to very high polynomial degrees for a piecewise constant polynomial approximation in time and if pressure boundary conditions are specified at least in one point the resulting system is in addition symmetric and positive definite this allows us to use even faster iterative solvers like the conjugate gradient method the flexibility and accuracy of high order space time dg methods on curved unstructured meshes allows to discretize even complex physical domains with very coarse grids in both space and time the proposed method is verified for approximation polynomials of degree up to four in space and time by solving a series of typical 3d test problems and by comparing the obtained numerical results with available exact analytical solutions or with other numerical or experimental reference data to the knowledge of the authors this is the first time that a space time discontinuous galerkin finite element method is presented for the three dimensional incompressible navier stokes equations on staggered unstructured tetrahedral grids high order staggered space time dg scheme for the 3d incompressible navier stokes equations primal grid based on curved tetrahedra dual grid based on non standard five point hexahedra new discretization of the viscous terms on the main grid using lifting operators on the dual grid very simple space time pressure correction algorithm providing also high order in time all linear systems have maximum sparsity and use the smallest possible optimal five point stencil

a robust and efficient hybrid cut cell ghost cell method with adaptive mesh refinement for moving boundaries on irregular domains abstract a new robust and efficient cartesian grid method is developed for the moving boundary problem on an arbitrary complex domain a difficult problem in the application of cut cell methods is the presence of degenerate cut cells which are defined as cut cells that are intersected by a boundary curve at more than two points a new strategy is proposed for handling the problem of degenerate cells within the cut cell methodology in the proposed approach gradient fluxes through all sections of the boundary curve intersecting a cut cell are computed using surface integrals with the consequence that all cut cells in the solution domain whether they are regular or degenerate are handled using the same procedure marker points on the boundary curve are used to define cubic splines which provide a high fidelity representation for the boundary curve from which various geometrical properties e g volume face areas centroid etc of cut cells can be determined with high accuracy in order to enhance the robustness of the present approach the concept of a ghost point for degenerate cut cells is introduced which facilitates the evaluation of gradient fluxes in the fluid domain this is advantageous as there is no longer any need to deal individually with each usually small split cut cell in consequence the method proposed here can be interpreted as a hybrid cut cell ghost cell method in which the conventional cut cell method is used to deal with regular cut cells and the ghost cell method is used to handle degenerate cut cells the accuracy and efficiency of this method can be improved further by application of an adaptive mesh refinement amr method based on a fully threaded tree data structure to the cut cells a multigrid acceleration technique is used to solve the resulting algebraic system of discretized equations six test cases for which exact solutions are available are used to demonstrate the accuracy and efficiency of the proposed algorithm for both fixed and moving boundary problems using a triangulated surface mesh to represent an internal boundary surface our proposed approach is generalized to deal with three dimensional fluid flow problems a test case of a three dimensional free surface problem is used to validate the generalization of our cartesian grid approach for complex boundaries in three dimensions

a divergence free condition compensated method for incompressible navier stokes equations the present study aims to develop a new formulation to effectively calculate the incompressible navier stokes solutions in non staggered grids the distinguished feature of the proposed method which avoids directly solving the divergence free equation is to add a rigorously derived source term to the momentum equation to ensure satisfaction of the fluid incompressibility for the sake of numerical accuracy dispersion relation preserving upwind scheme developed within the two dimensional context was employed to approximate the convection terms the validity of the proposed mass preserving navier stokes method is justified by solving two benchmark problems at high reynolds and rayleigh numbers based on the simulated navier stokes solutions the proposed formulation is shown to outperform the conventional segregated method in terms of the reduction of cpu time 2007 elsevier b v all rights reserved

lack of self averaging of the specific heat in the three dimensional random field ising model we apply the recently developed critical minimum energy subspace scheme for the investigation of the random field ising model we point out that this method is well suited for the study of this model the density of states is obtained via the wang landau and broad histogram methods in a unified implementation by employing the n fold version of the wang landau scheme the random fields are obtained from a bimodal distribution h i ifmmode pm else textpm fi 2 and the scaling of the specific heat maxima is studied on cubic lattices with sizes ranging from l 4 to l 32 observing the finite size scaling behavior of the maxima of the specific heats we examine the question of saturation of the specific heat the lack of self averaging of this quantity is fully illustrated and it is shown that this property may be related to the question mentioned above

designing correct fluid hydrodynamics on a rectangular grid using mrt lattice boltzmann approach while the lattice boltzmann method lbm has become a powerful numerical approach for solving complex flows the standard lattice boltzmann method typically uses a square lattice grid in two spatial dimensions and cubic lattice grid in three dimensions for inhomogeneous and anisotropic flows it is desirable to have a lbm model that utilizes a rectangular grid there were two previous attempts to extend the multiple relaxation time mrt lbm to a rectangular lattice grid in 2d however the resulting hydrodynamic momentum equation was not fully consistent with the navier stokes equation due to anisotropy of the transport coefficients in the present work a new mrt model with an additional degree of freedom is developed in order to match precisely the navier stokes equation when a rectangular lattice grid is used we first revisit the previous attempts to understand the origin and nature of anisotropic transport coefficients by conducting an inverse design analysis within the chapman enskog procedure then an additional adjustable parameter that governs the relative orientation in the energy normal stress subspace is introduced it is shown that this adjustable parameter can be used to fully eliminate the anisotropy of transport coefficients thus the exact navier stokes equation can be derived on a rectangular grid our theoretical findings are confirmed by numerical solutions using three two dimension benchmark problems i e the channel flow the cavity flow and the decaying taylor green vortex flow the numerical results demonstrate that the proposed model shows remarkably good performance with appropriate choice of model parameters

the random field ising model with an asymmetric and anisotropic bimodal probability distribution abstract the ising model in the presence of a random field drawn from the asymmetric and anisotropic trimodal probability distribution p h i p h i h 0 q h i h 0 r h i is investigated the partial probabilities p q r take on values within the interval 0 1 consistent with the constraint p q r 1 asymmetric distribution h i is the random field variable with basic absolute value h 0 strength is the competition parameter which is the ratio between the respective strength of the random magnetic field in the two principal directions z and z and is positive so that the random fields are competing anisotropic distribution this probability distribution is an extension of the bimodal one allowing for the existence in the lattice of non magnetic particles or vacant sites the current random field ising system displays mainly second order phase transitions which for some values of p q and h 0 are followed by first order phase transitions joined smoothly by a tricritical point occasionally two tricritical points appear implying another second order phase transition in addition to these points re entrant phenomena can be seen for appropriate ranges of the temperature and random field for specific values of p and q using the variational principle we write down the equilibrium equation for the magnetization and solve it for both phase transitions and at the tricritical point in order to determine the magnetization profile with respect to h 0 considered as an independent variable in addition to the temperature

high re solutions for incompressible flow using the navier stokes equations and a multigrid method the vorticity stream function formulation of the two dimensional incompressible navierstokes equations is used to study the effectiveness of the coupled strongly implicit multigrid csi mg method in the determination of high re fine mesh flow solutions the driven flow in a square cavity is used as the model problem solutions are obtained for configurations with reynolds number as high as 10 000 and meshes consisting of as many as 257 x 257 points for re 1000 the 129 x 129 grid solution required 1 5 minutes of cpu time on the amdahl 470 v 6 computer because of the appearance of one or more secondary vortices in the flow field uniform mesh refinement was preferred to the use of one dimensional gridclustering coordinate transformations the past decade has witnessed a great deal of progress in the area of computational fluid dynamics developments in computer technology hardware as well as in advanced numerical algorithms have enabled attempts to be made towards analysis and numerical solution of highly complex flow problems for some of these applications the use of simple iterative techniques to solve the navier stokes equations leads to a rather slow convergence rate for the solutions the solution convergence rate can be seriously affected if the coupling among the various governing differential equations is not properly honored either in the interior of the solution domain or at its boundaries the rate of convergence is also generally strongly dependent on such problem parameters as the reynolds number the mesh size and the total number of computational points this has led several researchers to examine carefully the recently emerging multigrid mg technique as a useful means for enhancing the convergence rate of iterative numerical methods for solving discretized equations at a number of computational grid points so large as to be considered impractical previously

a singular value decomposition svd based generalized finite difference gfd method for close interaction moving boundary flow problems in this paper we present a study on a singular value decomposition svd based generalized finite difference gfd method and a nodal selection scheme for moving body boundary flow problems formulated on a hybrid cartesian cum meshfree grid system the present study shows that the svd based method is more robust and accurate than the conventional least squares based gfd scheme a nodal selection scheme is also introduced to overcome the problem of numerical instability associated with the clustering of computational nodes such nodal clustering occurs dynamically when moving bodies or boundaries approach within close proximity of each other resulting in the overlap of their meshfree grids the nodal scheme is applied to close interaction flow problems as exemplified by the squeezing action of a circular cylinder through a very narrow slot and the close proximity bypass interaction of two oscillating circular cylinders

ising spin glass under continuous distribution random magnetic fields tricritical points and instability lines the effects of random magnetic fields are considered in an ising spin glass model defined in the limit of infinite range interactions the probability distribution for the random magnetic fields is a double gaussian which consists of two gaussian distributions centered respectively at h0 andh0 presenting the same width it is argued that such a distribution is more appropriate for a theoretical description of real systems than its simpler particular two well known limits namely the single gaussian distribution h0 and the bimodal one 0 the model is investigated by means of the replica method and phase diagrams are obtained within the replica symmetric solution critical frontiers exhibiting tricritical points occur for different values of with the possibility of two tricritical points along the same critical frontier to our knowledge it is the first time that such a behavior is verified for a spin glass model in the presence of a continuous distribution random field which represents a typical situation of a real system the stability of the replica symmetric solution is ana lyzed and the usual almeida thouless instability is verified for low temperatures it is verified that the higher temperature tricritical point always appears in the region of stability of the replica symmetric solution a condition involving the parameters h0 and for the occurrence of this tricritical point only is obtained analytically some of our results are discussed in view of experimental measurements available in the literature spin glass systems 1 5 continue to challenge many re searchers in the area of magnetism from the theoretical point of view its simplest version defined in terms of ising spin variables the so called ising spin glass isg represents one of the most fascinating problems in the physics of dis ordered magnets the isg mean field solution based on the infinite range interaction model as proposed by sherrington and kirkpatrick sk6 presents a quite nontrivial behav ior the correct low temperature solution of the sk model is defined in terms of a continuous order parameter function 7 i e an infinite number of order parameters associated with many low energy states a procedure which is usually de nominated as replica symmetry breaking rsb further more a transition in the presence of an external magnetic field known as the almeida thouless at line 8 is found in the solution of the sk model such a line separates a low temperature region characterized by rsb from a high temperature one where a simple one parameter solution de nominated as replica symmetric rs solution is stable the validity of the results of the sk model for the description of more realistic systems characterized by short range interac tions represents a very polemic question 5 recent numeri cal simulations claim the absence of an at line in the three dimensional short range isg 9 as well as along the non mean field region of a one dimensional isg characterized by long range interactions 10 however these results ob tained with rather small lattice size simulations do not rule out the possibility of a crossover to a different scenario at much larger lattice sizes or also for smaller fields and or temperatures one candidate for alternative theory to the sk model is the droplet model 11 based on domain wall renormalization group arguments for spin glasses 12 13 according to the droplet model the low temperature phase of any finite dimensional short range spin glass should be described in terms of a single thermodynamic state together of course with its corresponding time reversed counterpart i e essentially a rs type solution many important features of the isg still deserve an appropriate understanding within the droplet model scenario and in particular the validity of this model becomes questionable for increasing dimension alities where one expects the existence of a finite upper criti cal dimension above which the mean field picture should prevail

an anisotropic gls stabilized finite element method for incompressible flow problems abstract we consider a stabilized finite element approximation of incompressible flow problems in primitive velocity pressure variables which is based on a gls formulation equal order interpolation for the velocity and the pressure can be employed with this formulation the method introduced here is specially developed to be used on anisotropic finite element meshes with large element aspect ratios rather than using a single stabilization parameter within each element the jacobian matrix of the affine transformation from the reference element is employed for stabilization purposes stability and anisotropic error estimates in a suitable mesh dependent norm are proved for the linear stokes problem numerical results confirm the accuracy and robustness of the proposed method compared to similar previous stabilized schemes

a discontinuous hp finite element method for convection diffusion problems this paper presents a new method which exhibits the best features of both finite volume and finite element techniques special attention is given to the issues of conservation flexible accuracy and stability the method is elementwise conservative the order of polynomial approximation can be adjusted element by element and the stability is not based on the introduction of artificial diffusion but on the use of a very particular finite element formulation with discontinuous basis functions the method supports h p and hp approximations and can be applied to any type of meshes including non matching grids a priori error estimates and numerical experiments on representative model problems indicate that the method is robust and capable of delivering high accuracy

finite difference ghost point multigrid methods on cartesian grids for elliptic problems in arbitrary domains in this paper we present a numerical method for solving elliptic equations in an arbitrary domain described by a level set function with general boundary conditions dirichlet neumann robin etc on cartesian grids using finite difference discretization and non eliminated ghost values a system of n i n g equations in n i n g unknowns is obtained by finite difference discretization on the n i internal grid points and second order interpolation to define the conditions for the n g ghost values the resulting large sparse linear system is then solved by a multigrid technique the novelty of the papers can be summarized as follows general strategy to discretize the boundary condition to second order both in the solution and its gradient a relaxation of inner equations and boundary conditions by a fictitious time method inspired by the stability conditions related to the associated time dependent problem with a convergence proof for the first order scheme an effective geometric multigrid which maintains the structure of the discrete system at all grid levels it is shown that by increasing the relaxation step of the equations associated to the boundary conditions a convergence factor close to the optimal one is obtained several numerical tests including variable coefficients anisotropic elliptic equations and domains with kinks show the robustness efficiency and accuracy of the approach

the sherrington kirkpatrick spin glass model in the presence of a random field with a joint gaussian probability density function for the exchange interactions and random fields abstract the magnetic systems with disorder form an important class of systems which are under intensive studies since they reflect real systems such a class of systems is the spin glass one which combines randomness and frustration the sherrington kirkpatrick ising spin glass with random couplings in the presence of a random magnetic field is investigated in detail within the framework of the replica method the two random variables exchange integral interaction and random magnetic field are drawn from a joint gaussian probability density function characterized by a correlation coefficient the thermodynamic properties and phase diagrams are studied with respect to the natural parameters of both random components of the system contained in the probability density the de almeida thouless line is explored as a function of temperature and other system parameters the entropy for zero temperature as well as for non zero temperatures is partly negative or positive acquiring positive branches as h 0 increases

an improved unsteady unstructured artificial compressibility finite volume scheme for viscous incompressible flows part ii application in part i of this paper a preconditioned artificial compressibility scheme was developed for modelling laminar steady state and transient incompressible flows for a wide range of reynolds and rayleigh numbers in this part several examples of laminar incompressible problems are solved and discussed the influence of various ac parameters on robustness and convergence rates are assessed for a complex category of problems it is shown that the scheme developed in part i is an accurate robust and easy to use method for solving incompressible laminar flow problems over a wide range of flow regimes copyright 2002 john wiley sons ltd

general strong conservation formulation of navier stokes equations in nonorthogonal curvilinear coordinates the selection of primary dependent variables for the solution of navier stokes equations in the curvilinear body fitted coordinates is still an unsettled issue reported formulations with primitive variables involve contravariant velocity components cartesian components and velocity projections also known as resolutes most of the formulations result in a weak conservation form of the momentum equations which contain grid line curvature and divergence related coriolis and centrifugal terms this paper presents a general strong conservation formulation of the momentum equations allowing the flexibility in choosing the various forms of the velocity components as the dependent variables ambiguous issues relating geometrical topology and forms of governing equations are discussed and clarified computational results obtained with both strong and weak forms are presented and compared to known analytical experimental data the results confirm the soundness of the formulation 19 refs

a cartesian grid embedded boundary method for poisson s equation on irregular domains we present a numerical method for solving poisson s equation with variable coefficients and dirichlet boundary conditions on two dimensional regions the approach uses a finite volume discretization which embeds the domain in a regular cartesian grid we treat the solution as a cell centered quantity even when those centers are outside the domain cells that contain a portion of the domain boundary use conservative differencing of second order accurate fluxes on each cell volume the calculation of the boundary flux ensures that the conditioning of the matrix is relatively unaffected by small cell volumes this allows us to use multigrid iterations with a simple point relaxation strategy we have combined this with an adaptive mesh refinement amr procedure we provide evidence that the algorithm is second order accurate on various exact solutions and compare the adaptive and nonadaptive calculations

effective field theory for the ising model with a fluctuating exchange integral in an asymmetric bimodal random magnetic field a differential operator technique abstract the spin 1 2 ising model on a square lattice with fluctuating bond interactions between nearest neighbors and in the presence of a random magnetic field is investigated within the framework of the effective field theory based on the use of the differential operator relation the random field is drawn from the asymmetric and anisotropic bimodal probability distribution p h i p h i h 1 q h i c h 1 where the site probabilities p q take on values within the interval 0 1 with the constraint p q 1 h i is the random field variable with strength h 1 and c the competition parameter which is the ratio of the strength of the random magnetic field in the two principal directions z and z c is considered to be positive resulting in competing random fields the fluctuating bond is drawn from the symmetric but anisotropic bimodal probability distribution p j i j 1 2 j i j j j i j j where j and represent the average value and standard deviation of j i j respectively we estimate the transition temperatures phase diagrams for various values of the system s parameters c p h 1 susceptibility and equilibrium equation for magnetization which is solved in order to determine the magnetization profile with respect to t and h 1

an embedded boundary formulation for large eddy simulation of turbulent flows interacting with moving boundaries a non boundary conforming formulation for simulating complex turbulent flows with dynamically moving boundaries on fixed cartesian grids is proposed the underlying finite difference solver for the filtered incompressible navier stokes equations is based on a second order fractional step method on a staggered grid to satisfy the boundary conditions on an arbitrary immersed interface the velocity field at the grid points near the interface is reconstructed using momentum forcing without smearing the sharp interface the concept of field extension is also introduced to treat the points emerging from a moving solid body to the fluid laminar flow cases and large eddy simulations les are presented to demonstrate the formal accuracy and range of applicability of the method in particular simulations of laminar flow induced by the harmonic in line oscillation of a circular cylinder in quiescent fluid and from a transversely oscillating cylinder in a free stream are presented and compared to reference simulations and experiments les of turbulent flow over a traveling wavy wall and transitional flow through a bileaflet prosthetic heart valve are also shown all results are in very good agreement with reference results in the literature

ghost cell method for inviscid two dimensional flows on cartesian grids a new approach to the computation of inviscid flows using cartesian grid methods is presented the crux of the method is the curvature corrected symmetry technique ccst developed by the present authors for body fitted grids and reviewed here the method introduces ghost cells near the boundaries whose values are developed from an assumed flowfield model in the vicinity of the wall consisting of a vortex flow that satisfies the normal momentum equation and the nonpenetration condition the ccst boundary condition was shown to be substantially more accurate than traditional boundary condition approaches this improved boundary condition is adapted to a cartesian mesh formulation that we term the ghost body cell method in this method all cell centers exterior to the body are computed with fluxes at the four surrounding cell edges there is no need for special treatment corresponding to cut cells which complicate other cartesian mesh methods the merits of the method are indicated by the computation of the compressible flow about basic circular cylinders as well as of airfoil applications and detailed comparisons to body fitted grid computations

a ghost cell immersed boundary method for flow in complex geometry an efficient ghost cell immersed boundary method gcibm for simulating turbulent flows in complex geometries is presented a boundary condition is enforced through a ghost cell method the reconstruction procedure allows systematic development of numerical schemes for treating the immersed boundary while preserving the overall second order accuracy of the base solver both dirichlet and neumann boundary conditions can be treated the current ghost cell treatment is both suitable for staggered and non staggered cartesian grids the accuracy of the current method is validated using flow past a circular cylinder and large eddy simulation of turbulent flow over a wavy surface numerical results are compared with experimental data and boundary fitted grid results the method is further extended to an existing ocean model mitgcm to simulate geophysical flow over a three dimensional bump the method is easily implemented as evidenced by our use of several existing codes

an implicit boundary approach for viscous compressible high reynolds flows using a hybrid remeshed particle hydrodynamics method abstract we present an implicit boundary particle method with background mesh adaptation we use a brinkman penalisation to represent the boundary of the domain and a remeshed particle method to simulate viscous flow with high reynolds numbers a penalty term is added to the navier stokes equations to impose the boundary conditions the boundary conditions are enforced to a specific precision with no need to modify the numerical method or change the grid achieving an implicit approach for flow around complex boundaries geometries simulation the main idea of the brinkman penalisation method is to model the solid obstacle as a porous medium the governing equations for the compressible fluid and penalised navier stokes for the porous medium are solved simultaneously without need for interface conditions the accuracy of the method is tested for a number of benchmark problems starting with simple cases such as a periodic laminar flow in a channel poiseuille flow to more complex problems such as the lid driven cavity with high reynolds numbers the reflection and propagation of a compressible shock wave and finally swirling flow in a model two stroke diesel engine the remeshed particle mesh method coupled with brinkman penalisation provides a good quality simulation and the results are in agreement with analytical or reference solutions

damage spreading in the sandpile model of soc abstract we have studied the damage spreading defined in the text in the sandpile model of self organised criticality we have studied the variations of the critical time defined in the text and the total number of sites damaged at critical time as a function of system size both show the power law variation

adaptive variational multiscale methods for incompressible flow based on two local gauss integrations we consider variational multiscale vms methods with h adaptive technique for the stationary incompressible navier stokes equations the natural combination of vms with adaptive strategy retains the best features of both methods and overcomes many of their deficits a reliable a posteriori projection error estimator is derived which can be computed by two local gauss integrations at the element level finally some numerical tests are presented to illustrate the method s efficiency

wang landau study of the critical behavior of the bimodal 3d random field ising model we apply the wang landau method to the study of the critical behavior of the three dimensional random field ising model with a bimodal probability distribution for high values of the random field intensity we find that the energy probability distribution at the transition temperature is double peaked suggesting that the phase transition is first order on the other hand the transition looks continuous for low values of the field intensity in spite of the large sample to sample fluctuations observed the double peak in the probability distribution is always present for high fields

a cartesian ghost cell multigrid poisson solver for incompressible flows in this paper a simple cartesian ghost cell multigrid poisson solver is proposed for simulating incompressible fluid flows the flow field is discretized efficiently on a rectangular mesh in which solid bodies are immersed a small number of ghost mesh cells and their symmetric image cells are distributed in the vicinity of the solid boundary with the aid of the ghost and image cells the dirichlet and neumann boundary conditions can be implemented effectively chorin s fractional step projection method is adopted for the coupling of velocity and pressure for the solution of the navier stokes equations point wise gauss seidel iteration is used to solve the pressure poisson equation to speed up the convergence of the solution to the corresponding linear system sub level coarse meshes embedded with ghost and image cells are also introduced and operated in a sequential v cycle several test cases including the classical ideal incompressible flow around a cylinder a lid driven cavity flow and viscous flow past a fixed rotating cylinder are presented to demonstrate the accuracy and efficiency of the current approach 2010 john wiley sons ltd

sharp interface cartesian grid method i an easily implemented technique for 3d moving boundary computations a cartesian grid method is developed for the simulation of incompressible flows around stationary and moving three dimensional immersed boundaries the embedded boundaries are represented using level sets and treated in a sharp manner without the use of source terms to represent boundary effects the narrow band distance function field in the level set boundary representation facilitates implementation of the finite difference flow solver the resulting algorithm is implemented in a straightforward manner in three dimensions and retains global second order accuracy the accuracy of the finite difference scheme is established and shown to be comparable to finite volume schemes that are considerably more difficult to implement moving boundaries are handled naturally the pressure solver is accelerated using an algebraic multigrid technique adapted to be effective in the presence of moving embedded boundaries benchmarking of the method is performed against available numerical as well as experimental results

strong violation of critical phenomena universality wang landau study of the two dimensional blume capel model under bond randomness we study the pure and random bond versions of the square lattice ferromagnetic blume capel model in both the first order and second order phase transition regimes of the pure model phase transition temperatures thermal and magnetic critical exponents are determined for lattice sizes in the range l 20 100 via a sophisticated two stage numerical strategy of entropic sampling in dominant energy subspaces using mainly the wang landau algorithm the second order phase transition emerging under random bonds from the second order regime of the pure model has the same values of critical exponents as the two dimensional ising universality class with the effect of the bond disorder on the specific heat being well described by double logarithmic corrections our findings thus supporting the marginal irrelevance of quenched bond randomness on the other hand the second order transition emerging under bond randomness from the first order regime of the pure model has a distinctive universality class with nu 1 30 6 and beta nu 0 128 5 these results amount to a strong violation of universality principle of critical phenomena since these two second order transitions with different sets of critical exponents are between the same ferromagnetic and paramagnetic phases furthermore the latter of these two sets of results supports an extensive but weak universality since it has the same magnetic critical exponent but a different thermal critical exponent as a wide variety of two dimensional systems with and without quenched disorder in the conversion by bond randomness of the first order transition of the pure system to second order we detect by introducing and evaluating connectivity spin densities a microsegregation that also explains the increase we find in the phase transition temperature under bond randomness

a gridless boundary condition method for the solution of the euler equations on embedded cartesian meshes with multigrid the solution of the euler equations using a gridless boundary condition treatment on a patched embedded cartesian field mesh is described the gridless boundary treatment is implemented by means of a least squares fitting of the conserved flux variables using a cloud of nodes in the vicinity of the body the method allows for accurate treatment of the surface boundary conditions without the need for excessive refinement of the cartesian mesh additionally the method does not suffer from problems associated with thin body geometry or extremely fine cut cells near the body unlike some methods that consider a gridless or meshless treatment throughout the entire domain the use of a cartesian field mesh allows for effective implementation of multigrid acceleration and issues associated with global conservation are alleviated results are presented for transonic flow about single and dual naca 0012 airfoil configurations including a convergence study indicating the effectiveness of multigrid acceleration within the construct of the gridless boundary treatment where applicable comparisons to the flo52 body fitted euler code are presented to gauge the accuracy of the method

multicritical points and crossover mediating the strong violation of universality wang landau determinations in the random bond d 2 blume capel model the effects of bond randomness on the phase diagram and critical behavior of the square lattice ferromagnetic blume capel model are discussed the system is studied in both the pure and disordered versions by the same efficient two stage wang landau method for many values of the crystal field restricted here in the second order phase transition regime of the pure model for the random bond version several disorder strengths are considered we present phase diagram points of both pure and random versions and for a particular disorder strength we locate the emergence of the enhancement of ferromagnetic order observed in an earlier study in the ex first order regime the critical properties of the pure model are contrasted and compared to those of the random model accepting for the weak random version the assumption of the double logarithmic scenario for the specific heat we attempt to estimate the range of universality between the pure and random bond models the behavior of the strong disorder regime is also discussed and a rather complex and yet not fully understood behavior is observed it is pointed out that this complexity is related to the ground state structure of the random bond version

replica exchange algorithm and results for the three dimensional random field ising model the random field ising model with gaussian disorder is studied using a different monte carlo algorithm the algorithm combines the advantages of the replica exchange method and the two replica cluster method and is much more efficient than the metropolis algorithm for some disorder realizations three dimensional systems of size 24 3 are studied each realization of disorder is simulated at a value of temperature and uniform field that is adjusted to the phase transition region for that disorder realization energy and magnetization distributions show large variations from one realization of disorder to another for some realizations of disorder there are three well separated peaks in the magnetization distribution and two well separated peaks in the energy distribution suggesting a first order transition

calculation of incompressible viscous flows by an unconditionally stable projection fem this paper investigates the numerical performance of a finite element implementation of a new incremental fractional step method to compute steady and unsteady incompressible viscous flows under general boundary conditions and using unstructured meshes a variational framework is adopted which accommodates two different spaces for representing and approximating the velocity fields calculated respectively in the viscous and inviscid phases of the method but which leads to a very simple numerical scheme in terms of only one discrete velocity field an unconditionally stable semi implicit approximation of the nonlinear term is used to eliminate any time step restriction as far as the numerical stability is concerned numerical results for five test problems in two dimensions are reported to illustrate the flexibility of the proposed method

gerris a tree based adaptive solver for the incompressible euler equations in complex geometries an adaptive mesh projection method for the time dependent incompressible euler equations is presented the domain is spatially discretised using quad octrees and a multilevel poisson solver is used to obtain the pressure complex solid boundaries are represented using a volume of fluid approach second order convergence in space and time is demonstrated on regular statically and dynamically refined grids the quad octree discretisation proves to be very flexible and allows accurate and efficient tracking of flow features the source code of the method implementation is freely available

on the roles of minimization and linearization in least squares finite element models of nonlinear boundary value problems in this paper we examine the roles of minimization and linearization in the least squares finite element formulations of nonlinear boundary values problems the least squares principle is based upon the minimization of the least squares functional constructed via the sum of the squares of appropriate norms of the residuals of the partial differential equations in the present case we consider l 2 norms since the least squares method is independent of the discretization procedure and the solution scheme the least squares principle suggests that minimization should be performed prior to linearization where linearization is employed in the context of either the picard or newton iterative solution procedures however in the least squares finite element analysis of nonlinear boundary value problems it has become common practice in the literature to exchange the sequence of application of the minimization and linearization operations the main purpose of this study is to provide a detailed assessment on how the finite element solution is affected when the order of application of these operators is interchanged the assessment is performed mathematically through an examination of the variational setting for the least squares formulation of an abstract nonlinear boundary value problem and also computationally through the numerical simulation of the least squares finite element solutions of both a nonlinear form of the poisson equation and also the incompressible navier stokes equations the assessment suggests that although the least squares principle indicates that minimization should be performed prior to linearization such an approach is often impractical and not necessary

a cartesian grid embedded boundary method for the heat equation on irregular domains we present an algorithm for solving the heat equation on irregular time dependent domains it is based on the cartesian grid embedded boundary algorithm of johansen and colella j comput phys 147 2 60 85 for discretizing poisson s equation combined with a second order accurate discretization of the time derivative this leads to a method that is second order accurate in space and time for the case where the boundary is moving we convert the moving boundary problem to a sequence of fixed boundary problems combined with an extrapolation procedure to initialize values that are uncovered as the boundary moves we find that in the moving boundary case the use of crank nicolson time discretization is unstable requiring us to use the l sub 0 stable implicit runge kutta method of twizell gumel and arigu

universality and double critical end points a double critical end point in the two dimensional spin 3 2 blume capel model is studied via extensive monte carlo simulations the resultant scaling character of the probability distribution of the mixing scaling operators allows us to locate the double critical end point precisely and also to convincingly show that it indeed belongs to the same universality class as the critical points

on the role of polynomials in rbf fd approximations ii numerical solution of elliptic pdes rbf generated finite differences rbf fd have in the last decade emerged as a very powerful and flexible numerical approach for solving a wide range of pdes we find in the present study that combining polyharmonic splines phs with multivariate polynomials offers an outstanding combination of simplicity accuracy and geometric flexibility when solving elliptic equations in irregular or regular regions in particular the drawbacks on accuracy and stability due to runge s phenomenon are overcome once the rbf stencils exceed a certain size due to an underlying minimization property test problems include the classical 2 d driven cavity and also a 3 d global electric circuit problem with the earth s irregular topography as its bottom boundary the results we find are fully consistent with previous results for data interpolation

meshfree iterative stabilized taylor galerkin and characteristic based split cbs algorithms for incompressible n s equations abstract this paper presents two stabilized schemes of the fractional step algorithm using characteristic based split and taylor galerkin like based split respectively in the meshfree context an iterative procedure which makes the convective term satisfy the momentum conservation equation in an implicit sense is introduced into the two schemes to allow much larger time step sizes a modified version of finite increment calculus process for incompressibility stabilization is developed to avoid the calculation of high order spatial derivatives numerical experiments demonstrate the capability and stability of the proposed schemes of the meshfree based fractional step method in the simulation of incompressible flows

the random field ising model with asymmetric bimodal probability distribution abstract the ising model in the presence of a random field is investigated within the mean field approximation based on landau expansion the random field is drawn from the bimodal probability distribution p h p h h 0 1 p h h 0 where the probability p assumes any value within the interval 0 1 asymmetric distribution the prevailing transitions are of second order but for some values of p and h 0 first order phase transitions take place for smaller temperatures and higher h 0 thus confirming the existence of a tricritical point also the possible reentrant phenomena in the phase diagram t h 0 plane occur for appropriate values of p and h 0 using the variational principle we determine the equilibrium equation for magnetization and solve it for both transitions and at the tricritical point in order to determine the magnetization profile with respect to h 0

an immersed interface method for stokes flows with fixed moving interfaces and rigid boundaries we present an immersed interface method for solving the incompressible steady stokes equations involving fixed moving interfaces and rigid boundaries irregular domains the fixed moving interfaces and rigid boundaries are represented by a number of lagrangian control points in order to enforce the prescribed velocity at the rigid boundaries singular forces are applied on the fluid at these boundaries the strength of singular forces at the rigid boundary is determined by solving a small system of equations for the deformable interfaces the forces that the interface exerts on the fluid are calculated from the configuration position of the deformed interface the jumps in the pressure and the jumps in the derivatives of both pressure and velocity are related to the forces at the fixed moving interfaces and rigid boundaries these forces are interpolated using cubic splines and applied to the fluid through the jump conditions the positions of the deformable interfaces are updated implicitly using a quasi newton method bfgs within each time step in the proposed method the stokes equations are discretized via the finite difference method on a staggered cartesian grid with the incorporation of jump contributions and solved by the conjugate gradient uzawa type method numerical results demonstrate the accuracy and ability of the proposed method to simulate incompressible stokes flows with fixed moving interfaces on irregular domains

three time integration methods for incompressible flows with discontinuous galerkin boltzmann method abstract this paper presents three time integration methods for incompressible flows with finite element method in solving the lattice bgk boltzmann equation the space discretization is performed using nodal discontinuous galerkin method which employs unstructured meshes with triangular elements and high order approximation degrees the time discretization is performed using three different kinds of time integration methods namely direct decoupling and splitting from the storage cost temporal accuracy numerical stability and time consumption we systematically compare three time integration methods then benchmark fluid flow simulations are performed to highlight efficient time integration methods numerical results are in good agreement with others or exact solutions

the role of constraints within generalized nonextensive statistics the gibbs jaynes path for introducing statistical mechanics is based on the adoption of a specific entropic form sand of physically appropriate constraints for instance for the usual canonical ensemble one adopts i ii ipi 1 and iii ei eigenvalues of the hamiltonian u1 internal energy equilibrium consists in optimizing s1 with regard to pi in the presence of constraints ii and iii within the recently introduced nonextensive statistics i is generalized into sq k 1 ipiq q 1 q 1 reproduces s1 ii is maintained and iii is generalized in a manner which might involve piq in the present effort we analyze the consequences of some special choices for iii and their formal and practical implications for the various physical systems that have been studied in the literature to illustrate some mathematically relevant points we calculate the specific heat respectively associated with a nondegenerate two level system as well as with the classical and quantum harmonic oscillators

are damage spreading transitions generically in the universality class of directed percolation we present numerical evidence for the fact that the damage spreading transition in the domany kinzel automaton found by martinset al is in the same universality class as directed percolation we conjecture that also other damage spreading transitions should be in this universality class unless they coincide with other transitions as in the ising model with glauber dynamics and provided the probability for a locally damaged state to become healed is not zero

vorticity boundary condition and related issues for finite difference schemes this paper discusses three basic issues related to the design of finite difference schemes forunsteadyviscous incompressible flows using vorticity formulations the boundary condition for vorticity an efficient time stepping procedure and the relation between these schemes and the ones based on velocity pressure formulation we show that many of the newly developed global vorticity boundary conditions can actually be written as some local formulas derived earlier we also show that if we couple a standard centered difference scheme with third or fourth order explicit runge kutta methods the resulting schemes havenocell reynolds number constraints for high reynolds number flows these schemes are stable under the cfl condition given by the convective terms finally we show that the classical mac scheme is the same as thom s formula coupled with second order centered differences in the interior in the sense that one can define discrete vorticity in a natural way for the mac scheme and get the same values as the ones computed from thom s formula we use this to derive an efficient fourth order runge kutta time discretization for the mac scheme from the one for thom s formula we present numerical results for driven cavity flow at high reynolds number 105

steady viscous flow past a circular cylinder up to reynolds number 600 viscous flow past a circular cylinder becomes unstable around reynolds number re 40 with a numerical technique based on newton s method and made possible by the use of a supercomputer steady but unstable solutions have been calculated up to re 600 it is found that the wake bubble region with recirculating flow grows in length approximately linearly with re the width increases like re12 up to re 300 at which paint a transition to linear increase with re begins at the highest reynolds numbers we reached the wake resembles a pair of translating uniform vortices both touching the center line the cylinder moving in front with the same speed supplies the vorticity required to balance diffusion