adaptive hybrid grid methods an adaptive refinement and redistribution method is presented for use on hybrid grids composed of prismatic pyramidal and tetrahedral elements the combined refinement and redistribution scheme minimizes the computational time and memory required for the solver and maximizes the numerical accuracy grid refinement is achieved via a priori source placement and also solution based splitting of the edges of the grid elements the prismatic and pyramidal elements are divided directionally and the tetrahedral elements may be refined isotropically or directionally the prismatic grid redistribution scheme attracts or repels points that are close to the wall surface so as to better capture boundary layers a method is developed to place newly created boundary nodes on the actual splined surface instead of the previous discretized surface this ensures that the grid refinement always represents the geometric model accurately several examples are presented to demonstrate the a priori source placement the solution based grid refinement and the prismatic grid redistribution

numerical study of the turbulent flow past an airfoil with trailing edge separation presentation d une methode numerique par volume fini pour la resolution des equations de navier stokes bidimensionnelles incompressibles et stationnaires en coordonnees generales curvilignes application de la methode aux ecoulements turbulents sur des profils avec et sans separation au bord de sortie posterieur comparaison des calculs avec des donnees experimentales

a second order time accurate finite volume method for unsteady incompressible flow on hybrid unstructured grids a new second order time accurate fractional step method for solving unsteady incompressible navier stokes equations on hybrid unstructured grids is presented the nonstaggered grid method originally developed by rhie and chow 1983 aiaa j 21 1525 for steady flow and further extended by zang et al 1994 j comput phys 114 18 to unsteady flow on structured grids is employed in the present study to enforce mass conservation on hybrid unstructured grids the pressure and cartesian velocity components are defined at the center of each cell while the face normal velocities are defined at the mid points of the corresponding cell faces a second order fully implicit time advancement scheme is used for time integration and the resulting nonlinear equations are linearized without losing the overall time accuracy both the momentum and poisson equations are integrated with the finite volume method and the flow variables at the cell face are obtained using an interpolation scheme independent of cell shape the present numerical method is applied to four different benchmark problems and proves to be accurate and efficient

a note on overdispersed exponential families abstract the issue of creating overdispersion in a given one parameter one dimensional exponential family by extending it to a two parameter exponential family with the same support is considered an easily verifiable sufficient condition for this is derived it is shown that a large class of families satisfy this condition and that this class includes efron s 1986 and lindsay s 1986 family as special cases this class is also closely related to jorgensen s 1988 exponential dispersion models ump unbiased tests for testing overdispersion are exhibited and it is shown that in this context cox s overdispersion test is a special case a graphical display is developed to select a family of the general class which should be used with a given set of data to overdisperse a given target one parameter family two real data illustrations are given kr

a consistently formulated quick scheme for fast and stable convergence using finite volume iterative calculation procedures abstract previous applications of quick for the discretization of convective transport terms in finite volume calculation procedures have failed to employ a rigorous and systematic approach for consistently deriving this finite difference scheme instead earlier formulations have been established numerically by trial and error the new formulation for quick presented here is obtained by requiring that it satisfy four rules that guarantee physically realistic numerical solutions having overall balance careful testing performed for the wall driven square enclosure flow configuration shows that the consistently derived version of quick is more stable and converges faster than any of the formulations previously employed this testing includes the relative evaluation of boundary conditions approximated by second and third order finite difference schemes as well as calculations performed at higher reynolds numbers than previously reported

the calculation of some laminar flows using various discretisation schemes abstract for various laminar two dimensional flows the upwind hybrid and the quadratic finite difference schemes are evaluated the upwind and hybrid schemes are used in their normal forms the quadratic formulation leonard s quick scheme has in the past been found to be less stable than these two other schemes because it can on occasion generate both negative and positive influence coefficients two new forms of the quadratic formulation both of which always generate positive influence coefficients are presented for a uniform grid distribution and tested by reference to the results obtained from the upwind and hybrid schemes and data from other sources these two new schemes are found to be stable although one form seems to be sensitive to the size of the finite difference grid furthermore the solutions obtained using these new formulations are equal to or better than those obtained using the upwind and or the hybrid schemes it is concluded that these new formulations require further validation and to this end these new formulations are provided in a form that is easy to install into existing computer codes

multiblock hybrid grid finite volume method to solve flow in irregular geometries in this work a finite volume based finite element method is suitably developed for solving incompressible flow and heat transfer on collocated hybrid grid topologies the method is generally applicable to arbitrarily shaped elements and orientations and thus challenges the potential to unify many of the different grid topologies into a single formulation the key point in this formulation is the correct estimation of the convective and diffusive fluxes at the cell faces using a novel physical influence scheme this scheme remarkably enhances the achieved solution accuracy it is shown that the extended formulation is robust enough to treat any combination of multiblock meshes with dual element shape employments in this regard the solution domain is broken up into a number of different multiblock arrangements in which each block is filled with only one type of finite element shape the combined grid can decrease the computational time and memory requirements and increase the numerical accuracy the results of the extended formulation are validated against different benchmark and other solutions the current results are in excellent agreement with the other solutions without exhibiting any disturbances around the block boundaries

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 finite volume eulerian lagrangian localized adjoint method for solution of the advection dispersion equation a new mass conservative method for solution of the one dimensional advection dispersion equation is derived and discussed test results demonstrate that the finite volume eulerian lagrangian localized adjoint method fvellam outperforms standard finite difference methods in terms of accuracy and efficiency for solute transport problems that are dominated by advection for dispersion dominated problems the performance of the method is similar to that of standard methods like previous ellam formulations fvellam systematically conserves mass globally with all types of boundary conditions fvellam differs from other ellam approaches in that integrated finite differences instead of finite elements are used to approximate the governing equation this approach in conjunction with a forward tracking scheme greatly facilitates mass conservation the mass storage integral is numerically evaluated at the current time level and quadrature points are then tracked forward in time to the next level forward tracking permits straightforward treatment of inflow boundaries thus avoiding the inherent problem in backtracking as used by most characteristic methods of characteristic lines intersecting inflow boundaries fvellam extends previous ellam results by obtaining mass conservation locally on lagrangian space time elements details of the integration tracking and boundary algorithms are presented test results are given for problems in cartesian and radial coordinates

steady viscous flow in a triangular cavity steady recirculating viscous flow inside an equilateral triangular cavity is generated by translating one side the navier stokes equations are solved numerically using finite differences on a transformed geometry alternative numerical approaches and associated numerical difficulties are also discussed the results show a primary eddy and a series of secondary eddies at the stagnant corner for high reynolds numbers the interior of the primary eddy has constant vorticity but its value cannot be predicted by the mean squared law

non equilibrium critical behaviour on fractal lattices a simple one component surface reaction model exhibiting a critical point has been studied on deterministic fractal lattices with fractal dimension 1 df 2 results from time dependent simulations show a change in the value of the critical exponents with df two of the exponents interpolate very nicely between the values in one and two dimensions

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

adaptive finite volume upwind approach on mixed quadrilateral triangular meshes an adaptive cell vertex finite volume upwind approach on unstructured mixed quadrilateral triangular meshes where the quadrilaterals are directionally stretched in the flow regions having one dimensional features has been developed to solve the unsteady euler equations in the present approach the runge kutta time integration roe s riemann solver muscl differencing with characteristic interpolation variables a new treatment of the rotated extrapolation boundary condition and a modified technique of the global local regeneration for directionally stretched meshes are included by using different combinations of interpolation variables limiter functions and numerical implementations of boundary conditions a systematic study is made to understand the characteristics of the current approach in this work the isolated oblique shock problem shock reflection at a wall supersonic flow passing through a channel with a 4 circular arc bump transonic flows around single and two element airfoils as well as the shock propagation in a channel are investigated it is concluded that the present solution procedure demonstrates good convergence performance and provides accurate and high resolution results for the steady and unsteady inviscid flows

on the oscillatory dynamical behaviour of epidemic spreading in fractal media we present numerical evidence that dynamical physical processes that develop a time dependent characteristic length and take place in fractal media exhibiting spatial discrete scale invariance dsi with fundamental scaling ratio b may become coupled to the topology of the fractal leading to the observation of time dsi the hallmark of time dsi is the observation of a log periodic modulation of the dynamic or kinetic observables which is characterized by a well defined fundamental time scaling ratio both fundamental scaling ratios are linked according to b 1 z where z is the dynamic exponent characteristic of the physical process specifically we have studied the epidemic behaviour of the contact process cp in sierpinski carpets the cp exhibits second order irreversible phase transitions between an active regime and an absorbing state where the system is trapped without any escape possibility we observed that relevant dynamic observables such as the number of active sites the survival probability of the epidemics and the mean square displacement of the epidemic from the origin r2 t exhibit log periodic modulations by fitting the data we evaluate the fundamental time scaling ratio for various fractals and the corresponding dynamic exponents since at criticality one has that r2 t t2 z an independent estimation of the dynamic exponent can be performed in excellent agreement with results obtained by using the conjectured relationship for the fundamental scaling ratios b and

hierarchic hp edge element families for maxwell s equations on hybrid quadrilateral triangular meshes we construct and study a set of hierarchic basis functions for the galerkin discretisation of the space h curl 169 suitable for hybrid meshes containing both quadrilateral and triangular elements with arbitrary non uniform order polynomial approximation we investigate the conditioning and dispersive behaviour of the elements in addition numerical examples are shown which demonstrate the accuracy of the space for computing solutions of the time harmonic maxwell s equations that have singularities

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

regular article an accurate cartesian grid method for viscous incompressible flows with complex immersed boundaries a cartesian grid method has been developed for simulating two dimensional unsteady viscous incompressible flows with complex immersed boundaries a finite volume method based on a second order accurate central difference scheme is used in conjunction with a two step fractional step procedure the key aspects that need to be considered in developing such a solver are imposition of boundary conditions on the immersed boundaries and accurate discretization of the governing equation in cells that are cut by these boundaries a new interpolation procedure is presented which allows systematic development of a spatial discretization scheme that preserves the second order spatial accuracy of the underlying solver the presence of immersed boundaries alters the conditioning of the linear operators and this can slow down the iterative solution of these equations the convergence is accelerated by using a preconditioned conjugate gradient method where the preconditioner takes advantage of the structured nature of the underlying mesh the accuracy and fidelity of the solver is validated by simulating a number of canonical flows and the ability of the solver to simulate flows with very complicated immersed boundaries is demonstrated

parameter orthogonality and approximate conditional inference on propose une statistique du rapport de vraisemblance construite a partir de la distribution conditionnelle des observations etant donne les estimateurs du maximum de vraisemblance pour les parametres de nuisance

an unstructured hp finite element scheme for fluid flow and heat transfer in moving domains abstract this paper presents the formulation validation and application of a spectral hp algorithm for numerical solution of the navier stokes and heat scalar transport equations in arbitrarily moving complex geometries the new spectral element algorithm is based on the arbitrary lagrangian eulerian formulation and utilizes modal expansion of jacobi polynomials in mixed triangular and quadrilateral elements in two dimensions time integration is performed by stiffly stable schemes and can deliver up to third order time accuracy for transient problems test cases with sufficiently smooth solutions demonstrate spectral convergence and low phase dissipation error preliminary simulation results for micro mixers and micro heat spreaders are also presented

unstructured cartesian refinement with sharp interface immersed boundary method for 3d unsteady incompressible flows a novel numerical method is developed for solving the 3d unsteady incompressible navier stokes equations on locally refined fully unstructured cartesian grids in domains with arbitrarily complex immersed boundaries owing to the utilization of the fractional step method on an unstructured cartesian hybrid staggered non staggered grid layout flux mismatch and pressure discontinuity issues are avoided and the divergence free constraint is inherently satisfied to machine zero auxiliary hanging nodes are used to facilitate the discretization of the governing equations the second order accuracy of the solver is ensured by using multi dimension lagrange interpolation operators and appropriate differencing schemes at the interface of regions with different levels of refinement the sharp interface immersed boundary method is augmented with local near boundary refinement to handle arbitrarily complex boundaries the discrete momentum equation is solved with the matrix free newton krylov method and the krylov subspace method is employed to solve the poisson equation the second order accuracy of the proposed method on unstructured cartesian grids is demonstrated by solving the poisson equation with a known analytical solution a number of three dimensional laminar flow simulations of increasing complexity illustrate the ability of the method to handle flows across a range of reynolds numbers and flow regimes laminar steady and unsteady flows past a sphere and the oblique vortex shedding from a circular cylinder mounted between two end walls demonstrate the accuracy the efficiency and the smooth transition of scales and coherent structures across refinement levels large eddy simulation les past a miniature wind turbine rotor parameterized using the actuator line approach indicates the ability of the fully unstructured solver to simulate complex turbulent flows finally a geometry resolving les of turbulent flow past a complete hydrokinetic turbine illustrates the potential of the method to simulate turbulent flows past geometrically complex bodies on locally refined meshes in all the cases the results are found to be in very good agreement with published data and savings in computational resources are achieved

critical behaviour of the irreversible phase transitions of a dimer monomer process on fractal media the dynamic critical behaviour of a dimer monomer surface reaction process the zgb model of the type 1 2 a2 b to ab is studied on two different fractals namely a sierpinski carpet and percolating clusters which have almost the same fractal dimension df equivalent to 1 89 in both surfaces the model exhibits two continuous irreversible phase transitions for the sierpinski carpet the values of the critical exponents interpolate between those of directed percolation in 1 1 and 1 2 dimensions results corresponding to percolating clusters are not conclusive enough to assign the universality class of the model

implicit characteristic galerkin method for convection diffusion equations this paper presents a characteristic galerkin finite element method with an implicit algorithm for solving multidimensional time dependent convection diffusion equations the method is formulated on the basis of the combination of both the precise and the implicit numerical integration procedures aiming to reference particles the precise integration procedure with a 2n algorithm is taken as a tool to determine the material lagrangian derivative of the convective function in the operator splitting procedure the stability analysis of the algorithm and numerical results illustrate good performance of the present method in stability and accuracy copyright 2000 john wiley sons ltd

directed percolation in 2 1 dimensions the author presents results of monte carlo simulations for directed percolation in 2 1 dimensions very close to the percolation threshold his values for pc for bond and site percolation on the bcc and simple cubic lattices are more precise than previous estimates by one to two orders of magnitude the improvement on the critical exponents describing the behaviour at pc is less impressive but they are also substantially more precise than previous ones

a stable and accurate convective modelling procedure based on quadratic upstream interpolation a convective modelling procedure is presented which avoids the stability problems of central differencing while remaining free of the inaccuracies of numerical diffusion associated with upstream differencing for combined convection and diffusion the number of operations at each grid point is comparable to that of standard upstream pluscentral differencing however highly accurate solutions can be obtained with a grid spacing much larger than that required by conventional methods for comparable accuracy with obvious practical advantaged in terms of both speed and storage the algorithm is based on a conservative control volume formulation with cell wall values of each field variable written in terms of a quadratic interpolation using in any one coordinate direction the two adjacent nodal values together with the value at the next upstream node this results in a convective differencing scheme with greater formal accuracy than central differencing while retaining the basic stable convective sensitivity property of upstream weighted schemes the consistent treatment of diffusion terms is equivalent to central differencing with careful modelling numerical boundary conditions are not troublesome some idealized problems are studied showing the practical advantages of the method over other schemes in comparison with exact solutions an application to a complex unsteady two dimensional flow is briefly discussed

momentum variable procedure for solving compressible and incompressible flows navier stokes equations are solved for both compressible and incompressible flows using momentum component variables instead of the usual velocity variables as the dependent variables the numerical procedure is developed in a control volume based finite element context the procedure is determined in a pressure based algorithm rather than the density based algorithms which compressible methods normally use the proper selection of the connections between the variables on control volume surfaces and the main nodal values allow the use of a collocated grid arrangement the compressible and incompressible results of this algorithm are investigated by testing a number of test cases including the driven cavity an entrance region flow and a converging diverging nozzle flow the results indicate that the momentum component procedure is quite successful for solving compressible and incompressible flows within a single algorithm

streamline upwind petrov galerkin formulations for convection dominated flows with particular emphasis on the incompressible navier stokes equations abstract a new finite element formulation for convection dominated flows is developed the basis of the formulation is the streamline upwind concept which provides an accurate multidimensional generalization of optimal one dimensional upwind schemes when implemented as a consistent petrov galerkin weighted residual method it is shown that the new formulation is not subject to the artificial diffusion criticisms associated with many classical upwind methods the accuracy of the streamline upwind petrov galerkin formulation for the linear advection diffusion equation is demonstrated on several numerical examples the formulation is extended to the incompressible navier stokes equations an efficient implicit pressure explicit velocity transient algorithm is developed which accomodates several treatments of the incompressibility constraint and allows for multiple iterations within a time step the effectiveness of the algorithm is demonstrated on the problem of vortex shedding from a circular cylinder at a reynolds number of 100