grid generation techniques in computational fluid dynamics revue des differentes methodes on montre que les regions tridimensionnelles sont mieux traitees par fragmentation du champ en sous regions avec generation de grilles dans chaque sous region interet des grilles adaptatives couplees a des solutions physiques

exact mean field solutions of the asymmetric random average process we consider the asymmetric random average process arap with continuous mass variables and parallel discrete time dynamics studied recently by krug garcia and rajesh majumdar both j statist phys 99 2000 the model is defined by an arbitrary state independent fraction density function r with support on the unit interval we examine the exactness of mean field steady state mass distributions in dependence of and identify as a conjecture based on high order calculations the class of density functions yielding product measure solutions additionally the exact form of the associated mass distributions p m is derived using these results we show examplary the exactness of the mean field ansatz for monomial fraction densities r n 1 rn 2 with n 2 for verification we calculate the mass distributions p m explicitly and prove directly that product measure holds furthermore we show that even in cases where the steady state is not given by a product measure very accurate approximants can be found in the class

comparative study between two navier stokes algorithms for transonicairfoils a critical examination of several aspects of the numerical simulation of high reynolds number transonic airfoil flows is presented subcritical and supercritical flowfields about an aft cambered airfoil were generated by solving the mass averaged navier stokes equations with turbulence incorporated through an algebraic eddy viscosity model the governing equations were solved on curvilinear body fitted grids utilizing two different algorithms i e maccormack s explicit and beam warming implicit the numerical uncertainties associated with different schemes grid resolution artificial viscosity and far field boundary placement were investigated and found to be of the same order of magnitude or less than the corresponding uncertainties in the available experimental data comparison of computed and experimental results showed good prediction of all the essential flow features however detailed comparison of velocity profiles pointed out deficiencies of the turbulence model downstream of the shock wave boundary layer interaction in the airfoil cove and in the near wake thinlayer and navier stokes computed results were found to be in excellent agreement with each other

two dimensional elliptic grid solver using boundary grid control and curvature correction the thompson method of explicitly evaluating control function of the elliptic grid solver is employed to improve local grid quality around convex and concave boundaries the curvature correction is principally added to the grid lines around a boundary and is quickly attenuated as the grid points move inward the algebraic advancing front method is employed to estimate two levels of orthogonal grids for evaluating the control functions at the boundary if the grid equation based on the cauchy riemann relation with and as independent variables is employed numerical examinations show that a lengthy trial and error procedure is required to get a satisfactory grid distribution in contrast the method based on the cauchy riemann relation with x and y as independent variables which benefits from the maximum principle not only removes the undesired grid clustering and diluting easily but also effectively improves overall grid smoothness and slightly enhances boundary grid orthogonality

models of stress fluctuations in granular media we investigate in detail two models describing how stresses propagate and fluctuate in granular media the first one is a scalar model where only the vertical component of the stress tensor is considered in the continuum limit this model is equivalent to a diffusion equation where the r ole of time is played by the vertical coordinate plus a randomly varying convection term we calculate the response and correlation function of this model and discuss several properties in particular related to the stress distribution function we then turn to the tensorial model where the basic starting point is a wave equation which in the absence of disorder leads to a ray like propagation of stress in the presence of disorder the rays acquire a diffusive width and the angle of propagation is shifted a striking feature is that the response function becomes negative which suggests that the contact network is mechanically unstable to very weak perturbations the stress correlation function reveals characteristic features related to the ray like propagation which are absent in the scalar description our analytical calculations are confirmed and extended by a numerical analysis of the stochastic wave equation

conserved mass models and particle systems in one dimension in this paper we study analytically a simple one dimensional model of mass transport we introduce a parameter p that interpolates between continuous time dynamics p 0 limit and discrete parallel update dynamics p 1 for each p we study the model with i both continuous and discrete masses and ii both symmetric and asymmetric transport of masses in the asymmetric continuous mass model the two limits p 1 and p 0 reduce respectively to the q model of force fluctuations in bead packs s n coppersmith et al phys rev e 53 4673 1996 and the recently studied asymmetric random average process j krug and j garcia cond mat 9909034 we calculate the steady state mass distribution function p m assuming product measure and show that it has an algebraic tail for small m p m m where the exponent depends continuously on p for the asymmetric case we find p 1 p 2 p for 0 p 1 and 1 1 and for the symmetric case p 2 p 2 8 5p p 2 for all 0 p 1 we discuss the conditions under which the product measure ansatz is exact we also calculate exactly the steady state mass mass correlation function and show that while it decouples in the asymmetric model in the symmetric case it has a nontrivial spatial oscillation with an amplitude decaying exponentially with distance

three dimensional grid generation using elliptic equations with direct grid distribution control boundary fitted computational meshes are generated by solving a system of elliptic partial differential equations the grid points at the boundary surfaces are arbitrarily distributed the interior grid distribution is controlled by a technique which insures a grid line orthogonality at the boundaries the grid is automatically adjusted while the grid line orthogonality at the boundaries is achieved in an iterative process this technique is demonstrated for three different configurations desirable cell size and shape are obtained for the boundary shapes which normally cause poor grid distribution

boundary fitted coordinate systems for numerical solution of partial differential equations a review a comprehensive review of methods of numerically generating curvilinear coordinate systems with coordinate lines coincident with all boundary segments is given some general mathematical framework and error analysis common to such coordinate systems is also included the general categories of generating systems are those based on conformal mapping orthogonal systems nearly orthogonal systems systems produced as the solution of elliptic and hyperbolic partial differential equations and systems generated algebraically by interpolation among the boundaries also covered are the control of coordinate line spacing by functions embedded in the partial differential operators of the generating system and by subsequent stretching transformation dynamically adaptive coordinate systems coupled with the physical solution and time dependent systems that follow moving boundaries are treated references reporting experience using such coordinate systems are reviewed as well as those covering the system development

matrix product approach for the asymmetric random average process we consider the asymmetric random average process which is a one dimensional stochastic lattice model with nearest neighbour interaction but continuous and unbounded state variables first the explicit functional representations so called beta densities of all local interactions leading to steady states of product measure form are rigorously derived this also completes an outstanding proof given in a previous publication then we present an alternative solution for the processes with factorized stationary states by using a matrix product ansatz due to continuous state variables we obtain a matrix algebra in the form of a functional equation which can be solved exactly

variational approach by means of adjoint systems to structural optimization and sensitivity analysis ii structure shape variation abstract for a linear elastic structure the first variation of an arbitrary stress strain and displacement functionals corresponding to variation of shape of external boundaries or interfaces is derived by using the solutions for primary and adjoint systems the application to optimal design is next presented and the relevant optimally conditions are derived from general expressions the path independent integrals used in fracture mechanics are rederived as a particular case of general expressions

finite volume methods for two dimensional incompressible flows with complex boundaries abstract the paper discusses possible ways of developing accurate and efficient finite volume methods for complex incompressible flows the issues of boundary fitted grid generation choice of coupled or uncoupled procedures cartesian or grid aligned velocity components staggered or non staggered variable arrangement discretization methods solution algorithms and convergence acceleration by multigrid methods are addressed an example of a finite volume method for general two dimensional flows is described in some detail and applications of this method to a variety of flows are presented

model for force fluctuations in bead packs we study theoretically the complex network of forces that is responsible for the static structure and properties of granular materials we present detailed calculations for a model in which the fluctuations in the force distribution arise because of variations in the contact angles and the constraints imposed by the force balance on each bead of the pile we compare our results for the force distribution function for this model including exact results for certain contact angle probability distributions with numerical simulations of force distributions in random sphere packings this model reproduces many aspects of the force distribution observed both in experiment and in numerical simulations of sphere packings our model is closely related to some that have been studied in the context of self organized criticality we present evidence that in the force distribution context critical power law force distributions occur only when a parameter hidden in other interpretations is tuned our numerical mean field and exact results all indicate that for almost all contact distributions the distribution of forces decays exponentially at large forces

improvements on objective and constraint functions in domain optimization in this paper a sequential quadratic programming algorithm is efficiently coupled with the finite element package msc nastran in order to optimize the shape of two dimensional parts with piecewise constant thickness where linearized elasticity is used three different methods for gradient calculation with respect to the changing of the shape are also coupled to msc nastran the aim of this article is to give a study on difficulties in the convergence of the shape using usual objective and constraint functions and improvements on them to avoid these difficulties two examples are presented to illustrate the improvements made and to give numerical results

three dimensional elliptic grid generation with fully automatic boundary constraints a new procedure for generating smooth uniformly clustered three dimensional structured elliptic grids is presented here which formulates three dimensional boundary constraints by extending the two dimensional counterpart presented by the author earlier this fully automatic procedure obviates the need for manual specification of decay parameters over the six bounding surfaces of a given volume grid the procedure has been demonstrated here for the mars science laboratory msl geometries such as aeroshell and canopy as well as the inflatable aerodynamic decelerator iad geometry and a 3d analytically defined geometry the new procedure also enables generation of single block grids for such geometries because the automatic boundary constraints permit the decay parameters to evolve as part of the solution to the elliptic grid system of equations these decay parameters are no longer just constants as specified in the conventional approach but functions of generalized coordinate variables over a given bounding surface since these decay functions vary over a given boundary orthogonal grids around any arbitrary simply connected boundary can be clustered automatically without having to break up the boundaries and the corresponding interior or exterior domains into various blocks for grid generation the new boundary constraints are not limited to the simply connected regions only but can also be formulated around multiply connected and isolated regions in the interior the proposed method is superior to other methods of grid generation such as algebraic and hyperbolic techniques in that the grids obtained here are c 2 continuous whereas simple elliptic smoothing of algebraic or hyperbolic grids to enforce c 2 continuity destroys the grid clustering near the boundaries

structure of shape derivatives for nonsmooth domains abstract the object of this paper is to study the shape gradient and the shape hessian by the velocity speed method for arbitrary domains with or without constraints it makes the connection between methods using a family of transformations such as first or second order perturbations of the identity operator new definitions for shape derivatives are given they naturally extend existing theories for ck or lipchitzian domains to arbitrary domains without any smoothness conditions on their geometric boundary in this new framework extensions of the classical structure theorems are given for the shape gradient and the shape hessian

2d orthogonal grid generation with boundary point distribution control a numerical method for 2d orthogonal grid generation with control of the boundary point distribution is presented the method is based on the solution of a system of partial differential equations the grid cell aspect ratio the so called distortion function is calculated from its definition equation in the entire domain the method allows the specification of the boundary point distribution in all the boundaries and also the distance of the first grid node to the boundary the method is successfully applied to several geometries including geometries with grid singularities and grids around airfoils and cross sections of ship sterns

three dimensional grid generation using poisson equations a method for constructing a boundary fitted grid system for arbitrary three dimensional 3 d configurations is presented the grid generation procedure is formulated through the poison equations a feature of the scheme is that grid lines in the grid system are smothly interconnected between the boundary co ordinates the control of the grid distributions in the interior of the system has implemented by the forcing functions appearing in the poisson equations and by the boundary coordinates reasonable cell sizes and shapes are obtained even for extreme boundary shapes which normally tend to cause poorly controlled grid distributions

an exactly solvable dissipative transport model we introduce a class of one dimensional lattice models in which a quantity which may be thought of as an energy is either transported from one site to a neighbouring one or locally dissipated transport is controlled by a continuous bias parameter q which allows us to study symmetric as well as asymmetric cases we derive sufficient conditions for the factorization of the n body stationary distribution and give an explicit solution for the latter before briefly discussing physically relevant situations

application of bubnov galerkin formulation to orthogonal grid generation abstract a bubnov galerkin formulation is used to solve an elliptic grid generation system by using linear and quadratic isoparametric elements good orthogonality characteristics are obtained for symmetric and non symmetric physical domains using both complete boundary correspondence or a combination of dirichlet and neuman boundary conditions the method exhibits excellent stability and requires a low number of iterations to attain convergence results are compared with those presented in e d chikliwala and y c yortsos j comput phys 57 391 1985

new boundary constraints for elliptic systems used in grid generation problems new boundary constraints for elliptic partial differential equations as used in grid generation problems in generalized curvilinear coordinate systems are proposed in this paper these constraints based on the principle of local conservation of thermal energy in the vicinity of the boundaries are derived using the green s theorem they uniquely determine the so called decay parameters in the inhomogeneous terms of these elliptic systems these constraints are designed for boundary clustered grids where large gradients in physical quantities need to be resolved adequately it is observed that the present formulation also works satisfactorily for mild clustering therefore a closure for the decay parameter specification for elliptic grid generation problems has been provided resulting in a fully automated elliptic grid generation technique thus there is no need for a parametric study of these decay parameters since the new constraints fix them uniquely it is also shown that for neumann type boundary conditions these boundary constraints uniquely determine the solution to the internal elliptic problem thus eliminating the nonuniqueness of the solution of an internal boundary value grid generation problem with neumann boundary conditions

orthogonal mapping in two dimensions abstract a method for the generation of orthogonal boundary fitted curvilinear coordinates for arbitrary simply and doubly connected domains is developed on the basis of the theory of quasi conformal mappings of quadrilaterals and of previous work by ryskin and leal the method has useful applications in orthogonal grid generation in two dimensional and axi symmetric domains and in the extension of rapid elliptic solvers and spectral methods to complex geometries a new technique for the calculation of the conformal module of quadrilaterals is also presented

discretization of free surface flows and other moving boundary problems a system of elliptic partial differential equations and boundary conditions has been developed for generating boundary fitted element discretizations of two dimensional free and moving boundary problems terms in the differential equations are scaled for dimensional homogeneity and adjustable weighting of orthogonality smoothness and concentration of the coordinate mesh they govern grid points become finite element nodes mapped isoparametrically or subparametrically from a simple or patched computational domain concentration terms contain control functions and parameters that influence node spacing along each coordinate independently overall control is by patchwise parameters and functions successful selection of these to follow deforming flow regions is straightforward and is illustrated by analysis of steady and transient slide coating flows

a hybrid differential algebraic method for three dimensional grid generation an effective method is presented for generating three dimensional boundary fitted grids the technique is based on a two step procedure involving the solution of differential equations and algebraic interpolations a coarse grid with an arbitrarily given point distribution at all the boundaries is first generated by solving the poisson equations with the forcing functions being automatically adjusted during the grid generation to achieve orthogonality at the boundaries a fine grid with a desired concentration of grid lines is then obtained by fitting tricubic spline functions on the coarse grid a primary feature of the method is that the mesh spacing can be quickly and explicitly changed while retaining the smoothness over the entire field and the boundary orthogonality applications to a variety of geometries demonstrate the performance of the method

hyperbolic equation method of grid generation for enclosed regions in a recent study the authors combined the grid front marching method and the parabolic equation method in this study a similar idea is applied to extend the cordeva and barth hyperbolic equation method to enclosed regions

elliptic grid generation various types of generating systems for boundary conforming coordinate systems based on the numerical solution of systems of elliptic partial differential equations are discussed particular emphasis is given to the determination of functions in these equations which control the distribution of the curvilinear coordinate lines in the field

generation of orthogonal and nearly orthogonal coordinates with gridcontrol near boundaries a numerical procedure is presented for the generation of boundary fitted curvilinear coordinates with controllable mesh spacing and orthogonality the technique is based on a straightforward two step procedure involving the solution of poisson s equation the method is capable of generating orthogonal grids with partial control of the mesh spacing or nearly orthogonal grids with strict control of the mesh spacing the inhomogeneous terms in the poisson equations are automatically adjusted during the grid generation the technique is applicable to two dimensional simply connected regions typical of airfoils cascades diffusers and inlets

a laplacian equation method for numerical generation of boundary fitted 3d orthogonal grids abstract a sethod for generating boundary fitted orthogonal curvilinear grids in 3 dimensional space is described the mapping between the curvilinear coordinates and the cartesian coordinates is provided by a set of laplace equations which expressed in curvilinear coordinates involve the components of the metric tensor and are therefore non linear and coupled an iterative algorithm is described which achieves a numerical solution grids appropriate for the calculation of flow fields over complex topography or in complex flow passages as those found in turbomachinery and for other engineering applications can be constructed using the proposed method various examples are presented and plotted in perspective and data for the assessment of the properties of the resulting meshes is provided

elliptic grid generation based on laplace equations and algebraic transformations abstract an elliptic grid generation method is presented to generate boundary conforming grids in domains in 2d and 3d physical space and on minimal surfaces and parametrized surfaces in 3d physical space the elliptic grid generation method is based on the use of a composite mapping this composite mapping consists of a nonlinear transfinite algebraic transformation and an elliptic transformation the elliptic transformation is based on the laplace equations for domains or on the laplace beltrami equations for surfaces the algebraic transformation maps the computational space one to one onto a parameter space the elliptic transformation maps the parameter space one to one onto the domains or surfaces the composition of these two mappings is a differentiable one to one mapping from computational space onto the domains or surfaces and has a nonvanishing jacobian this composite mapping defines the grid point distribution in the interior of the domains or surfaces for domains and minimal surfaces the composite mapping obeys a nonlinear elliptic poisson system with control functions completely defined by the algebraic transformation the solution of the poisson systems is obtained by picard iteration and black box multigrid solvers for parametrized curved surfaces it is not necessary to define and solve a nonlinear elliptic poisson system instead a linear elliptic system and an inversion problem is solved to generate the grid in the interior of the surface

a numerical technique for two dimensional grid generation with grid control at all of the boundaries abstract a numerical technique is developed in the present investigation to generate grids by the use of the poisson equations orthogonal grids are obtained along all of the two boundaries 0 and max the stand off grid spacing between 0 and and between max and max can be controlled by employing a proper grid point distribution on the boundaries 0 and max thanks to the orthogonal boundary grids the present numerical technique is applicable to complex geometry by patching grids without slope discontinuity across the interface of the patches this technique also allows the poisson equations to generate coordinates for o type grid system and for periodic turbine cascades in the course of grid generation the magnitudes of the required control functions might be very large in a region where clustering grids are needed to guarantee a good numerical stability in spite of the values of the control functions the weighting function scheme along with the sis solver is employed through the examples illustrated in the present study the negative jacobian reported by previous investigators is shown not to arise from the use of the poisson equations it indeed comes from the truncation error of the central difference scheme used by them

exact tracer diffusion coefficient in the asymmetric random average process we study tracer diffusion in the continuous time asymmetric random average process which is an interacting particle system on generalizing the hammersley process from the equations of motion for the particle position correlations we obtain the exact tracer diffusion coefficient which is in agreement with a recent heuristic result by krug and garcia