an adaptive finite element method for transient compressible flows with moving boundaries a description is given of an adaptive finite element method for the simulation of two dimensional compressible flows with moving boundaries the method is implemented on an unstructured triangular grid and the mesh adaptation is achieved by local grid regeneration using an error estimation procedure coupled to an automatic triangular mesh generator two numerical examples are included to illustrate the numerical performance of the method

a high order numerical method for the helmholtz equation with nonstandard boundary conditions we describe a high order accurate methodology for the numerical simulation of time harmonic waves governed by the helmholtz equation our approach combines compact finite difference schemes that provide an inexpensive venue toward high order accuracy with the method of difference potentials developed by ryaben kii the latter can be interpreted as a generalized discrete version of the method of calderon s operators in the theory of partial differential equations the method of difference potentials can accommodate nonconforming boundaries on regular structured grids with no loss of accuracy due to staircasing it introduces a universal framework for treating boundary conditions of any type a significant advantage of this method is that changing the boundary condition within a fairly broad variety does not require any major changes to the algorithm and is computationally inexpensive in this paper we address various types of boundary conditions using the method of difference potentials we demonstrate th

complex adhm equations and sheaves on p 3 abstract we establish a 1 1 correspondence between certain classes of sheaves on p 3 and solutions of a complex version of the atiyah hitchin drinfeld manin equations we also show how relaxing of the locally free condition on sheaves is reflected on partial completions of the space of regular solutions we also introduce a new class of sheaves on p 3 closely related to ideal sheaves for curves within p 3

a procedure for efficient generation of solution adapted unstructured grids abstract an efficient procedure for generation of solution adapted unstructured grids is presented the grid generation procedure is based upon a delaunay triangulation scheme combined with new adaptive point source techniques with this method high quality solution adapted grids can be generated efficiently techniques are presented for obtaining adaptation sources which automatically detect relevant features in the flow field the overall procedure is coupled with a finite element flow solver computed solutions are presented which successfully demonstrate the overall procedure for a variety of aerospace configurations

a new mesh generation scheme for arbitrary planar domains this paper describes a new algorithm to generate interior nodes within any arbitrary multi connected regions the boundary nodes and the interior nodes are then linked up to form the best possible triangular elements by a completely revised technique in an efficient and stable manner owing to the generality of the central generation program the global domain is allowed to be divided into as many irregular subdomains as desired in order to model closely the actual physical situation moreover the boundaries of the sub domains are updated from time to time when necessary to include the possibilities of progressive refinement around a sharp corner generating radiating mesh from a prescribed node generating mesh between two circular arcs etc despite its flexibility and capabilities data for triangulation have been kept to a minimum by a logical input module no connectivity information between subregions is needed and common boundaries are defined once only all these features have contributed to a powerful method to generate 3 node or 6 node triangular element meshes of great variety within the most irregular heterogeneous regions

the pressure corrected ice finite element method for compressible flows on unstructured meshes a new implicit continuous fluid eulerian ice scheme for simulating a wide range of transient and steady inviscid and viscous compressible flows on unstructured finite elements is presented this new computational fluid dynamics scheme termed the pressure corrected ice finite element method pcice fem represents an advancement in massmomentum coupled pressure based schemes the governing hydrodynamic equations for this scheme consist of the conservative forms of the momentum balance navier stokes mass conservation and total energy equations the pcice fem scheme is developed as a predictor corrector scheme by performing a fractional step splitting of the semi implicit temporal discretization of the governing equations into an explicit predictor phase and a semi implicit pressure correction phase coupled by a pressure poisson solution the result of this predictor corrector formulation is that the pressure poisson equation is provided with sufficient internal energy information to avoid iteration with the semi implicit pressure correction equations the pcice fem scheme combines a modified form of the two step taylor galerkin fem scheme as an explicit predictor for the fractional momentum equations and a time weighted fem method for the semi implicit form of the mass conservation and the total energy equations the pcice fem scheme employs flux corrected transport fct as a high resolution filter for shock capturing the ability of the pcice fem scheme to accurately and efficiently simulate a wide variety of flows from nearly incompressible to highly compressible is demonstrated

prismatic grid generation for three dimensional complex geometries the paper describes generation of semiunstructu red prismatic grids for three dimensional complex geometries a new method of generation is presented which couples both algebraic and elliptic steps this combination yields low computation cost as well as smoothness of the grid main advantages of the developed grid generator are its direct control of grid orthogonality and spacing as well as its generality for treatment of three dimensional geometries the method marches a surface consisting of triangular faces away from the body surface employment of prismatic elements is a relatively new approach toward three dimensional complex geometry numerical simulations of viscous flows a body surface is covered with triangles which gives the geometric flexibility whereas the structure of the mesh in the direction normal to the surface provides better resolution of the viscous regions an f 16a aircraft geometry was included in the applications to investigate efficiency and to demonstrate robustness of the method in handling relatively complex topologies grid generation time for the entire aircraft domain was of the order of minutes on a workstation

tetrahedral mesh generation based on node insertion in crystal lattice arrangements and advancing front delaunay triangulation a method of unstructured technical mesh generation for general three dimensional domains is presented a conventional boundary representation is adopted as the basis for the description of solids with evolving geometry and topology the geometry of the surfaces is represented either analytically or by piecewise polynominal interpolation a preliminary surface mesh is generated by an advancing front method with the nodes inserted by hard sphere packing in physical space in accordance with a prescribed mesh density interior nodes are inserted in a face centered cubic fcc crystal lattice arrangements coupled to octree spatial subdivision with the local lattice parameter determined by a prespecified nodal density function prior to triangulation of the volume the preliminary surface mesh is preprocessed by a combination of local transformations and subdivisions in order to guarantee that the surface triangulation be a subcomplex of the volume delaunay triangulation a joint delaunay triangulation of the interior and boundary nodes which preserves the modified surface mesh is then constructed via an advancing front approach the resulting mesh is finally improved upon by the application of local transformations the overall time complexity of the mesher is o n log n the robustness and versatility of the approach as well as the good quality of the resulting meshes is demostrated with the aid of selected examples

implicit flux split euler schemes for unsteady aerodynamic analysis involving unstructured dynamic meshes improved algorithms for the solution of the time dependent euler equations are presented for unsteady aerodynamic analysis involving unstructured dynamic meshes the improvements have been developed recently to the spatial and temporal discretizations used by unstructured grid flow solvers the spatial discretization involves a flux split approach which is naturally dissipative and captures shock waves sharply with at most one grid point within the shock structure the temporal discretization involves an implicit time integration shceme using a gauss seidel relaxation procedure which is computationally efficient for either steady or unsteady flow problems for example very large time steps may be used for rapid convergence to steady state and the step size for unsteady cases may be selected for temporal accuracy rather than for numerical stability steady and unsteady flow results are presented for the naca 0012 airfoil to demonstrate applications of the new euler solvers the unsteady results were obtained for the airfoil pitching harmonically about the quarter chord the resulting instantaneous pressure distributions and lift and moment coefficients during a cycle of motion compare well with experimental data the paper presents a description of the euler solvers along with results and comparisons which assess the capability

error estimator and adaptive moving grids for finite volumes schemes a new adaptation technique has been developed for two and three dimensional grids based on relocation of the mesh nodes the flow is governed by the euler equations expressed in an euler lagrange form and the discretization uses a first order finite volume scheme based on roe s approximate riemann solver the grid is unstructured and its motion and evolution obey the physical and geometrical conservation laws the error is evaluated by a reconstructed higher order solution which is used to derive a forcing term to drive the motion of the grid nodes this is formulated so as to uniformly distribute the error while keeping the same grid connectivity the development is made for two and three dimensional grids although results are presented only for two dimensional flows he adaptation of the grid to the flow characteristics is widely recognized as a method to improve the solution accuracy and the overall computing efficiency of numerical schemes the moti vation is that since the grid is normally generated before knowing the flow behavior it is possible that the nodes distribution does not correspond to the solution requirements the adaptivity process is made up of two key elements an error estimator and an adaptation procedure the simplest error estimator used for finite volume schemes 1 2 is based on the physical behavior of the flowfield more specifically on the gradient of the density or the mach number the adaptation consists in refining and coarsening the mesh in regions of higher or lower gradients respectively the projection method developed by zienkiewicz and zhu3 4 is based on the observation that for finite elements discretization the solution is continuous whereas the derivatives are discontinuous at the interface of two elements those derivatives are projected in a space of continuous functions and the norm of the difference be tween this projection and the derivatives is used as a measure of the computational error for some problems the fluxes instead of derivatives are physically continuous in all of the domain and con sequently more appropriate to be projected in a space of continuous functions 5 babuska and rheinboldt6 propose an error estimator based on the solution of a local variational problem where the unknowns are the approximation errors the advantage consists in the reduction of the size of the linear system to be solved in compressible flows with shock waves or contact discontinu ities the variables can no longer be considered continuous the computed errors based on the solution gradient increase unbound edly with the adaptation of the discontinuity this acts as permanent source for grid refinement and could produce wrong results 7 paillere et al 8 use a wave model to evaluate the error for com pressible flows the model combines the effects of the divergence and rotational of the velocity to reduce the influence of disconti nuities the error is multiplied by a power of a characteristic length of the grid cell the adaptation procedure also considers a minimal local grid size

h morph an indirect approach to advancing front hex meshing h morph is a new automatic algorithm for the generation of a hexahedral dominant finite element mesh for arbitrary volumes the h morph method starts with an initial tetrahedral mesh and systematically transforms and combines tetrahedral into hexahedra it uses an advancing front technique where the initial front consists of a set of prescribed quadrilateral surface facets fronts are individually processed by recovering each of the six quadrilateral faces of a hexahedron from the tetrahedral mesh recovery techniques similar to those used in boundary constrained delaunay mesh generation are used tetrahedral internal to the six hexahedral faces are then removed and a hexahedron is formed at any time during the h morph procedure a valid mixed hexahedral tetrahedral mesh is in existence within the volume the procedure continues until no tetrahedral remain within the volume or tetrahedral remain which cannot be transformed or combined into valid hexahedral elements any remaining tetrahedral are typically towards the interior of the volume generally a less critical region for analysis transition from tetrahedral to hexahedra in the final mesh is accomplished through pyramid shaped elements advantages of the proposed method include its ability to conform to an existing quadrilateral surface mesh its ability to mesh without the need to decompose or recognize special classes of geometry and its characteristic well aligned layers of elements parallel to the boundary example test cases are presented on a variety of models

a general explicit or semi explicit algorithm for compressible and incompressible flows this note presents a rational basis for a unified finite element algorithm capable of dealing with a wide range of fluid flow in both steady and transient cases it is hoped that empiricism inherent in many previous approaches can be avoided and a sound basis provided the algorithm permits the use of equal interpolation for all variables by avoiding the need for the babuska brezzi constraints in regions where the flow is nearly incompressible the success of the algorithm which here is written for the non conservative equation form is demonstrated on several examples ranging from nearly incompressible through transonic regions to supersonic flows up to mild shocks such as those occurring in the examples presented in this paper no artificial viscosity is added at any stage the algorithm extends some concepts introduced in an earlier paper

mesh generation and adaptivity for the solution of compressible viscous high speed flows an implicit explicit procedure for the solution of the compressible navier stokes equations on unstructured triangular and tetrahedral meshes is outlined a procedure for constructing continuous lines made up of edges in the mesh is employed and the implicit equation system is solved via line relaxation the problem of generating and adapting unstructured meshes for viscous flow simulations is addressed a number of examples are included which demonstrate the numerical performance of the proposed procedures

an adaptive finite element procedure for compressible high speed flows abstract a two step explicit finite element procedure for obtaining time accurate solutions to the compressible euler equations is described the method is coupled with an adaptive mesh refinement process which enables steady state solutions of improved quality to be obtained

active shielding and control of noise we present a mathematical framework for the active control of time harmonic acoustic disturbances unlike many existing methodologies our approach provides for the exact volumetric cancellation of unwanted noise in a given predetermined region of space while leaving unaltered those components of the total acoustic field that are deemed friendly our key finding is that for eliminating the unwanted component of the acoustic field in a given area one needs to know relatively little in particular neither the locations nor structure nor strength of the exterior noise sources need to be known likewise there is no need to know the volumetric properties of the supporting medium across which the acoustic signals propagate except perhaps in the narrow area of space near the boundary perimeter of the domain to be shielded the controls are built based solely on the measurements performed on the perimeter of the region to be shielded moreover the controls themselves i e additional sources are also c

mathematical instanton bundles on p2n 1 soit e un fibre algebrique de rang 2n sur p c 2n 1 on dit e est un fibre instanton mathematique de nombre quantique k si e est simple a un polynome de chern c t e 1 1 t 2 k et une cohomologie naturelle h 9 e l dans 2n 1 l 0 on demontre que l ensemble mip 2n 1 k des classes d isomorphismes des fibres instanton mathematiques de nombre quantique k sur p c 2n 1 peuvent s identifier a un quotient mi p2n 1 k sk 2n 2k gl k c ou sk 2n 2k est la variete des modules de kronecker non degenerees symetriques simples de rang 2n 2k

moduli spaces of framed instanton bundles on cp 3 and twistor sections of moduli spaces of instantons on c 2 abstract we show that the moduli space m of framed instanton bundles on cp 3 is isomorphic as a complex manifold to a subvariety in the moduli of rational curves of the twistor space of the moduli space of framed instantons on r 4 we then use this characterization to prove that m is equipped with a torsion free affine connection with holonomy in sp 2 n c

boundary conditions for the numerical solution of elliptic equations in exterior regions elliptic equations in exterior regions frequently require a boundary condition at infinity to ensure the weill posedness of the problem examples of practical applications include the helmholtz equation and laplace s equation computational procedures based on a direct discretization of the elliptic problem require the replacement of the condition at infinity by a boundary condition on a finite artificial surface direct imposition of the condition at infinity along the finite boundary results in large errors a sequence of boundary conditions is developed which provides increasingly accurate approximations to the problem in the infinite domain estimates of the error due to the finite boundary are obtained for several cases computations are presented which demonstrate the increased accuracy that can be obtained by the use of the higher order boundary conditions the examples are based on a finite element formulation but finite difference methods can also be used

three dimensional unstructured mesh generation part 1 fundamental aspects of triangulation and point creation abstract the present paper introduces an alternative approach for delaunay triangulation in which the triangulation is mapped from an equivalent convex hull in a higher dimension furthermore some fundamental aspects of a point creation algorithm for unstructured mesh generation have been addressed based on numerical experiments a point spacing tensor and point insertion criterion have been introduced aiming to deal with anisotropic meshes

an approach to refining three dimensional tetrahedral meshes based on delaunay transformations a technique for refining three dimensional tetrahedral meshes is proposed in this paper the proposed technique is capable of treating arbitrary unstructured tetrahedral meshes convex or non convex with multiple regions resulting in high quality constrained delaunay triangulations the tetrahedra generated are of high quality nearly equilateral sliver tetrahedra which present a real problem to many algorithms are not produced with the new method the key to the generation of high quality tetrahedra is the iterative application of a set of topological transformations based on the voronoi delaunay theory and a reposition of nodes technique the computational requirements of the proposed technique are in linear relationship with the number of nodes and tetrahedra making it ideal for direct employment in a fully automatic finite element analysis system for 3 d adaptive mesh refinement application to some test problems is presented to show the effectiveness and applicability of the new method

a universal formulation of two equation models for adaptive computation of turbulent flows abstract this paper describes the application of a recently developed universal adaptive finite element algorithm to the simulation of several turbulent flows the objective of the present work is to show how the controlled accuracy of adaptive methods provides the means to perform careful quantitative comparisons of two equation models the formulation uses the logarithmic form of turbulence variables which naturally leads to a simple algorithm applicable to all two equation turbulence models the new methodology is free of ad hoc stability enhancement measures such as clipping and limiters which may often differ from one model to the other such techniques limit the predictive capability of a turbulence model and cloud the issues of a comparison study the present procedure results in one adaptive solver applicable to all two equation models the approach is demonstrated by comparing three popular turbulence models on a few non trivial compressible and incompressible flows we have chosen the following models the standard k model the k model of speziale and the k model of wilcox results show that accurate solutions can be obtained for all models and that systematic comparison of turbulence models can be made

an alternating digital tree adt algorithm for 3d geometric searching and intersection problems a searching algorithm is presented for determining which members of a set of n points in an n dimensional space lie inside a prescribed space subregion the algorithm is then extended to handle finite size objects as well as points in this form it is capable of solving problems such as that of finding the objects from a given set which intersect with a prescribed object the suitability of the algorithm is demonstrated for the problem of three dimensional unstructured mesh generation using the advancing front method

an implicit explicit scheme for compressible viscous high speed flows abstract an implicit explicit finite element based algorithm for the solution of 2d steady compressible viscous high speed flows is presented a structured grid is employed in the vicinity of solid walls and the implicit form of the algorithm is implemented in this region the explicit form of the algorithm is used in the remainder of the flow domain which is discretised with an unstructured assembly of triangles the quality of the computed solution is improved by the application of solution adaptive remeshing the computed results for two examples are compared with experimental observations to illustrate the performance of the proposed scheme

nondegenerate multidimensional matrices and instanton bundles in this paper we prove that the moduli space of rank 2n symplectic instanton bundles on p 2n 1 defined from the well known monad condition is affine this result was not known even in the case n 1 where by atiyah drinfeld hitchin and manin in 1978 the real instanton bundles correspond to self dual yang mills sp 1 connections over the 4 dimensional sphere the result is proved as a consequence of the existence of an invariant of the multi dimensional matrices representing the instanton bundles

adaptive finite element method for turbulent flow near a propeller we present an adaptive finite element method based on remeshing to solve incompressible turbulent free shear flow near a propeller solutions are obtained in primitive variables using a highly accurate finite element approximation on unstructured grids turbulence is modeled by a mixing length formulation two general purpose error estimators which take into account swirl and the variation or the eddy viscosity are presented and applied to the turbulent wake or a propeller the proposed adaptive scheme is robust reliable and cost effective

two dimensional mesh generation adaptive remeshing and refinement this paper discusses the generation of unstructured triangular meshes by the advancing front technique we also employ the technique to discretize surfaces a simple and effective algorithm for the specification of element sizes is described a similar idea is then applied to adaptive remeshing where a completely new mesh is created on the basis of the isolines of a certain important variable the isolines are obtained from the fe calculation based on the previous mesh in this paper attention is focused on the poisson s equation the optimal a priori error estimate for the problem is used to estimate the number of isolines needed for the remeshing when the estimated error exceeds the tolerance in only a small part of the domain the adaptive procedure is switched automatically to an adaptive refinement

finite element navier stokes calculation of three dimensional turbulent flow near a propeller les equations de navier stokes sont resolues par une methode d elements finis a fonction de penalite l helice est modelisee par un disque actuateur et le transport turbulent par une equation d energie cinetique turbulente

blockwise adaptivity for time dependent problems based on coarse scale adjoint solutions we describe and test an adaptive algorithm for evolution problems that employs a sequence of blocks consisting of fixed though nonuniform space meshes this approach offers the advantages of adaptive mesh refinement but with reduced overhead costs associated with load balancing remeshing matrix reassembly and the solution of adjoint problems used to estimate discretization error and the effects of mesh changes a major issue with a block adaptive approach is determining block discretizations from coarse scale solution information that achieve the desired accuracy we describe several strategies for achieving this goal using adjoint based a posteriori error estimates and we demonstrate the behavior of the proposed algorithms as well as several technical issues in a set of examples

unstructured grid generation using iterative point insertion and local reconnection a procedure is presented for efficient generation of high quality two or three dimensional unstructured grids of triangular or tetrahedral elements the present procedure uses an iterative point creation and insertion scheme wherein points are created using advancing front type point placement initially the connectivity for these generated points is obtained by directly subdividing the elements which contain them without regard to quality this connectivity is then improved by iteratively using local reconnection subject to a quality criterion for two dimensions a min max criterion is used and for three dimensions a delaunay in sphere criterion followed by a min max type criterion is used the overall procedure is applied repetitively until a complete field grid is generated with a desired point distribution grid quality and performance statistics are presented for a variety of two and three dimensional configurations the combined quality and efficiency attributes of this procedure appear to be a substantial improvement over existing methods

analysis of the zienkiewicz zhu a posteriori error estimator in the finite element method an a posteriori error estimator for finite element analysis proposed by zienkiewicz and zhu is analysed and shown to be effective and convergent in addition we analyse wider classes of estimators of which the zienkiewicz zhu estimator is a special case it is shown that some of these estimators will be asymptotically exact numerical evidence is presented supporting the analysis

compact 2d and 3d sixth order schemes for the helmholtz equation with variable wave number several studies have presented compact fourth order accurate finite difference approximation for the helmholtz equation in two or three dimensions several of these formulae allow for the wave number k to be variable other papers have extended this further to include variable coefficients within the laplacian which models non homogeneous materials in electromagnetism later papers considered more accurate compact sixth order methods but these were restricted to constant k in this paper we extend these compact sixth order schemes to variable k in both two and three dimensions results on 2d and 3d problems with known analytic solutions verify the sixth order accuracy we demonstrate that for large wave numbers the second order scheme cannot produce comparable results with reasonable grid sizes

direct implementation of high order bgt artificial boundary conditions abstract local artificial boundary conditions abcs for the numerical simulation of waves have been successfully used for decades most notably the boundary conditions due to engquist majda bayliss gunzburger turkel and higdon the basic idea behind these boundary conditions is that they cancel several leading terms in an expansion of the solution the larger the number of terms canceled the higher the order of the boundary condition and in turn the smaller the reflection error due to truncation of the original unbounded domain by an artificial outer boundary in practice however the use of local abcs has been limited to low orders first and second because higher order boundary conditions involve higher order derivatives of the solution which may harm well posedness and cause numerical instabilities they are also difficult to implement especially in finite elements a prominent exception is the development of local high order abcs based on auxiliary variables in the current paper we implement high order bayliss turkel abcs directly with no auxiliary variables yet no discrete approximation of the constituent high order derivatives either instead we represent the solution at the boundary as an expansion with respect to a continuous basis for the spherical artificial boundary the basis consists of eigenfunctions of the beltrami operator spherical harmonics which enable replacing the high order derivatives in the abcs with powers of the corresponding eigenvalues the continuous representation at the boundary is coupled to higher order compact finite differences inside the domain by the method of difference potentials mdp it maintains high order accuracy even when the boundary is not aligned with the discretization grid

an anisotropic zienkiewicz zhu type error estimator for 3d applications we extend the anisotropic zienkiewicz zhu a posteriori error estimator of proceedings of the enumath 2009 uppsala sweden 29 june 3 july 2009 to three dimensions like the standard zienkiewicz zhu estimator the proposed estimator is designed to be independent of the problem at hand is cheap to compute and easy to implement in contrast to the standard zienkiewicz zhu estimator the elementwise counterpart of the proposed estimator explicitly takes into account the geometrical properties of the actual tetrahedron thus in a wide variety of applications the estimator is able to detect the anisotropic features exhibited by the solution of the governing equations a metric based optimization procedure rigorously addressed drives the adaptation of the mesh it is shown numerically to yield quasi optimal triangulations dictating the accuracy vs number of elements behaviour despite being heuristic to some extent in practice the overall anisotropic adaptation procedure turns out to be effective copyright 2010 john wiley sons ltd

tetrahedral mesh generation in polyhedral regions based on convex polyhedron decompositions the input to the method consists of the boundary faces of the polyhedral region and possibly internal and hole interfaces plus the desired number of tetrahedra and other scalar parameters the region is decomposed into convex polyhedra in two stages so that tetrahedra of one length scale can be generated in each subregion a mesh distribution function which is either automatically constructed from the first stage convex polyhedron decomposition or supplied by the user is used to determine the tetrahedron sizes in the subregions then a boundary constrained triangulation is constructed in each convex polyhedron with local transformations being used to improve the quality of the tetahedra

a finite element formulation of compressible flows using various sets of independent variables abstract this paper presents a finite element method for the simulation of compressible flows the navier stokes and euler equations are solved in the conservation form using various sets of independent variables a variational formulation is developed based upon a variant of the petrov galerkin method and uses a shock capturing operator an adaptive algorithm based on a particular residual norm is proposed several numerical examples are presented to demonstrate the performances of each set of variables in solving compressible high speed flows

adaptive remeshing for compressible flow computations an adaptive mesh procedure for improving the quality of steady state solutions of the euler equations in two dimensions is described the procedure is implemented in conjunction with a finite element solution algorithm using linear triangular elements and an explicit time stepping scheme the mesh adaptation is accomplished by regeneration using information provided by the computed solution on the current mesh the meshes produced are characterised by the appearance of stretched elements in the vicinity of one dimensional flow features and can exhibit a large variation in element size this allows solutions of enhanced quality to be produced in a computationally efficient manner

numerical solution of the wave equation with variable wave speed on nonconforming domains by high order difference potentials abstract we solve the wave equation with variable wave speed on nonconforming domains with fourth order accuracy in both space and time this is accomplished using an implicit finite difference fd scheme for the wave equation and solving an elliptic modified helmholtz equation at each time step with fourth order spatial accuracy by the method of difference potentials mdp high order mdp utilizes compact fd schemes on regular structured grids to efficiently solve problems on nonconforming domains while maintaining the design convergence rate of the underlying fd scheme asymptotically the computational complexity of high order mdp scales the same as that for fd

an implicit finite element method for high speed flows a fast algorithm is presented for constructing continuous lines made up of element sides which pass once through each node of a general unstructured triangular mesh and which are generally aligned in prescribed directions the lines are used as the basis of an adaptive fully implicit unstructured grid procedure for the solution of two dimensional problems of steady compressible inviscid and laminar viscous high speed flows where the equation system is solved by line relaxation using a block tridiagonal equation solver for three dimensional laminar viscous simulations it is proposed to utilize an implicit explicit finite element formulation in the vicinity of solid walls a grid exhibiting structure in the normal direction is employed while away from this region the grid will be totally unstructured in the structured region lines in the normal direction to the wall are readily identified while lines in the surfaces parallel to the solid wall are constructed using the proposed two dimensional procedure the implicit algorithm is then used in the structured region and the equation solution is achieved via line relaxation an explicit form of the solution algorithm is used elsewhere to illustrate the performance of the proposed method solutions are obtained for both transonic inviscid and transonic and hypersonic laminar viscous problems in two dimensions the application of the proposed procedure to the solution of three dimensional hypersonic laminar viscous flow over a double ellipsoid configuration is also described

finite element method for computing turbulent propeller flow a numerical procedure based on the primitive variable navier stokes equations is applied to the simulation of the three dimensional axisymmetric flow near a propeller in a uniform flow the time averaged navier stokes equations are solved using both a mixed and a penalty function finite element method a new model is developed to compute axisymmetric viscous throughflow past propellers this is achieved by forcing the flow to be tangent to the mean stream surface between the blades this condition is enforced by introducing a lagrange multiplier that can be interpreted as the force applied by the blades on the fluid turbulence is modelled by a simple mixing length equation detailed comparison with wind tunnel measurements shows good prediction of velocity and pressure the present approach represents a first step toward the development of a viscous quasi three dimensional capability

surface mesh sizing control a method is presented for controlling element sizes on the interior of areas during surface meshing a delaunay background mesh is defined over which natural neighbour interpolation a neighbourhood based interpolation scheme is used to generate a sizing function the sizing function may be used to interpolate element sizes anisotropic stretching parameters or other surface characteristics required during meshing a brief description of natural neighbour interpolation is included and the sizing results obtained from this interpolation method are compared to those obtained using linear interpolation three specific applications are presented that utilize the sizing function namely boundary layer meshing surface curvature refinement and anisotropic mesh generation for these applications criteria used for augmenting the sizing function based on insertion of additional interior vertices into the background mesh are discussed copyright 2000 john wiley sons ltd

instantons and geometric invariant theory we show that the yang mills instantons can be described in terms of certain holomorphic bundles on the projective plane the proof uses explicit matrix descriptions arising from monads and an analysis of the corresponding groups of symmetries

an adaptive remeshing strategy for flows with moving boundaries and fluid structure interaction the primary objective of this work is to extend the capability of the arbitrary lagrangian eulerian ale based strategy for solving fluid structure interaction problems this is driven by the fact that the ale mesh movement techniques will not be able to treat problems in which fluid structure interface experiences large motion in addition for certain problems the need arises to capture accurately flow features such as a region with high gradients of the solution variables this can be achieved by incorporating an adaptive remeshing procedure into the solution strategy as in our previous works comput methods appl mech eng 2006 195 1633 1666 comput methods appl mech eng 2006 195 5754 5779 here the fluid flow is governed by the incompressible navier stokes equations and modelled by using stabilized low order velocity pressure finite elements the motion of the fluid domain is accounted for by an arbitrary lagrangian eulerian ale strategy the flexible structure is represented by means of appropriate standard finite element formulations while the motion of the rigid body is described by rigid body dynamics for temporal discretization of both fluid and solid bodies the discrete implicit generalized method is employed the resulting strongly coupled set of non linear equations is then solved by means of a novel partitioned solution procedure which is based on the newton raphson methodology and incorporates full linearization of the overall incremental problem within the adaptive solution strategy the quality of fluid mesh and the solution quality indicator are evaluated regularly and compared against the appropriate remeshing criteria to decide whether a remeshing step is required the adaptive remeshing procedure follows closely the standard computational procedure in which the adaptive remeshing process produces a mesh that can capture salient features of the flow field for the problems under consideration in this work the motion of the fluid boundary very often results in boundaries with very high curvatures and a fluid domain that contain areas with small cross sections to be able to generate meshes that give result with acceptable accuracy these local geometrical features need to be included in determining the element density distribution the numerical examples demonstrate the robustness and efficiency of the methodology copyright 2007 john wiley sons ltd

a taylor galerkin method for convective transport problems a method is described to derive finite element schemes for the scalar convection equation in one or more space dimensions to produce accurate temporal differencing the method employs forward time taylor series expansions including time derivatives of second and third order which are evaluated from the governing partial differential equation this yields a generalized time discretized equation which is successively discretized in space by means of the standard bubnov galerkin finite element method the technique is illustrated first in one space dimension with linear elements and euler leap frog and crank nicolson time stepping several interesting relations with standard galerkin and recently developed petrov galerkin methods emerge and the new taylor galerkin schemes are found to exhibit particularly high phase accuracy with minimal numerical damping the method is successively extended to deal with variable coefficient problems and multi dimensional situations

adaptive remeshing for three dimensional compressible flow computations an adaptive mesh procedure for computing steady state solutions of the compressible euler equations in three dimensions is presented the method is an extension of previous work in two dimensions the approach requires the coupling of a surface triangulator an automatic tetrahedral mesh generator a finite element flow solver and an error estimation procedure an example involving flow at high mach number is included to demonstrate the numerical performance of the proposed approach the example shows that the use of this form of adaptivity in three dimensions offers the potential of even greater computational savings than those attained in the corresponding two dimensional implementation

adaptative remeshing for viscous incompressible flows this paper presents an adaptive finite element procedure for solving viscous incompressible flows the methodology is based on adaptive remeshing for steady state problems the navier stokes equations for an incompressible fluid are solved in primitive variables by an uzawa algorithm using a highly accurate element the efficiency and convergence rate of the adaptive strategy are evaluated by solving problems with known analytical solutions finally the methodology is applied to the flow over a backward facing step and predictions are compared with experimental measurements the use of the proposed adaptive procedure is shown to lead to improved accuracy of the finite element predictions nomenclature c a constant e error in the solution h element size dissipation energy n number of elements in the mesh p pressure 5 step and fence height u velocity vector u v velocity components x y coordinates v gradient operator 6 element size predicted by adaptation module e strain rate tensor 1a v u v ut a stress tensor 2 e similarity variable in a boundary layer t relative error on a mesh h absolute viscosity of the fluid v kinematic viscosity of the fluid

centroidal voronoi tessellation based finite element superconvergence in this article a finding on finite element superconvergence is reported the laplacian operator with dirichlet boundary condition is considered the linear finite element solutions have an o h2 0 5 superconvergence in l2 norm at nodes on an almost equilateral triangular mesh generated based on centroidal voronoi tessellation for an arbitrary 2d bounded domain extensive numerical examples are presented to demonstrate the superconvergence property copyright 2008 john wiley sons ltd

adaptivity techniques for compressible inviscid flows abstract to enhance the resolution of numerically simulated flowfields grid adaptivity is vitally important further to afford complete flexibility in the spatial discretisation of the flow domain both structured unstructured and combinations of grid types are likely to be required hence the development of grid adaptivity techniques for general grids is important this paper discusses adaptivity achieved through point enrichment point derefinement and point movement applied on general grids a flexible data structure is described together with suitable strategies for adaptively refining a computational grid applications are presented of adaptive grid refinement for two dimensional compressible flow simulation

3d delaunay mesh generation coupled with an advancing front approach abstract this paper describes a fully automatic mesh generation method suitable for domains of any shape in r 3 initially a so called boundary mesh is generated wherein internal points are created using advancing front point placement and inserted using a delaunay method the algorithm combines the advantages of efficiency and nice mathematical properties of a delaunay approach with advancing front high quality point placement strategy several three dimensional examples are presented to demonstrate the overall efficiency and the relevance of the combined procedure the present method can be extended to isotropic or anisotropic adaptive mesh generation

enhanced error estimator for adaptive finite element analysis of 3d incompressible flow abstract this paper describes an enhanced error estimator for adaptive finite element analysis of three dimensional incompressible viscous flow the estimator uses a modified form of the recovery functional employed in the well known l 2 local patch recovery technique lpr originally proposed by zienkiewicz and zhu the modified recovery functional is obtained by penalizing the conventional recovery functional using the residual of the continuity equation for the constraint the enhanced estimator which we denote as lprc is tested on unstructured second order tetrahedral meshes using an analytical solution to the three dimensional incompressible navier stokes equations we report significant improvements in the effectiveness of the resulting error estimate both for interior and boundary nodes at virtually no additional computational cost the lprc estimator is particularly useful for flows in which stresses at the boundary of the computational domain play an important role such as in blood flow modeling although in this paper the lprc error estimator is tested exclusively on the 10 noded tetrahedral taylor hood element we expect that when applied to incompressible flows the lprc estimator will perform more effectively than the lpr estimator when used with other types of elements as well

high order numerical simulation of the transmission and scattering of waves using the method of difference potentials the method of difference potentials generalizes the method of calderon s operators from pdes to arbitrary difference equations and systems it offers several key advantages such as the capability of handling boundaries interfaces that are not aligned with the discretization grid variable coefficients and nonstandard boundary conditions in doing so the complexity of the algorithm remains comparable to that of an ordinary finite difference scheme on a regular structured grid previously we have applied the method of difference potentials to solving several variable coefficient interior helmholtz problems with fourth and sixth order accuracy we have employed compact finite difference schemes as a core discretization methodology those schemes enable high order accuracy on narrow stencils and hence require only as many boundary conditions as needed for the underlying differential equation itself numerical experiments corroborate the high order accuracy of our method for variable coefficients regular grids and non conforming boundaries in the current paper we extend the previously developed methodology to exterior problems we present a complete theoretical analysis of the algorithm as well as the results of a series of numerical simulations specifically we study the scattering of time harmonic waves about smooth shapes subject to various boundary conditions we also solve the transmission scattering problems in which not only do the waves scatter off a given shape but also propagate through the interface and travel across the heterogeneous medium inside in all the cases our methodology guarantees high order accuracy for regular grids and non conforming boundaries and interfaces

filling space with tetrahedra in the context of 3d finite element meshes various options for filling an indefinite space such as would be approached within a fine mesh with tetrahedra are considered this problem is not trivial as it is in 2 d since unlike equilateral triangles regular tetrahedra cannot be fitted together to fill space various groupings or assemblies which can be repeated indefinitely to fill space are considered by altering the shape of the tetrahedra in one of these to minimize a suitable function a unique shape of tetrahedron is obtained which optimizes the conditioning the mesh thus produced is shown to be better conditioned than alternatives based on assemblies of different shaped tetrahedra a number of conditioning measures are used to confirm this finally actual meshes which fit boundaries are briefly considered copyright 1999 john wiley sons ltd

on boundary conditions of the characteristic based split cbs algorithm for fluid dynamics this paper discusses alternative procedures which can be used in the application of boundary conditions for the cbs algorithm attention is focused on the problem of application of prescribed velocity and traction conditions the paper is illustrated with some incompressible flow problems although previously logical and correct boundary condition specifications were introduced the procedures outlined in this paper simplify calculations and generally make it more accurate copyright 2002 john wiley sons ltd

tetrahedral meshes from planar cross sections in biomedicine many three dimensional 3d objects are sampled in terms of slices such as computed tomography ct magnetic resonance imaging mri and ultrasound imaging it is often necessary to construct surface meshes from the cross sections for visualization and thereafter construct tetrahedra for the solid bounded by the surface meshes for the purpose of finite element analysis in ref 1 c bajaj e coyle and k lin graphical models and image processing 58 6 1996 524 543 we provided a solution to the construction of a surface triangular mesh from planar section contours here we provide an approach to tetrahedralize the solid region bounded by planar contours and the surface mesh it is a difficult task because the solid can be of high genus several through holes as well as have complicated branching regions we develop an algorithm to effectively reduce the solid into prismatoids and provide an approach to tetrahedralize the prismatoids our tetrahedralization approach is similar to the advancing front technique aft for its flexible control of mesh quality the main criticism of aft is that the remaining interior may be badly shaped or even untetrahedralizable the emphasis of our prismatoid tetrahedralization approach is on the characterization and prevention of untetrahedralizable parts ruppert and seidel j ruppert r seidel on the difficulty of tetrahedralizing three dimensional non convex polyhedra in proceedings 5th annual acm symposium comput geom 1989 p 380 392 have shown that the problem of deciding whether a polyhedron is tetrahedralizable without adding steiner points is np complete we characterize this problem under certain constraints and design one rule to reduce the chance of generating untetrahedralizable shapes the characterization also leads to the classification of two common untetrahedralizable categories which can be better processed if they do occur

a finite point method in computational mechanics applications to convective transport and fluid flow the paper presents a fully meshless procedure fo solving partial differential equations the approach termed generically the finite point method is based on a weighted least square interpolation of point data and point collocation for evaluating the approximation integrals some examples showing the accuracy of the method for solution of adjoint and non self adjoint equations typical of convective diffusive transport and also to the analysis of compressible fluid mechanics problem are presented

finite element solutions of the euler equations for transonic external flows we present a finite element newton galerkin scheme for the solution of the steady subsonic and transonic euler equations in primitive variable form the scheme is based on the explicit introduction of an artificial viscosity in the governing equations to provide the necessary dissipation for numerical stability the system of equations is linearized by a newton method and a direct solver is used for the resulting fully coupled system of algebraic equations

discrete calderon s projections on parallelepipeds and their application to computing exterior magnetic fields for frc plasmas confining dense plasma in a field reversed configuration frc is considered a promising approach to fusion numerical simulation of this process requires setting artificial boundary conditions abcs for the magnetic field because whereas the plasma itself occupies a bounded region within the frc coils the field extends from this region all the way to infinity if the plasma is modeled using single fluid magnetohydrodynamics mhd then the exterior magnetic field can be considered quasi static this field has a scalar potential governed by the laplace equation the quasi static abc for the magnetic field is obtained using the method of difference potentials in the form of a discrete calderon boundary equation with projection on the artificial boundary shaped as a parallelepiped the calderon projection itself is computed by convolution with the discrete fundamental solution on the three dimensional cartesian grid

compressible flowfield solutions with unstructured grids generated by delaunay triangulation a method is described that constructs three dimensional unstructured tetrahedral meshes using the delaunay triangulation criterion the approach includes an automatic point creation technique and ensures that given an initial surface triangulation which bounds a domain a valid boundary conforming assembly of tetrahedra is produced the efficiency of the proposed procedure reduces the computer time for the generation of realistic unstructured tetrahedral grids to the order of minutes on workstations of modest computational capabilities the grids generated are used with two finite element algorithms to simulate inviscid transonic compressible flows flow solutions for aerospace configurations are presented and computed results compared with experimental data

h adaptive finite element computation of time harmonic exterior acoustics problems in two dimensions abstract in this paper we carry out adaptive finite element computations of the helmholtz equation in two dimensions in the context of time harmonic exterior acoustics the purpose is to demonstrate potentially significant cost savings engendered through adaptivity for propagating solutions at moderate wave numbers ka 2 4 the computations are performed on meshes of linear triangles and are adapted to the solution by locally changing element sizes h refinement the adaptive procedure involves applying an explicit residual based a posteriori error estimator and an h adaptive strategy which were derived in a previous paper the adaptive meshes are then obtained through global mesh regeneration using an advancing front mesh generator two different finite element formulations are considered the galerkin and galerkin least squares gls methods the infinite physical domain is truncated by an artificial exterior boundary on which a fully coupled dirichlet to neumann dtn boundary condition is applied two different problems are computed plane wave scattering by a rigid infinite surface circular and square cross sections and nonuniform radiation from an infinite circular cylinder detailed cost studies with respect to an active column direct solver are performed for the nonuniform radiation problem the adaptive mesh is twenty times more cost effective than a uniform mesh for galerkin when coupled with the gls formulation the adaptive mesh is forty times more efficient than galerkin computations on a uniform mesh

adaptive finite element method for thermal flow problems this paper presents an adaptive finite element method based on remeshing to solve incompressible viscous flow problems including heat transfer effects by forced or free convection conjugate heat transfer problems are also considered solutions are obtained in primitive variables by an uzawa algorithm using a highly accurate finite element approximation on unstructured grids two error estimators are presented and compared on problems with known analytical solutions the methodology is then applied to a problem of practical interest and predictions are compared with experimental measurements and show very good agreement

efficient three dimensional delaunay triangulation with automatic point creation and imposed boundary constraints a method is described which constructs three dimensional unstructured tetrahedral meshes using the delaunay triangulation criterion several automatic point creation techniques will be highlighted and an algorithm will be presented which can ensure that given an initial surface triangulation which bounds a domain a valid boundary conforming assembly of tetrahedra will be produced statistics of measures of grid quality are presented for several grids the efficiency of the proposed procedure reduces the computer time for the generation of realistic unstructured tetrahedral grids to the order of minutes on workstations of modest computational capabilities

finite element navier stokes solver for unstructured grids a three dimensional finite element navier stokes solver has been developed for calculating transonic viscous flow on unstructured grids about complex aerodynamic configurations the solver employs a second orderaccurate space discretization of the navier stokes equations obtained from a galerkin weighted residual approximation time discretization is obtained using either an explicit two step lax wendroff scheme or an explicit multistep runge kutta scheme boundary conditions are implemented using a procedure based on the method of characteristi cs the overall solution procedure has been initially validated by calculating two and three dimensional inviscid and viscous transonic flows

a new approach to the development of automatic quadrilateral mesh generation a methodology for the automatic mesh generation of quadrilateral elements is proposed the methodology is based on the facts that i a region can always be subdivided entirely into quadrilaterals if the polygon which forms the boundary of the region has an even number of sides ii a quadrilateral can be formed by two triangles which share a common side by taking advantage of the techniques developed in an existing automatic triangular mesh generator quadrilateral meshes can be generated according to the distribution of user specified element size over the domain of interest in particular an automatic quadrilateral mesh generator based on the advancing front technique for triangular mesh generation1 is described techniques to improve the quality of the generated quadrilateral meshes are introduced the robustness and versatility of the mesh generator are demonstrated by a variety of examples

finite element euler computations in three dimensions an explicit finite element solution procedure for the three dimensional euler equations is presented the solution domain is automatically meshed using a tetrahedral mesh generator which is an extension of our previous two dimensional work several examples are included to illustrate the performance of the generator and solver an adaptive mesh regeneration procedure is used for the first time in three dimensions

generation of oriented three dimensional delaunay grids suitable for the control volume integration method a fully automatic algorithm for three dimensional mesh generation is presented the algorithm preserves the robustness and time efficiency of the finite octree technique replacing octrees by more general 2 4 8 trees it is capable of generating oriented meshes in a post processing step meshes are transformed in order to satisfy the delaunay criterion and so that non overlapping closed control volumes can be defined for each mesh point through edge bisectors the method is shown to be appropriate for modelling semiconductor devices where the control volume scheme is the method of choice due to the peculiarities of the partial differential equations involved and where locally refined and oriented meshes are essential to describe the relevant internal physical quantities adequately while keeping the number of mesh points practical

fast adaptive finite element scheme for viscous incompressible flows this paper presents an adaptive finite element procedure for solving viscous incompressible flows the methodology is based on adaptive remeshing for the solution of the steady state navier stokes equations for an incompressible fluid solutions are obtained in primitive variables by an uzawa algorithm using a highly accurate element two error estimators are presented and compared for a problem with a known analytical solution the methodology is then applied to a problem of practical interest and predictions are compared with experimental measurements the proposed adaptive scheme is shown to lead to improved accuracy of the finite element predictions c e e h l n p q q 5 u u v x y 6 v a v v nomenclature constant velocity error error in the solution element size dissipation energy plate length number of elements in the mesh pressure pressure error test function for pressure error step and fence height velocity vector velocity components test function for velocity error coordinates element size predicted by adaptation module strain rate tension vi vu vf 7 relative error on a mesh similarity variable in a boundary layer absolute viscosity of the fluid kinematic viscosity of the fluid deviatoric stress sensor 2pe gradient operator

an automatic adaptive meshing technique for delaunay triangulations abstract a new algorithm is described for adaptivity of delaunay triangulations it distinguishes between regions of mesh according to whether they are to be refined unaltered or coarsened the method automatically identifies nodes of the mesh which are candidates for deletion for a region to be coarsened a node deletion process is proposed and it is proved that the resulting triangulation is delaunay after coarsening the mesh retains a high quality for two reasons the first is because a set of nodes have been used to obtain the coarse mesh which are equi distant apart in some sense defined by the original mesh the second is because the triangulation is delaunay the mesh refinement procedure sub divides elements into a number of similar elements in the regions to be refined two dimensional examples demonstrate the quality of the mesh after coarsening refinement

unsteady euler algorithm with unstructured dynamic mesh for complex aircraft aerodynamic analysis an euler solution algorithm is presented for unsteady aerodynamic analysis of complex aircr aft configurations the flow solver involves a multistage runge kutta time stepping scheme that uses a finite volume spatial discretization on an unstructured grid made up of tetrahedra a significant contribution of the research is the development and implementation of a moving mesh algorithm that is employed for problems involving static or dynamic deformation of the aircraft the mesh algorithm is a general procedure that can treat realistic motions and deformations of complex aircraft configurations steady and unsteady results are presented for a supersonic fighter configuration to demonstrate applications of the euler solver and dynamic mesh algorithm the unsteady flow results were obtained for the aircraft oscillating harmonically in a complete vehicle bending mode effects of angle of attack and reduced frequency on instantaneous pressures and force responses were investigated the paper presents descriptions of the euler solver and dynamic mesh algorithm along with results that assess the capability

unsteady flow simulation using unstructured meshes transient flows involving moving boundaries are more difficult to simulate as the geometry of the computational domain changes with time regardless of the changes occurring in the solution the mesh must be modified during the computation in order to accommodate the changes in the geometry although the literature on this subject describes a number of different approaches for handling this type of problem the approach followed in this paper is to use unstructured mesh methods we consider initially the simulation of inviscid two dimensional transient flows involving moving bodies employing an extension of adaptivity procedures which have been successfully used for steady state problems with the error estimation procedure coupled to an automatic triangular mesh generator this approach is extended to produce a three dimensional capability using tetrahedral meshes a number of examples are included to illustrate the numerical performance of these methods

incompressibility without tears how to avoid restrictions of mixed formulation the severe restrictions of the babuska brezzi stability criteria permit only a limited number of interpolations for velocities displacements and pressure to be used for incompressible behaviour these restrictions preclude the use of many useful elements we show in this paper how such difficulties can be side stepped by seeking the steady state solution through the use of various time marching schemes this permits a simple iterative approach to incompressible or nearly incompressible problems of fluid mechanics or solid mechanics and provides a stimulus for the use of such procedures in metal forming flow etc

a stabilized finite point method for analysis of fluid mechanics problems in this paper a meshless procedure termed the finite point method for solving convection diffusion and fluid flow type problems is presented the method is based on the use of a weighted least square interpolation procedure together with point collocation for evaluating the approximation integrals special emphasis is given to the stabilization of the convective terms and the neumann boundary condition which has been found to be essential to obtain accurate results some examples of application to diffusive and convective transport and compressible flow problems using quadratic fp interpolations are presented

quantum instantons with classical moduli spaces we introduce a quantum minkowski space time based on the quantum group su 2 q extended by a degree operator and formulate a quantum version of the anti self dual yang mills equation we construct solutions of the quantum equations using the classical adhm linear data and conjecture that up to gauge transformations our construction yields all the solutions we also find a deformation of penrose s twistor diagram giving a correspondence between the quantum minkowski space time and the classical projective space p 3

adaptive refinement coarsening scheme for three dimensional unstructured meshes the paper describes the development and application of an adaptive algorithm for tetrahedral grids an initial unstructured grid is adapted by employing local division as well as deletion of the tetrahedral cells the process is dynamic and the adapted grid changes follow evolution of the solution adaptation of the cells consists of normal division of a tetrahedron into eight subcells as well as directional division into two or four subcells a major issue of such adaptive grid algorithms is elimination of hanging nodes that appear on the edges in the interface between the embedded and unembedded zones a novel technique has been developed for treatment of such interface cells that can be applied to eliminate any possible hanging node configuration in a simple way a special data structure based on octrees has been developed which is flexible to handle all different types of cell division deletion application cases include a moving source as well as transonic flow around the onera m6 wing

adaptive mesh generation for fluid mechanics problems in this study we give an in depth investigation of the adaptive procedures for compressible and incompressible flow problems many tests have been carried out with different error indicators for different problems these refinement procedures show that the interpolation error indicators are adequate to predict an accurate solution comparison between the gradient and curvature based error indicators show that the former yields better performance in most situations however we found that the latter indicators predict better motion in the recirculatory and unstable regions than the gradient based method many test cases have been presented for both compressible and incompressible flow problems in the later part of the paper we suggest a simple way of combining the curvature gradient indicators of different key variables and present an appropriate problem where it is applicable a wide coverage of relevant literature has also been presented in this paper copyright 2000 john wiley sons ltd

adaptive remeshing for the k epsilon model of turbulence an adaptive nite element method for solving incompressible turbulentows using the k model of turbulence is presented solutions are obtained in primitive variables using a highly accurate quadratic nite element on unstructured grids turbulence is modeled using the k model of turbulence two error estimators are presented that take into account in a rigorous way the relative importance of the errors in velocity pressure turbulence variables and eddy viscosity the ef ciency and convergence rate of the methodology are evaluated by solving problemswith known analytical solutions themethod isthen applied to turbulent free shearowsand predictions are compared to measurements nomenclature cl c1 c2 k model constants e error f body force h element size k element in the mesh k turbulent kinetic energy n outward unit vector p u production of turbulence p pressure u velocity vector