singularities in anisotropic steady state heat conduction using a boundary element method in many heat conduction problems boundaries with sharp corners or abrupt changes in the boundary conditions give rise to singularities of various types which tend to slow down the rate of convergence with decreasing mesh size of any standard numerical method used for obtaining the solution in this paper it is shown how this difficulty may be overcome in the case of an anisotropic medium by a modified boundary element method the standard boundary element method is modified to take account of the form of the singularity without appreciably increasing the amount of computation involved two test examples the first with a singularity caused by an abrupt change in a boundary condition and the second with a singularity caused by a sharp re entrant corner are investigated and numerical results are presented copyright 2002 john wiley sons ltd

robust computational algorithms for dynamic interface tracking in three dimensions front tracking provides sharp resolution of wave fronts through the active tracking of interfaces between distinct materials a major challenge to this method is to handle changes in the interface topology we describe two algorithms implemented in the front tracking code frontier to model dynamic changes in three dimensional interfaces the two methods can be combined to give a hybrid method that is superior to each individual method the success of these algorithms is shown by simulations of rayleigh taylor instability which is an interfacial instability driven by an acceleration directed across a material interface our numerical results are validated by comparing the numerical computation of the velocity of a single rising bubble with an analytic model for the bubble velocity

a viscosity solutions approach to shape from shading the problem of recovering a lambertian surface from a single two dimensional image may be written as a first order nonlinear equation which presents the disadvantage of having several continuous and even smooth solutions a new approach based on hamilton jacobi bellman equations and viscosity solutions theories enables one to study non uniqueness phenomenon and thus to characterize the surface among the various solutions a consistent and monotone scheme approximating the surface is constructed thanks to the dynamic programming principle and numerical results are presented

solution adaptive cartesian cell approach for viscous and inviscid flows a cartesian cell based approach for adaptively refined solutions of the euler and navier stokes equations in two dimensions is presented grids about geometrically complicated bodies are generated automatically by the recursive subdivision of a single cartesian cell encompassing the entire flow domain where the resulting cells intersect bodies polygonal cut cells are created using modified polygon clipping algorithms the grid is stored in a binary tree data structure that provides a natural means of obtaining cell to cell connectivity and of carrying out solution adaptive mesh refinement the euler and navier stokes equations are solved on the resulting grids using a finite volume formulation the convective terms are up winded a linear reconstruction of the primitive variables is performed providing input states to an approximate riemann solver for computing the fluxes between neighboring cells the results of a study comparing the accuracy and positivity of two classes of cell centered viscous gradient reconstruction procedures is briefly summarized adaptively refined solutions of the navier stokes equations are shown using the more robust of these gradient reconstruction procedures where the results computed by the cartesian approach are compared to theory experiment and other accepted computational results for a series of low and moderate reynolds number flows

eikonal equation based front propagation for arbitrary complex configurations this paper presents a front propagation method using the eikonal equation 1 in which represents the smallest euclidean distance field to the front to be propagated the offset capturing approach consists in first calculating the field over a uniform cartesian grid fully covering the front to be propagated and then constructing the iso curves or surfaces as the propagated result the calculation of uses a 3d numerical scheme the fast sweeping scheme validation for accuracy of the method is presented using academic test cases a real 3d industry application draft tube with two piers is successfully propagated and demonstrated using special boundary conditions to cope with inlet and outlet planes during front propagtion this application involves the propagation of a front that exhibits both concave and convex shape regions sharp corners and local tangent plane surface discontinuities as well as a multi connected domain copyright 2007 john wiley sons ltd

on absence and existence of the anomalous localized resonance without the quasi static approximation this paper considers transmission problems for the helmholtz equation with bodies that have negative material parameters such material parameters are used to model metals on optical frequencies and so called metamaterials as the absorption of the materials in the model tends to zero the fields may blow up when the speed of the blow up is suitable this is called the anomalous localized resonance alr in this paper we study this phenomenon and formulate a new condition the weak anomalous resonance w ar where the speed of the blow up of fields may be slower using this concept we can study the blow up of fields in the presence of negative material parameters without the commonly used quasi static approximation we give simple geometric conditions under which w ar or alr may or may not appear in particular we show that in a case of a curved layer of negative material with a strictly convex boundary neither alr nor w ar appears with nonzero frequencies i e in the dynamic range in dimensions

the method of fundamental solutions and condition number analysis for inverse problems of laplace equation this paper investigates the applications of the method of fundamental solutions together with the conditional number analysis to solve various inverse 2d laplace problems involving under specified and or over specified boundary conditions through the method of fundamental solutions and the condition number analysis it is numerically found that solutions of inverse laplace problems can be obtained without iteration or regularization for small noise levels since the method of fundamental solutions is a boundary type meshless numerical method that can automatically satisfy the governing equation however for larger values of noise levels regularization is still necessary to obtain promising result the present paper mainly focuses on the two types of numerical predictions of inverse 2d laplace problems 1 cauchy problem and 2 shape identification problem good quantitative agreement with the analytical solutions and other numerical methods for small perturbed boundary data is observed by using present meshless numerical scheme

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

hybrid prismatic tetrahedral grid generation for viscous flow applications a method for the automatic generation of unstructured grids composed of tetrahedra and prisms is proposed the prismatic semistructured grid is generated around viscous boundary surfaces and covers viscous regions whereas the tetrahedral grid covers the rest of the computational domain the delaunay approach for tetrahedral grid generation is used the proposed prismatic grid is structured in directions normal to the boundary faces but the number of prisms generated from one boundary face is variable from face to face unlike conventional prismatic grid generators this technique works well even in regions of cavities and gaps the delaunay background grid generated for surface nodes serves as an efficient data structure to check possible intersections of prisms particular attention is given to the boundary constraining problem a robust algorithm for the boundary recovery by edge swapping followed by a direct subdivision of tetrahedra is used grid examples for internal and external flow problems of complex shapes demonstrate the efficiency of the method

unstructured viscous grid generation by the advancing layers method a new method of generating unstructured triangular tetrahedral grids with high aspect ratio cells is proposed the method is based on new grid marching strategy referred to as advancing layers for construction of highly stretched cells in the boundary layer and the conventional advancing front technique for generation of regular equilateral cells in the inviscid flow region unlike the existing semi structured viscous grid generation techniques the new procedure relies on a totally unstructured advancing front grid strategy resulting in a substantially enhanced grid flexibility and efficiency the method is conceptually simple but powerful capable of producing high quality viscous grids for complex configurations with ease a number of two dimensional triangular grids are presented to demonstrate the methodology the basic elements of the method however have been primarily designed with three dimensional problems in mind making it extendible for tetrahedral viscous grid generation

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

unstructured mel modelling of nonlinear unsteady ship waves an unstructured mixed eulerian lagrangian model mel is described for the simulation of the nonlinear wave body interaction as opposed to the structured model used widely in this field in present model the free surface is interpolated accurately using a polynomial scheme coupled with the moving least squares method and is triangulated with a local interrogation method coupled with the advancing front method to provide a high quality mesh a new method is devised to update the free surface intersection with the body based on the desingularized boundary integral method double desingularized point sources are used for a control point at the intersection with one inside the body and the other above the free surface to satisfy both the body and free surface boundary conditions over there the desingularized point sources are positioned in terms of the element sizes as well as solid angles of the boundary surface so as to avoid possible overcrowding of the sources at the corners of the surface solid angles on the surface are computed analytically using the spherical triangle theory as an illustration the algorithm is used to simulate the wave generation for a wigley hull which impulsively starts to move at a constant speed on a calm water surface the anticipated kelvin ship wave pattern is well simulated the wave profiles along the hull agree well with the measured results of nobeless and mccarthy proceedings of the 2nd dtnsrdc workshop maryland 1983 pp 5 35 as compared to a structured approach the unstructured model reduces the cpu time and memory requirements and being robust in handling complex geometries is more versatile in practical applications

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

tetrahedral unstructured navier stokes method for turbulent flows a method is presented for solving the navier stokes equations for turbulent flow problems on three dimensional unstructured grids spatial discretization is accomplished by a cell centered finite volume formulation using an accurate linear reconstruction scheme and upwind flux differencing time is advanced by an implicit backward euler time stepping scheme flow turbulence effects are modeled by the spalart allmaras one equation model which is coupled with a wall function to reduce the number of cells in the sublayer region of the boundary layer a systematic assessment of the method is presented to devise guidelines for more strategic application of the technology to complex problems the assessment includes the accuracy in predictions of the skin friction coefficient law of the wall behavior and surface pressure for a flat plate turbulent boundary layer and for the onera m6 wing under a high reynolds number transonic separated flow condition

bounds on herglotz functions and fundamental limits of broadband passive quasistatic cloaking using a sum rule we derive new bounds on herglotz functions that generalize those given in bernland et al j phys a math theor 44 14 145205 2011 and gustafsson and sjoberg new j phys 12 4 043046 2010 these bounds apply to a wide class of linear passive systems such as electromagnetic passive materials among these bounds we describe the optimal ones and also discuss their meaning in various physical situations like in the case of a transparency window where we exhibit sharp bounds then we apply these bounds in the context of broadband passive cloaking in the quasistatic regime to refute the following challenging question is it possible to construct a passive cloaking device that cloaks an object over a whole frequency band our rigorous approach although limited to quasistatics gives quantitative limitations on the cloaking effect over a finite frequency range by providing inequalities on the polarizability tensor associated with the cloaking device we emphasize that our resul

hybrid prismatic tetrahedral grid generation for viscous flows around complex geometries a method for the generation of hybrid prismatic tetrahedral grids is described for complex three dimensional geometries including multibody domains and employed for viscous flows around an aircraft the prisms cover the region close to each body s surface while tetrahedra are created elsewhere a special method is presented that allows the generation of single block nonoverlapping prismatic meshes even in complex geometries that contain narrow gaps and cavities examples of cases treated by this method include wing engine configurations as well as multi element wings the second development is a combined octree advancing front method for the generation of the tetrahedra of the hybrid mesh the main feature of this octree based tetrahedra generator is that it does not require the creation of a background mesh by the user for the determination of the grid spacing and stretching parameters these are determined via an automatically generated octree the hybrid grid generator is robust geometry independent and requires no user intervention the suitability of hybrid meshes for capturing viscous flow phenomena is demonstrated by simulation of viscous flows around a high speed civil transport type of aircraft configuration reduction in computer resources has been substantial allowing flow simulations to be performed on workstations rather than supercomputers

the boundary element solution of the cauchy steady heat conduction problem in an anisotropic medium in this paper the iterative algorithm proposed by kozlov et al for the cauchy problem for the laplace equation is extended in order to solve the cauchy steady state heat conduction problem in an anisotropic medium the iterative algorithm is numerically implemented using the boundary element method bem the convergence and the stability of the numerical method as well as various types of accuracy convergence and stopping criteria are investigated the numerical results obtained confirm that provided an appropriate stopping regularization criterion is imposed then the iterative bem produces a convergent and stable numerical solution with respect to increasing the number of boundary elements and decreasing the amount of noise added into the input data an efficient stopping regularization criterion to cease the iterative process is proposed and the rate of convergence of the algorithm is improved by using various relaxation procedures between iterations a new concept of a variable relaxation factor is proposed analytical formulae for the coefficients of the matrices resulting from the direct application of the bem in an anisotropic medium are also presented copyright 2000 john wiley sons ltd

the method of fundamental solutions for inverse boundary value problems associated with the steady state heat conduction in anisotropic media in this paper the method of fundamental solutions is applied to solve some inverse boundary value problems associated with the steady state heat conduction in an anisotropic medium since the resulting matrix equation is severely ill conditioned a regularized solution is obtained by employing the truncated singular value decomposition while the optimal regularization parameter is chosen according to the l curve criterion numerical results are presented for both two and three dimensional problems as well as exact and noisy data the convergence and stability of the proposed numerical scheme with respect to increasing the number of source points and the distance between the fictitious and physical boundaries and decreasing the amount of noise added into the input data respectively are analysed a sensitivity analysis with respect to the measure of the accessible part of the boundary and the distance between the internal measurement points and the boundary is also performed the numerical results obtained show that the proposed numerical method is accurate convergent stable and computationally efficient and hence it could be considered as a competitive alternative to existing methods for solving inverse problems in anisotropic steady state heat conduction copyright 2005 john wiley sons ltd

variational principles for complex conductivity viscoelasticity and similar problems in media with complex moduli linear processes in media with dissipation arising in conductivity optics viscoelasticity etc are considered time periodic fields in such media are described by linear differential equations for complex valued potentials the properties of the media are characterized by complex valued tensors for example by complex conductivity or complex elasticity tensors variational formulations are suggested for such problems the functionals whose euler equations coincide with the original ones are constructed four equivalent variational principles are obtained two minimax and two minimal ones the functionals of the obtained minimal variational principles are proportional to the energy dissipation averaged over the period of oscillation the last principles can be used in the homogenization theory to obtain the bounds on the effective properties of composite materials with complex valued properties tensors

limiting absorption principle and well posedness for the time harmonic maxwell equations with anisotropic sign changing coefficients we study the limiting absorption principle and the well posedness of maxwell equations with anisotropic sign changing coefficients in the time harmonic domain the starting point of the analysis is to obtain cauchy problems associated with two maxwell systems using a change of variables we then derive a priori estimates for these cauchy problems using two different approaches the fourier approach involves the complementing conditions for the cauchy problems associated with two elliptic equations which were studied in a general setting by agmon douglis and nirenberg the variational approach explores the variational structure of the cauchy problems of the maxwell equations as a result we obtain general conditions on the coefficients for which the limiting absorption principle and the well posedness hold moreover these new conditions are of a local character and easy to check our work is motivated by and provides general sufficient criteria for the stability of electromagnetic fields in the context of negative index metamaterials

efficient unstructured mesh generation by means of delaunay triangulation and bowyer watson algorithm this work is devoted to the description of an efficient unstructured mesh generation method entirely based on the delaunay triangulation the distinctive characteristic of the proposed method is that point positions and connections are computed simultaneously this result is achieved by taking advantage of the sequential way in which the bowyer watson algorithm computes the delaunay triangulation two methods are proposed which have great geometrical flexibility in that they allow us to treat domains of arbitrary shape and topology and to generate arbitrarily nonuniform meshes the methods are computationally efficient and are applicable both in two and three dimensions

global dense multiscale reconstruction for a billion points we present a variational approach for surface reconstruction from a set of oriented points with scale information we focus particularly on scenarios with nonuniform point densities due to images taken from different distances in contrast to previous methods we integrate the scale information in the objective and globally optimize the signed distance function of the surface on a balanced octree grid we use a finite element discretization on the dual structure of the octree minimizing the number of variables the tetrahedral mesh is generated efficiently with a lookup table which allows to map octree cells to the nodes of the finite elements we optimize memory efficiency by data aggregation such that robust data terms can be used even on very large scenes the surface normals are explicitly optimized and used for surface extraction to improve the reconstruction at edges and corners

influence of impingement edge geometry on cavity flow oscillations and back portion of the airfoil is shown in figs 2b and 2c respectively the smooth transition of the grid from one type to another and the decency of the grid at sharp corners and between close surfaces are clearly shown which indicate excellent compatibility and communication between the two grid strategies as controlled by a common background grid the grid was generated using a silicon graphics iris 4d 210 vox workstation the code s performance is about 360 triangles s on that workstation and 2350 triangles s on a cray y mp the total turnaround time required for generating a grid around a complex geometry including the setup time is about 1 h to examine the fidelity of the grids generated with the present method a turbulent viscous flow computation was performed on the grid shown in fig 2 the flow solution was obtained with an available node based upwind flow solver8 using the baldwinearth turbulence model at a mach number of 0 2 an angle of attack of 16 2 deg and a reynolds number of 9 x 106 comparisons for surface pressure distributions and velocity profiles are shown in figs 3a and 3b respectively excellent agreement with experimental data confirms the viability of the generated grid concluding remarks a new method of unstructured viscous grid generation has been introduced the approach is conceptually simple but powerful and capable of producing high quality viscous unstructured grids for complex configurations with ease being based on a totally unstructured grid strategy the method is fully automatic and flexible and thus alleviates the difficulties stemming from the structural limitations of the existing structured or semi unstruct ured techniques because of an efficient grid marching strategy and a simple front detection algorithm the method is highly efficient and operational on small workstations the method is also self sufficient for insertion of grid points in the boundary layer and beyond the method has been applied to two dimensional problems with satisfactory results the basic elements of the technique however have been primarily designed for its subsequent extension for generating three dimensional highly stretched tetrahedral grids which is currently in progress the full benefit of the method will be realized for generation of three dimensi onal viscous grids where the complexity of the problem becomes excessive

a variational perspective on cloaking by anomalous localized resonance a body of literature has developed concerning cloaking by anomalous localized resonance the mathematical heart of the matter involves the behavior of a divergence form elliptic equation in the plane rm div a x rm grad u x f x the complex valued coefficient has a matrix shell core geometry with real part equal to 1 in the matrix and the core and 1 in the shell one is interested in understanding the resonant behavior of the solution as the imaginary part of a x decreases to zero so that ellipticity is lost most analytical work in this area has relied on separation of variables and has therefore been restricted to radial geometries we introduce a new approach based on a pair of dual variational principles and apply it to some non radial examples in our examples as in the radial setting the spatial location of the source f plays a crucial role in determining whether or not resonance occurs

cloaking due to anomalous localized resonance in plasmonic structures of confocal ellipses if a core of dielectric material is coated by a plasmonic structure of negative dielectric material with nonzero loss parameter then anomalous localized resonance may occur as the loss parameter tends to zero and the source outside the structure can be cloaked in this paper we consider cloaking by anomalous localized resonance calr on structures where the core and the shell are confocal ellipses for such structures we compute the critical elliptic radii such that for any source inside it calr takes place and for any source outside it calr does not take place the method of this paper uses the spectral analysis of the neumann poincare type operator associated with two interfaces the boundaries of the core and the shell which was developed in h ammari g ciraolo h kang h lee and g w milton arch ration mech anal 208 2013 pp 667 692

a fast sweeping method for eikonal equations in this paper a fast sweeping method for computing the numerical solution of eikonal equations on a rectangular grid is presented the method is an iterative method which uses upwind difference for discretization and uses gauss seidel iterations with alternating sweeping ordering to solve the discretized system the crucial idea is that each sweeping ordering follows a family of characteristics of the corresponding eikonal equation in a certain direction simultaneously the method has an optimal complexity of o n for n grid points and is extremely simple to implement in any number of dimensions monotonicity and stability properties of the fast sweeping algorithm are proven convergence and error estimates of the algorithm for computing the distance function is studied in detail it is shown that 2 n gauss seidel iterations is enough for the distance function in n dimensions an estimation of the number of iterations for general eikonal equations is also studied numerical examples are used to verify the analysis

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

intergrid boundary definition method for overset unstructured grid approach the use of the overset concept for the unstructured grid method is relatively unexplored however the overset approach can extend the applicability of the unstructured grid method for real engineering problems without much need for code development the multiple moving body problem is one of those applications improvement in local resolution for euler navier stokes computations on unstructured grids is another use of the overset concept an efficient and robust algorithm to localize the intergrid boundaries for the overset unstructured grid method is proposed simplicity and automation in the intergrid boundary definition are realized using the wall distance as a basic parameter the neighbor to neighbor jump search algorithm is efficiently utilized in the method the robustness and efficiency of the search is improved by the use of subsidiary grids that are generated as a byproduct of the delaunay triangulation method the basic procedure of the present method is described for a multielement airfoil problem the effects of the overset method on the solution accuracy and the convergence are tested by onera m6 wing

quality estimates and stretched meshes based on delaunay triangulations any other vertex is exploited for the automation of the grid generation process moreover delaunay grids have many interesting properties an extensive documentation of which can be found in ref 10 in the following we will first describe the different elements of frod the derivation of the background mesh as well as the vertex generation for the viscous and inviscid regions the latter half of this paper presents the quality measures that can be derived for the isotropic vertex generation part

geometry parameterization method for multidisciplinary applications a technique is described for parameterizing geometries in a manner suitable for numerical simulations used in design optimization the new methodology referred to as control grids is flexible easy to use extendable and applicable to multidisciplinary design optimization although significantly different than free form deformation the present method provides many similar capabilities comparisons between the current technique and free form deformation are provided to highlight the advantages and disadvantages of each method the new parameterization technology is described and demonstrated in both two and three dimensions for single and multidisciplinary applications

fast sweeping methods for eikonal equations on triangular meshes the original fast sweeping method which is an efficient iterative method for stationary hamilton jacobi equations relies on natural ordering provided by a rectangular mesh we propose novel ordering strategies so that the fast sweeping method can be extended efficiently and easily to any unstructured mesh to that end we introduce multiple reference points and order all the nodes according to their l p metrics to those reference points we show that these orderings satisfy the two most important properties underlying the fast sweeping method 1 these orderings can cover all directions of information propagating efficiently 2 any characteristic can be decomposed into a finite number of pieces and each piece can be covered by one of the orderings we prove the convergence of the new algorithm the computational complexity of the algorithm is nearly optimal in the sense that the total computational cost consists of o m flops for iteration steps and o m rm log m flops for sorting at the predetermined initialization step which can be efficiently optimized by adopting a linear time sorting method where m is the total number of mesh points extensive numerical examples demonstrate that the new algorithm converges in a finite number of iterations independent of mesh size

flow simulation using generalized static and dynamic grids a new approach is presented for a e ow simulation system using generalized grids in a generalized grid the physical domain of interest is decomposed into cells with an arbitrary number of edges or faces the grid can be of structured unstructured or hanging node type or an arbitrary combination of the types a cell face based data structure is used to storethegrid information a e ow simulation system is developed forgeneralized gridsthat can handle static and dynamic grids the full navier stokes equations in the integral form are taken as the relations that govern the e uid e ow a cell centered e nite volume scheme is developed for solving these governing equations the numerical e ux across the cell faces is evaluated by an upwind scheme based on roe s approximate riemann solver a higher order scheme is formulated by utilizing taylor s series expansion and green s theorem limiter functions are used to preserve monotonocity the skin friction coefe cient is used to evaluate the accuracy of the limiterfunctions thegeneralized minimalresidualmethod isutilized tosolvethesparselinearsystem ofequations resulting from thelinearization of the e ux vectors thespalart allmaras one equation turbulence model has been implemented for the generalized grids and is used to evaluate the turbulent viscosity for dynamically moving bodies the equations of classical mechanics are used to predict the trajectory based on the external aerodynamic and body forces a variety of computational examples are presented to demonstratethe wide rangeof applications and the results are compared with experimental data whenever available

shape reconstruction and volume meshing for complex solids the reconstruction of a solid surface from a series of cross sections and the generation of a volume mesh that conforms with a prescribed surface are issues that arise in numerous applications we describe an approach to both these problems that is based on the generation of a tetrahedral mesh which automatically captures a triangulation of the surface points a simple algorithm for introducing a set of interior points permits a simple partition of the volume mesh into two disjoint sets of tetrahedra such that one set determines the interior of the solid while the second determines the exterior

an entropy satisfying boundary layer surface mesh generation a method is presented to generate surface boundary layers the novelty of the method consists in a uniform treatment of the concave and convex regions based on offsetting the initial front in particular concave situations are enforced to respect the entropy satisfying solution local solutions of the offset of edges in the planes and triangles in the three dimensional space are also given showing the relationship between normal computation distance extrusion and the generalized voronoi diagram the boundary layer mesh generation is cast as a weak solution of the eikonal equation computed locally layer by layer to mimic the hyperbolic character of the eikonal equation augmented by a possibly nonbijective mapping between layers this provides a theoretical framework to rely on for practical answers such as configurations where the adjacent topologies to a boundary layer may be curved or at least not aligned with the offset direction or if the boundary layer mesh must be generated as a mapping betw

analysis of plasmon resonance on smooth domains using spectral properties of the neumann poincare operator abstract we investigate in a quantitative way the plasmon resonance at eigenvalues and the essential spectrum the accumulation point of eigenvalues of the neumann poincare operator on smooth domains we first extend the symmetrization principle so that the single layer potential becomes a unitary operator from h 1 2 onto h 1 2 we then show that the resonance at the essential spectrum is weaker than that at eigenvalues it is shown that anomalous localized resonance occurs at the essential spectrum on ellipses and cloaking due to anomalous localized resonance does occur on ellipses like on the core shell structure considered in 19 it is shown that cloaking due to anomalous localized resonance does not occur at the essential spectrum on three dimensional balls

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

implicit method for the computation of unsteady flows on unstructured grids an implicit method for the computation of unsteady flows on unstructured grids is presented following a finite difference approximation for the time derivative the resulting nonlinear system of equations is solved at each time step by using an agglomeration multigrid procedure the method allows for arbitrarily large time steps and is efficient in terms of computational effort and storage inviscid and viscous unsteady flows are computed to validate the procedure the issue of the mass matrix which arises with vertex centered finite volume schemes is addressed the present formulation allows the mass matrix to be inverted indirectly a mesh point movement and reconnection procedure is described that allows the grids to evolve with the motion of bodies as an example of flow over bodies in relative motion flow over a multi element airfoil system undergoing deployment is computed

high order discontinuous galerkin method for computation of turbulent flows this paper presents a high order discontinuous galerkin method for computation of compressible turbulent flows in three space dimensions a modified spalart and allmaras turbulence model is implemented and discretized to the same order of accuracy as that for the reynolds averaged navier stokes equations the creation of curvilinear meshes for arbitrary three dimensional configurations is achieved through the aid of a computational analysis programming interface which enables direct communications with the computer aided design module to determine the true positions of surface quadrature points for high order geometric representations a modified linear elasticity approach is used sequentially and is of crucial importance for reshaping the interior mesh to allow high aspect ratio curved elements in turbulent boundary layers requirements of the mesh parameters including the wall spacing and viscous stretching factor are studied and it is concluded that for attached turbulent flows the conventional s

simulation of flows with strong shocks with an adaptive conservative scheme in the present work numerical simulations of unsteady flows with moving shocks are presented an unsteady mesh adaptation method based on error equidistribution criteria is adopted to capture the most important flow features the modifications to the topology of the grid are locally interpreted in terms of continuous deformation of the finite volumes built around the nodes the arbitrary lagrangian eulerian formulation of the euler equations is then applied to compute the flow variable over the new grid without resorting to any explicit interpolation step the numerical results show an increase in the accuracy of the solution together with a strong reduction of the computational costs with respect to computations with a uniform grid using a larger number of nodes

simulation of vortex breakdown using adaptive grid refinement with vortex center identification a topological feature adaptation method is proposed to compute vortical flows around a delta wing at high incidence vortex center identification based on the locally applied critical point method is utilized as an indicator of the grid refinement using rivara s bisection algorithm the three dimensional navier stokes equations are solved using the hybrid unstructured grid the computed results show that the refinement at the vortex core is effective to improve the numerical accuracy of the flow around a delta wing the present feature adaptive refinement is especially effective to improve the prediction of the vortex breakdown positions at high incidence

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

surface mesh generation by means of steiner triangulations a method is presented for the efficient and automatic generation of unstructured grids on surfaces the overall procedure uses a steiner triangulation where sites are added in arbitrary order and hence the tracking of fronts is not needed in the algorithm the connectivity of the new points is initially generated by direct subdivision and further improved by using local reconnection the lawson s method is used to obtain a delaunay tessellation but other reconnection criteria may be used with minor modifications e g minimise the maximum angle the mesh generation procedure uses an approximate physical space grid to define the surface during the grid generation process at the end the mapped space coordinates are transformed back to the actual surface the field point distribution is controlled by an element size function obtained from the solution of a laplace equation whose boundary conditions are derived from the boundary node information additional control is possible by prescribing dummy boundaries the combination of grid smoothing and the elimination of nodes of degree 3 4 pairs of nodes of degree 5 and nodes of degree higher than 7 as a postprocessing step has proved to be an efficient tool to improve the grid quality results are presented which demonstrate that high quality unstructured grids can be efficiently generated on surfaces using the present method

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

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

curvature flow and entropy conditions applied to grid generation we describe a numerical technique to generate logically rectangular body fitted interior and exterior grids the technique is based on solving a hamilton jacobi type equation for a propagating level set function using techniques borrowed from hyperbolic conservation laws coordinate grid lines are kept smooth through curvature terms which regularize the equation of motion and upwind difference schemes which satisfy the correct entropy conditions of front propagation the resulting algorithm can be used to generate two and three dimensional interior and exterior grids around reasonably complex bodies which may contain sharp corners and significant variations in curvature the technique may also be easily extended to problems of boundary fitted moving grids

octree advancing front method for generation of unstructured surface and volume meshes amethodisdescribedforthegeneration ofunstructuredgridsforcomplexthree dimensionalgeometriesincluding multibodydomains acombinedoctree advancing frontmethod ispresentedforgenerationoftheunstructured surface mesh as well as the tetrahedral volume mesh the unique feature of this generator is that a special octree provides the local length scales of the mesh which can vary signi cantly this octree is automatically created and eliminates the need for a user constructed background mesh to determine the grid spacing and stretching parameters the grid generator isrobust isgeometry independent and requires minimal userinteraction a techniqueis also presented for generation of anisotropic surface meshes that result in a signi cant reduction in the number of triangular faces automatic local remeshing is also employed to improve the quality of the tetrahedral mesh the geometry independence of the octree advancing front method is demonstrated through both surface and volume

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

spectral resolution of the neumann poincare operator on intersecting disks and analysis of plasmon resonance the purpose of this paper is to investigate the spectral nature of the neumann poincare operator on the intersecting disks which is a domain with the lipschitz boundary the complete spectral resolution of the operator is derived which shows in particular that it admits only the absolutely continuous spectrum no singularly continuous spectrum and no pure point spectrum we then quantitatively analyze using the spectral resolution the plasmon resonance at the absolutely continuous spectrum

structured background grids for generation of unstructured grids by advancing front method a new method of background grid construction is introduced for generation of unstructured grids using the advancing front technique unlike the conventional triangular tetrahedral background grids that are difficult to construct and usually inadequate in performance the new method exploits the simplicity of uniform cartesian meshes and the superiority of the elliptic grid point distribution for unstructured grid generation the approach is analogous to solving a steady state heat conduction problem with discrete heat sources the spacing parameters of grid points are distributed over the nodes of a cartesian background grid by solving a poisson equation to increase the control over the grid point distribution a directional clustering approach is developed the new method is convenient to use and provides better grid quality and flexibility some sample two dimensional results are presented to demonstrate the power of the method

reordering of hybrid unstructured grids for lower upper symmetric gauss seidel computations this note is devoted to the three dimensional hybrid grid implementation of the lu sgs method the original method was based on sweeps through grid node numbers and was applied to two dimensional euler computations unfortunately in its original formulation the method cannot be vectorized in addition the method is not compatible with commonly used edge based data structure to fit the method to the three dimensional computations on a vector supercomputer grid reordering is necessary it was applied to the cell centered finite volume method

markov chain approximations for deterministic control problems with affine dynamics and quadratic cost in the control we consider the construction of markov chain approximations for an important class of deterministic control problems the emphasis is on the construction of schemes that can be easily implemented and which possess a number of highly desirable qualitative properties the class of problems covered is that for which the control is affine in the dynamics and with quadratic running cost this class covers a number of interesting areas of application including problems that arise in large deviations risk sensitive and robust control robust filtering and certain problems in computer vision examples are given as well as a proof of convergence

a versatile sharp interface immersed boundary method for incompressible flows with complex boundaries a sharp interface immersed boundary method for simulating incompressible viscous flow past three dimensional immersed bodies is described the method employs a multi dimensional ghost cell methodology to satisfy the boundary conditions on the immersed boundary and the method is designed to handle highly complex three dimensional stationary moving and or deforming bodies the complex immersed surfaces are represented by grids consisting of unstructured triangular elements while the flow is computed on non uniform cartesian grids the paper describes the salient features of the methodology with special emphasis on the immersed boundary treatment for stationary and moving boundaries simulations of a number of canonical two and three dimensional flows are used to verify the accuracy and fidelity of the solver over a range of reynolds numbers flow past suddenly accelerated bodies are used to validate the solver for moving boundary problems finally two cases inspired from biology with highly complex three dimensional bodies are simulated in order to demonstrate the versatility of the method

an advancing front delaunay triangulation algorithm designed for robustness abstract a new algorithm is described for generating an unstructured mesh about an arbitrary two dimensional configuration mesh points are generated automatically by the algorithm in a manner which ensures a smooth variation of elements and the resulting triangulation constitutes the delaunay triangulation of these points the algorithm combines the mathematical elegance and efficiency of delaunay triangulation algorithms with the desirable point placement features boundary integrity and robustness that are traditionally associated with advancing front type mesh generation strategies the method offers increased robustness over previous algorithms in that it cannot fail regardless of the initial boundary point distribution and the prescribed cell size distribution throughout the flow field

a folding unfolding algorithm for the construction of semi structured layers in hybrid grid generation abstract a method is presented for generating semi structured layers in hybrid grids suitable for high reynolds number flow simulations it can produce superior quality grids around convex and concave ridges of the domain compared to a standard prismatic or advancing layers generator in a first step hybrid quadrilateral triangular grids are employed to cluster the surface grid towards sharp corners and ridges starting from this surface grid as an initial front for the volume grid generation a prismatic and hexahedral layers generation technique is used containing degenerate faces to add or remove elements in convex or concave areas of the geometry respectively the method can automatically create structured like grids in concave gaps and better discretize the space around convex ridges to improve overall accuracy the final grid remains conforming to not complicate the solver and post processing requirements several examples illustrate the application of the method

numerical solution of the cauchy problem for steady state heat transfer in two dimensional functionally graded materials the application of the method of fundamental solutions to the cauchy problem for steady state heat conduction in two dimensional functionally graded materials fgms is investigated the resulting system of linear algebraic equations is ill conditioned and therefore regularization is required in order to solve this system of equations in a stable manner this is achieved by employing the zeroth order tikhonov functional while the choice of the regularization parameter is based on the l curve method numerical results are presented for both smooth and piecewise smooth geometries the convergence and the stability of the method with respect to increasing the number of source points and the distance between the source points and the boundary of the solution domain and decreasing the amount of noise added into the input data respectively are analysed

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