extension of finite volume compressible flow solvers to multi dimensional variable density zero mach number flows when attempting to compute unsteady variable density flows at very small or zero mach number using a standard finite volume compressible flow solver one faces at least the following difficulties i spatial pressure variations vanish as the mach numberm

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

three dimensional front tracking we describe a three dimensional front tracking algorithm discuss its numerical implementation and present studies to validate the correctness of this approach based on the results of the two dimensional computations we expect three dimensional front tracking to significantly improve computational efficiencies for problems dominated by discontinuities in some cases for which the interface computations display considerable numerical sensitivity we expect a greatly enhanced capability

moment of fluid interface reconstruction method in multi material arbitrary lagrangian eulerian mmale algorithms a new lagrangian interface evolution method to use in a multi material ale mmale algorithm is proposed the input data set for the method consists of the volume fractions after the lagrangian step and the orientation position of the interfaces before this step in the present work the moment of fluid mof method is used at the end of the ale cycle to provide required interface information for this method compared to traditional reconstruction methods in addition to the volume fractions the proposed method incorporates the configuration of the interfaces in the calculations the effect of compressibility is also considered in prioritizing the materials the capability of the method is assessed by testing its potential to track interfaces through large topology change in the domains which contain two or more materials numerical results for these tough test problems provide enough evidence for the accuracy and robustness of the proposed method

a robust and efficient polyhedron subdivision and intersection algorithm for three dimensional mmale remapping the multi material arbitrary lagrangian eulerian mmale method is an effective way to simulate the multi material flow with severe surface deformation comparing with the traditional arbitrary lagrangian eulerian ale method the mmale method allows for multiple materials in a single cell which overcomes the difficulties in grid refinement process in recent decades many researches have been conducted for the lagrangian rezoning and surface reconstruction phases but less attention has been paid to the multi material remapping phase especially for the three dimensional problems due to two complex geometric problems the polyhedron subdivision and the polyhedron intersection in this paper we propose a clipping and projecting algorithm for polyhedron intersection whose basic idea comes from the commonly used method by grandy 1999 29 and jia et al 2013 34 our new algorithm solves the geometric problem by an incremental modification of the topology based on segmentplane intersections a comparison with jia et al 2013 34 shows our new method improves the efficiency by 55 to 65 when calculating polyhedron intersections moreover the instability caused by the geometric degeneracy can be thoroughly avoided because the geometry integrity is preserved in the new algorithm we also focus on the polyhedron subdivision process and describe an algorithm which could automatically and precisely tackle the various situations including convex non convex and multiple subdivisions numerical studies indicate that by using our polyhedron subdivision and intersection algorithm the volume conversation of the remapping phase can be exactly preserved in the mmale simulation

the discrete duality finite volume method for stokes equations on three dimensional polyhedral meshes we develop a discrete duality finite volume method for the three dimensional steady stokes problem with a variable viscosity coefficient on polyhedral meshes under very general assumptions on the mesh which may admit nonconforming polyhedrons we prove the stability and well posedness of the scheme we also prove the convergence of the numerical approximation to the velocity velocity gradient and pressure and derive a priori estimates for the corresponding approximation error final numerical experiments confirm the theoretical predictions

solution adaptive grid strategies based on point redistribution solution adaptive grid strategies based on the redistribution of a fixed number of points are described in this paper the redistribution is performed using weight functions that vary based on significant flow features the weight functions are evaluated using an equidistribution principle in this paper emphasis is placed on the development of weight functions applicable to compressible flows exhibiting large scale separated vortical flows vortex vortex and vortex surface interactions separated shear layers and multiple shocks of diaerent intensities algebraic elliptic and parabolic methods of grid generation have been utilized for structured grid redistribution additionally a point movement scheme is presented for generalized structured unstructured hybrid grid adaptation computer aided geometry design cagd techniques are combined with redistribution schemes to maintain the fidelity of solid boundaries in particular solid boundaries are represented using non uniform rational b splines nurbs a grid generation software system parallel multiblock adaptive grid generation pmag using an elliptic redistribution scheme is also described with emphasis placed on the parallel implementation for multiblock structured grids with unstructured blocking topologies and on interpolation issues computational examples demonstrating the influence of diaerent weight functions and grid redistribution strategies are presented 2000 elsevier science s a all rights reserved

an hybrid finite volume finite element method for variable density incompressible flows this paper is devoted to the numerical simulation of variable density incompressible flows modeled by the navier stokes system we introduce an hybrid scheme which combines a finite volume approach for treating the mass conservation equation and a finite element method to deal with the momentum equation and the divergence free constraint the breakthrough relies on the definition of a suitable footbridge between the two methods through the design of compatibility condition in turn the method is very flexible and allows to deal with unstructured meshes several numerical tests are performed to show the scheme capabilities in particular the viscous rayleigh taylor instability evolution is carefully investigated

a general non iterative riemann solver for godunov s method abstract godunov s method is characterized by the use of a riemann problem solution to resolve discontinuities at the interface between cells the major drawback of this method is the difficulty and the high cost of solving the nonlinear riemann problem exactly especially for materials with complex equations of state this paper describes a simplified and noniterative approximate riemann solver which is characterized by only two material dependent parameters for a given material these parameters are the local speed of sound and a parameter which is directly related to the shock density ratio in the limit of strong shocks these parameters are conveniently obtained from a linear fit to the experimental data for the shock hugoniot in various materials the approximate riemann solver retains the essential quadratic nonlinearity which enables it to deal with the whole range of cases from weak sound waves to strong shocks

artificial compressibility characteristics based schemes for variable density incompressible multispecies flows part ii multigrid implementation and numerical tests the paper presents an investigation of the accuracy and efficiency of artificial compressibility characteristics based cb schemes for variable density incompressible flows the cb schemes have been implemented in conjunction with a multigrid method for accelerating numerical convergence and a fourth order explicit runge kutta method for the integration of the governing equations in time the implementation of the cb schemes is obtained in conjunction with first second and third order interpolation formulas for calculating the variables at the cell faces of the computational volume the accuracy and efficiency of the schemes are examined against analytical and experimental results for diffusion broadening in two and three dimensional microfluidic channels a problem that has motivated the development of the present methods moreover unsteady inviscid simulations have been performed for variable density mixing layer the computations revealed that accuracy and efficiency depend on the cb scheme design the best multigrid convergence rates were exhibited by the conservative cb scheme which is obtained by the fully conservative formulation of the variable density incompressible equations

a critical analysis of rayleigh taylor growth rates abstract recent simulations of rayleigh taylor instability growth rates display considerable spread we provide evidence that differences in numerical dissipation effects mass diffusion and viscosity due to algorithmic differences and differences in simulation duration are the dominant factors that produce such different results within the simulation size and durations explored here we provide evidence that the principal discrepancies are due to numerical dispersion through comparison of simulations using different algorithms we present new 3d front tracking simulations that show tentative agreement with the range of reported experimental values we begin an exploration of new physical length scales that may characterize a transition to a new rayleigh taylor mixing regime

untangling of 2d meshes in ale simulations a procedure is presented to untangle unstructured 2d meshes containing inverted elements by node repositioning the inverted elements may result from node movement in arbitrary lagrangian eulerian ale simulations of continuum mechanics problems with large shear deformation such as fluid flow and metal forming meshes with inverted elements may also be created due to the limitations of mesh generation algorithms particularly for nonsimplicial mesh generation the untangling procedure uses a combination of direct node placement based on geometric computation of the feasible set and node repositioning driven by numerical optimization of an objective function that achieves its minimum on a valid mesh it is shown that a combination of the feasible set based method and the optimization method achieves the best results in untangling complex 2d meshes preliminary results are also presented for untangling of 3d unstructured meshes by the same approach

structured mesh adaption space accuracy and interpolation methods abstract in this paper we review the main stages of the construction of a variational method to optimize and to adapt two and three dimensional structured grids the formalism and the notation presented enable a constructive and comprehensive description of the adaption process the major part of this paper is devoted to the study of various interpolation methods which are used for the correct space localization of the adaption for cell center cell vertex recovery and for overlapping grids interpolation in particular the behavior of the linear interpolation least square minimization and taylor series expansion methods are investigated several examples of the methods described and the combination of adaption and interpolation are presented showing their possibilities

a cell by cell anisotropic adaptive mesh ale scheme for the numerical solution of the euler equations in this paper a cell by cell anisotropic adaptive mesh technique is added to an existing staggered mesh lagrange plus remap finite element ale code for the solution of the euler equations the quadrilateral finite elements may be subdivided isotropically or anisotropically and a hierarchical data structure is employed an efficient computational method is proposed which only solves on the finest level of resolution that exists for each part of the domain with disjoint or hanging nodes being used at resolution transitions the lagrangian equipotential mesh relaxation and advection solution remapping steps are generalised so that they may be applied on the dynamic mesh it is shown that for a radial sod problem and a two dimensional riemann problem the anisotropic adaptive mesh method runs over eight times faster

the construction of compatible hydrodynamics algorithms utilizing conservation of total energy the principal goal of all numerical algorithms is to represent as faithfully and accurately as possible the underlying continuum equations to which a numerical solution is sought however in the transformation of the equations of fluid dynamics into discretized form important physical properties are either lost or obeyed only to an approximation that often becomes worse with time this is because the numerical methods used to form the discrete analog of these equations may only represent them to some order of local truncation error without explicit regard to global properties of the continuum system although a finite truncation error is inherent to all discretization methods it is possible to satisfy certain global properties such as conservation of mass momentum and total energy to numerical roundoff error the purpose of this work is to show how these equations can be differenced compatibly so that they obey the aforementioned properties in particular it is shown how conservation of total energy can be utilized as an intermediate device to achieve this goal for the equations of fluid dynamics written in lagrangian form and with a staggered spatial placement of variables for any number of dimensions and in any coordinate system for staggered spatial variables it is shown how the momentum equation and the specific internal energy equation can be derived from each other in a simple and generic manner by use of the conservation of total energy this allows for the specification of forces that can be of an arbitrary complexity such as those derived from an artificial viscosity or subzonal pressures these forces originate only in discrete form nonetheless the change in internal energy caused by them is still completely determined the procedure given here is compared to the method of support operators to which it is closely related difficulties with conservation of momentum volume and entropy are also discussed the proper treatment of boundary conditions and differencing with respect to time are detailed

a projection fem for variable density incompressible flows abstract this work describes a new finite element projection method for the computation of incompressible viscous flows of nonuniform density one original idea of the proposed method consists in factorizing the density variable partly outside and partly inside the time evolution operator in the momentum equation to prevent spatial discretization errors in the mass conservation to affect the kinetic energy balance of the fluid it is shown that unconditional stability in the incremental version of the projection method is possible provided two projections are performed per time step in particular a second order accurate bdf projection method is presented and its numerical performance is illustrated by test computations and comparisons

lagrangian gas dynamics in two dimensions and lagrangian systems we propose a new and canonical way of writing the equations of gas dynamics in lagrangian coordinates in two dimensions as a weakly hyperbolic system of conservation laws one part of the system is called the physical part and contains physical variables the other part is the geometrical part we show that the physical part is symmetrizable we show that the weak hyperbolicity is due to shear contact discontinuities free divergence constraints play an important role in the system we prove the l2 stability of the physical part of the system based on this formulation we derive a new conservative and entropy consistent finite volume numerical scheme we prove the stability of the numerical scheme numerical results show the potential interest of this approach various examples born infeld mhd 3d lagrangian gas dynamics can be written using the same abstract formalism

adaptive zoning for singular problems in two dimensions abstract winslow s method for the automatic generation of computation meshes is extended to adaptively vary the zone sizes and orthogonality of grid lines in the resulting mesh through simple analysis and numerical examples the adaptive mesh is shown to give significant increases in accuracy in the computation of singular problems

measurement error in the explanatory variable of a binary regression regression calibration and integrated conditional likelihood in studies of residential radon and lung cancer in epidemiology one approach to investigating the dependence of disease risk on an explanatory variable in the presence of several confounding variables is by fitting a binary regression using a conditional likelihood thus eliminating the nuisance parameters when the explanatory variable is measured with error the estimated regression coefficient is biased usually towards zero motivated by the need to correct for this bias in analyses that combine data from a number of case control studies of lung cancer risk associated with exposure to residential radon two approaches are investigated both employ the conditional distribution of the true explanatory variable given the measured one the method of regression calibration uses the expected value of the true given measured variable as the covariate the second approach integrates the conditional likelihood numerically by sampling from the distribution of the true given measured explanatory variable the two approaches give very similar point estimates and confidence intervals not only for the motivating example but also for an artificial data set with known properties these results and some further simulations that demonstrate correct coverage for the confidence intervals suggest that for studies of residential radon and lung cancer the regression calibration approach will perform very well so that nothing more sophisticated is needed to correct for measurement error

compressible multiphase semi implicit method with moment of fluid interface representation a unified method for simulating multiphase flows using an exactly mass momentum and energy conserving cell integrated semi lagrangian advection algorithm is presented the deforming material boundaries are represented using the moment of fluid method the new algorithm uses a semi implicit pressure update scheme that asymptotically preserves the standard incompressible pressure projection method in the limit of infinite sound speed the asymptotically preserving attribute makes the new method applicable to compressible and incompressible flows including stiff materials enabling large time steps characteristic of incompressible flow algorithms rather than the small time steps required by explicit methods shocks are captured and material discontinuities are tracked without the aid of any approximate or exact riemann solvers simulations of underwater explosions and fluid jetting in one two and three dimensions are presented which illustrate the effectiveness of the new algorithm at efficiently computing multiphase flows containing shock waves and material discontinuities with large impedance mismatch

numerical solution of the quasilinear poisson equation in a nonuniform triangle mesh a finite difference method using a nonuniform triangle mesh is described for the numerical solution of the nonlinear two dimensional poisson equation s 0 where is a function of or its derivatives sis a function of position and or its normal derivative is specified on the boundary the finite difference equations are solved by successive overrelaxation the triangle mesh which is constructed numerically by solving laplace s equation is easily adapted to nonrectangular boundaries and interfaces examples of numerical results are given for the magnetostatic problem with iron and other possible applications are mentioned

error estimate and the geometric corrector for the upwind finite volume method applied to the linear advection equation this paper deals with the upwind finite volume method applied to the linear advection equation on a bounded domain and with natural boundary conditions we introduce what we call the geometric corrector which is a sequence associated with every finite volume mesh in mathbf r nd and every nonvanishing vector mathbf a of mathbf r nd first we show that if the continuous solution is regular enough and if the norm of this corrector is bounded by the mesh size then an order one error estimate for the finite volume scheme occurs afterwards we prove that this norm is indeed bounded by the mesh size in several cases including the one where an arbitrary coarse conformal triangular mesh is uniformly refined in two dimensions computing numerically exactly this corrector allows us to state that this result might be extended under conditions to more general cases such as the one with independent refined meshes

compatible energy conserving bounds preserving remap of hydrodynamic fields for an extended ale scheme abstract from the very origins of numerical hydrodynamics in the lagrangian work of von neumann and richtmyer 83 the issue of total energy conservation as well as entropy production has been problematic because of well known problems with mesh deformation lagrangian schemes have evolved into arbitrary lagrangian eulerian ale methods 39 that combine the best properties of lagrangian and eulerian methods energy issues have persisted for this class of methods we believe that fundamental issues of energy conservation and entropy production in ale require further examination the context of the paper is an ale scheme that is extended in the sense that it permits cyclic or periodic remap of data between grids of the same or differing connectivity the principal design goals for a remap method then consist of total energy conservation bounded internal energy and compatibility of kinetic energy and momentum we also have secondary objectives of limiting velocity and stress in a non directional manner keeping primitive variables monotone and providing a higher than second order reconstruction of remapped variables in particular the new contributions fall into three categories associated with energy conservation and entropy production reconstruction and bounds preservation of scalar and tensor fields and conservative remap of nonlinear fields the paper presents a derivation of the methods details of implementation and numerical results for a number of test problems the methods requires volume integration of polynomial functions in polytopal cells with planar facets and the requisite expressions are derived for arbitrary order

a finite volume ventcell schwarz algorithm for advection diffusion equations this paper provides a new fully discrete domain decomposition algorithm for the advection diffusion reaction equation it relies on the optimized ventcell schwarz algorithm with a finite volume discretization of the subdomain problems the scheme includes a wide range of advection fluxes with a special treatment on the boundary a complete analysis of the scheme is presented and the convergence of the algorithm to a discrete approximation of the equation using a modified convective flux is proved numerical illustrations of the efficiency of the discrete ventcell schwarz algorithm are given

interactive method of variational grid generation abstract in the paper the elliptic variational grid generation technique based on methods of optimal control for distributed systems is presented the interactive nature of the method consists in adaptive changing of the golas of correction steps in the process of grid generation the corrections concern orthogonality and uniformity of the mesh

analysis of a finite volume method for a bone growth system in vivo this paper is devoted to the convergence analysis of a finite volume method and numerical simulations of a reaction cross diffusion system arising from a bone growth model this model describes the evolution of mesenchymal stem cells osteoblasts bone matrix and osteogenic growth factor we propose a numerical scheme based on an implicit finite volume method constructed on an orthogonal mesh lack of the regularity of the approximate system is overcome by stability results which allow to obtain estimates on the translates apply the kolmogorov theorem in order to get compactness and show the convergence of the proposed scheme the efficiency and robustness of the scheme are shown in simulating a situation in bone growth the healing of a skull fracture in rats

the performance of functional methods for correcting non gaussian measurement error within poisson regression corrected excess risk of lung cancer mortality in relation to radon exposure among french uranium miners a broad variety of methods for measurement error me correction have been developed but these methods have rarely been applied possibly because their ability to correct me is poorly understood we carried out a simulation study to assess the performance of three error correction methods two variants of regression calibration the substitution method and the estimation calibration method and the simulation extrapolation simex method features of the simulated cohorts were borrowed from the french uranium miners cohort in which exposure to radon had been documented from 1946 to 1999 in the absence of me correction we observed a severe attenuation of the true effect of radon exposure with a negative relative bias of the order of 60 on the excess relative risk of lung cancer death in the main scenario considered that is when me characteristics previously determined as most plausible from the french uranium miners cohort were used both to generate exposure data and to correct for me at the analysis stage all three error correction methods showed a noticeable but partial reduction of the attenuation bias with a slight advantage for the simex method however the performance of the three correction methods highly depended on the accurate determination of the characteristics of me in particular we encountered severe overestimation in some scenarios with the simex method and we observed lack of correction with the three methods in some other scenarios for illustration we also applied and compared the proposed methods on the real data set from the french uranium miners cohort study copyright 2012 john wiley sons ltd

isogeometric analysis of lagrangian hydrodynamics axisymmetric formulation in the rz cylindrical coordinates a recent isogeometric analysis iga formulation of lagrangian shock hydrodynamics 4 is extended to the 3d axisymmetric case the euler equations of compressible hydrodynamics are formulated using the rz cylindrical coordinates and are discretized in the weak form using nurbs based iga artificial shock viscosity and internal energy projection are added to stabilize the formulation the resulting discretization exhibits good accuracy and robustness properties it also gives exact symmetry preservation on the appropriately constructed meshes several benchmark examples are computed to examine the performance of the proposed formulation

an adaptive level set approach for incompressible two phase flows we present a numerical method using the level set approach for solving incompressible two phase flow with surface tension in the level set approach the free surface is represented as the zero level set of a smooth function this has the effect of replacing the advection of density which has steep gradients at the free surface with the advection of the level set function which is smooth in addition the free surface can merge or break up with no special treatment we maintain the level set function as the signed distance from the free surface in order to accurately compute flows with high density ratios and stiff surface tension effects in this work we couple the level set scheme to an adaptive projection method for the incompressible navier stokes equations in order to achieve higher resolution of the free surface with a minimum of additional expense we present two dimensional axisymmetric and fully three dimensional results of air bubble and water drop computations

a family of linearity preserving schemes for anisotropic diffusion problems on arbitrary polyhedral grids a family of cell centered finite volume schemes are proposed for anisotropic diffusion problems on arbitrary polyhedral grids with planar facets the derivation of the schemes is done under a general framework through a certain linearity preserving approach the key ingredient of our algorithm is to employ solely the so called harmonic averaging points located at the cell interfaces to define the auxiliary unknowns which not only makes the interpolation procedure for auxiliary unknowns simple and positivity preserving but also reduces the stencil of the schemes the final schemes are cell centered with a small stencil of 25 point on the structured hexahedral grids moreover the schemes satisfy the local conservation condition treat discontinuity exactly and allow for a simple stability analysis a second order accuracy in the l2 norm and a first order accuracy in the h1 norm are observed numerically on general distorted meshes in case that the diffusion tensor is anisotropic and discontinuous

covariate measurement errors and parameter estimation in a failure time regression model summary estimation in cox s failure time regression model is considered when the regression vector is subject to measurement error a hazard function model is induced for the failure rate given the measured covariate and a partial likelihood function is derived for the relative risk parameters this partial likelihood function may involve the baseline hazard function as well as the regression parameter but useful inference techniques arise for testing whether the regression parameter equals zero and for more general inferences in important special cases explicit consideration is given to testing equality of survival curves when group membership is subject to misclassification and to relative risk estimation with normally distributed covariates approaches to regression estimation using the overall likelihood function and a marginal likelihood function based on failure time ranks are also indicated illustration of the possible effect of covariate errors on relative risk estimation is provided

a 3d discrete duality finite volume method for nonlinear elliptic equations discrete duality finite volume ddfv schemes have recently been developed in two dimensions to approximate nonlinear diffusion problems on general meshes in this paper a three dimensional extension of these schemes is proposed the construction of this extension is detailed and its main properties are proved a priori bounds well posedness and error estimates the practical implementation of this scheme is easy numerical experiments are presented to illustrate its good behavior

correction of logistic regression relative risk estimates and confidence intervals for systematic within person measurement error errors in the measurement of exposure that are independent of disease status tend to bias relative risk estimates and other measures of effect in epidemiologic studies toward the null value two methods are provided to correct relative risk estimates obtained from logistic regression models for measurement errors in continuous exposures within cohort studies that may be due to either random unbiased within person variation or to systematic errors for individual subjects these methods require a separate validation study to estimate the regression coefficient lambda relating the surrogate measure to true exposure in the linear approximation method the true logistic regression coefficient beta is estimated by beta lambda where beta is the observed logistic regression coefficient based on the surrogate measure in the likelihood approximation method a second order taylor series expansion is used to approximate the logistic function enabling closed form likelihood estimation of beta confidence intervals for the corrected relative risks are provided that include a component representing error in the estimation of lambda based on simulation studies both methods perform well for true odds ratios up to 3 0 for higher odds ratios the likelihood approximation method was superior with respect to both bias and coverage probability an example is provided based on data from a prospective study of dietary fat intake and risk of breast cancer and a validation study of the questionnaire used to assess dietary fat intake

a two dimensional nodal riemann solver based on one dimensional riemann solver for a cell centered lagrangian scheme we develop a new and more general formula for the construction of two dimensional nodal riemann solver for a cell centered lagrangian scheme developed by maire and his co workers which allows us to use general one dimensional riemann solvers that have intermediate velocity and pressure in the construction the old formula for the scheme used in the papers of maire et al is only a special case of our new formula we present an entropy discussion which indicates that the schemes with nodal solvers constructed following the old formula which can only use the 1d riemann solvers satisfying our strong entropy condition are usually numerically very dissipative to develop numerically less dissipative schemes we introduce a so called weak entropy condition and present a one dimensional riemann solver that satisfies the weak entropy condition but not the strong entropy condition analysis shows that the scheme using this 1d solver is numerically less dissipative than the schemes using solvers satisfying the strong condition finally several numerical examples are presented to show that our new formula works well and the scheme using the one dimensional solver satisfying the weak entropy condition improves the accuracy in smooth region resolution around rarefaction waves and two dimensional symmetry however it sometimes produces small velocity oscillations and mesh distortions

a decoupled and positivity preserving discrete duality finite volume scheme for anisotropic diffusion problems on general polygonal meshes abstract we suggest a new positivity preserving discrete duality finite volume ddfv scheme for anisotropic diffusion problems on general polygonal meshes like existing ddfv schemes this scheme is built on the primary and dual meshes and has finite volume fv equations for both vertex and cell centered unknowns the transpose of the coefficient matrix for the fv equations of the cell centered unknowns is an m matrix while that for the vertex unknowns is not an m matrix but a symmetric and positive definite matrix by employing a certain truncation technique for the vertex unknowns the positivity preserving property for both categories of unknowns is guaranteed local conservation is strictly maintained for the cell centered unknowns and conditionally maintained for the vertex unknowns since the fv equations of the vertex unknowns can be solved independently the two sets of fv equations are decoupled in contrast to existing nonlinear positivity preserving schemes the new scheme requires no nonlinear iterations for linear problems for nonlinear problems the positivity preserving mechanism of the new scheme is decoupled from its nonlinear iteration so that any nonlinear solver can be adopted moreover the positivity of the discrete solution is proved and the well posedness is analyzed rigorously for linear problems in numerical experiments the new scheme is examined extensively and compared with two positivity preserving cell centered schemes and a nonlinear ddfv scheme numerical results show that the present ddfv scheme achieves second order accuracy and preserves the positivity of the solution for heterogeneous and anisotropic problems on severely distorted grids the high efficiency of the scheme is also demonstrated by the comparison of computation time and number of nonlinear iterations

a two dimensional mesh moving technique for time dependent partial differential equations abstract we discuss an adaptive mesh moving technique that can be used with a finite difference or finite element scheme to solve initial boundary value problems for systems of partial differential equations in two space dimensions and time the mesh moving technique is based on an algebraic node movement function determined from the geometry and propagation of regions having significant discretization error indicators our procedure is designed to be flexible so that it can be used with many existing finite difference and finite element methods to test the mesh moving algorithm we implemented it in a system code with an initial mesh generator and a maccormack finite difference scheme on quadrilateral cells for hyperbolic vector systems of conservation laws results are presented for several computational examples the moving mesch scheme reduces dispersive errors near shocks and wave fronts and thereby reduces grid requirements necessary to compute accurate solutions while increasing computational efficiency

a two dimensional unstructured cell centered multi material ale scheme using vof interface reconstruction we present a new cell centered multi material arbitrary lagrangian eulerian ale scheme to solve the compressible gas dynamics equations on two dimensional unstructured grid our ale method is of the explicit time marching lagrange plus remap type namely it involves the following three phases a lagrangian phase wherein the flow is advanced using a cell centered scheme a rezone phase in which the nodes of the computational grid are moved to more optimal positions a cell centered remap phase which consists of interpolating conservatively the lagrangian solution onto the rezoned grid the multi material modeling utilizes either concentration equations for miscible fluids or the volume of fluid vof capability with interface reconstruction for immiscible fluids the main original feature of this ale scheme lies in the introduction of a new mesh relaxation procedure which keeps the rezoned grid as close as possible to the lagrangian one in this formalism the rezoned grid is defined as a convex combination between the lagrangian grid and the grid resulting from condition number smoothing this convex combination is constructed through the use of a scalar parameter which is a scalar function of the invariants of the cauchy green tensor over the lagrangian phase regarding the cell centered remap phase we employ two classical methods based on a partition of the rezoned cell in terms of its overlap with the lagrangian cells the first one is a simplified swept face based method whereas the second one is a cell intersection based method our multi material ale methodology is assessed through several demanding two dimensional tests the corresponding numerical results provide a clear evidence of the robustness and the accuracy of this new scheme

a quasi elliptic transformation for moving boundary problems with large anisotropic deformations we have developed a quasi elliptic set of equations for generating a discretization mesh that optimally conforms to an entire domain that undergoes large deformations in primarily one direction we have applied this method to the axisymmetric problem of the transient displacement of a viscous liquid by a high pressure gas the liquid initially fills completely a tube the diameter of which may be constant or change smoothly suddenly or periodically along its finite length key ingredients for the success of the proposed transformation are limiting the orthogonality requirements on the mesh and employing an improved node distribution function along the deforming boundary the retained orthogonal term along with the penalty method for the imposition of the boundary conditions overcome the inherent restrictions of a conformal transformation producing meshes of high quality this term also eliminates the discontinuous slopes of the coordinate lines that are normal to the free surface these usually arise due to the harmonic transformation around highly deforming surfaces the mathematical anisotropy in the mesh generating equations directly corresponds to the physical one when the initially straight and normal to the axis of symmetry air fluid interface at the tube entrance develops mostly along the axial direction generating a long open bubble moreover the generalized node distribution imposes an optimal discretization of the bubble surface itself combining this scheme with the mixed finite element method produces a powerful tool with extended robustness and accuracy in order to reduce the computational cost the resulting set of equations is solved with a non linear gauss seidel technique and a variable time step specific applications of the proposed scheme are presented

some aspects of measurement error in explanatory variables for continuous and binary regression models a simple form of measurement error model for explanatory variables is studied incorporating classical and berkson cases as particular forms and allowing for either additive or multiplicative errors the work is motivated by epidemiological problems and therefore consideration is given not only to continuous response variables but also to logistic regression models the possibility that different individuals in a study have errors of different types is also considered the relatively simple estimation procedures proposed for use with cohort data and case control data are checked by simulation under the assumption of various error structures the results show that even in situations where conventional analysis yields slope estimates that are on average attenuated by a factor of approximately 50 per cent estimates obtained using the proposed amended likelihood functions are within 5 per cent of their true values the work was carried out to provide a method for the analysis of lung cancer risk following residential radon exposure but it should be applicable to a wide variety of situations

on the conservative and accurate cfd approximations for moving meshes and moving boundaries we are concerned with the conservative approximations of compressible flows in the context of moving mesh or interface tracking this paper makes a review of some numerical approaches based on the geometrical conservation law gcl property for computation with moving mesh or moving boundary those methods are reformulated and some comparisons are made we also propose a methodology to approximate accurately the mesh point trajectories and obtain accurate geometrical parameters in 2d and 3d satisfying the gcl property for time accurate schemes higher order geometrical parameters also act as a stabilization of the approximation the numerical effects of the higher order trajectories are illustrated for a 2d moving airfoil the efficiency of a mesh relaxation based on the modified linear elasticity equations is demonstrated for 3d computations of flow behavior in the combustion chamber of a four valves piston engine

reducing the entropy production in a collocated lagrange remap scheme the eulerian scheme described in this article aims to perform efficient and accurate compressible multimaterial fluid flows simulations we use a second order collocated lagrange remap scheme based on the eucclhyd lagrangian scheme maire et al 2007 26 which is conservative and uses acoustic riemann solvers the entropy production is studied and a correction is proposed to improve accuracy in isentropic flows by adding correction fluxes the scheme is thus kept conservative in mass momentum and total energy a vof plic interface reconstruction is added to the scheme results are presented that assess the dissipation reduction

a posteriori error estimation for the discrete duality finite volume discretization of the laplace equation an efficient and fully computable a posteriori error bound is derived for the discrete duality finite volume discretization of the laplace equation on very general two dimensional meshes the main ingredients are the equivalence of this method with a finite element like scheme and tools from the finite element framework numerical tests are performed with a stiff solution on highly nonconforming locally refined meshes and with a singular solution on triangular meshes

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

a cell centered lagrangian scheme for two dimensional compressible flow problems we present a new lagrangian cell centered scheme for two dimensional compressible flows the primary variables in this new scheme are cell centered i e density momentum and total energy are defined by their mean values in the cells the vertex velocities and the numerical fluxes through the cell interfaces are not computed independently contrary to standard approaches but are evaluated in a consistent manner due to an original solver located at the nodes the main new feature of the algorithm is the introduction of four pressures on each edge two for each node on each side of the edge this extra degree of freedom allows us to construct a nodal solver which fulfills two properties first the conservation of momentum and total energy is ensured second a semidiscrete entropy inequality is provided in the case of a one dimensional flow the solver reduces to the classical godunov acoustic solver it can be considered as its two dimensional generalization many numerical tests are presented they are representative test cases for compressible flows and demonstrate the robustness and the accuracy of this new solver

high order multi material ale hydrodynamics we present a new approach for multi material arbitrary lagrangian eulerian ale hydrodynamics simulations based on high order finite elements posed on high order curvilinear meshes the method builds on and extends our previous work in the lagrangian v a dobrev t v kolev and r n rieben siam j sci comput 34 2012 pp b606 b641 and remap r w anderson et al internat j numer methods fluids 77 2015 pp 249 273 phases of ale and depends critically on a functional perspective that enables subzonal physics and material modeling v a dobrev et al internat j numer methods fluids 82 2016 pp 689 706 curvilinear mesh relaxation is based on node movement which is determined through the solution of an elliptic equation the remap phase is posed in terms of advecting state variables between two meshes over a fictitious time interval the resulting advection equation is solved by a discontinuous galerkin dg formulation combined with a customized flux corrected transpor

review of some adaptive node movement techniques in finite element and finite difference solutions of partial differential equations abstract this article summarizes the results of a literature search for adaptive numerical methods of solving partial differential equations the methods discussed involve the adaptive movement of nodes so as to obtain a low level of solution truncation error while minimizing the number of nodes used in the calculation such methods are applicable to the solution of nonstationary flow problems that contain moving regions of rapid change in the flow variables surrounded by regions of relatively smooth variation flows with shock waves contact surfaces slip streams phase change interfaces and boundary layers can be modelled with great precision by these methods it will be shown that significant economies of execution can be attained if nodes are moved so that they remain concentrated in regions of rapid variation of the flow variables

error estimate for finite volume scheme we study the convergence of a finite volume scheme for the linear advection equation with a lipschitz divergence free speed in r d we prove a h1 2 error estimate in the l 0 t l1 norm for bv data this result was expected from numerical experiments and is optimal

applications and generalizations of variational methods for generating adaptive meshes abstract generating computation meshes for irregular regions have been of interest to a lot of people in many areas of research for a long time one technique that has met with sucess over the long run has been to generate methods using an elliptic equation or a system of elliptic equations the technique in its simplest form uses a system of laplace equations which are solved by direct or iterative methods as people gained more experience with this method source terms were added to the laplace equations to gain additional control of the mesh in variable coefficients of the derivatives were added for further flexibility in this paper the authors work with a method that systematically generates a set of elliptic equations without having to explicitly perturb a set of laplace equations with source terms and variable coefficients this technique uses the variational methods often associated with elliptic equations following this introduction they briefly discuss the variational formulation in two dimensional cartesian geometry then the formulation will be generalized to three dimensions next several three dimensional test problems will be shown after displaying these three dimensional test results the author wil the exhibit an application of the mesh generation technique in two dimensions this application involves generating an adaptive mesh for a supersonic flow past a step in a wind tunnel author

time dependent viscous incompressible navier stokes equations the finite difference galerkin formulation and streamfunction algorithms abstract the finite difference galerkin fdg method is extended to time dependent incompressible navier stokes equations two algorithm development examples are given that use a staggered grid and centered differencing scheme for the primitive variables mass balance is used to solve the essential problems associated with applying the fdg method the use of the fdg method with this underlying discretization is shows to be the discrete analog of the continuum manipulations that lead to the fourth order streamfunction equation asymptotic and time evolution results obtained with a crank nicolson adams basforth algorithm are compared with published computations for re 400 1000 and 3200

algebraic mesh quality metrics quality metrics for structured and unstructured mesh generation are placed within an algebraic framework to form a mathematical theory of mesh quality metrics the theory based on the jacobian and related matrices provides a means of constructing classifying and evaluating mesh quality metrics the jacobian matrix is factored into geometrically meaningful parts a nodally invariant jacobian matrix can be defined for simplicial elements using a weight matrix derived from the jacobian matrix of an ideal reference element scale and orientation invariant algebraic mesh quality metrics are defined the singular value decomposition is used to study relationships between metrics equivalence of the element condition number and mean ratio metrics is proved the condition number is shown to measure the distance of an element to the set of degenerate elements algebraic measures for skew length ratio shape volume and orientation are defined abstractly with specific examples given two combined metrics shape volume and shape volume orientation are algebraically defined and examples of such metrics are given algebraic mesh quality metrics are extended to nonsimplicial elements a series of numerical tests verifies the theoretical properties of the metrics defined

achieving finite element mesh quality via optimization of the jacobian matrix norm and associated quantities part i a framework for surface mesh optimization structured mesh quality optimization methods are extended to optimization of unstructured triangular quadrilateral and mixed finite element meshes n ew interpretations of well known nodally bssed objective functions are made possible using matrices and matrix norms the matrix perspective also suggests several new objective functions particularly significant is the interpretation of the oddy metric and the smoothness objective functions in terms of the condition number of the metric tensor and jacobian matrix respectively objective functions are grouped according to dimensionality to form weighted combinations a simple unconstrained local optimum is computed using a modiiied n ewton iteration the optimization approach was implemented in the cubit mesh generation code and tested on several problems results were compared against several standard element based quaiity measures to demonstrate that good mesh quality can be achieved with nodally based objective functions

a general topology godunov method we describe a numerical technique for solving 2 dimensional compressible multimaterial problems using a general topology mesh multimaterial problems are characterized by the presence of interfaces whose shapes may become arbitrarily complex in the course of dynamic evolution computational methods based on more conventional fixed connectivity quadrilateral meshes do not have adequate flexibility to follow convoluted interface shapes and frequently fail due to excessive mesh distortion the present method is based on a mesh of arbitrary polygonal cells because this mesh is dual to a triangulation its topology is unrestricted and it is able to accommodate arbitrary boundary shapes additionally this mesh is able to quickly and smoothly change local mesh resolution thus economizing on the number of mesh cells and it is able to improve mesh isotropy because in a region of uniform mesh the cells tend to become regular hexagons the underlying algorithms are based on those of the caveat code these consist of an explicit finite volume cell centered arbitrary lagrangian eulerian ale technique coupled with the godunov method which together are readily adaptable to a general topology mesh several special techniques have been developed for this extension to a more general mesh they include an interface propagation scheme based on huygens construction a near lagrangian mesh rezoning algorithm that minimizes advection while enhancing mesh regularity an efficient global remapping algorithm that is capable of conservatively transferring quantities from one general mesh to another and various mesh restructering algorithms such as mesh reconnection smoothing and point addition and deletion

a high order projection method for tracking fluid interfaces in variable density incompressible flows we present a numerical method for computing solutions of the incompressible euler or navier stokes equations when a principal feature of the flow is the presence of an interface between two fluids with different fluid properties the method is based on a second order projection method for variable density flows using an approximate projection formulation the boundary between the fluids is tracked with a second order volume of fluid interface tracking algorithm we present results for viscious rayleigh taylor problems at early time with equal and unequal viscosities to demonstrate the convergence of the algorithm we also present computational results for the rayleigh taylor instability in air helium and for bubbles and drops in an air water system without surface tension to demonstrate the behavior of the algorithm on problems with large density and viscosity contrasts

simulation extrapolation estimation in parametric measurement error models we describe a simulation based method of inference for parametric measurement error models in which the measurement error variance is known or at least well estimated the method entails adding add

generation of computational grids using optimization a method for generation of computational grids using principles of nonlinear programming optimization is described grids are generated so that certain discrete measures of grid smoothness and orthogonality are max imized using a fast iterative optimization procedure the method can also be used to improve an existing grid ir respective of the method used for its generation if the original grid contains regions of overlap nonpositive jacobian this method is capable of unraveling the grid and making it useful for computations the iterative op timization procedure is efficient due to the use of a conjugate direction method with exact line searching examples are given of the application of this technique to two and three dimensional computational grids the extension of the method to generate solution adaptive grids is discussed n the past few years there has been a great deal of interest in the development of computational grid generation techniques1 for discretizing complex regions for the numerical solution of partial differential equations the commonly used grid generation methods have achieved a high degree of sophistication and ease of use however for complex con figurations the existing methods do not always produce ac ceptable grids for computations grid quality deterioration is especially apparent in three dimensional grid generation methods and when two dimensional grids are combined to form a three dimensio nal grid 2 3 in addition to grid quality problems many methods suffer from computational ineffi ciency for these reasons the authors have perceived a need for a grid generatio n method that could be used to improve the quality of a given computational grid in addition the method should be capable of serving as a stand alone grid generation procedure independent of other techniques the basic concept behind this grid generation method is to assume from the outset that the grid to be generated or op timized consists of straight line segments joining the nodal grid points this is in contrast to methods that solve elliptic parabolic or hyperbolic partial differential equations or use conformal mapping these methods are based on con tinuous not discrete coordinate transformations and therefore suffer from discretization errors for any grid con sisting of a finite number of grid points the grid generation technique described herein formulates discrete measures of grid smoothness and orthogonality at each grid point and therefore does not suffer from truncation errors on coarse grids these measures of grid quality are then minimized us ing a conjugate direction procedure with exact line searching the resulting grids are optimal with respect to the particular smoothness and orthogonality measures chosen and there are many possible choices for their exact forms the next section describes the formulation of the method followed by some typical results of using this method to im prove existing grids or generate new grids finally exten sions of the method for generating solution adaptive grids are discussed and other areas of possible future research are pointed out analysis the formulation of the method will be illustrated for two dimensional grids the details of the method for the three dimensional case are given in the appendix we will discuss the grid generation method by first noting similarities with the saltzman brackbill4 variational grid generation method in the variational method two func tionals are introduced that provide measures of grid smoothness

coordinate system control adaptive meshes the discussion of the formulation and properties of the adaptive mesh algorithm is as complete as space permits as should be clear from the discussion adaptive gridding is most useful for singular perturbation problems where localized regions with large gradients develop spontaneously often choosing the correct weight function is not trivial and sometimes it is appropriate to cause the mesh to respond to structure in several dependent variables simultaneously

angular momentum preserving cell centered lagrangian and eulerian schemes on arbitrary grids we address the conservation of angular momentum for cell centered discretization of compressible fluid dynamics on general grids we concentrate on the lagrangian step which is also sufficient for eulerian discretization using lagrange remap starting from the conservative equation of the angular momentum we show that a standard riemann solver a nodal one in our case can easily be extended to update the new variable this new variable allows to reconstruct all solid displacements in a cell and is analogous to a partial discontinuous galerkin dg discretization we detail the coupling with a second order muscl extension all numerical tests show the important enhancement of accuracy for rotation problems and the reduction of mesh imprint for implosion problems the generalization to axi symmetric case is detailed

uniform in time convergence of numerical methods for non linear degenerate parabolic equations gradient schemes is a framework that enables the unified convergence analysis of many numerical methods for elliptic and parabolic partial differential equations conforming and non conforming finite element mixed finite element and finite volume methods we show here that this framework can be applied to a family of degenerate non linear parabolic equations which contain in particular the richards stefan s and leray lions models and we prove a uniform in time strong in space convergence result for the gradient scheme approximations of these equations in order to establish this convergence we develop several discrete compactness tools for numerical approximations of parabolic models including a discontinuous ascoli arzela theorem and a uniform in time weak in space discrete aubin simon theorem the model s degeneracies which occur both in the time and space derivatives also requires us to develop a discrete compensated compactness result

on the elliptic mesh generation in domains containing multiple inclusions and undergoing large deformations we present an improved method to generate a sequence of structured meshes even when the physical domain contains deforming inclusions this method belongs to the class of arbitrary lagrangian eulerian ale methods for solving moving boundary problems its tools are either a separate mappings of the domain boundaries and enforcing the node distribution on lines emanating from singular points or b domain decomposition and separate mappings of each subdomain using suitable coordinate systems the latter is shown to be more versatile and general in both cases a set of elliptic equations is used to generate the grid extending in this way the method advanced by dimakopoulos and tsamopoulos y dimakopoulos j a tsamopoulos a quasi elliptic transformation for moving boundary problems with large anisotropic deformations j comput phys 192 2003 494 522 we shall present examples where this earlier method and all other mesh generating methods which are based on a conformal mapping or solving a quasi elliptic set of pdes fail to produce an acceptable mesh and accurate solutions in such geometries furthermore in contrast to other methods appropriate boundary conditions and constraints such as orthogonality of specific mesh lines and prespecified node distributions on them can be easily implemented along a specific part of the domain or its boundary hence no attractive terms at specific corners or singular points are needed to increase the mesh resolution around the moving interfaces while keeping low the memory requirements and the computational time a local mesh refinement technique has been incorporated as well the method is demonstrated in two challenging examples where no remeshing is required in spite of the large domain deformations in the first one the transient growth of two bubbles embedded in a viscoelastic filament undergoing stretching in the axial direction is examined while in the second one the linear and non linear dynamics of two bubbles in a viscous medium are determined in an acoustic field the large elasticity of the filament in the first case or the large inertia in the second case coupled with the externally induced large deformations of the liquid domain requires the accurate calculation which is achieved by the method we propose herein the governing equations are solved using the finite element galerkin method with appropriate modifications to solve the hyperbolic constitutive equation of a viscoelastic fluid these are coupled with an implicit euler method for time integration or with arnoldi s algorithm for normal mode analysis

covariate measurement error in logistic regression abstract in a logistic regression model when covariates are subject to measurement error the naive estimator obtained by regressing on the observed covariates is asymptotically biased this document introduces a bias adjusted estimator and two estimators appropriate for normally distributed measurement errors a functional maximum likelihood estimator and an estimator which exploits the consequences of sufficiency the four proposals are studied asymptotically under conditions which are appropriate when the measurement error is small a small monte carlo study illustrates the superiority of the measurement error estimators in certain situations additional keywords mathematical models

stabilization of cell centered compressible lagrangian methods using subzonal entropy this work deals with the stabilization of early stages of lagrangian calculations of compressible gas dynamics in the context of cell centered discretization we describe a totally conservative algorithm based on an entropy analysis of the distortion of a lagrangian mesh it prevents the tangling of the mesh while remaining consistent and conservative in mass momentum and total energy the method described can be applied to any cell centered lagrangian scheme in this article we detail the extension to the cell centered glace scheme published in carre et al 2009 g carre s del pino b despres e labourasse a cell centered lagrangian hydrodynamics scheme on general unstructured meshes in arbitrary dimension j comput phys 228 2009 5160 5183 numerical tests are proposed to assess the accuracy and robustness

finite volume schemes on unstructured grids for non local models application to the simulation of heat transport in plasmas in the so called spitzer harm regime equations of plasma physics reduce to a nonlinear parabolic equation for the electronic temperature coming back to the derivation of this limiting equation through hydrodynamic regime arguments one is led to construct a hierarchy of models where the heat fluxes are defined through a non local relation which can be reinterpreted as well by introducing coupled diffusion equations we address the question of designing numerical methods to simulate these equations the basic requirement for the scheme is to be asymptotically consistent with the spitzer harm regime furthermore the constraints of physically realistic simulations make the use of unstructured meshes unavoidable we develop a finite volume scheme based on vertex based discretization which reaches these objectives we discuss on numerical grounds the efficiency of the method and the ability of the generalized models in capturing relevant phenomena missed by the asymptotic problem

isentropic correction for collocated lagrange remap scheme abstract we study an eulerian scheme of lagrange remap type which simulates compressible multi material fluid flows the lagrangian phase is based on a collocated scheme called eucclhyd explicit unstructured cell centered lagrangian hydrodynamics maire et al 2007 whereas the remap phase uses alternate directions with interface reconstruction of plic type the eucclhyd scheme which is built on the resolution of acoustic riemann problems at nodes is totally conservative second order in time and space and captures shock waves accurately however the intrinsic entropy production is inaccurate for isentropic flows rarefaction expansion waves isentropic compression in this framework we suggest a correction inspired by braeunig 2016 to improve accuracy in flows with isentropic behavior this is achieved by modifying the scheme in order to nullify the entropy production in expansion zones