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

a new interface tracking method the polygonal area mapping method we present a new method the polygonal area mapping pam method for tracking a non diffusive immiscible material interface between two materials in two dimensional incompressible flows this method represents material areas explicitly as piecewise polygons traces characteristic points on polygon boundaries along pathlines and calculates new material areas inside interface cells via polygon clippings in a discrete manner the new method has very little spatial numerical diffusion and tracks the interface singularities naturally and accurately in addition to high accuracy the pam method can be directly used on either a structured rectangular mesh or an unstructured mesh without any modifications the mass conservation is enforced by heuristic algorithms adjusting the volume of material polygons the results from a set of widely used benchmark tests show that the pam method is superior to existing volume of fluid vof methods

on adaptive estimation in stationary arma processes on demontre la normalite asymptotique locale puis on construit des estimateurs localement asymptotiquement minimax

a cartesian grid embedded boundary method for hyperbolic conservation laws we present a second order godunov algorithm to solve time dependent hyperbolic systems of conservation laws on irregular domains our approach is based on a formally consistent discretization of the conservation laws on a finite volume grid obtained from intersecting the domain with a cartesian grid we address the small cell stability problem associated with such methods by hybridizing our conservative discretization with a stable nonconservative discretization at irregular control volumes and redistributing the difference in the mass increments to nearby cells in a way that preserves stability and local conservation the resulting method is second order accurate in l 1 for smooth problems and is robust in the presence of large amplitude discontinuities intersecting the irregular boundary

adaptive tetrahedral meshing in free surface flow an unstructured three dimensional moving mesh algorithm is developed for free surface flows with the capability of simulating large deformation a robust edge swapping algorithm and an optimization based mesh smoothing algorithm are used to improve mesh quality as the interface deforms the edge swapping algorithm uses an optimal swap sequence to transform configurations with several tetrahedra sharing a common edge the optimization based mesh smoothing relocates vertex position so that the minimum quality of the incident cells is maximized also edge contraction and bisection are used to adjust the mesh resolution according to surface curvature these local refinements effectively maintain good mesh quality and appropriate mesh size while avoiding global re meshing this scheme s robustness and accuracy are demonstrated with deforming liquid ligaments periodic jets and colliding droplets

moment of fluid analytic reconstruction on 2d cartesian grids moment of fluid mof is a piecewise linear interface reconstruction method that tracks fluid through its volume fraction and centroid which are deduced from the zeroth and first moments we present a method that replaces the original minimization stage by an analytic reconstruction algorithm on bi dimensional cartesian grids this algorithm provides accurate results for a lower computational cost than the original minimization algorithm when more than two fluids are involved this algorithm can be used coupled with the minimization algorithm although this paper deals with cartesian grids everything remains valid for any meshes that are made of rectangular cells

adaptive moment of fluid method a novel adaptive mesh refinement amr strategy based on the moment of fluid mof method for volume tracking of evolving interfaces is presented moment of fluid method is a new interface reconstruction and volume advection method using volume fractions as well as material centroids the mesh refinement criterion is based on the deviation of the actual centroid obtained by interface reconstruction from the reference centroid given by moment advection process the centroid error indicator detects not only high curvature regions but also regions with complicated subcell structures like filaments a new lagrange remap scheme is presented for advecting moments which includes lagrangian backtracking polygon intersection based remapping and forward tracking to define the material centroid the effectiveness and efficiency of amr mof method is demonstrated with classical test problems such as zalesak s disk and reversible vortex problem the comparison with previously published results for these problems shows the superior accuracy of the amr mof method over other methods in addition two new test cases with severe deformation rates are introduced namely droplet deformation and s shape deformation problems for further demonstration of the capabilities of the amr mof method

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

the repair paradigm new algorithms and applications to compressible flow the repair paradigm leads to several algorithms for redistributing mass momentum and energy while adhering to local maximum principles as an adjunct to the remapping step in certain compressible flow codes that use remapping such as arbitrary lagrangian eulerian codes or for just redistributing mass in advection codes in the case of advection of a concentration repair keeps the newly computed concentration in a cell between the maximum and minimum concentrations in neighboring old cells thus guaranteeing at least that the new concentration is between zero and one for compressible flow density velocity and internal energy are similarly constrained while maintaining conservation of mass momentum and total energy in this way positive density and internal energy are achieved as a side effect we propose a new algorithm combining both local and global repair that maintains causality and is efficient in a parallel computational setting the local global algorithm is independent of the order in which the distribution is performed and it maintains 1d symmetry this is applied to advection in two dimensions and to among others the leblanc problem the sedov problem and an interacting 2d blast wave problem the latter is done with a lagrangian code for which rezoning remapping and repair are essential

reconstructing volume tracking a new algorithm for the volume tracking of interfaces in two dimensions is presented the algorithm is based upon a well defined second order geometric solution of a volume evolution equation the method utilizes local discrete material volume and velocity data to track interfaces of arbitrarily complex topology a linearity preserving piecewise linear interface geometry approximation ensures that solutions generated retain second order spatial accuracy second order temporal accuracy is achieved by virtue of a multidimensional unsplit time integration scheme we detail our geometrically based solution method in which material volume fluxes are computed systematically with a set of simple geometric tasks we then interrogate the method by testing its ability to track interfaces through large controlled topology changes whereby an initially simple interface configuration is subjected to vortical flows numerical results for these strenuous test problems provide evidence for the algorithm s improved solution quality and accuracy

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 robust mof method applicable to severely deformed polygonal mesh abstract the mof moment of fluid method is an accurate approach for interface reconstruction in numerical simulation of multi material fluid flow so far most works focus on improving its accuracy and efficiency such as developing analytic reconstruction method and deducing the iteration schemes based on high order derivatives of the objective function in this paper we mainly concern on improving its robustness especially for severely deformed polygonal meshes in which case the objective function has multiple minimum value points by using an efficient method for solving multiple roots of the nonlinear equation in large scope a new algorithm is developed to enhance robustness of the mof method the main idea of this algorithm is as follows the first derivative of the objective function is continuous so the minimum value points of the objective function must be the zero points of the first derivative instead of finding the zero points of the first derivative directly we turn to calculating the minimum value points also zero points of the square of the first derivative which is a convex function on a neighborhood of each zero point applying the properties of convex function the neighbor of each extreme minimum point of it can be obtained efficiently then each zero point of the square of the first derivative can be obtained using the iterative formula in its neighbor finally by comparing the values of the objective function at these zero points of the first derivative the global minimum value point of the objective function can be found and is the desired solution the new algorithm only uses the first derivative of the objective function it doesn t need an initial guess for the solution which has to be carefully chosen in previous works numerical results are presented to demonstrate the accuracy and robustness of this new algorithm the results show that it is applicable to severely deformed polygonal mesh even with concave cells

on estimation and adaptive estimation for locally asymptotically normal families locally asymptotically minimax lam estimates are constructed for locally asymptotically normal lan families under very mild additional assumptions adaptive estimation is also considered and a sufficient condition is given for an estimate to be locally asymptotically minimax adaptive incidently it is shown that a well known lower bound due to hajek 1972 for the local asymptotic minimax risk is not sharp

efficient estimation of banach parameters in semiparametric models abtract consider a semiparametric model with a euclidean parameter and an infinite dimensional parameter to be called banach parameter assume there exists an efficient estimator of the euclidean parameter when the value of the euclidean parameter is known there exists an estimator of the banach parameter which depends on this value and is efficient within this restricted model substituting the efficient estimator of the euclidean parameter for the value of this parameter in the estimator of the banach parameter one obtains an efficient estimator of the banach parameter for the full semiparametric model with the euclidean parameter unknown this heredity property of efficiency completes estimation in semiparametric models in which the euclidean parameter has been estimated efficiently typically estimation of both the euclidean and the banach parameter is necessary in order to describe the random phenomenon under study to sufficient extent since efficient estimators are asymptotically linear the above substitution method is a particular case of substituting asymptotically linear estimators of a euclidean parameter into estimators that are asymptotically linear themselves and that depend on this euclidean parameter this more general substitution case is studied for its own sake as well and a heredity property for asymptotic linearity is proved

incremental remapping as a transport advection algorithm there are two fundamentally different strategies for solving the standard transport or continuity equation corresponding to whether it is expressed as a partial differential equation or as an integral statement of conservation the more common approach is to discretize the partial differential equation and to march the solution forward in time the alternative method is to project cell volumes along lagrangian trajectories as far forward or backward in time as desired and then to remap the resulting density distribution onto some target mesh this latter approach is known as remapping remapping has many advantages not the least of which is that the time step is limited only by accuracy considerations but it tends to be expensive and complex in this paper we show that if the time step is made sufficiently short such that trajectories are confined to the nearest neighbor cells then the remapping may be written as a flux form transport algorithm and it becomes nearly as simple and efficient as standard transport schemes the resulting method called incremental remapping retains most of the advantages of general remapping these include a geometric basis for transport b compatibility of associated tracer transport with simple tracer advection i e retention of tracer monotonicity properties and c efficient handling of multiple tracers since each additional tracer adds only a relatively small incremental cost

a new volume of fluid advection algorithm a new vof advection algorithm is presented termed the stream scheme the algorithm uses a linear piecewise method for free surface reconstruction coupled to a unique fully multidimensional method of cell boundary flux integration the performance of the new algorithm is compared against other vof advection algorithms using a variety of standard advection tests in general the performance of the stream scheme appears superior to existing multidimensional and dimensionally split advection algorithms

estimating invariant laws of linear processes by u statistics suppose we observe an invertible linear process with independent mean zero innovations and with coefficients depending on a finite dimensional parameter and we want to estimate the expectation of some function under the stationary distribution of the process the usual estimator would be the empirical estimator it can be improved using the fact that the innovations are centered we construct an even better estimator using the representation of the observations as infinite order moving averages of the innovations then the expectation of the function under the stationary distribution can be written as the expectation under the distribution of an infinite series in terms of the innovations and it can be estimated by a u statistic of increasing order also called an infinite order u statistic in terms of the estimated innovations the estimator can be further improved using the fact that the innovations are centered this improved estimator is optimal if the coefficients of the linear process are estimated optimally the variance reduction of our estimator over the empirical estimator can be considerable

space time discontinuous galerkin finite element method for two fluid flows a novel numerical method for two fluid flow computations is presented which combines the space time discontinuous galerkin finite element discretization with the level set method and cut cell based interface tracking the space time discontinuous galerkin stdg finite element method offers high accuracy an inherent ability to handle discontinuities and a very local stencil making it relatively easy to combine with local hp refinement the front tracking is incorporated via cut cell mesh refinement to ensure a sharp interface between the fluids to compute the interface dynamics the level set method lsm is used because of its ability to deal with merging and breakup also the lsm is easy to extend to higher dimensions small cells arising from the cut cell refinement are merged to improve the stability and performance the interface conditions are incorporated in the numerical flux at the interface and the stdg discretization ensures that the scheme is conservative as long as the numerical fluxes are conservative the numerical method is applied to one and two dimensional two fluid test problems using the euler equations

reachability of a set of facets for linear affine systems with n 1 inputs this note provides new necessary and sufficient conditions for an n dimensional linear affine system with n 1 inputs to reach an exit facet or set of exit facets of a simplex the conditions reduce the original np hard necessary and sufficient conditions to a set of at most n lp problems

homogeneous state feedback stabilization of homogenous systems we show that for any asymptotically controllable homogeneous system in euclidean space not necessarily lipschitz at the origin there exists a homogeneous control lyapunov function and a homogeneous possibly discontinuous state feedback law stabilizing the corresponding sampled closed loop system if the system satisfies the usual local lipschitz condition on the whole space we obtain semiglobal stability of the sampled closed loop system for each sufficiently small fixed sampling rate if the system satisfies a global lipschitz condition we obtain global exponential stability for each sufficiently small fixed sampling rate the control lyapunov function and the feedback are based on the lyapunov exponents of a suitable auxiliary system and admit a numerical approximation

the repair paradigm and application to conservation laws repair is a conservative post processing procedure to be used in numerical methods for hyperbolic conservation laws in order to preserve certain qualitative characteristics of the numerical solution such as positivity of density and internal energy by means of redistribution of conserved quantities such as mass momentum and total energy among the cells of the mesh in this paper we describe the repair paradigm and prove several theorems which form a theoretical foundation for the repair procedures we consider two applications of repair and present corresponding numerical results the first application deals with improving properties of the remapping conservative interpolation stage of arbitrary lagrangian eulerian ale methods for the gas dynamics equations in which the solution is conservatively transferred from one mesh to another one requirement for remapping is that the interpolated density and internal energy on the new mesh have to stay positive another desirable property is that the remapping procedure should not create new extrema for the velocity field for various reasons these properties may not be satisfied especially for high order methods repair plays a supplemental role by bringing gas dynamics quantities into physically justified bounds another application of repair is to improve the quality of numerical methods for advection of some scalar tracer field with prescribed divergence free velocity field in which case the advection equation can be written as a conservation law and therefore the total amount of tracer is conserved we show how the repair procedure allows us to reduce oscillations in a numerical solution obtained by a formally high order method repair offers an alternative to more classical methods of reducing oscillations and maintaining positivity

two phase flows on interface refined grids modeled with vof staggered finite volumes and spline interpolants abstract a two phase 2d model that combines the volume of fluid vof method with implicit staggered finite volumes discretization of the navier stokes equation is presented staggered finite volumes are developed on the basis of nonconforming crouzeix raviart finite elements where all components of the velocity lie in the middle of the element edges and the pressure degrees of freedom are found in the centers of mass of the elements staggered finite volumes extend marker and cell mac regular staggered grids to unstructured mesh a linear saddle point problem resulting from either the discretization or the newton method is solved for all unknown pressures and velocities interface is represented with spline interpolants which follow the vof distribution adaptive mesh refinement is used to obtain a high level of uniform refining at the domain of dependence of the interface the aligned grid is obtained by irregular refining of the cells which are intersected by a curve the boundaries of its elements coincide with the slope segments going through the intersections of the curve with the underlying regular elements boundary the deformable computational grids are used only to discretize the navier stokes equation the advection of volume fractions is done on the advection mesh which corresponds to highest regular refining on the computational grid approximation of the surface tension on spline interpolants offers a straightforward way to describe correctly the pressure jumps on interface fitted staggered grids this allows deletion of the anomalous currents around a statical bubble and their effective reduction in real simulations on the aligned grid the continuity of the viscous stress is modeled exactly due to the finite volume approach using the proposed numerical techniques single bubble rise is analyzed

nonlinear regulation the piecewise linear approach this paper approaches nonlinear control problems through the use of discrete time piecewise linear systems these are systems whose next state and output maps are both described by pl maps i e by maps which are affine on each of the components of a finite polyhedral partition various results on state and output feedback observers and inverses standard for linear systems are proved for pl systems many of these results are then used in the study of more general both discrete and continuous time systems using suitable approximations

gerris a tree based adaptive solver for the incompressible euler equations in complex geometries an adaptive mesh projection method for the time dependent incompressible euler equations is presented the domain is spatially discretised using quad octrees and a multilevel poisson solver is used to obtain the pressure complex solid boundaries are represented using a volume of fluid approach second order convergence in space and time is demonstrated on regular statically and dynamically refined grids the quad octree discretisation proves to be very flexible and allows accurate and efficient tracking of flow features the source code of the method implementation is freely available

data based identification and control of nonlinear systems via piecewise affine approximation the piecewise affine pwa model represents an attractive model structure for approximating nonlinear systems in this paper a procedure for obtaining the pwa autoregressive exogenous arx autoregressive systems with exogenous inputs models of nonlinear systems is proposed two key parameters defining a pwarx model namely the parameters of locally affine subsystems and the partition of the regressor space are estimated the former through a least squares based identification method using multiple models and the latter using standard procedures such as neural network classifier or support vector machine classifier having obtained the pwarx model of the nonlinear system a controller is then derived to control the system for reference tracking both simulation and experimental studies show that the proposed algorithm can indeed provide accurate pwa approximation of nonlinear systems and the designed controller provides good tracking performance

a perspective on adaptive modeling and meshing am m the purpose of this study is to develop an integrated approach to adaptive modeling in conjunction with adaptive meshing this involves consideration of the modeling error from various sources and the discretization error in the numerical scheme adapting the model to control error due to geometry boundary data constitutive relations and model parameters can be integrated with adaptive mesh control to improve numerical reliability other factors such as stabilization by artificial dissipation and regularization are considered a class of hybrid algorithms are developed to combine these approaches

fourth order interface tracking in two dimensions via an improved polygonal area mapping method we present an improved pam ipam method as the first fourth order interface tracking method whose convergence rates are independent of c 1 derivative discontinuities of the interface as an improved version of the polygonal area mapping pam method q zhang and p l f liu j comput phys 227 2008 pp 4063 4088 the accuracy of the ipam method is achieved via i augmenting the abstract data structure of pam to faithfully represent multiple components of material regions within a single cell ii removing restrictive assumptions of pam iii adjusting the volume of represented cell material regions via polygon ear removal and iv maintaining a relation h l r hh alpha between the eulerian grid size h and the lagrangian length scale that measures the distance between adjacent interface markers unlike volume of fluid methods and level set methods merging and separation of the tracked material is not automatically handled by the ipam method instead flexible subgrid resolutions

a conservative adaptive projection method for the variable density incompressible navier stokes equations in this paper we present a method for solving the equations governing time dependent variable density incompressible flow in two or three dimensions on an adaptive hierarchy of grids the method is based on a projection formulation in which we first solve advection diffusion equations to predict intermediate velocities and then project these velocities onto a space of approximately divergence free vector fields our treatment of the first step uses a specialized second order upwind method for differencing the nonlinear convection terms that provides a robust treatment of these terms suitable for inviscid and high reynolds number flow density and other scalars are advected in such a way as to maintain conservation if appropriate and free stream preservation our approach to adaptive refinement uses a nested hierarchy of logically rectangular girds with simultaneous refinement of the girds in both space and time the integration algorithm on the grid hierarchy is a recursive procedure in which coarse grids are advanced in time fine grids are advanced multiple steps to reach the same time as the coarse grids and the data at different levels are then synchronized the single grid algorithm is described briefly but the emphasis here is on the time stepping procedure for the adaptive hierarchy numerical examples are presented to demonstrate the algorithms s accuracy and convergence properties and illustrate the behavior of the method an additional example demonstrates the performance of the method on a more realistic problem namely a three dimensional variable density shear layer

a hybrid level set volume constraint method for incompressible two phase flow a second order hybrid level set volume constraint method hlsvc for numerically simulating deforming boundaries is presented we combine the hlsvc interface advection algorithm with a two phase flow solver in order to numerically capture deforming bubbles and drops whose actual volume s fluctuate about fixed target volume s three novel developments are described 1 a new method for enforcing a volume constraint in which the number of bubbles and drops can change due to merging or splitting 2 a new second order semi lagrangian narrow band level set reinitialization algorithm and 3 validation of a two phase flow numerical method by comparison with linear stability analysis results for a co flowing liquid jet in gas the new interface capturing method is tested on benchmark problems in which the velocity is prescribed passive advection of interfaces and in which the velocity is determined by the incompressible navier stokes equations for two phase flow the error in interface position when using the hybrid level set volume constraint method is reported for many benchmark problems in polar coordinates cylindrical coordinates and on an adaptive grid in which one criteria of adaptivity is the magnitude of the interface curvature

on a family of unsplit advection algorithms for volume of fluid methods volume of fluid vof methods are widely used for the interface tracking problem yet rigorous analyses of them are rare this paper presents such an analysis for incompressible flows by combining the theories of ordinary differential equations differential geometry and boolean algebra based on the concept of donating region dr q zhang siam rev 55 2013 pp 443 461 the author classifies the fluxing particles of a fixed control volume into four categories and derives three analytical solutions for the advection equation of the color function one edgewise solution provides a unified view of dr based advection algorithms for vof methods while another cellwise solution serves as the theoretical foundation of the recent polygonal area mapping method the well known second order convergence rates of streamline based vof advection algorithms are proved rigorously potential deterioration of this second order convergence is also discussed for several subtle issues such as exact mass conservation a

mimetic finite difference methods for diffusion equations on non orthogonal non conformal meshes mimetic discretizations based on the support operators methodology are derived for non orthogonal locally refined quadrilateral meshes the second order convergence rate on non smooth meshes is verified with numerical examples

an improved plic vof method for tracking thin fluid structures in incompressible two phase flows a drawback common to plic schemes is the difficulty of reconstructing the interface when filaments of a thickness smaller than the cell size are present in this work we present an improvement of the reconstruction method proposed by lopez et al a volume of fluid method based on multidimensional advection and spline interface reconstruction j comput phys 195 2004 718 for two dimensional flows which allows tracking fluid structures thinner than the cell size by allowing the interface to be represented in each cell by two non contiguous linear segments the method is based on using markers that are placed every time step at the mid points of the reconstructed cell interface segments the markers are used to improve the orientation and location of the interface segments although the method essentially remains of a vof type numerical tests show that a substantial improvement in accuracy is achieved over previous volume of fluid methods and that the proposed method compares well even with a recent hybrid markers and volume of fluid method

an accurate adaptive solver for surface tension driven interfacial flows a method combining an adaptive quad octree spatial discretisation geometrical volume of fluid interface representation balanced force continuum surface force surface tension formulation and height function curvature estimation is presented the extension of these methods to the quad octree discretisation allows adaptive variable resolution along the interface and is described in detail the method is shown to recover exact equilibrium to machine accuracy between surface tension and pressure gradient in the case of a stationary droplet irrespective of viscosity and spatial resolution accurate solutions are obtained for the classical test case of capillary wave oscillations an application to the capillary breakup of a jet of water in air further illustrates the accuracy and efficiency of the method the source code of the implementation is freely available as part of the gerris flow solver

adaptive estimation in time series models in a framework particularly suited for many time series models we obtain a lan result under quite natural and economical conditions this enables us to construct adaptive estimators for part of the euclidean parameter in these semiparametric models special attention is directed to group models in time series with the important subclass of models with time varying location and scale our set up is confronted with the existing literature and as examples we reconsider linear regression and arma tar and arch models