adaptive unstructured volume remeshing ii application to two and three dimensional level set simulations of multiphase flow in part i adaptive unstructured volume remeshing i the method j comput phys in press we presented an adaptive remeshing algorithm that automatically adjusts the size of the elements of meshes of unstructured triangles 2d and unstructured tetrahedra 3d with time and position in the computational domain in order to efficiently resolve the relevant physical scales here we illustrate the performance of an implementation of the algorithm in finite element level set simulations of deformable droplet and fluid fluid interface interactions breakup and coalescence in multiphase flows the wide range of length scales characterizing the dynamics are accurately resolved as demonstrated by comparison to experiments and to theoretical and sharp interface boundary integral numerical results the computational cost is found to be competitive even with respect to boundary integral methods for the first time using an interface capturing level set method we successfully simulate the inertia driven impact and rebound of a liquid droplet from a liquid interface and find agreement with recent experimental results

a quadratic spline based interface quasi reconstruction algorithm for accurate tracking of two phase flows a new quadratic spline based interface quasi reconstruction algorithm is presented which provides an accurate and continuous representation of the interface in a multiphase domain and facilitates the direct estimation of local interfacial curvature the fluid interface in each of the mixed cells is represented by piecewise parabolic curves and an initial discontinuous plic approximation of the interface is progressively converted into a smooth quadratic spline made of these parabolic curves the conversion is achieved by a sequence of predictor corrector operations enforcing function c 0 and derivative c 1 continuity at the cell boundaries using simple analytical expressions for the continuity requirements the efficacy and accuracy of the current algorithm has been demonstrated using standard test cases involving reconstruction of known static interface shapes and dynamically evolving interfaces in prescribed flow situations these benchmark studies illustrate that the present algorithm performs excellently as compared to the other interface reconstruction methods available in literature quadratic rate of error reduction with respect to grid size has been observed in all the cases with curved interface shapes only in situations where the interface geometry is primarily flat the rate of convergence becomes linear with the mesh size the flow algorithm implemented in the current work is designed to accurately balance the pressure gradients with the surface tension force at any location as a consequence it is able to minimize spurious flow currents arising from imperfect normal stress balance at the interface this has been demonstrated through the standard test problem of an inviscid droplet placed in a quiescent medium finally the direct curvature estimation ability of the current algorithm is illustrated through the coupled multiphase flow problem of a deformable air bubble rising through a column of water

new approaches to robust minimum variance filter design this paper is concerned with the design of robust filters that ensure minimum filtering error variance bounds for discrete time systems with parametric uncertainty residing in a polytope two efficient methods for robust kalman filter design are introduced the first utilizes a recently introduced relaxation of the quadratic stability requirement of the stationary filter design the second applies the new method of recursively solving a semidefinite program sdp subject to linear matrix inequalities lmis constraints to obtain a robust finite horizon time varying filter the proposed design techniques are compared with other existing methods it is shown via two examples that the results obtained by the new methods outperform all of the other designs

level set approach to mean curvature flow in arbitrary codimension we develop a level set theory for the mean curvature evolution of surfaces with arbitrary co dimension thus generalizing the previous work 8 15 on hypersurfaces the main idea is to surround the evolving surface of co dimension k in r by a family of hypersurfaces the level sets of a function evolving with normal velocity equal to the sum of the d k smallest principal curvatures the existence and the uniqueness of a weak level set solution is easily established using mainly the results of 8 and the theory of viscosity solutions for second order nonlinear parabolic equations the level set solutions coincide with the classical solutions whenever the latter exist the proof of this connection uses a careful analysis of the squared distance from the surfaces it is also shown that varifold solutions constructed by brakke 7 are included in the level set solutions the idea of surrounding the evolving surface by a family of hypersurfaces with a certain property is related to the barriers of de giorgi an introduction to the theory of barriers and his connection to the level set solutions is also provided

generalized tunstall codes for sources with memory tunstall codes are variable to fixed length codes that maximize the expected number of source letters per dictionary string for discrete memoryless sources we analyze a generalization of tunstall coding to sources with memory and demonstrate that as the dictionary size increases the number of code letters per source symbol comes arbitrarily close to the minimum among all variable to fixed length codes of the same size we also find the asymptotic relationship between the dictionary size and the average length of a dictionary entry

asymptotic behavior of the lempel ziv parsing scheme and digital search trees the lempel ziv parsing scheme finds a wide range of applications most notably in data compression and algorithms on words it partitions a sequence of length n into variable phrases such that a new phrase is the shortest substring not seen in the past as a phase the parameter of interest is the number mn of phrases that one can construct from a sequence of length n in this paper for the memoryless source with unequal probabilities of symbols generation we derive the limiting distribution of mn which turns out to be normal this proves a long standing open problem in fact to obtain this result we solved another open problem namely that of establishing the limiting distribution of the internal path length in a digital search tree the latter is a consequence of an asymptotic solution of a multiplicative differential functional equation often arising in the analysis of algorithms on words interestingly enough our findings are proved by a combination of probabilistic techniques such as renewal equation and uniform integrability and analytical techniques such as mellin transform differential functional equations de poissonization and so forth in concluding remarks we indicate a possibility of extending our results to markovian models

modelling merging and fragmentation in multiphase flows with surfer we introduce a new numerical method called surfer for the simulation of two and three dimensional flows with several fluid phases and free interfaces between them we consider incompressible fluids obeying the navier stokes equation with newtonian viscosity in the bulk of each phase capillary forces are taken into account even when interfaces merge or break up fluid interfaces are advanced in time using an exactly volume conserving variant of the volume of fluid algorithm thus allowing for full symmetry between fluid phases the navier stokes equation is solved using staggered finite differences on a mac grid and a split explicit time differencing scheme while incompressibility is enforced using an iterative multigrid poisson solver capillary effects are represented as a stress tensor computed from gradients of the volume fraction function this formulation is completely independent of the topology of interfaces and relatively easy to implement in 3d it also allows exact momentum conservation in the discretized algorithm numerical spurious effects or parasite currents are noticed and compared to similar effects in boltzmann lattice gas methods for immiscible fluids simulations of droplets pairs colliding in 2d and in 3d are shown interface reconnection is performed easily despite the large value of capillary forces during reconnection

an arbitrary lagrangian eulerian method for moving boundary problems and its application to jumping over water we develop an ale arbitrary lagrangian eulerian moving mesh method suitable for solving two dimensional and axisymmetric moving boundary problems including the interaction between a free surface and a solid structure this method employs a body fitted grid system where the gas liquid interface and solid liquid interface are lines of the grid system and complicated dynamic boundary conditions are incorporated naturally and accurately in a finite volume formulation the resulting nonlinear system of mass and momentum conservation is then solved by a fractional step projection method the method is validated on the uniform flow passing a cylinder a two dimensional flow with a solid structure and several problems of bubble dynamics axi symmetrical flows with a free surface for both steady and unsteady flows good agreement with other theoretical numerical and experimental results is obtained a further application is the investigation of a two dimensional mechanical strider a mass spring system interacting with a water surface demonstrating the ability of the method in handling the interaction between a solid structure and a free surface we find that the critical compression required to jump off the water surface varies linearly with spring constant for stiff springs and algebraically with exponent 0 7 for weak springs

variational formulations for surface tension capillarity and wetting the interest in the simulation of flows with significant surface tension effects has grown significantly in recent years this has been driven by the substantial advances made in the measurement and manufacturing of microscopic systems since at small length scales surface phenomena are dominant in this article surface tension capillarity and wetting effects are discussed in terms of the virtual work principle and shape sensitivity starting from first principles and arriving at variational formulations that are adequate for numerical treatment by finite elements for example to make the exposition self contained some elements of differential geometry are recalled using a formulation that is fully in cartesian coordinates and may thus be more friendly to readers not familiar with covariant derivatives all necessary results are proved in this cartesian formulation several numerical examples computed with a finite element level set formulation are used to illustrate this challenging physical problem

a direct time integral thinc scheme for sharp interfaces abstract this paper describes an improved multi dimensional tangent of hyperbola interface capturing thinc scheme that uses a direct time integration of the hyperbolic tangent function the new time integral thinc scheme is based on the assumption that the interface remains unchanged and moves with the velocity of the cell center during a computational time step a time varying hyperbolic tangent function representing the two phase distribution is then constructed and directly integrated in time compared with existing thinc methods that generally use third order total variation diminishing runge kutta rk3 schemes to update the volume fraction the proposed method requires only one reconstruction step thus reducing the computational cost several classical advection tests have been implemented and the results indicate that the proposed direct time integral thinc method 1 achieves computational errors close to those of the rk3 scheme at a computational cost that is close to that of the first order explicit scheme and 2 preserves better boundedness of the volume fractions than the original rk3 based thinc methods when using a larger steepness parameter and higher courant numbers the proposed approach is employed with the incompressible navier stokes equations to solve a 2d dambreak problem and the numerical results agree well with the corresponding experimental data demonstrating the applicability of the direct time integral thinc method

interface reconstruction with least squares fit and split advection in three dimensional cartesian geometry in this paper we present and analyze different volume of fluid vof reconstruction and advection algorithms that approximate the interface separating two immiscible fluids in the three dimensional space the paper describes the improvement of the reconstruction when a least square fit algorithm which minimizes a distance functional is applied its performance is tested for several smooth surfaces against other simple reconstruction methods then eulerian lagrangian and mixed split advection schemes are presented and analyzed in particular one advection method is discussed that conserves mass exactly for a divergence free velocity field thus allowing computations to machine precision

a relationship between stabilized finite element methods and the galerkin method with bubble functions abstract a relation between stabilized finite element methods and the galerkin method employing interpolations with bubble functions is established for the advective diffusive model and for the linearized compressible navier stokes equations the bubble functions are shown to help in stabilizing the advective operator without recourse to upwinding or any other numerical strategy in particular for the advective diffusive model the galerkin method employing piecewise linears with bubble functions is shown to be equivalent to the streamline upwind petrov galerkin supg method in the diffusive limit

robust filtering via semidefinite programming with applications to target tracking in this paper we propose a novel finite horizon discrete time time varying filtering method based on the robust semidefinite programming sdp technique the proposed method provides robust performance in the presence of norm bounded parameter uncertainties in the system model the robust performance of the proposed method is achieved by minimizing an upper bound on the worst case variance of the estimation error for all admissible systems our method is recursive and computationally efficient in our simulations the new method provides superior performance to some of the existing robust filtering approaches in particular when applied to the problem of target tracking the new method has led to a significant improvement in tracking performance our work shows that the robust sdp technique and the interior point algorithms can bring substantial benefits to practically important engineering problems

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

finite horizon robust kalman filter design we study the problem of finite horizon kalman filtering for systems involving a norm bounded uncertain block a new technique is presented for robust kalman filter design this technique involves using multiple scaling parameters that ran be optimized by solving a semidefinite program the use of optimized scaling parameters leads to an improved design a recursive design method that can be applied to real time applications is also proposed

sharp interface immersed boundary level set method for wave body interactions a sharp interface cartesian grid method for the large eddy simulation of two phase turbulent flows interacting with moving bodies is presented the overall approach uses a sharp interface immersed boundary formulation and a level set ghost fluid method for solid fluid and fluid fluid interface treatments respectively a four step fractional step method is used for velocity pressure coupling and a lagrangian dynamic smagorinsky subgrid scale model is adopted for large eddy simulations a simple contact angle boundary condition treatment that conforms to the immersed boundary formulation is developed a variety of test cases of different scales ranging from bubble dynamics water entry and exit landslide generated waves to ship hydrodynamics are performed for validation extensions for high reynolds number ship flows using wall layer models are also considered

flair fluz line segment model for advection and interface reconstruction abstract a computational technique for solving fluid problems with free surfaces and interfaces is presented the conventional cell volume fraction approach is employed for tracking the interfaces however for surface advection and its reconstruction a new and more accurate flair flux line segment model for advection and interface reconstruction algorithm is developed the surface is approximated by a set of line segments fitted at the boundary of every two neighboring computational cells a criterion is developed for identifying the line segment orientation by inspecting the cell volume fractions the new cell volume fraction field is obtained by integrating the advected area underneath the interface line segment as an example this technique is applied to the capillary driven viscous flow of an initially elliptic two dimensional fluid zone the problem is posed mathematically as a solution of the navier stokes equations with moving free surface boundary conditions the damping motion of the fluid zone is observed through transport of the free surface which is related to the instantaneous internal velocity field under the influence of surface tension and viscous forces

generalized navier boundary condition and geometric conservation law for surface tension we consider two fluid flow problems in an arbitrary lagrangian eulerian ale framework the purpose of this work is twofold first we address the problem of the moving contact line namely the line common to the two fluids and the wall second we perform a stability analysis in the energy norm for various numerical schemes taking into account the gravity and surface tension effects the problem of the moving contact line is treated with the so called generalized navier boundary conditions owing to these boundary conditions it is possible to circumvent the incompatibility between the classical no slip boundary condition and the fact that the contact line of the interface on the wall is actually moving the energy stability analysis is based in particular on an extension of the geometry conservation law gcl concept to the case of moving surfaces this extension is useful to study the contribution of the surface tension the theoretical and computational results presented in this paper allow us to propose a strategy which offers a good compromise between efficiency stability and artificial diffusion

a level set approach for computing solutions to incompressible two phase flow a level set approach for computing solutions to incompressible two phase flow is presented the interface between the two fluids is considered to be sharp and is described as the zero level set of a smooth function a new treatment of the level set method allows us to efficiently maintain the level set function as the signed distance from the interface we never have to explicitly reconstruct or find the zero level set consequently we are able to handle arbitrarily complex topologies large density and viscosity ratios and surface tension on relatively coarse grids we use a second order projection method along with a second order upwinded procedure for advecting the momentum and level set equations we consider the motion of air bubbles and water drops we also compute flows with multiple fluids such as air oil and water

second order accurate volume of fluid algorithms for tracking material interfaces we introduce two new volume of fluid interface reconstruction algorithms and compare the accuracy of these algorithms to four other widely used volume of fluid interface reconstruction algorithms we find that when the interface is smooth e g continuous with two continuous derivatives the new methods are second order accurate and the other algorithms are first order accurate we propose a design criteria for a volume of fluid interface reconstruction algorithm to be second order accurate namely that it reproduce lines in two space dimensions or planes in three space dimensions exactly we also introduce a second order unsplit volume of fluid advection algorithm that is based on a second order finite difference method for scalar conservation laws due to bell dawson and shubin we test this advection algorithm by modeling several different interface shapes propagating in two simple incompressible flows and compare the results with the standard second order operator split advection algorithm although both methods are second order accurate when the interface is smooth we find that the unsplit algorithm exhibits noticeably better resolution in regions where the interface has discontinuous derivatives such as at corners

an absolutely stabilized finite element method for the stokes problem on presente une formulation a elements finis absolument stabilisee pour le probleme de stokes on etablit des estimations d erreurs optimales dans la norme l 2 pour l approximation des champs de vitesses et de pressions

high order ale schemes for incompressible capillary flows the spatial discretization of problems with moving boundaries is considered incorporating the temporal evolution of not just the mechanical variables but also of the nodal positions of the moving mesh the outcome is a system of differential algebraic equations dae of index 2 or in the case of inertialess flow just 1 from the dae formulation it its possible to define strategies to build schemes of arbitrary accuracy we introduce here several schemes of order 2 and 3 that avoid the solution of a nonlinear system involving simultaneously the mechanical variables and the geometrical ones this class of schemes has been the one adopted by the majority of practitioners of computational fluid dynamics up to now the proposed schemes indeed achieve the design accuracy and further show stability restrictions that are not significantly more severe than those of popular first order schemes the numerical experimentation is performed on capillary problems discretized by both div stable p 2 p 1 p 1 p 1 and equal order p 1 p 1 stabilized finite elements and incorporating surface tension and triple contact line effects

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

a self adaptive oriented particles level set method for tracking interfaces a new method for tracking evolving interfaces by lagrangian particles in conjunction with a level set approach is introduced this numerical technique is based on the use of time evolution equations for fundamental vector and tensor quantities defined on the front and represents a new and convenient way to couple the advantages of the eulerian description given by a level set function f to the use of lagrangian massless particles the term oriented points out that the information advected by the particles not only concern the spatial location but also the local outward normal vector n to the interface c and the second fundamental tensor the shape operator n the particles are exactly located upon c and provide all the requested information for tracking the interface on their own in addition a self adaptive mechanism suitably modifies at each time step the markers distribution in the numerical domain each particle behaves both as a potential seeder of new markers on c so as to guarantee an accurate reconstruction of the interface and a de seeder to avoid any useless gathering of markers and to limit the computational effort the algorithm is conceived to avoid any transport equation for f and to confine the level set function to the role of a mere post processing tool thus all the numerical diffusion problems usually affecting the level set methodology are removed the method has been tested both on 2d and 3d configurations it carries out a fast reconstruction of the interface and its accuracy is only limited by the spatial resolution of the mesh

an interface reconstruction method based on analytical formulae for 2d planar and axisymmetric arbitrary convex cells in this paper we propose a non iterative interface reconstruction method for 2d planar and axisymmetric geometries that is valid for arbitrary convex cells and intended to be used in multi material simulation codes with sharp interface treatment for instance assuming that the normal vector to the interface is known we focus on the computation of the line constant so that the polygon resulting from the cell interface intersection has the requested volume to this end we first decompose the cell in trapezoidal elements and then propose a new approach to derive an exact formula for the trapezoids volumes this formula derived for both the planar and axisymmetric cases is used to first bracket and then find the line constant that exactly matches the prescribed volume the computational efficiency of the proposed method is demonstrated over a large number of reproducible conditions and against two existing methods

a new finite element formulation for computational fluid dynamics viii the galerkin least squares method for advective diffusive equations abstract galerkin least squares finite element methods are presented for advective diffusive equations galerkin least squares represents a conceptual simplification of supg and is in fact applicable to a wide variety of other problem types a convergence analysis and error estimates are presented

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

a mesh dependent model for applying dynamic contact angles to vof simulations typical vof algorithms rely on an implicit slip that scales with mesh refinement to allow contact lines to move along no slip boundaries as a result solutions of contact line phenomena vary continuously with mesh spacing this paper presents examples of that variation a mesh dependent dynamic contact angle model is then presented that is based on fundamental hydrodynamics and serves as a more appropriate boundary condition at a moving contact line this new boundary condition eliminates the stress singularity at the contact line the resulting problem is thus well posed and yields solutions that converge with mesh refinement numerical results are presented of a solid plate withdrawing from a fluid pool and of spontaneous droplet spread at small capillary and reynolds numbers

a finite volume hllc based scheme for compressible interfacial flows with surface tension shock waves are often used in experiments to create a shear flow across liquid droplets to study secondary atomization similar behavior occurs inside of supersonic combustors scramjets under startup conditions but it is challenging to study these conditions experimentally in order to investigate this phenomenon further a numerical approach is developed to simulate compressible multiphase flows under the effects of surface tension forces the flow field is solved via the compressible multicomponent euler equations i e the five equation model discretized with the finite volume method on a uniform cartesian grid the solver utilizes a total variation diminishing tvd third order rungekutta method for time marching and second order tvd spatial reconstruction surface tension is incorporated using the continuum surface force csf model fluxes are upwinded with a modified hartenlaxvan leer contact hllc approximate riemann solver an interface compression scheme is employed to counter numerical diffusion of the interface the present work includes modifications to both the hllc solver and the interface compression scheme to account for capillary force terms and the associated pressure jump across the gasliquid interface a simple method for numerically computing the interface curvature is developed and an acoustic scaling of the surface tension coefficient is proposed for the non dimensionalization of the model the model captures the surface tension induced pressure jump exactly if the exact curvature is known and is further verified with an oscillating elliptical droplet and mach 1 47 and 3 shock droplet interaction problems the general characteristics of secondary atomization at a range of weber numbers are also captured in a series of simulations

an arbitrary lagrangian eulerian finite element method for solving three dimensional free surface flows abstract this paper discusses numerical solution of unsteady three dimensional free surface flows the governing equilibrium equations are written in the framework of the arbitrary lagrangian eulerian kinematic description the corresponding variational formulation is established afterwards since the variational problems are nonlinear with respect to the moving coordinates a second order approximate variational problem is derived after a consistent linearization of the referential motion stability of the discrete formulations is ensured with the help of a new stabilization method a robust preconditioned gmres algorithm is then used to solve the resulting set of nonlinear equations finally the computational algorithms are assessed through numerical studies of various problems a large sloshing flow in a three dimensional reservoir a discharge flow from a reservoir simulation of a liquid vortex produced inside a cylindrical container with a disk rotating at the bottom and a three dimensional practical hydraulic problem

a method for computing flow fields around moving bodies abstract a new method for computing flow fields with arbitrarily moving boundaries is proposed under the concept of lie derivatives the field equations in general moving coordinates are derived which consist of several kinds of equations for example one written in viviand s conservative form according to our formulation it is natural and reasonable to consider that the computational coordinates fitted to the body move in space contrary to the usual computational procedures the two dimensional incompressible navier stokes equations in gemeral moving coordinates are solved by a finite difference method the present calculations are made for a the blood flow in human ventricle and b the dynamic stall process on oscillating airfoil consequently it is shown that the flows generated by moving bodies can easily be analyzed by the present method

h 2 robust filter design with performance certificate via convex programming in this paper a new approach to h 2 robust filter design is proposed both continuous and discrete time invariant systems subject to polytopic parameter uncertainty are considered after a brief discussion on some of the most expressive methods available for h 2 robust filter design a new one based on a performance certificate calculation is presented the performance certificate is given in terms of the gap produced by the robust filter between lower and upper bounds of a minimax programming problem where the h 2 norm of the estimation error is maximized with respect to the feasible uncertainties and minimized with respect to all linear rational and causal filters the calculations are performed through convex programming methods developed to deal with linear matrix inequality lmi many examples borrowed from the literature to date are solved and it is shown that the proposed method outperforms all other designs

robust kalman filtering for uncertain discrete time systems this paper is concerned with the problem of a kalman filter design for uncertain discrete time systems the system under consideration is subjected to time varying norm bounded parameter uncertainty in both the state and output matrices the problem addressed is the design of a linear filter such that the variance of the filtering error is guaranteed to be within a certain bound for all admissible uncertainties furthermore the guaranteed cost can be optimized by appropriately searching a scaling design parameter

a linear matrix inequality approach to robust h sub spl infin filtering we consider the robust h sub spl infin filtering problem for a general class of uncertain linear systems described by the so called integral quadratic constraints iqcs this problem is important in many signal processing applications where noise nonlinearity quantization errors time delays and unmodeled dynamics can be naturally described by iqcs the main contribution of this paper is to show that the robust h spl infin filtering problem can be solved using linear matrix inequality lmi techniques which are numerically efficient owing to recent advances in convex optimization the paper deals with both continuous and discrete time uncertain linear systems

robustness measures for linear systems with application to stability radii of hurwitz and schur polynomials in this paper we consider robustness measures stability radii for system matrices which are subjected to structured real and complex perturbations of the form a a bdc where b c are given matrices our object is twofold a to present a number of new results mainly concerning the real stability radius and its differences from the complex one b to give an overview of our approach to the robustness analysis of linear state space systems including basic properties and characterizations of the complex stability radius applying the results to the special case where a is in companion form and b 0 0 0 1 t we are able to determine stability radii for hurwitz and schur polynomials under arbitrary complex and real affine perturbations of the coefficient vector computable formulae are obtained and illustrated by several examples

a nitsche cut finite element method for the oseen problem with general navier boundary conditions abstract in this work a nitsche based imposition of generalized navier conditions on cut meshes for the oseen problem is presented other methods from literature dealing with the generalized navier condition impose this condition by means of substituting the tangential robin condition in a classical galerkin way these methods work fine for a large slip length coefficient but lead to conditioning and stability issues when it approaches zero we introduce a novel method for the weak imposition of the generalized navier condition which remains well posed and stable for arbitrary choice of slip length including zero the method proposed here builds on the formulation done by juntunen and stenberg 2009 they impose a robin condition for the poisson problem by means of nitsche s method for an arbitrary combination of the dirichlet and neumann parts of the condition the analysis conducted for the proposed method is done in a similar fashion as in massing et al 2018 but is done here for a more general type of boundary condition the analysis proves stability for all flow regimes and all choices of slip lengths also an l 2 optimal estimate for the velocity error is shown which was not conducted in the previously mentioned work a numerical example is carried out for varying slip lengths to verify the robustness and stability of the method with respect to the choice of slip length even though proofs and formulations are presented for the more general case of an unfitted grid method they can easily be reduced to the simpler case of a boundary fitted grid with the removal of the ghost penalty stabilization terms

relations between redundancy patterns of the shannon code and wave diffraction patterns of partially disordered media the average redundancy of the shannon code rn as a function of the block length n is known to exhibit two very different types of behavior depending on the rationality or irrationality of certain parameters of the source it either converges to 1 2 as n grows without bound or it may have a nonvanishing oscillatory quasi periodic pattern around the value 1 2 for all large n in this paper we make an attempt to shed some insight into this erratic behavior of rn by drawing an analogy with the realm of physics of wave propagation in particular the elementary theory of scattering and diffraction it turns out that there are two types of behavior of wave diffraction patterns formed by crystals which are correspondingly analogous to the two types of patterns of rn when the crystal is perfect the diffraction intensity spectrum exhibits very sharp peaks a k a bragg peaks at wavelengths of full constructive interference these wavelengths correspond to the frequencies of the harmonic waves of the oscillatory mode of rn on the other hand when the crystal is imperfect and there is a considerable degree of disorder in its structure the bragg peaks disappear and the behavior of this mode is analogous to the one where rn is convergent

temporal evolution of periodic disturbances in two layer couette flow the time dependent motion for a two layer couette flow consisting of fluids of different viscosities is simulated numerically by using an algorithm based on the volume of fluid vof method interfacial tension is included via a continuous surface force csf algorithm the algorithm is fine tuned to handle the motion which is driven by a shear induced interfacial instability due to the viscosity stratification the code is validated against linear theory two prototypical situations are presented one at a moderately high reynolds number and the other at a lower reynolds number the initial condition is seeded with the eigenmode of largest growth rate with amplitudes that are varied from those that capture the linear regime to larger values for nonlinear regimes issues of free surface advection and viscosity interpolation are discussed the onset of nonlinearity occurs at the interface and is quadratic followed by wave steepening

cellwise conservative unsplit advection for the volume of fluid method we present a cellwise conservative unsplit ccu advection scheme for the volume of fluid method vof in 2d contrary to other schemes based on explicit calculations of the flux balances the ccu advection adopts a cellwise approach where the pre images of the control volumes are traced backwards through the flow map the donating regions of the fluxes are calculated via the streaklines of the grid intersections represented as polygonal chains whose vertices are determined by backward tracing of particles injected in the flow at different times high order accuracy is obtained from the fourth order runge kutta method where intermediate velocities along pathlines are determined with quadratic temporal and bicubic spatial interpolations the volumes of the donating regions are corrected in order to fulfill the discrete continuity of incompressible flows consequently the calculation produces non overlapping donating regions and pre images with conforming edges to their neighbors resulting in the conservativeness and the boundedness liquid volume fraction inside the interval 0 1 of the ccu advection scheme finally the update of the liquid volume fractions is computed from the intersections of the pre image polygons with the reconstructed interfaces the ccu scheme is tested on several benchmark tests for the vof advection together with the standard piecewise linear interface calculation plic the geometrical errors of the ccu compare favorably with other unsplit vof plic schemes finally potential improvements of the vof method with the use of more precise interface representation techniques and the future extension of the ccu scheme to 3d are discussed cellwise vof update through backward tracing of the cell s pre image accuracy enhanced via bicubic spatial interpolation and polygonal chain streakline the ccu advection scheme is fully conservative and bounded no limitation on the courant number geometrical errors dominated by plic interface representation errors

robust discrete time minimum variance filtering the bounded variance filtered estimation of the state of an uncertain linear discrete time system with an unknown norm bounded parameter matrix is considered an upper bound on the variance of the estimation error is found for all admissible systems and estimators are derived that minimize the latter bound we treat the finite horizon time varying case and the infinite time case where the nominal system model is time invariant in the special stationary case where it is known that the uncertain system is time invariant we provide a robust filter for all uncertainties that still keep the system asymptotically stable

volume of fluid interface tracking with smoothed surface stress methods for three dimensional flows motivated by the need for three dimensional methods for interface calculations that can deal with topology changes we describe a numerical scheme built from a volume of fluid interface tracking technique that uses a piecewise linear interface calculation in each cell momentum balance is computed using explicit finite volume finite differences on a regular cubic grid surface tension is implemented by the continuous surface stress or continuous surface force method examples and verifications of the method are given by comparing simulations to analytical results and experiments for sedimenting droplet arrays and capillary waves at finite reynolds number in the case of a pinching pendant drop both three dimensional and axisymmetric simulations are compared to experiments agreement is found both before and after the reconnections

optimal selection of the bubble function in the stabilization of the p1 p1 element for the stokes problem in this paper we propose a criterion for the selection of the local stabilizing function of the mini discretization of the stokes problem we then show how the application of this criterion to nonconforming approximation leads to a particularly simple solution

numerical methods for tracking interfaces an overview is given of special numerical methods for tracking discontinuous fronts and interfaces these methods include surface tracking methods based on connected marker points along the interface volume tracking methods that track the volume occupied by the solution regions bounded by the interfaces and moving mesh methods where the underlying mesh is aligned and moved with the interface the pros and cons of the current methods are discussed and a new method is proposed that overcomes some of the difficulties encountered in approximating equations with multiple interacting interfaces

an interface reconstruction method based on an analytical formula for 3d arbitrary convex cells in this paper we are interested in an interface reconstruction method for 3d arbitrary convex cells that could be used in multi material flow simulations for instance we assume that the interface is represented by a plane whose normal vector is known and we focus on the volume matching step that consists in finding the plane constant so that it splits the cell according to a given volume fraction we follow the same approach as in the recent authors publication for 2d arbitrary convex cells in planar and axisymmetrical geometries namely we derive an analytical formula for the volume of the specific prismatoids obtained when decomposing the cell using the planes that are parallel to the interface and passing through all the cell nodes this formula is used to bracket the interface plane constant such that the volume matching problem is rewritten in a single prismatoid in which the same formula is used to find the final solution the proposed method is tested against an important number of reproducible configurations and shown to be at least five times faster

asymptotic average redundancy of huffman and other block codes we study asymptotically the redundancy of huffman and other codes it has been known from the inception of the huffman 1952 code that in the worst case its redundancy defined as the excess of the code length over the optimal ideal code length is not more than one however to the best of our knowledge no precise asymptotic results have been reported in literature thus far we consider here a memoryless binary source generating a sequence of length n distributed as binomial n p with p being the probability of emitting 0 based on the results of stubley 1994 we prove that for p 1 2 1 m 1 2 sup 1 m 2 sup m o spl rho sup n spl alpha n m rational where spl alpha log sub 2 1 p p and spl beta log sub 2 1 p spl rho x x is the fractional part of x the appearance of the fractal like function explains the erratic behavior of the huffman redundancy and its resistance to succumb to a precise analysis as a side result we prove that the average redundancy of the shannon block code is as n spl rarr spl infin r sub n sup s 1 2 o 1 spl alpha irrational 1 2 1 m 1 2 o spl rho sup n spl alpha n m rational where spl rho 1 finally we derive the redundancy of the golomb 1966 code for the geometric distribution which can be viewed as a special case of the huffman and shannon codes golomb s code redundancy has only oscillating behavior i e there is not convergent mode these findings are obtained by analytic methods such as theory of distribution of sequences modulo 1 and fourier series

space time discontinuous galerkin method for nonlinear water waves a space time discontinuous galerkin dg finite element method for nonlinear water waves in an inviscid and incompressible fluid is presented the space time dg method results in a conservative numerical discretization on time dependent deforming meshes which follow the free surface evolution the algorithm is higher order accurate both in space and time and closely related to an arbitrary lagrangian eulerian ale approach a detailed derivation of the numerical algorithm is given including an efficient procedure to solve the nonlinear algebraic equations resulting from the space time discretization numerical examples are shown on a series of model problems to demonstrate the accuracy and capabilities of the method

on the average redundancy rate of the lempel ziv code in this paper we settle a long standing open problem concerning the average redundancy r sub n of the lempel ziv 78 lz78 code we prove that for a memoryless source the average redundancy rate attains asymptotically er sub n a spl delta n log n o log log n log sup 2 n where a is an explicitly given constant that depends on source characteristics and spl delta x is a fluctuating function with a small amplitude we also derive the leading term for the kth moment of the number of phrases we conclude by conjecturing a precise formula on the expected redundancy for a markovian source the main result of this paper is a consequence of the second order properties of the lempel ziv algorithm obtained by jacquet and szpankowski 1995 these findings have been established by analytical techniques of the precise analysis of algorithms we give a brief survey of these results since they are interesting in their own right and shed some light on the probabilistic behavior of pattern matching based data compression

a geometrical area preserving volume of fluid advection method a new class of algorithms that preserve mass exactly for incompressible flows on a cartesian mesh are presented they amount to piecewise linear area preserving mappings of tessellations of the plane they are equivalent to volume of fluid vof advection methods which are decomposed into an eulerian implicit scheme in one direction followed by a lagrangian explicit step in the other one it is demonstrated that mass conservation is exact for incompressible flows and that there are no undershoots or overshoots of the volume fraction which thus always remains constrained between 0 and 1

phase field computations for ternary fluid flows we present a new phase field model for three component immiscible liquid flows with surface tension in the phase field approach the classical sharp interface between the two immiscible fluids is replaced by a transition region across which the properties of fluids change continuously the proposed method incorporates a chemical potential which can eliminate the unphysical phase field profile and a continuous surface tension force formulation from which we can calculate the pressure field directly from the governing equations the capabilities of the method are demonstrated with several examples we compute the ternary phase separation via spinodal decomposition equilibrium phase field profiles pressure field distribution and a three interface contact angle resulting from a spreading liquid lens on an interface the numerical results show excellent agreement with analytical solutions

on the redundancy of optimal codes with limited word length some limitations are given on the redundancy of d ary codes with maximal codeword length l an upper bound that improves on a previous result of e n gilbert 1971 is given it is then shown that the redundancy of these constrained codes is very close to that of the unconstrained huffman codes when the number of codewords n is such that nd sup 1 l becomes negligible a tight bound is given on the redundancy when only the most likely probabilities are known in the binary case a tight lower bound is given on the redundancy when only the least likely probability is known

a direct comparison between volume and surface tracking methods with a boundary fitted coordinate transformation and third order upwinding a volume tracking vt and a front tracking ft algorithm are implemented and compared for locating the interface between two immiscible incompressible newtonian fluids in a tube with a periodically varying circular cross section initially the fluids are stationary and stratified in an axisymmetric arrangement so that one is around the axis of the tube core fluid and the other one surrounds it annular fluid a constant pressure gradient sets them in motion with both vt and ft a boundary fitted coordinate transformation is applied and appropriate modifications are made to adopt either method in this geometry the surface tension force is approximated using the continuous surface force method all terms appearing in the continuity and momentum equations are approximated using centered finite differences in space and one sided forward finite differences in time in each time step the incompressibility condition is enforced by a transformed poisson equation which is linear in pressure this equation is solved by either direct lu decomposition or a multigrid iterative solver when the two fluids have the same density the former method is about 3 5 times faster but when they do not the multigrid solver is as much as 10 times faster than the lu decomposition when the interface does not break and the reynolds number remains small the accuracy and rates of convergence of vt and ft are comparable the well known failure of centered finite differences arises as the reynolds number increases and leads to non physical oscillations in the interface and failure of both methods to converge with mesh refinement these problems are resolved and computations with reynolds as large as 500 converged by approximating the convective terms in the momentum equations by third order upwind differences using lagrangian polynomials when the volume of the core fluid or the weber number decrease increasing the importance of interfacial tension and leading to breakup of the interface forming a drop of core fluid the ft method converges faster with mesh refinement than the vt method and upwinding may be required finally examining the generation of spurious currents around a stationary bubble in the tube for ohnesorge numbers between 0 1 and 10 it is found that the maximum velocity remains approximately the same in spite mesh refinements when vt is applied whereas it is of the same order of magnitude for the coarsest mesh and monotonically decreases with mesh refinement when ft is applied

a fast pressure correction method for incompressible two fluid flows we have developed a new pressure correction method for simulating incompressible two fluid flows with large density and viscosity ratios the method s main advantage is that the variable coefficient poisson equation that arises in solving the incompressible navier stokes equations for two fluid flows is reduced to a constant coefficient equation which can be solved with an fft based fast poisson solver this reduction is achieved by splitting the variable density pressure gradient term in the governing equations the validity of this splitting is demonstrated from our numerical tests and it is explained from a physical viewpoint in this paper the new pressure correction method is coupled with a mass conserving volume of fluid method to capture the motion of the interface between the two fluids but in general it could be coupled with other interface advection methods such as level set phase field or front tracking first we verified the new pressure correction method using the capillary wave test case up to density and viscosity ratios of 10 000 then we validated the method by simulating the motion of a falling water droplet in air and comparing the droplet terminal velocity with an experimental value next the method is shown to be second order accurate in space and time independent of the vof method and it conserves mass momentum and kinetic energy in the inviscid limit also we show that for solving the two fluid navier stokes equations the method is 10 40 times faster than the standard pressure correction method which uses multigrid to solve the variable coefficient poisson equation finally we show that the method is capable of performing fully resolved direct numerical simulation dns of droplet laden isotropic turbulence with thousands of droplets using a computational mesh of 1024 3 points

free surface flows under impacting droplets a numerical method which fulfils the free surface boundary conditions and extrapolates the fluid velocity into empty grid cells outside the fluid region on a fixed cartesian grid system is presented the complex three dimensional vortex structures formed via surface vortex interaction and induction between vortices have been computed using the proposed technique implemented within a level set method for both vertical and oblique droplet impacts in incompressible fluids the present results have been validated through numerical tests which confirm zero tangential shear at the free surface and comparisons with experimental observations of cavity and vortex ring formation underneath the impact location in some cases transitions from a concentric vortex ring to a fully three dimensional vortex structure has been confirmed whilst the primary vortex ring is initiated at the highly curved contact surface between the droplet and receiving surface azimuthal instabilities are manifested in the shear layer around the cavity crater developing after the vertical impact resulting in axial counter rotating vorticity between the cavity and descending vortex ring underlying mechanisms which induce local deformation of the free surface creating a so called scar due to the sub surface vortices at the oblique impacts are also discussed

virtual bubbles and galerkin least squares type methods ga l s abstract the equivalence between stabilized finite element methods or galerkin least squares tyoe methods ga l s and the standard galerkin method with bubble functions is established in an abstract framework the results are applicable to various finite element spaces including high order elements and applications to the advective diffusive model and to the stokes problem are presented illustrating the potential of the abstract theory introduced here

an algorithm for prescribed mean curvature using isogeometric methods we present a newton type algorithm to find parametric surfaces of prescribed mean curvature with a fixed given boundary in particular it applies to the problem of minimal surfaces the algorithm relies on some global regularity of the spaces where it is posed which is naturally fitted for discretization with isogeometric type of spaces we introduce a discretization of the continuous algorithm and present a simple implementation using the recently released isogeometric software library igatools finally we show several numerical experiments which highlight the convergence properties of the scheme

a computational framework for free surface fluid flows accounting for surface tension abstract this work is concerned with the simulation of incompressible newtonian fluid flow problems with free surfaces in the presence of surface tension the computational framework presented is based on the stabilised velocity pressure finite element method the movement and deformation of the computational domain are accounted for by employing the arbitrary lagrangian eulerian ale description of the fluid kinematics the numerical model is extended to incorporate surface tension effects a novel partitioned solution procedure is developed based on the newton raphson methodology which incorporates full linearisation of the overall incremental problem several numerical examples are provided to demonstrate the efficiency of the methodology

solution techniques for multi physics problems with application to computational nonlinear aeroelasticity this paper presents an efficient parallel distributed methodology for solving multi physic problems this methodology is based on functional and geometric decompositions solution algorithms for coupled problems are discussed all these techniques are illustrated for the case of cfd based aeroelasticity a numerical study is performed for the agrad 445 6 aeroelastic test case 2005 elsevier ltd all rights reserved

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

a finite element method for the numerical solution of the coupled cahn hilliard and navier stokes system for moving contact line problems in this paper a semi implicit finite element method is presented for the coupled cahn hilliard and navier stokes equations with the generalized navier boundary condition for the moving contact line problems in our method the system is solved in a decoupled way for the cahn hilliard equations a convex splitting scheme is used along with a p1 p1 finite element discretization the scheme is unconditionally stable a linearized semi implicit p2 p0 mixed finite element method is employed to solve the navier stokes equations with our method the generalized navier boundary condition is extended to handle the moving contact line problems with complex boundary in a very natural way the efficiency and capacity of the present method are well demonstrated with several numerical examples

godunov type method on non structured meshes for three dimensional moving boundary problems abstract this paper presents a numerical method for the computation of compressible flows in domains whose boundaries move in a well defined predictable manner the method uses the space time formulation by godunov while the discretization is conducted on non structured tetrahedral meshes using roe s approximate riemann solver an implicit time stepping and a muscl type interpolation the computation of the geometrical parameters required to take into account the movement of the boundaries is described examples including the calculation of the flow in the cylinder of an internal combustion engine illustrates the possibilities of the method

linear estimation in krein spaces ii applications we have shown that several interesting problems in h sup spl infin filtering quadratic game theory and risk sensitive control and estimation follow as special cases of the krein space linear estimation theory developed in part i we show that all these problems can be cast into the problem of calculating the stationary point of certain second order forms and that by considering the appropriate state space models and error gramians we can use the krein space estimation theory to calculate the stationary points and study their properties the approach discussed here allows for interesting generalizations such as finite memory adaptive filtering with varying sliding patterns

average redundancy of the shannon code for markov sources it is known that for memoryless sources the average and maximal redundancy of fixed to variable length codes such as the shannon and huffman codes exhibit two modes of behavior for long blocks it either converges to a limit or it has an oscillatory pattern depending on the irrationality or rationality respectively of certain parameters that depend on the source in this paper we extend these findings concerning the shannon code to the case of a markov source we provide a precise characterization of the convergent versus oscillatory behavior of the shannon code redundancy for a class of irreducible periodic and aperiodic markov sources these findings are obtained by analytic methods such as fourier fejer series analysis and spectral analysis of matrices

a continuum method for modeling surface tension abstract a new method for modeling surface tension effects on fluid motion has been developed interfaces between fluids of different properties or colors are represented as transition regions of finite thickness across which the color variable varies continuously at each point in the transition region a force density is defined which is proportional to the curvature of the surface of constant color at that point it is normalized so that the conventional description of surface tension on an interface is recovered when the ratio of local transition region thickness to local radius of curvature approaches zero the continuum method eliminates the need for interface reconstruction simplifies the calculation of surface tension enables accurate modeling of two and three dimensional fluid flows driven by surface forces and does not impose any modeling restrictions on the number complexity or dynamic evolution of fluid interfaces having surface tension computational results for two dimensional flows are given to illustrate the properties of the method

a new method to h2 robust filter design abstract in this paper a new method to h 2 robust filter design is proposed both continuous and discrete time settings are considered for systems subject to polytopic parameter uncertainty lower and upper bounds of the true cost are determined in order to evaluate the degree of sub optimality of the proposed robust filter the design method is based on the parametrization of all robust filters as a convex combination of kalman filters associated to each vertex of the uncertainty domain among all feasible filters the one minimizing a guaranteed h 2 cost of the estimation error is determined by a pure convex programming problem expressed in terms of linear matrix inequalities lmis the order of the robust filter is generally greater than the order of the plant a fact that contributes to reduce conservatism the proposed design technique is compared with other methods available in the literature in several examples solved the proposed method outperforms all other designs

a robust h sub 2 filtering approach and its application to equalizer design for communication systems in this paper we aim at developing a robust h sub 2 filtering approach to the design of robust equalizers for communication systems the contents of this paper mainly include two parts first we present a robust h sub 2 filter design method for general multi input multioutput linear systems with norm bounded uncertainties in the system matrices based on the linear matrix inequality technique the characteristics of the equalization problem are taken into account in the filtering model considered here the advantage of the proposed method is that we can find the optimal solution to robust h sub 2 filtering problem at a reasonable computational burden second we apply the above method to the design of robust equalizers two generic examples are studied one for a single transmit and receive antenna system and another for a multiple transmit and receive antenna system both analytical and simulation results show that robust h sub 2 equalizer outperforms the zero forcing equalizer in both bit error rate and mean square errors in the whole simulated range of the signal to noise ratio snr when the channel is perturbed from its nominal value while for the nominal channel the robust h sub 2 equalizer performs better than the zero forcing equalizer when the snr is lower but it performs worse than the zero forcing equalizer when the snr is higher

numerical simulation of free surface incompressible liquid flows surrounded by compressible gas a numerical model for the three dimensional simulation of liquid gas flows with free surfaces is presented the incompressible navier stokes equations are assumed to hold in the liquid domain in the gas domain the velocity is disregarded the pressure is supposed to be constant in each connected component of the gas domain and follows the ideal gas law the gas pressure is imposed as a normal force on the liquid gas interface an implicit splitting scheme is used to decouple the physical phenomena given the gas pressure on the interface the method described in j comput phys 155 1999 439 int j numer meth fluids 42 7 2003 697 is used to track the liquid domain and to compute the velocity and pressure fields in the liquid then the connected components of the gas domain are found using an original numbering algorithm finally the gas pressure is updated from the ideal gas law in each connected component of gas the implementation is validated in the frame of mould filling numerical results in two and three space dimensions show that the effect of pressure in the bubbles of gas trapped by the liquid cannot be neglected

a parallel eulerian interface tracking lagrangian point particle multi scale coupling procedure this paper presents a parallel eulerian lagrangian multi scale coupling procedure for two phase flows at the fully resolved scale the dynamically evolving phase interface is tracked using a eulerian approach in regions of the flow where the phase interface geometry can no longer be resolved adequately separated small scale liquid structures are described by a lagrangian point particle approach the coupling procedure of these two descriptions consists of an efficient parallel algorithm that identifies tracked liquid candidate structures removes them from the resolved eulerian description and inserts them into the lagrangian description preserving their position mass momentum and lower order shape while in principle applicable to level set volume of fluid and marker particle interface tracking methods for the fully resolved scale this paper focuses on examples from atomization simulations using the refined level set grid method

a front tracking method for viscous incompressible multi fluid flows abstract a method to simulate unsteady multi fluid flows in which a sharp interface or a front separates incompressible fluids of different density and viscosity is described the flow field is discretized by a conservative finite difference approximation on a stationary grid and the interface is explicitly represented by a separate unstructured grid that moves through the stationary grid since the interface deforms continuously it is necessary to restructure its grid as the calculations proceed in addition to keeping the density and viscosity stratification sharp the tracked interface provides a natural way to include surface tension effects both two and three dimensional full numerical simulations of bubble motion are presented

a computational framework for fluid structure interaction finite element formulation and applications abstract this work is concerned with the modelling of the interaction of fluid flow with flexibly supported rigid bodies the fluid flow considered is governed by the incompressible navier stokes equations and modelled by employing stabilised low order velocity pressure finite elements the motion of the fluid domain is accounted for by an arbitrary lagrangian eulerian ale strategy the rigid body motion excited by the fluid flow is restricted by the elastic and damping properties of the supports for the temporal discretisation the discrete implicit generalised method is employed the resulting strongly coupled set of nonlinear equations is solved by means of a novel partitioned solution procedure which is based on the newton raphson methodology and incorporates full linearisation of the overall incremental problem the strong coupling is resolved and optimal convergence of the residuals is achieved several numerical examples are presented to demonstrate the robustness and efficiency of the methodology the examples clearly capture the phenomena of vortex induced oscillations and galloping

complexity of strings in the class of markov sources shannon s self information of a string is generalized to its complexity relative to the class of finite state machine fsm defined sources unlike an earlier generalization the new one is valid for both short and long strings the definition is justified in part by a theorem stating that asymptotically the mean complexity provides a tight lower bound for the mean length of all so called regular codes this also generalizes shannon s noiseless coding theorem for a large subclass of fsm sources a simple algorithm is described for computing the complexity

applications of convex optimization in signal processing and digital communication in the last two decades the mathematical programming community has witnessed some spectacular advances in interior point methods and robust optimization these advances have recently started to significantly impact various fields of applied sciences and engineering where computational efficiency is essential this paper focuses on two such fields digital signal processing and communication in the past the widely used optimization methods in both fields had been the gradient descent or least squares methods both of which are known to suffer from the usual headaches of stepsize selection algorithm initialization and local minima with the recent advances in conic and robust optimization the opportunity is ripe to use the newly developed interior point optimization techniques and highly efficient software tools to help advance the fields of signal processing and digital communication this paper surveys recent successes of applying interior point and robust optimization to solve some core problems in these two fields the successful applications considered in this paper include adaptive filtering robust beamforming design and analysis of multi user communication system channel equalization decoding and detection throughout our emphasis is on how to exploit the hidden convexity convex reformulation of semi infinite constraints analysis of convergence complexity and performance as well as efficient practical implementation

goal oriented error estimation and adaptivity for free boundary problems the domain map linearization approach in free boundary problems the accuracy of a goal quantity of interest depends on both the accuracy of the approximate solution and the accuracy of the domain approximation we develop duality based a posteriori error estimates for functional outputs of solutions of free boundary problems that include both sources of error the derivation of an appropriate dual problem linearized adjoint is however nonobvious for free boundary problems to derive an appropriate dual problem we present the domain map linearization approach in this approach the free boundary problem is first transformed into an equivalent problem on a fixed reference domain after which the dual problem is obtained by linearization with respect to the domain map we show for a bernoulli type free boundary problem that this dual problem corresponds to a poisson problem with a nonlocal robin type boundary condition furthermore we present numerical experiments that demonstrate the effectivity of the dual based error estimate and its usefulness in goal oriented adaptive mesh refinement

an all speed relaxation scheme for interface flows with surface tension we consider interface flows where compressibility and capillary forces surface tension are significant these flows are described by a non conservative unconditionally hyperbolic multiphase model the numerical approximation is based on finite volume method for unstructured grids at the discrete level the surface tension is approximated by a volume force csf formulation the interface physical properties are recovered by designing an appropriate linearized riemann solver relaxation scheme that prevents spurious oscillations near material interfaces for low speed flows a preconditioning linearization is proposed and the low mach asymptotic is formally recovered numerical computations for a bubble equilibrium converge to the required laplace law and the dynamic of a drop falling under gravity is in agreement with experimental observations