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

gensmac a computational marker and cell method for free surface flows in general domains abstract a computer program for solving two dimensional incompressible viscous fluid flow in general domains is described this is based on the simplified marker and cell technique but it has a number of novel features a user supplied data file of coordinates prescribes the fluid domain which can be quite general and needs only to be connected with a view to parallelisation the momentum equations are solved explicitly but an automatic step changing routine optimises the stability restriction a conjugate gradient solver is used to invert the discrete poisson equation an accurate approximation to the stress conditions on the free surface is adopted the code is written in structured fortran with features from fortran 90 the efficacy of the code is illustrated by applying it to some industrial problems

a mixed variational method for linear coupled thermoelastic analysis abstract a variational method for linear coupled quasi static thermoelastic analysis is presented the variational support is a statement in terms of displacement temperature stress and heat flux the statement is based on the hybrid stress formulation for the elastic part and on the mixed flux temperature formulation for the thermal one and includes the rate dependent terms of the energy balance equations and the initial condition a finite element model for the semidiscrete analysis is developed within this variational framework and a guideline for implementing a family of thermoelastic finite elements is given some test cases enlighten the effectiveness and reliability of the approach proposed

the three dimensional eulerian lagrangian marker and micro cell method for the simulation of free surface flows a new method is presented for the simulation of three dimensional incompressible free surface fluid flow problems the new technique the eulerian lagrangian marker and micro cell elmmc method is capable of simulating incompressible fluid flow problems in cartesian coordinates where the free surface can undergo severe deformations including impact with solid boundaries and impact between converging fluid fronts the method is also capable of handling the breakup of a fluid front from the main body of the fluid as well as their eventual coalescence the basic solution methodology solves the continuity and the navier stokes equations with a projection scheme and is even able to incorporate a basic k e turbulence modeling capability new approaches are presented for the advection of the free surface as well as for the calculation of the tentative velocity final velocity and pressure fields the capabilities of the new method are demonstrated by comparing numerical results with experimental studies while the convergence of the new method is demonstrated by spatial and temporal refinement studies

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

simulations of multiphase flows with multiple length scales using moving mesh interface tracking with adaptive meshing in multiphase flows the length scales of thin regions such as thin films between nearly touching drops and thin threads formed during the interface pinch off are usually several orders of magnitude smaller than the size of the drops in this paper a number of extra length criteria for adaptive meshes are developed and implemented in the moving mesh interface tracking method to solve these multiple length scale problems with high fidelity a nominal length scale based on the solutions of laplace s equations with the unit normal vectors of surfaces as the boundary conditions is proposed for the adaptive mesh refinement in the thin regions for almost flat interfaces boundaries which are near to the thin regions the averaged length of the interior edges sharing the two nodes with the boundary edge is introduced for the mesh adaptation the averaged length of the interfacial edges is used for the interior elements near the interfaces but outside of the thin regions for the interior mesh away from the interfaces boundaries different averaged length scales based on the initial mesh are employed for the adaptive mesh refining and coarsening numerous cases are simulated to demonstrate the capability of the proposed schemes in handling multiple length scales which include the relaxation and necking of an elongated droplet droplet droplet head on approaching droplet wall interactions and a droplet pair in a shear flow the smallest length resolved for the thin regions is three orders of magnitude smaller than the largest characteristic length of the problem

numerical simulation of axisymmetric free surface flows this paper describes an extension of the gensmac code for solving two dimen sional free surface flows to axisymmetric flows like gensmac the technique is finite difference based and embodies but considerably extends the smac simplified marker and cell ideas it incorporates adaptive time stepping and an accurate representation of the free surfaces while at the same time only uses surface particles to define the free surfaces greatly increasing the computational speed in addition it employs a graphic interface with solid modeling techniques to provide enhanced three dimensional visualization various simulations are undertaken to illustrate and validate typical flows both g i taylor s viscous jet plunging into a fluid and a liquid drop splashing onto a fluid are simulated also the important industrial application of container filling is illustrated finally a comparison is made with the linear theory of standing waves and the code is validated by a numerical convergence study

morse index of some min max critical points i application to multiplicity results on donne un resultat general sur des bornes inferieures pour des indices de morse de points critiques obtenus par des principes de min max en combinant cette information avec une inegalite semiclassique on obtient des estimations pointues sur la croissance de certaines valeurs critiques a partir desquelles on deduit de nouveaux resultats de multiplicite pour des solutions d equations elliptiques semi lineaires d ordre 2

existence of multiple positive solutions of subcritical semilinear elliptic problems in exterior strip domains abstract in this paper we consider the subcritical semilinear elliptic problem u u k x u p f x in u 0 in u h 0 1 where 0 n 3 1 p n 2 n 2 and is an exterior strip domain in r n under some suitable conditions on k and f we show that there exists a positive constant depending on k and f such that has exactly two solutions if 0 and no solution if furthermore if there exists a positive constant k 0 such that k x k 0 for x and f is bounded in then has at least one solution for

multidimensional upwind methods for hyperbolic conservation laws abstract we present a class of second order conservative finite difference algorithms for solving numerically time dependent problems for hyperbolic conservation laws in several space variables these methods are upwind and multidimensional in that the numerical fluxes are obtained by solving the characteristic form of the full multidimensional equations at the zone edge and that all fluxes are evaluated and differenced at the same time in particular operator splitting is not used correct behavior at discontinuities is obtained by the use of solutions to the riemann problem and by limiting some of the second order terms numerical results are presented which show that the methods described here yield the same high resolution as the corresponding operator split methods

a front tracking front capturing method for the simulation of 3d multi fluid flows with free surfaces a method for simulating incompressible imiscible unsteady newtonian multi fluid flows with free surfaces is described a sharp interface separates fluids of different density and viscosity surface and interfacial tensions are also considered and the required curvature is geometrically approximated at the fronts by a least squares quadratic fitting to remove small undulations at the fronts a mass conserving filter is employed the numerical method employed to solve the navier stokes equations is based on the gensmac 3d front tracking method the velocity field is computed using a finite difference scheme on an eulerian grid the free surface and the interfaces are represented by an unstructured lagrangian grid moving through an eulerian grid the method was validated by comparing the numerical results with analytical results for a number of simple problems complex numerical simulations show the capability and emphasize the robustness of this new method

short note on reducing interface curvature computation errors in the height function technique a detailed analysis of the errors involved in computing the interface curvature from volume fraction distributions using a height function technique is presented an improved version of the height function technique is proposed based on introducing a correction of the height function discretization error estimated from the local osculating spheres at interface points by using this error correction and an appropriate discretization of the partial derivatives of the height function a substantial improvement in the accuracy of the interface curvature computation can be efficiently achieved

radiation models for thermal flows at low mach number simplified approximate models for radiation are proposed to study thermal effects in low mach flow in open tunnels the governing equations for fluid dynamics are derived by applying a low mach asymptotic in the compressible navier stokes problem based on an asymptotic analysis we show that the integro differential equation for radiative transfer can be replaced by a set of differential equations which are independent of angle variable and easy to solve using standard numerical discretizations as an application we consider a simplified fire model in vehicular tunnels the results presented in this paper show that the proposed models are able to predict temperature in the tunnels accurately with low computational cost

efficient implementation of thinc scheme in this paper we improve the multi dimensional thinc tangent of hyperbola for interface capturing scheme f xiao y honma t kono a simple algebraic interface capturing scheme using hyperbolic tangent function int j numer meth fluid 48 2005 1023 the thinc scheme is a vof volume of fluid type method in the original thinc scheme one dimensional thinc scheme was straightforwardly used for multi dimensional cases in this paper we propose the wlic weighed line interface calculation method to extend the thinc scheme to multi dimension in the wlic method the interface is reconstructed by taking an average of line interfaces along x y and z coordinates with the weights calculated from surface normal the wlic method can extend the thinc scheme to multi dimension while maintaining simplicity of implementation and achieve a higher accuracy than the original thinc scheme the wlic method can readily extend the thinc scheme to three dimension

some variational principles for linear coupled thermoelasticity guided by the principle of virtual work the governing equations describing the physical behavior of a thermoelastic continuum were expressed as the euler lagrange equations of certain variational principles the differential variational principles were formulated for the thermoelastic continuum with or without an internal surface of discontinuity by introducing the dislocation potentials and lagrange undetermined multipliers these principles were shown to recover some of the earlier variational principles as special cases and their reciprocals were also recorded

simulation of free surface flows in a distributed memory environment abstract a parallel technique for a distributed memory machine based on domain decomposition for solving the navier stokes equations in cartesian and cylindrical coordinates in two dimensions with free surfaces is described it is based on the code by tome and mckee j comp phys 110 1994 171 186 and tome ph d thesis university of strathclyde glasgow 1993 which in turn is based on the smac method by amsden and harlow report la 4370 los alamos scientific laboratory 1971 which solves the navier stokes equations in three steps the momentum and poisson equations and particle movement these equations are discretized by explicit and 5 point finite differences the parallelization is performed by splitting the computation domain into vertical panels and assigning each of these panels to a processor all the computation can then be performed using nearest neighbour communication test runs comparing the performance of the parallel with the serial code and a discussion of the load balancing question are presented pvm is used for communication between processes

a numerical method for the incompressible navier stokes equations based on an approximate projection in this method we present a fractional step discretization of the time dependent incompressible navier stokes equations the method is based on a projection formulation in which we first solve diffusion convection equations to predict intermediate velocities which are then projected onto the space of divergence free vector fields our treatment of the diffusion convection step uses a specialized second order upwind method for differencing the nonlinear convective terms that provides a robust treatment of these terms at a high reynolds number in contrast to conventional projection type discretizations that impose a discrete form of the divergence free constraint we only approximately impose the constraint i e the velocity field we compute is not exactly divergence free the approximate projection is computed using a conventional discretization of the laplacian and the resulting linear system is solved using conventional multigrid methods numerical examples are presented to validate the second order convergence of the method for euler finite reynolds number and stokes flow a second example illustrating the behavior of the algorithm on an unstable shear layer is also presented

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

numerical simulation of particle transport in a drift ratchet the directed transport of microparticles depending on their size is the basis for particle sorting methods that are of utmost importance in for example life sciences a drift ratchet is a brownian motor that allows for such a directed transport hereby the particle motion is induced by a combination of the brownian motion and asymmetries stemming for example from the domain s geometry electrical fields or transient pressure boundary conditions we simulate a particular drift ratchet which consists of a matrix of pores with asymmetrically oscillating diameter wherein a fluid with suspended particles is pumped forward and backward and where the particles long term transport direction depends on their size thus this setup allows for continuous and parallel particle separation which has been shown experimentally however for a deeper understanding and for an optimized parameters choice further investigations i e simulations are necessary in this paper we present first results achieved with our parallel three dimensional simulation codes applied to a still simplified scenario this simplification is necessary to isolate different phenomena e g asymmetries and brownian motion to check their relevance for the particle transport the simulation codes are based on adaptive cartesian grids in combination with finite volume and finite element discretizations cartesian grids allow for a very efficient implementation of the solver algorithms and an efficient balanced parallelization via domain decomposition the achieved simulation results show the effectiveness of our approach and give some strong hints on a directed particle transport already with the simplified model we used here

on an alleged philosophers stone concerning variational principles with subsidiary conditions in general the lagrange multiplier method lmm is used to incorporate subsidiary conditions into variational principles the lagrange multipliers represent an additional field of independent variables the attempt to satisfy subsidiary conditions without employing additional independent unknowns has led to the development of simplified variational principles svp they are characterized by expressing lagrange multipliers in terms of original field variables by means of the euler lagrange equations for the multipliers providing their physical interpretation in the first part of the theoretical investigation systems with infinitely many degrees of freedom are studied it is shown that the euler lagrange equations of a lmm based on a modification of the principle of minimum of potential energy pmipe do not hold unconditionally that is for arbitrary subsidiary conditions for the corresponding svp the second part of the theoretical investigation is concerned with systems with a finite number of degrees of freedom the finite element method fem is employed to discuss and compare the characteristics of the lmm and of the corresponding svp contrary to the former the latter are found to be problem dependent several shortcomings of the svp are listed including the possibility of obtaining an infinite sequence of singular coefficient matrices in the process of a systematic mesh refinement consequently convergence of finite element solutions to the true solution in the limit of finite element representations is not guaranteed the theoretical findings are corroborated by the results of a detailed numerical study

a discrete geometric approach for simulating the dynamics of thin viscous threads we present a numerical model for the dynamics of thin viscous threads based on a discrete lagrangian formulation of the smooth equations the model makes use of a condensed set of coordinates called the centerline spin representation the kinematic constraints linking the centerline s tangent to the orientation of the material frame is used to eliminate two out of three degrees of freedom associated with rotations based on a description of twist inspired from discrete differential geometry and from variational principles we build a full fledged discrete viscous thread model which includes in particular a discrete representation of the internal viscous stress consistency of the discrete model with the classical smooth equations for thin threads is established formally our numerical method is validated against reference solutions for steady coiling the method makes it possible to simulate the unsteady behavior of thin viscous threads in a robust and efficient way including the combined effects of inertia stretching bending twisting large rotations and surface tension

a conservative phase field method for solving incompressible two phase flows in this paper a conservative phase field method based on the work of sun and beckermann y sun c beckermann sharp interface tracking using the phase field equation j comput phys 220 2007 626 653 for solving the two and three dimensional two phase incompressible navier stokes equations is proposed the present method can preserve the total mass as the cahn hilliard equation but the calculation and implementation are much simpler than that the dispersion relation preserving schemes are utilized for the advection terms while the helmholtz smoother is applied to compute the surface tension force term to verify the proposed method several benchmarks are examined and shown to have good agreements with previous results it also shows that the satisfactions of mass conservations are guaranteed

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

a finite difference technique for solving a time strain separable k bkz constitutive equation for two dimensional moving free surface flows this work is concerned with the numerical solution of the k bkz integral constitutive equation for two dimensional time dependent free surface flows the numerical method proposed herein is a finite difference technique for simulating flows possessing moving surfaces that can interact with solid walls the main characteristics of the methodology employed are the momentum and mass conservation equations are solved by an implicit method the pressure boundary condition on the free surface is implicitly coupled with the poisson equation for obtaining the pressure field from mass conservation a novel scheme for defining the past times t is employed the finger tensor is calculated by the deformation fields method and is advanced in time by a second order runge kutta method this new technique is verified by solving shear and uniaxial elongational flows furthermore an analytic solution for fully developed channel flow is obtained that is employed in the verification and assessment of convergence with mesh refinement of the numerical solution for free surface flows the assessment of convergence with mesh refinement relies on a jet impinging on a rigid surface and a comparison of the simulation of a extrudate swell problem studied by mitsoulis 2010 44 was performed finally the new code is used to investigate in detail the jet buckling phenomenon of k bkz fluids

an asymptotic preserving numerical scheme for kinetic equations in the low mach number limit a numerical scheme for the nonstationary boltzmann equation in the incompressible navier stokes limit is developed the scheme is induced by the asymptotic analysis of the navier stokes limit for the boltzmann equation it works uniformly for all ranges of mean free paths in the limit the scheme reduces to the chorin projection method for the incompressible navier stokes equation numerical results for different physical situations are shown and the uniform convergence of the scheme is established numerically

prost a parabolic reconstruction of surface tension for the volume of fluid method volume of fluid vof methods are popular for the direct numerical simulation of time dependent viscous incompressible flow of multiple liquids as in any numerical method however it has its weaknesses namely for flows in which the capillary force is the dominant physical mechanism the lack of convergence with spatial refinement or convergence to a solution that is slightly different from the exact solution has been documented in the literature a well known limiting case for this is the existence of spurious currents for the simulation of a spherical drop with zero initial velocity these currents are present in all previous versions of vof algorithms in this paper we develop an accurate representation of the body force due to surface tension which effectively eliminates spurious currents we call this algorithm prost parabolic reconstruction of surface tension there are several components to this procedure including the new body force algorithm improvements in the projection method for the navier stokes solver and a higher order interface advection scheme the curvature to the interface is calculated from an optimal fit for a quadratic approximation to the interface over groups of cells

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 second order projection method for the incompressible navier stokes equations in this paper we describe a second order projection method for the time dependent incom pressible navier stokes equations as in the original projection method developed by chorin we first solve diffusion convection equations to predict intermediate velocities which are then projected onto the space of divergence free vector fields by introducing more coupling between the diffusion onvection step and the projection step we obtain a temporal discretiza tion that is second order accurate our treatment of the diffusion convection step uses a specialized higher order godunov method for differencing the nonlinear convective terms that provides a robust treatment of these terms at high reynolds number the godunov procedure is second order accurate for smooth flow and remains stable for discontinuous initial data even in the zero viscosity limit we approximate the projection directly using a galerkin procedure that uses a local basis for discretely divergence free vector fields numerical results are presented validating the convergence properties of the method we also apply the method to doubly periodic shear layers to assess the performance of the method on more difficult

a monolithic conservative level set method with built in redistancing abstract we introduce a new level set method for representing evolving interfaces in the case of divergence free velocity fields the new method satisfies a conservation principle conservation is important for many applications such as modeling two phase incompressible flow in the present implementation the conserved quantity is defined as the integral of a smoothed characteristic function the new approach embeds level sets into a volume of fluid formulation the evolution of an approximate signed distance function is governed by a conservation law for its smoothed sign the non linear level set transport equation is regularized by adding a flux correction term that assures a non singular jacobian and penalizes deviations from a distance function the result is a locally conservative level set method with built in elliptic redistancing the continuous model is monolithic in the sense that the level set transport model the volume of fluid law of mass conservation and the minimization problem that preserves the approximate distance function property are incorporated into a single equation there is no need for any extra stabilization artificial compression flux limiting redistancing mass correction and other numerical fixes which are commonly used in level set or volume of fluid methods in addition there is just one free parameter that controls the strength of regularization and penalization in the model the accuracy and conservation properties of the monolithic finite element level set method are illustrated by the results of numerical studies for passive advection of free interfaces

a second order projection method for variable density flows this paper describes a second order projection method for variabledensity incompressible flows the method is suitable for both finite amplitude density variations and for fluids that are modeled using a boussinesq approximation it is based on a second order fractional step scheme in which diffusion convection terms are advanced without enforcing the incompressibility condition and the resulting intermediate velocity field is then projected onto the space of discretely divergencefree vector fields the nonlinear convection terms are treated using a godunov type procedure that is second order for smooth flow and remain stable and non oscillatory for nonsmooth flows with low fluid viscosities the method is described for finite amplitude density variation and the simplifications for a boussinesq approximation are sketched numerical results are presented that validate the convergence properties of the method and demonstrate its performance on more realistic problems

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

two phase electrohydrodynamic simulations using a volume of fluid approach a numerical methodology to simulate two phase electrohydrodynamic flows under the volume of fluid paradigm is proposed the electric force in such systems acts only at the interface and is zero elsewhere in the two fluids continuum surface force representations are derived for the electric field force in a system of dielectric dielectric and conducting conducting fluids on the basis of analytical calculations for simple flow problems we propose a weighted harmonic mean interpolation scheme to smoothen the electric properties in the diffused transition region interface it is shown that a wrong choice of interpolation scheme weighted arithmetic mean may lead to a transition region thickness dependent electric field in the bulk we simulate a set of problems with exact or approximate analytical solutions to validate the numerical model proposed a coupled level set and volume of fluid clsvof algorithm has been used for simulations presented here

a monotonicity preserving conservative sharp interface flow solver for high density ratio two phase flows this paper presents a novel approach for solving the conservative form of the incompressible two phase navier stokes equations in order to overcome the numerical instability induced by the potentially large density ratio encountered across the interface the proposed method includes a volume of fluid type integration of the convective momentum transport a monotonicity preserving momentum rescaling and a consistent and conservative ghost fluid projection that includes surface tension effects the numerical dissipation inherent in the volume of fluid treatment of the convective transport is localized in the interface vicinity enabling the use of a kinetic energy conserving discretization away from the singularity two and three dimensional tests are presented and the solutions shown to remain accurate at arbitrary density ratios the proposed method is then successfully used to perform the detailed simulation of a round water jet emerging in quiescent air therefore suggesting the applicability of the proposed algorithm to the computation of realistic turbulent atomization

a level set formulation of eulerian interface capturing methods for incompressible fluid flows a level set formulation is derived for incompressible immiscible navier stokes equations separated by a free surface the interface is identified as the zero level set of a smooth function eulerian finite difference methods based on this level set formulation are proposed these methods are robust and efficient and are capable of computing interface singularities such as merging and reconnection numerical experiments are presented to demonstrate the effectiveness of the methods

an effective implementation of surface tension using the marker and cell method for axisymmetric and planar flows this work presents a method for simulating axisymmetric and planar free surface flows dominated by surface tension forces the surface tension effects are incorporated into the free surface boundary conditions through the computation of the capillary pressure the required curvature is evaluated by fitting a least squares curve to the free surface using the tracking markers in the cell and in its close neighbors to avoid short wavelength perturbations on the free surface a mass conserving local four point stencil filter is employed this filter is an extension of the trapezoidal subgrid undulations removal tsur method the tsur technique consists of modifying the positions of two internal markers of the four point stencil in such a way that the surface length and the curvature are minimized while still preserving the volume the computation of the curvature is modified at cells adjacent to solid boundaries in order to apply contact angle boundary conditions to identify neighboring cells efficiently an implementation is effected through a dual representation of the cell data in addition to a matrix representation a list structure is also employed which permits the representation of specific groups of cells and associated data this technique was implemented in the gensmac code and it has been proved to be robust the code is shown to produce accurate results when compared with exact solutions of selected fluid dynamical problems involving surface tension additionally it is demonstrated that the method is applicable to complex free surface flows such as containers filling splashing drops and bursting bubbles

nonexistence and existence results of an optimal control problem governed by a class of multisolution semilinear elliptic equations abstract an optimal control problem governed by a class of multisolution semilinear elliptic equations is studied in this paper it is pointed out that the control domain and cost functional are nonconvex by analyzing the maximum condition for an optimal relaxed control one nonexistence and some existence results of an optimal pair are obtained the idea of using relaxed controls is mainly derived from the paper lou 2007 by lou where a linear and well posed controlled system was considered the present paper is mainly devoted to discussing the case not contained in lou 2007

an unstructured finite volume procedure for simulating flows with moving fronts abstract the correct prediction of moving fronts is of utmost importance in mold injection due to the complexity of the computational domains encountered in this engineering application finite element methods fem are widely used for predicting the fluid flow the prediction of the position of the front are however usually done using finite differences because of local mass conservation requirements this paper presents a finite volume method for simulating flows with moving fronts using voronoi discretization where the conservation principles are obeyed in solving the flow variables inside the domain as well as in the moving front the method extends the knowledge of the classical finite volume method for structured grids to unstructured grids

an implicit technique for solving 3d low reynolds number moving free surface flows this paper describes the development of an implicit finite difference method for solving transient three dimensional incompressible free surface flows to reduce the cpu time of explicit low reynolds number calculations we have combined a projection method with an implicit technique for treating the pressure on the free surface the projection method is employed to uncouple the velocity and the pressure fields allowing each variable to be solved separately we employ the normal stress condition on the free surface to derive an implicit technique for calculating the pressure at the free surface numerical results demonstrate that this modification is essential for the construction of methods that are more stable than those provided by discretizing the free surface explicitly in addition we show that the proposed method can be applied to viscoelastic fluids numerical results include the simulation of jet buckling and extrudate swell for reynolds numbers in the range 0 01 0 5

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

a quasivariational principle for fluid solid interaction discussion it was shown that the straightforward application of the ritz procedure with piecewise cubic hermitian interpolation functions in order to produce time finite element equations will result in an unstable algorithm this is a rather disappointing result if one refers e g to the second order static equilibrium problem of a rod for which the same interpolation model works so well in the authors opinion in order to get a better understanding of this phenomenon one must refer to the parent matrix k before the initial or the boundary conditions are imposed the degeneracy of k represents the need of the number of the essential conditions that must be imposed in order to make the formulation well defined for the given problem the parent matrix of eqs 4 and 5 is singular of degeneracy 1 this is exactly the single rigid body motion that must be removed in order to make the formulation for the static rod problem well defined however in the dynamic problem both the initial displacement and velocity are essential conditions that must be imposed in order to make the formulation well defined indeed the parent matrix of the modified elements eqs 12 and 13 is singular of degeneracy 2 and both the initial displacement and velocity must be imposed in order to solve the equations

coupling a local adaptive grid refinement technique with an interface sharpening scheme for the simulation of two phase flow and free surface flows using vof methodology suppression of the numerical diffusion of the volume fraction field the coupling of a sharpening method with adaptive local grid refinement technique testing of hric and cicsam vof schemes in numerical experiments application of this methodology in real physics problems good agreement against analytical solutions for droplet gravitational acceleration this study presents the implementation of an interface sharpening scheme on the basis of the volume of fluid vof method as well as its application in a number of theoretical and real cases usually modelled in literature more specifically the solution of an additional sharpening equation along with the standard vof model equations is proposed offering the advantage of restraining interface numerical diffusion while also keeping a quite smooth induced velocity field around the interface this sharpening equation is solved right after volume fraction advection however a novel method for its coupling with the momentum equation has been applied in order to save computational time the advantages of the proposed sharpening scheme lie on the facts that a it is mass conservative thus its application does not have a negative impact on one of the most important benefits of vof method and b it can be used in coarser grids as now the suppression of the numerical diffusion is grid independent the coupling of the solved equation with an adaptive local grid refinement technique is used for further decrease of computational time while keeping high levels of accuracy at the area of maximum interest interface the numerical algorithm is initially tested against two theoretical benchmark cases for interface tracking methodologies followed by its validation for the case of a free falling water droplet accelerated by gravity as well as the normal liquid droplet impingement onto a flat substrate results indicate that the coupling of the interface sharpening equation with the hric discretization scheme used for volume fraction flux term not only decreases the interface numerical diffusion but also allows the induced velocity field to be less perturbed owed to spurious velocities across the liquid gas interface with the use of the proposed algorithmic flow path coarser grids can replace finer ones at the slight expense of accuracy

an efficient interface preserving level set redistancing algorithm and its application to interfacial incompressible fluid flow in sussman smereka and osher j comp phys 94 1994 pp 146 159 a numerical scheme was presented for computing incompressible air water flows using the level set method crucial to the above method was a new iteration method for maintaining the level set function as the signed distance from the zero level set in this paper we implement a constraint along with higher order difference schemes in order to make the iteration method more accurate and efficient accuracy is measured in terms of the new computed signed distance function and the original level set function having the same zero level set we apply our redistancing scheme to incompressible flows with noticeably better resolved results at reduced cost we validate our results with experiment and theory we show that our distance level set scheme with the added constraint competes well with available interface tracking schemes for basic advection of an interface we perform basic accuracy checks and more stringent tests involving complicated interfacial structures as with all level set schemes our method is easy to implement

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 numerical study of the kernel conformation transformation for transient viscoelastic fluid flows this work presents a numerical application of a generic conformation tensor transformation for simulating highly elastic flows of non newtonian fluids typically observed in computational rheology in the kernel conformation framework 14 the conformation tensor constitutive law for a viscoelastic fluid is transformed introducing a generic tensor transformation function the numerical stability of the application of the kernel conformation for highly elastic flows is ultimately related with the specific kernel function used in the matrix transformation but also to the existence of singularities introduced either by flow geometry or by the characteristics of the constitutive equation in this work we implement this methodology in a free surface marker and cell discretization methodology implemented in a finite differences method the main contributions of this work are two fold on one hand we demonstrate the accuracy of this kernel conformation formulation using a finite differences method and free surfaces on the other hand we assess the numerical efficiency of specific kernel functions at high weissenberg number flows the numerical study considers different viscoelastic fluid flow problems including the poiseuille flow in a channel the lid driven cavity flow and the die swell free surface flow the numerical results demonstrate the adequacy of this methodology for high weissenberg number flows using the oldroyd b model we analyze a generic conformation tensor transformation for simulating the hwnp the numerical scheme is constructed in the context of finite differences the numerical study considers transient benchmarks in computational rheology complex flows are solved including the die swell free surface problem

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

coupled thermoelastic shell equations with second sound for high frequency vibrations of temperature dependent materials guided by the three dimensional theory of coupled thermoelasticity with second sound a system of shear deformable shell equations is consistently derived in invariant differential and variational forms for the high frequency vibrations of temperature dependent materials the first part of the paper is concerned with a unified variational principle describing the fundamental equations of thermoelasticity the differential type of variational principle is presented by expressing hamilton s principle for the thermal part of a thermoelastic region and then combining it with its mechanical part in the second part the hierarchic system of non isothermal shell equations is systematically established by use of the variational principle together with mindlin s kinematic hypothesis for shells the system of two dimensional approximate equations which may take account of all the significant mechanical and thermal effects including the temperature dependency of material governs the extensional thickness shear flexural and torsional as well as coupled vibrations of shells of uniform thickness lastly in the third part emphasis is placed on certain cases involving special material geometry and kinematics besides a theorem is devised so as to enumerate the initial and boundary conditions sufficient for the uniqueness in solutions of the system of non isothermal shell equations

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 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 coupled level set and volume of fluid method for computing 3d and axisymmetric incompressible two phase flows we present a coupled level set volume of fluid clsvof method for computing 3d and axisymmetric incompressible two phase flows this method combines some of the advantages of the volume of fluid method with the level set method to obtain a method which is generally superior to either method alone we present direct comparisons between computations made with the clsvof method and computations made with the level set method the volume of fluid method and the boundary integral method we also compare our computations to the exact solution for an oscillating ellipse due to lamb and experimental results obtained for a rising gas bubble in liquid obtained by hnat and buckmaster our computational examples focus on flows in which surface tension forces and changes in topology are dominant features of the flow

a front tracking method for the computations of multiphase flow direct numerical simulations of multiphase flows using a front tracking method are presented the method is based on writing one set of governing equations for the whole computational domain and treating the different phases as one fluid with variable material properties interfacial terms are accounted for by adding the appropriate sources as functions at the boundary separating the phases the unsteady navier stokes equations are solved by a conventional finite volume method on a fixed structured grid and the interface or front is tracked explicitly by connected marker points interfacial source terms such as surface tension are computed on the front and transferred to the fixed grid advection of fluid properties such as density is done by following the motion of the front the method has been implemented for fully three dimensional flows as well as for two dimensional and axisymmetric ones first the method is described for the flow of two or more isothermal phases the representation of the moving interface and its dynamic restructuring as well as the transfer of information between the moving front and the fixed grid are discussed applications and extensions of the method to homogeneous bubbly flows atomization flows with variable surface tension solidification and boiling are then presented

numerical simulation of viscoelastic flows using integral constitutive equations a finite difference approach this work presents a numerical technique for simulating incompressible isothermal viscoelastic flows of fluids governed by the upper convected maxwell ucm and k bkz kaye bernstein kearsley and zapas integral models the numerical technique described herein is an extension of the gensmac method to the solution of the momentum and mass conservation equations to include integral constitutive equations the governing equations are solved by the finite difference method on a staggered grid using a marker and cell approach the finger tensor b t t is computed in an eulerian framework using the ideas of the deformation fields method however improvements to the deformation fields method are introduced the finger tensor b t x t is obtained by a second order accurate method and the stress tensor t x t is computed by a second order quadrature formula the numerical method presented in this work is validated by comparing the predictions of velocity and stress fields in two dimensional fully developed channel flow of a maxwell fluid with the corresponding analytic solutions furthermore the flow through a planar 4 1 contraction is investigated and the numerical results were compared with the corresponding experimental data finally the ucm and the k bkz models were used to simulate the planar 4 1 contraction flow over a wide range of reynolds and weissenberg numbers and the numerical results obtained are in agreement with published data

numerical solution of the ericksen leslie dynamic equations for two dimensional nematic liquid crystal flows a finite difference method for solving nematic liquid crystal flows under the effect of a magnetic field is developed the dynamic equations of nematic liquid crystals given by the ericksen leslie dynamic theory are employed these are expressed in terms of primitive variables and solved employing the ideas behind the gensmac methodology tome and mckee 1994 tome et al 2002 38 41 these equations are nonlinear partial differential equations consisting of the mass conservation equation and the balance laws of linear and angular momentum by employing fully developed flow assumptions an analytic solution for steady 2d channel flow is found the resulting numerical technique was then in part validated by comparing numerical solutions against this analytic solution convergence results are presented to demonstrate the capabilities of the numerical method the flow of a nematic liquid crystal through various complex geometries are then simulated results are obtained for l shaped channels and planar 4 1 contraction for several values of reynolds and ericksen numbers

a hybrid particle level set method for improved interface capturing in this paper we propose a new numerical method for improving the mass conservation properties of the level set method when the interface is passively advected in a flow field our method uses lagrangian marker particles to rebuild the level set in regions which are underresolved this is often the case for flows undergoing stretching and tearing the overall method maintains a smooth geometrical description of the interface and the implementation simplicity characteristic of the level set method our method compares favorably with volume of fluid methods in the conservation of mass and purely lagrangian schemes for interface resolution the method is presented in three spatial dimensions