three dimensional volume conserving immersed boundary model for two phase fluid flows abstract we present a volume preserving scheme for two phase immiscible incompressible flows using an immersed boundary method ibm in a three dimensional space the two phase ibm employs a mixture of eulerian and lagrangian variables where the fluid interface is represented by discrete lagrangian markers exerting surface tension forces to the eulerian fluid domain and the markers are advected by the fluid velocity the interactions between the lagrangian markers and the fluid variables are linked by the discretized dirac delta function the present study extends the previous two dimensional research li et al volume preserving immersed boundary methods for two phase fluid flows int j numer meth fluids 69 2012 842 858 to the three dimensional space the key idea of the proposed method is relocating surface points along the normal directions to conserve the total volume we perform a number of numerical experiments to show the efficiency and accuracy of the proposed method

some remarks on the flux free finite element method for immiscible two fluid flows we give some theoretical considerations on the the flux free finite element method for the generalized stokes interface problem arising from the immiscible two fluid flow problems in the flux free finite element method the flux constraint is posed as another lagrange multiplier to keep the zero flux on the interface as a result the mass of each fluid is expected to be preserved at every time step we first study the effect of discontinuous coefficients viscosity and density on the error of the standard finite element approximations very carefully then the analysis is extended to the flux free finite element method

a localized re initialization equation for the conservative level set method the conservative level set methodology for interface transport is modified to allow for localized level set re initialization this approach is suitable to applications in which there is a significant amount of spatial variability in level set transport the steady state solution of the modified re initialization equation matches that of the original conservative level set provided an additional eikonal equation is solved which can be done efficiently through a fast marching method fmm implemented within the context of the accurate conservative level set method acls desjardins et al 2008 6 the fmm solution of this eikonal equation comes at no additional cost a metric for the appropriate amount of local re initialization is proposed based on estimates of local flow deformation and numerical diffusion the method is compared to standard global re initialization for two test cases yielding the expected results that minor differences are observed for zalesak s disk and improvements in both mass conservation and interface topology are seen for a drop deforming in a vortex finally the method is applied to simulation of a viscously damped standing wave and a three dimensional drop impacting on a shallow pool negligible differences are observed for the standing wave as expected for the last case results suggest that spatially varying re initialization provides a reduction in spurious interfacial corrugations improvements in the prediction of radial growth of the splashing lamella and a reduction in conservation errors as well as a reduction in overall computational cost that comes from improved conditioning of the pressure poisson equation due to the removal of spurious corrugations

a new level set model for multimaterial flows we propose a new level set model for representing multimaterial flows in multiple space dimensions instead of associating a level set function with a specific fluid material the function is associated with a pair of materials and the interface that separates them a voting algorithm collects sign information from all level set functions and determines material designation to represent a general m material configuration m m 1 2 level set functions need to be accounted for problems of practical interest use far fewer functions as not all pairs of materials share an interface and level set functions that coincide are grouped together under this model regions of potential material ambiguity i e overlaps or vacuum are markedly reduced in size in 2d ambiguous regions are points as opposed to lines in material based level set models in 3d they are lines as opposed to surfaces the model produces excellent results without the need for reinitialization thereby avoiding additional computational costs and preventing excessive numerical diffusion

an arbitrary order runge kutta discontinuous galerkin approach to reinitialization for banded conservative level sets abstract we present a runge kutta discontinuous galerkin method for solving conservative reinitialization in the context of the conservative level set method 18 19 this represents an extension of the method recently proposed by owkes and desjardins 21 by solving the level set equations on the refined level set grid 9 and projecting all spatially dependent variables into the full basis used by the discontinuous galerkin discretization by doing so we achieve the full k 1 order convergence rate in the l 1 norm of the level set field predicted for rkdg methods given kth degree basis functions when the level set profile thickness is held constant with grid refinement shape and volume errors for the 0 5 contour of the level set on the other hand are found to converge between first and second order we show a variety of test results including the method of manufactured solutions reinitialization of a circle and sphere zalesak s disk and deforming columns and spheres all showing substantial improvements over the high order finite difference traditional level set method studied for example by herrmann 9 we also demonstrate the need for kth order accurate normal vectors as lower order normals are found to degrade the convergence rate of the method

an optimization based approach to enforcing mass conservation in level set methods this paper presents a new conservative level set method for numerical simulation of evolving interfaces a pde constrained optimization problem is formulated and solved in an iterative fashion the proposed optimal control procedure constrains the level set function to satisfy a conservation law for the corresponding heaviside function the target value of the state variable is defined as the solution to the standard level set transport equation the gradient of the control variable corrects the convective flux in the nonlinear state equation so as to enforce mass conservation while minimizing deviations from the target state a relaxation term is added when it comes to the design of an iterative solver for the nonlinear system the potential of the optimization based approach is illustrated by two numerical examples

bounded renormalization with continuous penalization for level set interface capturing methods in this work a reinitialization procedure oriented to regularize the level set ls function field is presented in ls approximations for two fluid flow simulations a scalar function indicates the presence of one or another phase and the interface between them in general the advection of such function produces a degradation of some properties of the ls function such as the smoothness of the transition between phases and the correct position of the interface the methodology introduced here denominated bounded renormalization with continuous penalization consists of solving by the finite element method a partial differential equation with certain distinguishing properties with the aim of keeping the desirable properties of the ls function the performance of the strategy is evaluated for several typical cases in one two and three dimensional domains for both the advection and the renormalization stages copyright 2010 john wiley sons ltd

a stabilized mixed finite element method for darcy flow we develop new stabilized mixed finite element methods for darcy flow stability and an a priori error estimate in the stability norm are established a wide variety of convergent finite elements present themselves unlike the classical galerkin formulation which requires highly specialized elements an interesting feature of the formulation is that there are no mesh dependent parameters numerical tests confirm the theoretical results 2002 elsevier science b v all rights reserved

extended discontinuous galerkin methods for two phase flows the spatial discretization summary this work discusses a discontinuous galerkin dg discretization for two phase flows the fluid interface is represented by a level set and the dg approximation space is adapted such that jumps and kinks in pressure and velocity fields can be approximated sharply this adaption of the original dg space which can be performed on the fly for arbitrary interface shapes is referred to as extended discontinuous galerkin by combining this ansatz with a special quadrature technique one can regain spectral convergence properties for low regularity solutions which is demonstrated by numerical examples this work focuses on the aspects of spatial discretization and special emphasis is devoted on how to overcome problems related to quadrature small cut cells and condition number of linear systems temporal discretization will be discussed in future works copyright 2016 john wiley sons ltd

an eulerian interface sharpening algorithm for compressible two phase flow the algebraic thinc approach article history we describe a novel interface sharpening approach for efficient numerical resolution of a compressible homogeneous two phase flow governed by a quasi conservative five equation model of allaire et al 2001 1 the algorithm uses a semi discrete wave propagation method to find approximate solution of this model numerically in the algorithm in regions near the interfaces where two different fluid components are present within a cell the thinc tangent of hyperbola for interface capturing scheme is used as a basis for the reconstruction of a sub grid discontinuity of volume fractions at each cell edge and it is complemented by a homogeneous equilibrium consistent technique that is derived to ensure a consistent modeling of the other interpolated physical variables in the model in regions away from the interfaces where the flow is single phase standard reconstruction scheme such as muscl or weno can be used for obtaining high order interpolated states these reconstructions are then used as the initial data for riemann problems and the resulting fluctuations form the basis for the spatial discretization time integration of the algorithm is done by employing a strong stability preserving runge kutta method numerical results are shown for sample problems with the mie gruneisen equation of state for characterizing the materials of interests in both one and two space dimensions that demonstrate the feasibility of the proposed method for interface sharpening of compressible two phase flow to demonstrate the competitiveness of our approach we have also included results obtained using the anti diffusion interface sharpening method

a gradient augmented level set method for unstructured grids we present and test a gradient augmented level set method for unstructured grids which has been designed to allow for easy integration in parallel flow solvers the means to this end is a hermite formulation where the gradient is stored and advected as an independent variable along with the level set function the method uses narrow band storage in conjunction with a fast marching method which is also designed to take advantage of the gradient augmentation we demonstrate through standard passive advection test cases that the proposed method is able to compute interface motion with performance comparable to popular high performing methods on structured grids

isotropic finite volume discretization finite volume methods traditionally employ dimension by dimension extension of the one dimensional reconstruction and averaging procedures to achieve spatial discretization of the governing partial differential equations on a structured cartesian mesh in multiple dimensions this simple approach based on tensor product stencils introduces an undesirable grid orientation dependence in the computed solution the resulting anisotropic errors lead to a disparity in the calculations that is most prominent between directions parallel and diagonal to the grid lines in this work we develop isotropic finite volume discretization schemes which minimize such grid orientation effects in multidimensional calculations by eliminating the directional bias in the lowest order term in the truncation error explicit isotropic expressions that relate the cell face averaged line and surface integrals of a function and its derivatives to the given cell area and volume averages are derived in two and three dimensions respectively it is found that a family of isotropic approximations with a free parameter can be derived by combining isotropic schemes based on next nearest and next next nearest neighbors in three dimensions use of these isotropic expressions alone in a standard finite volume framework however is found to be insufficient in enforcing rotational invariance when the flux vector is nonlinear and or spatially non uniform the rotationally invariant terms which lead to a loss of isotropy in such cases are explicitly identified and recast in a differential form various forms of flux correction terms which allow for a full recovery of rotational invariance in the lowest order truncation error terms while preserving the formal order of accuracy and discrete conservation of the original finite volume method are developed numerical tests in two and three dimensions attest the superior directional attributes of the proposed isotropic finite volume method prominent anisotropic errors such as spurious asymmetric distortions on a circular reaction diffusion wave that feature in the conventional finite volume implementation are effectively suppressed through isotropic finite volume discretization furthermore for a given spatial resolution a striking improvement in the prediction of kinetic energy decay rate corresponding to a general two dimensional incompressible flow field is observed with the use of an isotropic finite volume method instead of the conventional discretization c 2014 elsevier inc all rights reserved

boundary conditions at fluid permeable interfaces in porous media a variational approach abstract a general set of boundary conditions at fluid permeable interfaces between dissimilar fluid filled porous matrices is established starting from an extended hamilton rayleigh principle these conditions do include friction and inertial effects once linearized they encompass boundary conditions relative to volume darcy brinkman and to surface saffman beavers joseph dissipation effects

efficient computations for high density ratio rising bubble flows using a diffused interface coupled lattice boltzmann level set scheme a mass conserving diffused interface coupled lattice boltzmann level set scheme is proposed and numerically studied for the simulation of high density and viscosity ratio multiphase flows the approach is based on the pressure evolution formulation of the lattice boltzmann equation which is then coupled with the level set equation to capture a diffused level set function multiple relaxation time collision and isotropic force discretization techniques are employed to further reinforce the stability and accuracy of the lbm solver and a monolithic approach is employed to convect the level set function with minimal computations to preserve a smooth density profile we present extensive investigations for numerical accuracy through performing benchmark simulations for rising bubble problems it is observed that the proposed scheme is successful in producing accurate results as compared to those from high precision 2d finite element solutions in hysing et al 2009 offering a remarkable improvement in mass conservation and characteristic benchmark quantities upon our previous sharp interface coupled model described in safi and turek 2014 moreover parallel scalability of the coupled lb scheme is shown to be preserved through performing efficient cpu and gpgpu based computations

variational implementation of immersed finite element methods dirac distributions are often crucial components of the solid fluid coupling operators in immersed solution methods for fluid structure interaction fsi problems this is certainly so for methods like the immersed boundary method ibm or the immersed finite element method ifem where dirac distributions are approximated via smooth functions by contrast a truly variational formulation of immersed methods does not require the use of dirac distributions either formally or practically this has been shown in the finite element immersed boundary method feibm where the variational structure of the problem is exploited to avoid dirac distributions at both the continuous and the discrete level in this paper we generalize the feibm to the case where an incompressible newtonian fluid interacts with a general hyperelastic solid specifically we allow i the mass density to be different in the solid and the fluid ii the solid to be either viscoelastic of differential type or purely elastic and iii the solid to be either compressible or incompressible at the continuous level our variational formulation combines the natural stability estimates of the fluid and elasticity problems in immersed methods such stability estimates do not transfer to the discrete level automatically due to the non matching nature of the finite dimensional spaces involved in the discretization after presenting our general mathematical framework for the solution of fsi problems we focus in detail on the construction of natural interpolation operators between the fluid and the solid discrete spaces which guarantee semi discrete stability estimates and strong consistency of our spatial discretization

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

a conservative level set method for two phase flow ii in this paper we continue to develop and study the conservative level set method for incompressible two phase flow with surface tension introduced in j comput phys 210 2005 225 246 we formulate a modification of the reinitialization and present a theoretical study of what kind of conservation we can expect of the method a finite element discretization is presented as well as an adaptive mesh control procedure numerical experiments relevant for problems in petroleum engineering and material science are presented for these problems the surface tension is strong and conservation of mass is important problems in both two and three dimensions with uniform as well as non uniform grids are studied from these calculations convergence and conservation is studied good conservation and convergence are observed

an ale pfem method for the numerical simulation of two phase mixture flow abstract a new finite element method is proposed to simulate two phase mixture problems with free surfaces and or large moving boundaries the two phases are treated as interpenetrating continua within a two fluid model in contrast to the conventional two fluid model formulations in which the governing equations are written in the eulerian eulerian description the modified two fluid model has the governing equations of one fluid phase written in the lagrangian description while the respective equations of the other phase is formulated in the arbitrary lagrangian eulerian ale description with relative velocities defined with respect to the moving mesh associated with the first fluid phase the finite element method fem together with stabilization techniques the characteristic based split cbs and the algebraic flux correction afc method is employed to solve the equations numerically in space and time the nodes of the computational mesh are updated together with the flow of the phase described in the lagrangian description the computational mesh is updated by applying techniques used in the so called particle finite element method pfem characterized by regenerating the mesh in each computational step according to the updated nodal positions while the current boundary of the domain is identified using shape method the performance of the method is demonstrated by means of three 2d and 3d examples including a mixing process of two fluids in a stirred tank a free surface flow a 3d two phase channel flow a phase separation problem and the flow of two immiscible fluids

a reformulation of the conservative level set reinitialization equation for accurate and robust simulation of complex multiphase flows abstract this paper presents an accurate and robust reinitialization equation for the conservative level set that does not significantly deform stationary surfaces the compression and diffusion term of the reinitialization equation are reformulated to use a distance level set directly mapped from the conservative level set the normals are calculated using a distance level set reconstructed from the interface using a fast marching method increasing robustness and allowing the use of high order non tvd transport schemes using this new reinitialization equation we present results for canonical test cases such as zalesak s disk and spurious currents which show significant improvement a simulation of a liquid gas jet with r e 5000 is also presented to demonstrate the volume conservation properties of the method in more complex flows

formulation and finite element implementation of a multiplicative model of coupled poro plasticity at finite strains under fully saturated conditions in this paper we present the formulation and numerical analysis of a finite deformation model of coupled poro plasticity fully saturated conditions are assumed the model is based on a multiplicative decomposition of the deformation gradient in elastic and plastic parts together with an additive elastoplastic decomposition of the fluid content the final relations describing the evolution of the different fields are then obtained in the thermodynamic framework furnished by the principle of maximum plastic dissipation the particular case of an associated drucker prager model in effective stresses is considered as a model example a complete characterization of the dissipative structure of the problem of evolution is described through the derivation of an a priori stability estimate we describe in detail the finite element implementation of the model in the context of staggered algorithms for the solution of the physically coupled problem finally we present representative numerical simulations to illustrate the features of the proposed models in particular the case of strain localization in globally undrained conditions is studied in the proposed framework

optimal source codes for timely updates a transmitter observing a sequence of independent and identically distributed random variables seeks to keep a receiver updated about its latest observations the receiver need not be apprised about each symbol seen by the transmitter but needs to output a symbol at each time instant t if at time t the receiver outputs the symbol seen by the transmitter at time u t leq t the age of information at the receiver at time t is t u t we study the design of lossless source codes that enable transmission with minimum average age at the receiver we show that the asymptotic minimum average age can be attained up to a constant gap by the shannon codes for a tilted version of the original pmf generating the symbols which can be computed easily by solving an optimization problem furthermore we exhibit an example with alphabet mathcal x where shannon codes for the original pmf incur an asymptotic average age of a factor o sqrt log mathcal x more than that achieved by our codes underlying our prescription for optimal codes is a new variational formula for integer moments of random variables which may be of independent interest also we discuss possible extensions of our formulation to randomized schemes and to the erasure channel and include a treatment of the related problem of source coding for minimum average queuing delay

an conservative anti diffusion technique for the level set method abstract a novel conservative level set method is introduced for the approximation of two phase incompressible fluid flows the method builds on recent conservative level set approaches and utilizes an entropy production to construct a balanced artificial diffusion and artificial anti diffusion the method is self tuning maximum principle preserving suitable for unstructured meshes and neither re initialization of the level set function nor reconstruction of the interface is needed for long time simulation computational results in one two and three dimensions are presented for finite element and finite volume implementations of the method

toward efficient and accurate interface capturing on arbitrary hybrid unstructured grids the thinc method with quadratic surface representation and gaussian quadrature abstract a novel interface capturing scheme is proposed to compute moving interface on arbitrary hybrid unstructured grids different from conventional volume of fluid vof schemes that require complicated geometric manipulations for interface reconstructions the present method can be viewed as a hybrid geometric algebraic type vof approach i e the interface is implictly retrieved from an algebraic function that effectively makes use of the geometrical information such as normal direction and curvature of the interface unlike previous versions of the thinc tangent of hyperbola interface capturing method the interface is represented by a quadratic surface for grid cells of arbitrary shapes in this scheme the gaussian quadrature is used to estimate the integration of the cell wise multi dimensional hyperbolic tangent reconstruction function which is then used to retrieve the interface from the volume fraction value of the target cell the gaussian quadrature is also used to compute the numerical fluxes from the reconstruction function numerical accuracy for reconstruction and flux computation can be effectively improved by increasing quadrature points the whole solution procedure follows the finite volume method for advection transport and is thus simple and easy to use for cells of arbitrary shapes as verified in the benchmark tests in this paper the presented scheme so called thinc qq thinc method with quadratic surface representation and gaussian quadrature scheme shows significantly improved geometrical fidelity of interface representation particularly for curved surface despite algorithmic simplicity the solution quality of thinc qq is comparable to other existing vof methods with plic geometrical interface reconstructions and thus an accurate and efficient vof scheme of great practical significance for unstructured grids

an arbitrary lagrangian eulerian finite element formulation for a poroelasticity problem stemming from mixture theory abstract a finite element formulation is developed for a poroelastic medium consisting of an incompressible hyperelastic skeleton saturated by an incompressible fluid the governing equations stem from mixture theory and the application is motivated by the study of interstitial fluid flow in brain tissue the formulation is based on the adoption of an arbitrary lagrangian eulerian ale perspective we focus on a flow regime in which inertia forces are negligible the stability and convergence of the formulation is discussed and numerical results demonstrate agreement with the theory

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 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

a cartesian based embedded geometry technique with adaptive high order finite differences for compressible flow around complex geometries an immersed boundary methodology to solve the compressible navier stokes equations around complex geometries in cartesian fluid dynamics solvers is described the objective of the new approach is to enable smooth reconstruction of pressure and viscous stresses around the embedded objects without spurious numerical artifacts a standard level set represents the boundary of the object and defines a fictitious domain into which the flow fields are smoothly extended boundary conditions on the surface are enforced by an approach inspired by analytic continuation each fluid field is extended independently constrained only by the boundary condition associated with that field unlike most existing methods no jump conditions or explicit derivation of them from the boundary conditions are required in this approach numerical stiffness that arises when the fluid solid interface is close to grid points of the mesh is addressed by preconditioning in addition the embedded geometry technique is coupled with a stable high order adaptive discretization that is enabled around the object boundary to enhance resolution the stencils used to transition the order of accuracy of the discretization are derived using the summation by parts technique that ensures stability applications to shock reflections shock ramp interactions and supersonic and low mach number flows over two and three dimensional geometries are presented

benchmark computations for 3d two phase flows following our previous work on the application of the diffuse interface coupled lattice boltzmann level set lb ls approach to benchmark computations for 2d rising bubble simulations this paper investigates the performance of the coupled scheme in 3d two phase flows in particular the use of different lattice stencils e g d3q15 d3q19 and d3q27 is studied and the results for 3d rising bubble simulations are compared with regard to isotropy and accuracy against those obtained by finite element and finite difference solutions of the navierstokes equations it is shown that the method can eventually recover the benchmark solutions provided that the interface region is aptly refined by the underlying lattice following the benchmark simulations the application of the method in solving other numerically subtle problems e g binary droplet collision and droplet splashing on wet surface under high re and we numbers is presented moreover implementations on general purpose gpus are pursued where the computations are adaptively refined around the critical parts of the flow

delta function approximations in level set methods by distance function extension in a k tornberg b engquist numerical approximations of singular source terms in differential equations j comput phys 200 2004 462 488 it was shown for simple examples that the then m

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 conservative level set method for contact line dynamics a new model for simulating contact line dynamics is proposed we apply the idea of driving contact line movement by enforcing the equilibrium contact angle at the boundary to the conservative level set method for incompressible two phase flow e olsson g kreiss a conservative level set method for two phase flow j comput phys 210 2005 225 246 a modified reinitialization procedure provides a diffusive mechanism for contact line movement and results in a smooth transition of the interface near the contact line without explicit reconstruction of the interface we are able to capture contact line movement without loosing the conservation numerical simulations of capillary dominated flows in two space dimensions demonstrate that the model is able to capture contact line dynamics qualitatively correct

level set reinitialization at a contact line when a level set signed distance function is reinitialized in the vicinity of a contact line there is a blind spot that prevents an accurate reconstruction of a signed distance function the numerical method can create parasitic velocity currents near this region if additional contact line physics are included the parasitic velocity currents would pollute the solution and alter the physical behavior in this study a modified reinitialization routine is proposed that combines the standard hamilton jacobi equation with a relaxation equation for those grid cells along a wall in the blind spot two test cases an angled fluid wedge zero curvature and a circular fluid arc constant curvature are used to evaluate the numerical error induced by different methods the proposed method has less numerically induced interface distortion than other techniques examined furthermore this routine can be easily extended to three dimensions drops sliding on a wall are simulated in both two and three dimensions to demonstrate the advantages of this method a spreading fluid interface further shows that this method allows contact lines to merge naturally

unified adaptive variational multiscale method for two phase compressible incompressible flows in this paper we present a new stabilized finite element method to solve the two phase compressible incompressible fluid flow problems using the level set method an anisotropic mesh adaptation with a regularized interface is adopted to deal with the high discontinuity in the material properties the coupling between the pressure and the flow velocity is ensured by introducing mass conservation terms in the momentum equation therefore the same set of primitive unknowns and equations is described for both phases the unified system is solved using a new derived variational multiscale stabilized finite element method it is tested on three time dependent liquid gas interface problems the numerical results show good stability and accuracy properties permitting also to deal with important compressibility effect high density ratio and extremely stretched anisotropic elements

stabilized finite element method for incompressible flows with high reynolds number in the following paper we discuss the exhaustive use and implementation of stabilization finite element methods for the resolution of the 3d time dependent incompressible navier stokes equations the proposed method starts by the use of a finite element variational multiscale vms method which consists in here of a decomposition for both the velocity and the pressure fields into coarse resolved scales and fine unresolved scales this choice of decomposition is shown to be favorable for simulating flows at high reynolds number we explore the behaviour and accuracy of the proposed approximation on three test cases first the lid driven square cavity at reynolds number up to 50 000 is compared with the highly resolved numerical simulations and second the lid driven cubic cavity up to re 12 000 is compared with the experimental data finally we study the flow over a 2d backward facing step at re 42 000 results show that the present implementation is able to exhibit good stability and accuracy properties for high reynolds number flows with unstructured meshes

a high order and interface preserving discontinuous galerkin method for level set reinitialization abstract a high order numerical method for interface preserving level set reinitialization is presented in this paper in the interface cells the gradient of the level set function is determined by a weighted local projection scheme and the missing additive constant is determined such that the position of the zero level set is preserved in the non interface cells we compute the gradient of the level set function by solving a hamilton jacobi equation as a conservation law system using the discontinuous galerkin method following the work by hu and shu siam j sci comput 21 1999 660 690 the missing constant is then recovered by the continuity of the level set function while taking into account the characteristics to handle highly distorted initial conditions we develop a hybrid numerical flux that combines the lax friedrichs flux and the penalty flux our method is stable for non trivial test cases and handles singularities away from the interface very well when derivative singularities are present on the interface a second derivative limiter is designed to suppress the oscillations at least n 1 th order accuracy in the interface cells and nth order in the whole domain are observed for smooth solutions when nth degree polynomials are used two dimensional test cases are presented to demonstrate superior properties such as accuracy long term stability interface preserving capability and easy treatment of contact lines we also show some preliminary results on the pinch off process of a pendant drop where topological changes of the fluid interface are involved our method is readily extendable to three dimensions and adaptive meshes

optimal control for mass conservative level set methods this paper presents two different versions of an optimal control method for enforcing mass conservation in level set algorithms the proposed pde constrained optimization procedure corrects a numerical solution to the level set transport equation so as to satisfy a conservation law for the corresponding heaviside function in the original version of this method conservation errors are corrected by adding the gradient of a scalar control variable to the convective flux in the state equation in the present paper we investigate the use of vector controls the alternative formulation offers additional flexibility and requires less regularity than the original method the nonlinear system of first order optimality conditions is solved using a standard fixed point iteration the new methodology is evaluated numerically and compared to the scalar control approach

connectivity free front tracking method for multiphase flows with free surfaces in this study a connectivity free front tracking method is developed to simulate multiphase flows with free surfaces this method is based on the point set method which does not require any connectivities between interfacial points to represent the interface the main advantage of the connectivity free approach is the easiness in re constructing the interface when large topology change occurs it requires an indicator field to be constructed first based on the existing interface and the surface curvature and normal are then computed using the indicator field here we adopt the reproducing kernel particle method rkpm interpolation function that provides the ability to deal with free surface flows and the flexibility of using non uniform meshes when local fine resolution is needed a points regeneration scheme is developed to construct smooth interfaces and to automatically handle topology changes the mass conservation is verified by performing a single vortex advection test several 2 d and 3 d numerical tests including an oscillating droplet dam breaking two droplet impacting and multi bubble merging are presented to show the accuracy and the robustness of the method

minimum delay codes huffman s algorithm finds a prefix free binary code on a weighted alphabet which minimizes the expected length of the code string for a single symbol a definition is given for the expected delay for a prefix free binary code on a weighted alphabet it is the expected time between a request to transmit the symbol and the completion of that transmission assuming a channel with fixed capacity where requests are queued an o n 5 time o n 3 space convex hull algorithm is given that finds a code of minimal expected delay where n is the size of the alphabet it is conjectured that the algorithm has substantially lower time and space complexities in the worst case and still lower in the average case the heart of the proof of polynomial time complexity is the convex hull theorem which states that under certain conditions a binary tree that minimizes one penalty measure can be changed to a binary tree that minimizes a second penalty measure in a carefully controlled sequence of changes called elementa

an overview of projection methods for incompressible flows a series of numerical issues related to the analysis and implementation of fractional step methods for incompressible flows are addressed in this paper these methods are often referred to in the literature as projection methods and can be classified into three classes namely the pressure correction methods the velocity correction methods and the consistent splitting methods for each class of schemes theoretical and numerical convergence results available in the literature are reviewed and open questions are discussed the essential results are summarized in a table which could serve as a useful reference to numerical analysts and practitioners published by elsevier b v msc 65n35 65n22 65f05 35j05

level set jet schemes for stiff advection equations the semijet method abstract many interfacial phenomena in physical and biological systems are dominated by high order geometric quantities such as curvature here a semi implicit method is combined with a level set jet scheme to handle stiff nonlinear advection problems the new method offers an improvement over the semi implicit gradient augmented level set method previously introduced by requiring only one smoothing step when updating the level set jet function while still preserving the underlying methods higher accuracy sample results demonstrate that accuracy is not sacrificed while strict time step restrictions can be avoided

calculation of incompressible viscous flows by an unconditionally stable projection fem this paper investigates the numerical performance of a finite element implementation of a new incremental fractional step method to compute steady and unsteady incompressible viscous flows under general boundary conditions and using unstructured meshes a variational framework is adopted which accommodates two different spaces for representing and approximating the velocity fields calculated respectively in the viscous and inviscid phases of the method but which leads to a very simple numerical scheme in terms of only one discrete velocity field an unconditionally stable semi implicit approximation of the nonlinear term is used to eliminate any time step restriction as far as the numerical stability is concerned numerical results for five test problems in two dimensions are reported to illustrate the flexibility of the proposed method

a novel representation of the surface tension force for two phase flow with reduced spurious currents abstract a new numerical model for the solution of the single fluid formulation of the incompressible navier stokes equations for two phase flows is presented the model couples an interface front tracking algorithm to a solver of the navier stokes equations based on the finite element method the interface line is described by an ordered set of markers which are advected along the flow streamlines and from the knowledge of their position the local normal and mean curvature are calculated the local mean curvature has been extended to the whole computational domain and the singular surface tension force has been transformed within the framework of the variational formulation into a regular volume force isoparametric taylor hood elements have been used to discretize the navier stokes equations the resulting system has been solved with a fully multigrid method coupled with a vanka like smoother the model has been tested with a dynamical system characterized by a droplet surrounded by another fluid equilibrium solutions described by the laplace s law are reproduced with great accuracy with a very low level of spurious currents which disappear completely if the exact value of the curvature is used damped oscillations are investigated in terms of the oscillation period the damping coefficient and the critical reynolds number for the transition from periodic to aperiodic regimes good agreement with theoretical solutions and the results of other numerical models has been found when the comparison is applicable

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

development of a dispersively accurate conservative level set scheme for capturing interface in two phase flows a two step interface capturing scheme implemented within the framework of conservative level set method is developed in this study to simulate the gas water two phase fluid flow in addition to solving the pure advection equation which is used to advect the level set function for tracking interface both nonlinear and stabilized features are taken into account for the level set function so that a sharply varying interface can be stably predicted to preserve the conservative property the mapping given by x x u t is performed between two coordinates x and x for the advection diffusion equation in a flow field with velocity u to capture the interface the flux term capable of compressing the level set contours is also adopted in the construction of linear inviscid burgers equation which is indispensable in the level set method to resolve the physically sharp interface without incurring contact discontinuity oscillations a damping term which is nonlinear in terms of the level set function and can render an adequate artificial diffusion to stabilize the contact surface is added into the reinitialization step in the modified level set method for accurately predicting the level set function the advection scheme for solving the linear inviscid burgers equation in the advection step of the modified level set method is developed to accommodate the true dispersion relation the solution computed from the resulting two dimensional dispersion relation preserving advection scheme can minimize the phase error less artificial damping is needed to damp the oscillations in the vicinity of contact surface and the interface can be less numerically smeared for the sake of programming simplicity the incompressible two phase flow will be discretized in non staggered grids without incurring checkerboard oscillations by the developed explicit compact scheme for the approximation of pressure gradient terms for the verification of the proposed two dimensional dispersion relation preserving scheme and the non staggered incompressible flow solver three benchmark problems have been chosen in this study the proposed conservative level set method for capturing the interface in incompressible fluid flows is also verified by solving the dam break bubble rising in water droplet falling in water and rayleigh taylor instability problems good agreements with the referenced solutions are demonstrated for all the four investigated problems

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

source coding for quasiarithmetic penalties whereas huffman coding finds a prefix code minimizing mean codeword length for a given finite item probability distribution quasiarithmetic or quasilinear coding problems have the goal of minimizing a generalized mean of the form rho 1 sigmaipirho li where li denotes the length of the ith codeword p i denotes the corresponding probability and rho is a monotonically increasing cost function such problems proposed by campbell have a number of diverse applications several cost functions are shown here to yield quasiarithmetic problems with simple redundancy bounds in terms of a generalized entropy a related property also shown here involves the existence of optimal codes for well behaved cost functions optimal codes always exist for possibly infinite alphabet sources having finite generalized entropy an algorithm is introduced for finding binary codes optimal for convex cost functions this algorithm which can be extended to other minimization utilities can be performed using quadratic time and linear space this reduces the computational complexity of a problem involving minimum delay in a queue allows combinations of previously considered problems to be optimized and greatly expands the set of problems solvable in quadratic time and linear space

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

a ghost fluid level set methodology for simulating multiphase electrohydrodynamic flows with application to liquid fuel injection in this paper we present the development of a sharp numerical scheme for multiphase electrohydrodynamic ehd flows for a high electric reynolds number regime the electric potential poisson equation contains ehd interface boundary conditions which are implemented using the ghost fluid method gfm the gfm is also used to solve the pressure poisson equation the methods detailed here are integrated with state of the art interface transport techniques and coupled to a robust high order fully conservative finite difference navier stokes solver test cases with exact or approximate analytic solutions are used to assess the robustness and accuracy of the ehd numerical scheme the method is then applied to simulate a charged liquid kerosene jet

a novel roe solver for incompressible two phase flow problems abstract in this paper a novel roe type riemann solver is developed for solving incompressible two phase flow problems the two phase flow is modeled by coupling the artificial compressibility based navier stokes equations and an interface advection equation in a conservative level set framework the proposed roe solver does not assume a locally constant density field while evaluating the flux jacobian as a result the solver is capable of capturing the exact jump conditions across the contact and shear waves which in turn helps in enhancing the accuracy of the interface motion moreover mass conservation characteristics are significantly improved by adopting conservative level set framework together with finite volume discretization of the system of equations a dual time stepping method with explicit pseudo time marching scheme is used for modeling the unsteady terms the efficacy of the proposed solver is demonstrated using various standard incompressible two phase flow problems involving low amplitude sloshing broken dam rayleigh taylor instability and droplet splash

a consistent solution of the re initialization equation in the conservative level set method in this paper a new re initialization method for the conservative level set function is put forward first it has been shown that the re initialization and advection equations of the conservative level set function are mathematically equivalent to the re initialization and advection equations of the localized signed distance function next a new discretization for the spatial derivatives of the conservative level set function has been proposed this new discretization is consistent with the re initialization procedure and it guarantees a second order convergence rate of the interface curvature on gradually refined grids the new re initialization method does not introduce artificial deformations to stationary and non stationary interfaces even when the number of re initialization steps is large we derive the re initialization equation of the localized signed distance function we show the analytical relation between the vof and ls methods we introduce the consistent method for computation of the interface curvature the new re initialization method does not deform interfaces and conserves mass second order convergence of curvature is achieved with second order accurate method

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

an oriented particle level set method based on surface coordinates in this work we present a new method for tracking evolving interfaces like the adaptive oriented particle level set method aopls ianniello and mascio 2010 it uses a combination of unconnected particles containing geometric information and a level set function to track the interface in the present method the geometric information solved for in each particle is a set of tangent vectors and the corresponding curvature tensor of the interface compared to the aopls method the amount of geometric data stored in each particle is roughly halved while still retaining a description of the interface that includes both orientation and curvature a mechanism for ensuring a sufficiently dense distribution of particles on the interface is also included from the information stored in each particle a continuous representation of the interface is obtained by transferring the information to a level set function stored on an eulerian grid unlike the aopls method the present method takes the curvature into account when the zero level set is constructed this results in significant improvements in regions of high curvature two different formulations of the new method have been explored in the first the tangent vectors deform purely according to the velocity field in the second the tangent vectors are forced to coincide with the principal directions of the surface both formulations are shown to be applicable