an h adaptive method in the generalized finite differences abstract this paper describes an h adaptive method in generalized finite difference gfd to solve second order partial differential equations these equations representing the behaviour of many physical processes the explicit difference formulae obtained make it possible to propose an a posteriori error indicator which serves as starting point for an h adaptive method to improve the solution by selectively adding nodes to the domain this paper also analyses the influence of key parameters as the number of nodes to add in each step or the minimum distance between nodes through the analysis of the obtained solutions for different types of differential equations

weak efficiency for multiobjective variational problems abstract sometimes to locate efficient solutions for multiobjective variational problems mvps is quite costly so in this paper we tackle the study of weakly efficient solutions for mvps a new concept of weak vector critical point which generalizes other ones already existent and a new class of pseudoinvex functions are introduced we will apply a new approach to prove that the new class of pseudoinvex functions is equivalent to the class of functions whose weak vector critical points are weakly efficient solution for mvps

enhancement of stability and accuracy of the moving particle semi implicit method as a lagrangian gridless particle method the mps moving particle semi implicit method has been proven useful in a wide range of engineering applications up to now most of mps applications have been limited to problems with compressive stress states this paper investigates the performance and stability of mps method in simulation of more general hydrodynamic problems including those characterized by tensile stresses or by changes in the stress states it is shown that mps based simulations are prone to become destabilized in presence of attractive interparticle forces this instability appears to be similar to the so called tensile instability in sph method two new modifications namely a modified poisson pressure equation and a corrective matrix for pressure gradient model are proposed to resolve this shortcoming these two new modifications together with two previously proposed improvements are shown to stabilize and enhance the performance of mps method

simulation of surface tension in 2d and 3d with smoothed particle hydrodynamics method the methods for simulating surface tension with smoothed particle hydrodynamics sph method in two dimensions and three dimensions are developed in 2d surface tension model the sph particle on the boundary in 2d is detected dynamically according to the algorithm developed by dilts g a dilts moving least squares particle hydrodynamics ii conservation and boundaries international journal for numerical methods in engineering 48 2000 1503 1524 the boundary curve in 2d is reconstructed locally with lagrangian interpolation polynomial in 3d surface tension model the sph particle on the boundary in 3d is detected dynamically according to the algorithm developed by haque and dilts a haque g a dilts three dimensional boundary detection for particle methods journal of computational physics 226 2007 1710 1730 the boundary surface in 3d is reconstructed locally with moving least squares mls method by transforming the coordinate system it is guaranteed that the interface function is one valued in the local coordinate system the normal vector and curvature of the boundary surface are calculated according to the reconstructed boundary surface and then surface tension force can be calculated surface tension force acts only on the boundary particle density correction is applied to the boundary particle in order to remove the boundary inconsistency the surface tension models in 2d and 3d have been applied to benchmark tests for surface tension the ability of the current method applying to the simulation of surface tension in 2d and 3d is proved

optimality and duality for nondifferentiable multiobjective variational problems abstract the concept of efficiency is used to formulate duality for nondifferentiable multiobjective variational problems wolfe and mond weir type vector dual problems are formulated by using the generalized schwarz inequality and a characterization of efficient solution we established the weak strong and converse duality theorems under generalized f convexity assumptions

on efficiency and duality for multiobjective variational control problems with f ρ convexity abstract the concept of efficiency pareto optimum is used to formulate duality for multiobjective variational control problems wolfe and mond weir type duals are formulated under the generalized f convexity on the functions involved weak and strong duality theorems are proved

mixed type duality for multiobjective variational problems with generalized f ρ convexity a mixed type dual for multiobjective variational problems is formulated several duality theorems are established relating properly efficient solutions of the primal and dual variational problems under generalized f convexity static mixed type dual multiobjective problems are particular cases of these problems

on efficiency and duality for multiobjective variational problems abstract the concept of efficiency pareto optimum is used to formulate duality for multiobjective variational problems wolfe and mond weir type duals are formulated under generalized f convexity assumptions on the functions involved weak and strong duality theorems are proved

duality for nondifferentiable static multiobjective variational problems involving generalized f ϱ convex functions using the generalized schwarz inequality we establish some weak duality theorems for nondifferentiable static multiobjective variational problems involving generalized f convex functions later in the sequel we introduce three dual models for the nondifferentiable static multiobjective fractional variational problems and derive weak duality results for such programs

duality for multiobjective fractional generalized control problems with f ρ f ρ convexity abstract the concept of efficiency is used to formulate duality for multiobjective fractional control problems wolfe and mond weier type duals are formulated using the generalized f convexity on the functions involved we establish the weak and strong duality theorems for multiobjective fractional generalized control problems

symmetric duality for a class of nondifferentiable multi objective fractional variational problems abstract we introduce a symmetric dual pair for a class of nondifferentiable multi objective fractional variational problems weak strong converse and self duality relations are established under certain invexity assumptions the paper includes extensions of previous symmetric duality results for multi objective fractional variational problems obtained by kim lee and schaible d s kim w j lee s schaible symmetric duality for invex multiobjective fractional variational problems j math anal appl 289 2004 505 521 and symmetric duality results for the static case obtained by yang wang and deng x m yang s y wang x t deng symmetric duality for a class of multiobjective fractional programming problems j math anal appl 274 2002 279 295 to the dynamic case

improved incompressible smoothed particle hydrodynamics method for simulating flow around bluff bodies in this article we present numerical solutions for flow over an airfoil and a square obstacle using incompressible smoothed particle hydrodynamics isph method with an improved solid boundary treatment approach referred to as the multiple boundary tangents mbt method it was shown that the mbt boundary treatment technique is very effective for tackling boundaries of complex shapes also we have proposed the usage of the repulsive component of the lennard jones potential ljp in the advection equation to repair particle fractures occurring in the sph method due to the tendency of sph particles to follow the stream line trajectory this approach is named as the artificial particle displacement method numerical results suggest that the improved isph method which is consisting of the mbt method artificial particle displacement and the corrective sph discretization scheme enables one to obtain very stable and robust sph simulations the square obstacle and naca airfoil geometry with the angle of attacks between 0 and 15 were simulated in a laminar flow field with relatively high reynolds numbers we illustrated that the improved isph method is able to capture the complex physics of bluff body flows naturally such as the flow separation wake formation at the trailing edge and the vortex shedding the sph results are validated with a mesh dependent finite element method fem and excellent agreements among the results were observed

accuracy and stability in incompressible sph isph based on the projection method and a new approach the stability and accuracy of three methods which enforce either a divergence free velocity field density invariance or their combination are tested here through the standard taylor green and spin down vortex problems while various approaches to incompressible sph isph have been proposed in the past decade the present paper is restricted to the projection method for the pressure and velocity coupling it is shown that the divergence free isph method cannot maintain stability in certain situations although it is accurate before instability sets in the density invariant isph method is stable but inaccurate with random noise like disturbances the combined isph combining advantages in divergence free isph and density invariant isph can maintain accuracy and stability although at a higher computational cost redistribution of particles on a fixed uniform mesh is also shown to be effective but the attraction of a mesh free method is lost a new divergence free isph approach is proposed here which maintains accuracy and stability while remaining mesh free without increasing computational cost by slightly shifting particles away from streamlines although the necessary interpolation of hydrodynamic characteristics means the formulation ceases to be strictly conservative this avoids the highly anisotropic particle spacing which eventually triggers instability importantly pressure fields are free from spurious oscillations up to the highest reynolds numbers tested

a lattice boltzmann scheme for incompressible multiphase flow and its application in simulation of rayleigh taylor instability in this paper we propose a new lattice boltzmann scheme for simulation of multiphase flow in the nearly incompressible limit the new scheme simulates fluid flows based on distribution functions the interfacial dynamics such as phase segregation and surface tension are modeled by incorporating molecular interactions the lattice boltzmann equations are derived from the continuous boltzmann equation with appropriate approximations suitable for incompressible flow the numerical stability is improved by reducing the effect of numerical errors in calculation of molecular interactions an index function is used to track interfaces between different phases simulations of the two dimensional rayleigh taylor instability yield satisfactory results the interface thickness is maintained at 3 4 grid spacings throughout simulations without artificial reconstruction steps

an improved multiphase lattice boltzmann flux solver for three dimensional flows with large density ratio and high reynolds number an improved multiphase lattice boltzmann flux solver mlbfs is proposed in this work for effective simulation of three dimensional 3d multiphase flows with large density ratio and high reynolds number as a finite volume scheme the mlbfs originally proposed in 27 applies the finite volume method to solve for macroscopic flow variables directly the fluxes are reconstructed locally at each cell interface by using the standard lbm solutions due to the modeling error of the standard lbm the reconstructed fluxes deviate from those in the navier stokes equations and to compensate this error a complex tensor is introduced in the original mlbfs however the computation of the tensor introduces additional complexity and usually needs a relatively thicker interface thickness to maintain numerical stability which makes the solver be complex and inefficient in the 3d case to remove this drawback in this work a theoretical analysis to the formulations obtained from the chapman enskog expansion is conducted it is shown that the modeling error can be effectively removed by modifying the computation of the equilibrium density distribution function with this improvement the proposed 3d mlbfs not only avoids the calculation of the compensation tensor but also is able to maintain numerical stability with very thin interface thickness several benchmark cases including the challenging droplet impacting on a dry surface head on collisions of binary droplets and droplet splashing on a thin film with density ratio 1000 and reynolds number up to 3000 are studied to validate the proposed solver the obtained results agree well with the published data

an mps based particle method for simulation of multiphase flows characterized by high density ratios by incorporation of space potential particle concept abstract simulation of multiphase flows characterized by high density ratios is targeted by using a refined particle method the proposed method is founded on moving particle semi implicit mps method which is a projection based particle method the proposed method comprises of a decoupled two step computational algorithm through application of a consistent scheme for coupling the light heavy phases by incorporating the concept of space potential particles spp the proposed coupling scheme guarantees the continuity of pressure and space volume conservation at the phase interface without any need for commonly applied density smoothing averaging schemes or application of numerical stabilizing terms verification of the proposed multiphase particle method is conducted through the simulations of four benchmark tests and the method is shown to possess acceptable accuracy and convergence properties

an hamiltonian interface sph formulation for multi fluid and free surface flows in the present work a new sph model for simulating interface and free surface flows is presented this formulation is an extension of the one discussed in colagrossi and landrini 2003 and is related to the one proposed by hu and adams 2006 to study multi fluid flows the new sph scheme allows an accurate treatment of the discontinuity of quantities at the interface such as the density and permits to model flows where both interfaces and a free surface are present the governing equations are derived following a lagrangian variational principle leading to an hamiltonian system of particles the proposed formulation is validated on test cases for which reference solutions are available in the literature

a lagrangian particle level set method we present a novel particle level set method for capturing interfaces the level set equation is solved in a lagrangian frame using particles that carry the level set information a key aspect of the method involves a consistent remeshing procedure for the regularization of the particle locations when the particle map gets distorted by the advection field the lagrangian description of the level set method is inherently adaptive and exact in the case of solid body motions the efficiency and accuracy of the method is demonstrated in several benchmark problems in two and three dimensions involving pure advection and curvature induced motion of the interface the simplicity of the particle description is shown to be well suited for real time simulations of surfaces involving cutting and reconnection as in virtual surgery environments

variational and momentum preservation aspects of smooth particle hydrodynamic formulations this paper presents a new variational framework for various existing smooth particle hydrodynamic sph techniques and presents a new corrected sph formulation the linear and angular momentum preserving properties of sph formulations are also discussed the paper will show that in general in order to preserve angular momentum the sph equations must correctly evaluate the gradient of a linear velocity field a corrected algorithm that combines kernel correction with gradient correction is presented the paper will illustrate the theory presented with several examples relating to simple free surface flows

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

pressure boundary conditions for computing incompressible flows with sph in smoothed particle hydrodynamics sph methods for fluid flow incompressibility may be imposed by a projection method with an artificial homogeneous neumann boundary condition for the pressure poisson equation this is often inconsistent with physical conditions at solid walls and inflow and outflow boundaries for this reason open boundary flows have rarely been computed using sph in this work we demonstrate that the artificial pressure boundary condition produces a numerical boundary layer that compromises the solution near boundaries we resolve this problem by utilizing a rotational pressure correction scheme with a consistent pressure boundary condition that relates the normal pressure gradient to the local vorticity we show that this scheme computes the pressure and velocity accurately near open boundaries and solid objects and extends the scope of sph simulation beyond the usual periodic boundary conditions

a new surface tension formulation for multi phase sph using a reproducing divergence approximation in this paper we propose a new surface tension formulation for multi phase smoothed particle hydrodynamics sph to obtain a stable and accurate scheme for surface curvature a new reproducing divergence approximation without the need for a matrix inversion is derived furthermore we introduce a density weighted color gradient formulation to reflect the reality of an asymmetrically distributed surface tension force we validate our method with analytic solutions and demonstrate convergence for different cases furthermore we show that our formulation can handle phase interfaces with density and viscosity ratios of up to 1000 and 100 respectively finally complex three dimensional simulations including breakup of an interface demonstrate the capabilities of our method

front tracking with moving least squares surfaces the representation of interfaces by means of the algebraic moving least squares amls technique is addressed this technique in which the interface is represented by an unconnected set of points is interesting for evolving fluid interfaces since there is no surface connectivity the position of the surface points can thus be updated without concerns about the quality of any surface triangulation we introduce a novel amls technique especially designed for evolving interfaces applications that we denote ramls for robust amls the main advantages with respect to previous amls techniques are increased robustness computational efficiency and being free of user tuned parameters further we propose a new front tracking method based on the lagrangian advection of the unconnected point set that defines the ramls surface we assume that a background eulerian grid is defined with some grid spacing h the advection of the point set makes the surface evolve in time the point cloud can be regenerated at any time in particular we regenerate it each time step by intersecting the gridlines with the evolved surface which guarantees that the density of points on the surface is always well balanced the intersection algorithm is essentially a ray tracing algorithm well studied in computer graphics in which a line ray is traced so as to detect all intersections with a surface also the tracing of each gridline is independent and can thus be performed in parallel several tests are reported assessing first the accuracy of the proposed ramls technique and then of the front tracking method based on it comparison with previous eulerian lagrangian and hybrid techniques encourage further development of the proposed method for fluid mechanics applications

homogenization of the navier stokes equations in open sets perforated with tiny holes i abstract framework a volume distribution of holes this paper treats the homogenization of the stokes or navier stokes equations with a dirichlet boundary condition in a domain containing many tiny solid obstacles periodically distributed in each direction of the axes for example in the three dimensional case the obstacles have a size of e3 and are located at the nodes of a regular mesh of size e a suitable extension of the pressure is used to prove the convergence of the homogenization process to a brinkman type law in which a linear zero order term for the velocity is added to a stokes or navier stokes equation

simulating free surface flows with sph the sph smoothed particle hydrodynamics method is extended to deal with free surface incompressible flows the method is easy to use and examples will be given of its application to a breaking dam a bore the simulation of a wave maker and the propagation of waves towards a beach arbitrary moving boundaries can be included by modelling the boundaries by particles which repel the fluid particles the method is explicit and the time steps are therefore much shorter than required by other less flexible methods but it is robust and easy to program

homogenization of a non stationary stokes flow in porous medium including a layer abstract we study the behavior of the solution to the non stationary stokes equations in a porous medium with characteristic size of the pores e and containing a thin fissure 0 x n of width the limit when e and tend to zero gives the homogenized behavior of the flow which depends on the comparison between e and

an incompressible multi phase sph method an incompressible multi phase sph method is proposed in this method a fractional time step method is introduced to enforce both the zero density variation condition and the velocity divergence free condition at each full time step to obtain sharp density and viscosity discontinuities in an incompressible multi phase flow a new multi phase projection formulation in which the discretized gradient and divergence operators do not require a differentiable density or viscosity field is proposed numerical examples for taylor green flow capillary waves drop deformation in shear flows and for rayleigh taylor instability are presented and compared to theoretical solutions or references from literature the results suggest good accuracy and convergence properties of the proposed method

a necessary and sufficient condition for duality in multiobjective variational problems abstract in this paper we move forward in the study of duality and efficiency in multiobjective variational problems we introduce new classes of pseudoinvex functions and prove that not only it is a sufficient condition to establish duality results but it is also necessary moreover these functions are characterized in order that all kuhn tucker or fritz john points are efficient solutions recent papers are improved we provide an example to show this improvement and illustrate these classes of functions and results

multi fluid flows with the particle finite element method abstract particle methods are those in which the problem is represented by a discrete number of particles each particle moves accordingly with its own mass and the external internal forces applied on it in this paper the particle finite element method based on finite element shape functions is used to solve the continuous fluid mechanics equations in the case of heterogeneous density to evaluate the external applied forces to each particle the incompressible navier stokes equations are solved at each time step using a lagrangian formulation all the information in the fluid is transmitted via the particles all kinds of density heterogeneous fluids and multiphase flows with internal interfaces including or not free surfaces breaking waves and fluid separations may be easily solved with this methodology

second order symmetric duality in mathematical programming with f convexity abstract under second order f convexity f concavity and second order f pseudoconvexity f pseudoconcavity appropriate second order duality results for pair of wolfe and mond weir type second order symmetric dual nonlinear programming problems are established these second order duality results are then used to formulate wolfe type and mond weir type second order minimax mixed integer dual programs and symmetric duality theorem is established under separability and second order f convexity f concavity of the kernel function f x y second order symmetric dual fractional mixed integer programs are studied using the above programs moreover second order self duality theorems for the above pairs are obtained assuming f x y to be skew symmetric

a constant density approach for incompressible multi phase sph a constant density approach which corrects intermediate density errors by adjusting the half time step velocity with exact projection is proposed for the multi phase sph method developed in our previous work x y hu n a adams an incompressible multi phase sph method j comput phys 227 2007 264 278 as no prescribed reference pressure is required the present approach introduces smaller numerical viscosity and allows to simulate flows with unprecedentedly high density ratios by the projection sph method numerical examples for taylor green flow capillary waves and for rayleigh taylor instability are presented and compared to theoretical solutions or references from the literature

duality for a class of multiobjective control problems with generalized invexity abstract b mond and i smart j math anal appl 136 1988 325 333 defined a kind of invexity and discussed the duality and sufficiency in scalar control problems with such invexity d bhatia and p kumar j math anal appl 189 1995 676 692 defined another kind of invexity corresponding generalized invexity and discussed the duality for multiobjective control problems with such generalized invexity in this paper the duality results for multiobjective control problems with mond and smart s generalized invexity are discussed

darcy s law for slow viscous flow past a stationary array of bubbles we examine slow viscous flow past a concentrated bed of small stationary viscous bubbles of a second fluid and derive darcy s law relating the average fluid velocity to the overall pressure gradient and body force

sph with the multiple boundary tangent method in this article we present an improved solid boundary treatment formulation for the smoothed particle hydrodynamics sph method benchmark simulations using previously reported boundary treatments can suffer from particle penetration and may produce results that numerically blow up near solid boundaries as well current sph boundary approaches do not properly treat curved boundaries in complicated flow domains these drawbacks have been remedied in a new boundary treatment method presented in this article called the multiple boundary tangent mbt approach in this article we present two important benchmark problems to validate the developed algorithm and show that the multiple boundary tangent treatment produces results that agree with known numerical and experimental solutions the two benchmark problems chosen are the lid driven cavity problem and flow over a cylinder the sph solutions using the mbt approach and the results from literature are in very good agreement these solutions involved solid boundaries but the approach presented herein should be extendable to time evolving free surface boundaries copyright 2008 john wiley sons ltd

weakly efficient solutions and pseudoinvexity in multiobjective control problems abstract in this paper we introduce new pseudoinvexity conditions on functionals involved in a multiobjective control problem called w kt pseudoinvexity and w fj pseudoinvexity we prove that all kuhn tucker or fritz john points are weakly efficient solutions if and only if these conditions are fulfilled we relate weakly efficient solutions to optimal solutions of weighting control problems we generalize recently obtained optimality results of known mathematical programming problems and control problems we illustrate these results with an example

hamiltonian moving particle semi implicit hmps method for incompressible fluid flows particle methods are meshless simulation techniques in which motion of continua is approximated by discrete dynamics of a finite number of particles and thus have a great degree of flexibility for instance in dealing with the complex motion of surfaces or boundaries in this paper a particle method is developed from a direct discretization of the lagrangian for inviscid incompressible fluid flows the discretized lagrangian is transformed into a hamiltonian with holonomic constraints that stem from the incompressibility condition the rattle algorithm that is a symplectic scheme for holonomically constrained hamiltonian systems is adopted so that the resulting particle method inherits structures possessed by the partial differential equations that govern inviscid incompressible flows the algorithm of the particle method is semi implicit so we call it the hamiltonian moving particle semi implicit hmps method some numerical tests indicate the excellence of the hmps method in conservation of mechanical energy as well as linear and angular momenta

efficient solutions in v kt pseudoinvex multiobjective control problems a characterization in this paper we introduce a new condition on functionals involved in a multiobjective control problem for which we define the v kt pseudoinvex control problem we prove that a v kt pseudoinvex control problem is characterized so that a kuhn tucker point is an efficient solution we generalize recently obtained optimality results of known mathematical programming problems and control problems we illustrate these results with an example

comparisons of weakly compressible and truly incompressible algorithms for the sph mesh free particle method in the smoothed particle hydrodynamics sph discretisation method for the navier stokes equations the most widespread method to solve for pressure and mass conservation is the weakly compressible assumption wcsph this includes hydraulics applications and leads to some drawbacks such as severe artificial pressure fluctuations and a limitation to very small time steps related to the wcsph mach number and explicit method this paper presents comparisons of a semi implicit and truly incompressible sph isph algorithm with the classical wcsph method showing how some of the problems encountered in wcsph have been resolved by using isph to simulate incompressible flows mathematical models are presented before describing sph formalism several standard boundary conditions are introduced and special attention is given to tracking the surface particles the lid driven cavity flow re 400 and 1000 is performed as a benchmarking test a bluff body test case a square cylinder in a closed channel re d 20 and 100 based on the cylinder diameter shows that pressure fields extracted from wcsph are very unreliable whereas isph predict pressures and forces in closer agreement with classical finite volume cfd methods dam breaking cases with dry or wet beds downstream are then presented to highlight free surface flow and rapid dynamics effects the wcsph and isph results are generally verified with reference data from experiment and or another numerical method all the comparisons show improvement with isph and good agreement in general

the particle finite element method a powerful tool to solve incompressible flows with free surfaces and breaking waves summary particle methods are those in which the problem is represented by a discrete number of particles each particle moves accordingly with its own mass and the external internal forces applied to it particle methods may be used for both discrete and continuous problems in this paper a particle method is used to solve the continuous fluid mechanics equations to evaluate the external applied forces on each particle the incompressible navier stokes equations using a lagrangian formulation are solved at each time step the interpolation functions are those used in the meshless finite element method and the time integration is introduced by an implicit fractional step method in this manner classical stabilization terms used in the momentum equations are unnecessary due to lack of convective terms in the lagrangian formulation once the forces are evaluated the particles move independently of the mesh all the information is transmitted by the particles fluid structure interaction problems including free fluid surfaces breaking waves and fluid particle separation may be easily solved with this methodology copyright 2004 john wiley sons ltd

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

generalized type i invexity and duality in multiobjective variational problems abstract in this paper we introduce new classes of generalized v type i invex functions for variational problems and consider a multiobjective variational problem vp a number of sufficiency results are established using lagrange multiplier conditions under various types of generalized v type i invexity requirements duality results are obtained for mond weir type duals under the above generalized v type i invexity assumptions and their generalizations

a level set method for computing solutions to viscoelastic two phase flow abstract a finite element code based on the level set method is developed for simulating the motion of viscoelastic two phase flow problems this method is a generalization of the finite difference approach described in 1 4 for computing solutions to two phase problems of inviscid and viscous fluids the marchuk yanenko operator splitting technique is used to decouple the difficulties associated with the nonlinear convection term the incompressibility constraint the viscoelastic term and the interface motion problem the nonlinear convection problem is solved using a least squares conjugate gradient algorithm and the stokes like problem is solved using a conjugate gradient algorithm the constitutive equation is solved using a scheme that guarantees the positive definiteness of the configuration tensor while the convection term in the constitutive equation is discretized using a third order upwinding scheme the code is verified by performing a convergence study to show that the results are independent of the mesh and time step sizes using our code we have studied the deformation of drops in simple shear and pressure driven flows and of bubbles in gravity driven flows over a wide range of dimensionless capillary ca and deborah numbers de for a newtonian bubble rising in a quiescent viscoelastic liquid we find that there are limiting values of the parameters de and ca above which the bubble assumes a characteristic shape with a cusp like trailing edge the front of the bubble however remains round as the local viscoelastic and viscous stresses act to round the bubble in a pressure driven flow the drop is stretched so that its front which is closer to the channel center remains round and the trailing edge which is closer to the channel wall becomes sharp these numerical results are in agreement with the experimental observations

multiphase lattice boltzmann flux solver for incompressible multiphase flows with large density ratio a multiphase lattice boltzmann flux solver mlbfs is proposed in this paper for incompressible multiphase flows with low and large density ratios in the solver the flow variables at cell centers are given from the solution of macroscopic governing differential equations navier stokes equations recovered by multiphase lattice boltzmann lb model by the finite volume method at each cell interface the viscous and inviscid fluxes are evaluated simultaneously by local reconstruction of solution for the standard lattice boltzmann equation lbe the forcing terms in the governing equations are directly treated by the finite volume discretization the phase interfaces are captured by solving the phase field cahn hilliard equation with a fifth order upwind scheme unlike the conventional multiphase lb models which restrict their applications on uniform grids with fixed time step the mlbfs has the capability and advantage to simulate multiphase flows on non uniform grids the proposed solver is validated by several benchmark problems such as two phase co current flow taylor couette flow in an annulus rayleigh taylor instability and droplet splashing on a thin film at density ratio of 1000 with reynolds numbers ranging from 20 to 1000 numerical results show the reliability of the proposed solver for multiphase flows with high density ratio and high reynolds number

a robust weakly compressible sph method and its comparison with an incompressible sph summary this paper presents a comparative study for the weakly compressible wcsph and incompressible isph smoothed particle hydrodynamics methods by providing numerical solutions for fluid flows over an airfoil and a square obstacle improved wcsph and isph techniques are used to solve these two bluff body flow problems it is shown that both approaches can handle complex geometries using the multiple boundary tangents mbt method and eliminate particle clustering induced instabilities with the implementation of a particle fracture repair procedure as well as the corrected sph discretization scheme wcsph and isph simulation results are compared and validated with those of a finite element method fem the quantitative comparisons of wcsph isph and fem results in terms of strouhal number for the square obstacle test case and the pressure envelope surface traction forces and velocity gradients on the airfoil boundaries as well as the lift and drag values for the airfoil geometry indicate that the wcsph method with the suggested implementation produces numerical results as accurate and reliable as those of the isph and fem methods copyright 2011 john wiley sons ltd

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

numerical investigation of newtonian and non newtonian multiphase flows using isph method we have presented a multiphase incompressible smoothed particle hydrodynamics method with an improved interface treatment procedure to demonstrate the effectiveness of the interface treatment which can handle multiphase flow problems with high density and viscosity ratios we have modeled several challenging two phase flow problems namely single vortex flow square droplet deformation droplet deformation in shear flow and finally the newtonian bubble rising in viscous and viscoelastic liquids the proposed interface treatment includes the usage of i different smoothing functions in this work cubic spline kernel function for discretizing equations associated with the calculation of the surface tension force while the quintic spline for the discretization of governing equations and the relevant boundary conditions and ii a new discretization scheme for calculating the pressure gradient it is shown that with the application of the improved interface treatment it becomes possible to model multiphase flow problems with the density and viscosity ratios up to 1000 and 100 respectively while using standard projection method the utilization of cubic spline for the continuum surface force model significantly improves the quality of the calculated interface thereby eliminating the interphase particle penetrations and in turn leading to the calculation of more accurate velocity and pressure fields

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

direct numerical simulation of interfacial instabilities a consistent conservative all speed sharp interface method we present a conservative and consistent numerical method for solving the navier stokes equations in flow domains that may be separated by any number of material interfaces at arbitrarily high density viscosity ratios and acoustic impedance mismatches subjected to strong shock waves and flow speeds that can range from highly supersonic to near zero mach numbers a principal aim is prediction of interfacial instabilities under superposition of multiple potentially active modes rayleigh taylor kelvin helmholtz richtmyer meshkov as found for example with shock driven immersed fluid bodies locally oblique shocks accordingly we emphasize fidelity supported by physics based validation including experiments consistency is achieved by satisfying the jump discontinuities at the interface within a conservative 2nd order scheme that is coupled in a conservative manner to the bulk fluid motions the jump conditions are embedded into a riemann problem solved exactly to provide the pressures and velocities along the interface which is tracked by a level set function to accuracy of o dx 5 dt 4 subgrid representation of the interface is achieved by allowing curvature of its constituent interfacial elements to obtain o dx 3 accuracy in cut cell volume with attendant benefits in calculating cell geometric features and interface curvature o dx 3 overall the computation converges at near theoretical o dx 2 spurious currents are down to machine error and there is no time step restriction due to surface tension our method is built upon a quadtree like adaptive mesh refinement infrastructure when necessary this is supplemented by body fitted grids to enhance resolution of the gas dynamics including flow separation shear layers slip lines and critical layers comprehensive comparisons with exact solutions for the linearized rayleigh taylor and kelvin helmholtz problems demonstrate excellent performance sample simulations of liquid drops subjected to shock waves demonstrate for the first time ab initio numerical prediction of the key interfacial features and phenomena found in recent experimental and theoretical studies of this class of problems t g theofanous aerobreakup of newtonian and viscoelastic liquids ann rev fluid mech 43 2011 661 690

duality with bf type i functions for a class of nondifferentiable multiobjective variational problems a class of bf type i functions and its extensions are introduced in the continuous case an example is presented in support utilizing these new concepts sufficient optimality conditions and duality results are presented for multiobjective variational problems involving arbitrary norms

effective models of the navier stokes flow in porous media with a thin fissure abstract we consider the navier stokes equations in a bounded domain consisting of two porous media with a thin fissure 0 x n of width between them we suppose the porous medium having a periodic structure with a period e and consider the limit when e and tend to zero the effective behaviors in porous media and the fissure are determined which depend on the comparison between e and