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

analysis of the parareal time parallel time integration method the parareal algorithm is a method to solve time dependent problems parallel in time it approximates parts of the solution later in time simultaneously to parts of the solution earlier in time in this paper the relation of the parareal algorithm to space time multigrid and multiple shooting methods is first briefly discussed the focus of the paper is on new convergence results that show superlinear convergence of the algorithm when used on bounded time intervals and linear convergence for unbounded intervals

a fast numerical method for solving the three dimensional stokes equations in the presence of suspended particles abstract a new fast numerical method for solving the three dimensional stokes equations in the presence of suspended particles is presented the fluid dynamics equations are solved on a lattice a particle is represented by a set of points each of which moves at the local fluid velocity and is not constrained to lie on the lattice these points are coupled by forces which resist deformation of the particle these forces contribute to the force density in the stokes equations as a result a single set of fluid dynamics equations holds at all points of the domain and there are no internal boundaries particle size shape and deformability may be prescribed computational work increases only linearly with the number of particles so large numbers 500 1000 of particles may be studied efficiently the numerical method involves implicit calculation of the particle forces by minimizing an energy function and solution of a finite difference approximation to the stokes equations using the fourier toeplitz method the numerical method has been implemented to run on all cray computers the implementation exploits the cray s vectorized arithmetic and on machines with insufficient central memory it performs efficient disk 1 o while storing most of the data on disk applications of the method to sedimentation of one two and many particle systems are described trajectories and settling speeds for two particle sedimentation and settling speed for multiparticle sedimentation from initial distributions on a cubic lattice or at random give good quantitative agreement with existing theories

an error bound for a discrete reduced order model of a linear multivariable system the design of feasible controllers for high dimension multivariable systems can be greatly aided by a method of model reduction in order for the design based on the order reduction to include a guarantee of stability it is sufficient to have a bound on the model error previous work has provided such a bound for continuous time systems for algorithms based on balancing in this note an linftybound is derived for model error for a method of order reduction of discrete linear multivariable systems based on balancing

study of phase field lattice boltzmann models based on the conservative allen cahn equation conservative phase field cpf equations based on the allen cahn model for interface tracking in multiphase flows have become more popular in recent years especially in the lattice boltzmann lb community this is largely due to their simplicity and improved efficiency and accuracy over their cahn hilliard based counterparts additionally the improved locality of the resulting lb equation lbe for the cpf models makes them more ideal candidates for lb simulation of multiphase flows on nonuniform grids particularly within an adaptive mesh refinement framework and massively parallel implementation in this regard some modifications intended as improvements have been made to the original cpf lbe proposed by geier et al phys rev e 91 063309 2015 pleee81539 375510 1103 physreve 91 063309 which require further examination the goal of the present study is to conduct a comparative investigation into the differences between the original cpf model proposed by geier et al phys rev e 91 063309 2015 pleee81539 375510 1103 physreve 91 063309 and the so called improvements proposed by ren et al phys rev e 94 023311 2016 2470 004510 1103 physreve 94 023311 and wang et al phys rev e 94 033304 2016 2470 004510 1103 physreve 94 033304 using the chapman enskog analysis we provide a detailed derivation of the governing equations in each model and then examine the efficacy of the above mentioned models for some benchmark problems several test cases have been designed to study different configurations ranging from basic yet informative flows to more complex flow fields and the results are compared with finite difference simulations furthermore as a development of the previously proposed cpf lbe model axisymmetric formulations for the proposed model by geier et al phys rev e 91 063309 2015 pleee81539 375510 1103 physreve 91 063309 are derived and presented finally two benchmark problems are designed to compare the proposed axisymmetric model with the analytical solution and previous work we find that the accuracy of the model for interface tracking is roughly similar for different models at high viscosity ratios high density ratios and relatively high reynolds numbers while the original cfp lbe without the additional time dependent terms outperforms the so called improved models in terms of efficiency particularly on distributed parallel machines

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

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

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

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

monotonic parareal control for quantum systems following encouraging experimental results in quantum control numerical simulations have known significant improvements through the introduction of efficient optimization algorithms yet the computational cost still prevents using these procedures for high dimensional systems often present in quantum chemistry using parareal framework we present here a time parallelization of these schemes which allows us to reduce significantly their computational cost while still finding convenient controls

lattice boltzmann model for free surface flow and its application to filling process in casting a generalized lattice boltzmann model to simulate free surface is constructed in both two and three dimensions the proposed model satisfies the interfacial boundary conditions accurately a distinctive feature of the model is that the collision processes is carried out only on the points occupied partially or fully by the fluid to maintain a sharp interfacial front the method includes an anti diffusion algorithm the unknown distribution functions at the interfacial region are constructed according to the first order chapman enskog analysis the interfacial boundary conditions are satisfied exactly by the coefficients in the chapman enskog expansion the distribution functions are naturally expressed in the local interfacial coordinates the macroscopic quantities al the interface are extracted from the least square solutions of a locally linearized system obtained from the known distribution functions the proposed method does not require any geometric front construction and is robust for any interfacial topology simulation results of realistic filling process are presented rectangular cavity in two dimensions and hammer box campbell box sheffield box and motorblock in three dimensions to enhance the stability at high reynolds numbers various upwind type schemes are developed free slip and no slip boundary conditions are also discussed

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

fast algorithm based on tt m fe system for space fractional allen cahn equations with smooth and non smooth solutions abstract in this article a fast algorithm based on time two mesh tt m finite element fe scheme which aims at solving nonlinear problems quickly is considered to numerically solve the nonlinear space fractional allen cahn equations with smooth and non smooth solutions the implicit second order scheme containing both implicit crank nicolson scheme and second order backward difference method is applied to time direction a fast tt m method is used to increase the speed of calculation and the fe method is developed to approximate the spacial direction the tt m fe algorithm includes the following main computing steps firstly a nonlinear implicit second order fe scheme on the time coarse mesh c is solved by a nonlinear iterative method secondly based on the chosen initial iterative value a linearized fe system on time fine mesh c is solved where some useful coarse numerical solutions are found by the lagrange s interpolation formula the analysis for both stability and a priori error estimates are made in detail finally three numerical examples with smooth and non smooth solutions are provided to illustrate the computational efficiency in solving nonlinear partial differential equations from which it is easy to find that the computing time can be saved

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

analysis of high order fast interface tracking methods fast high order methods for the propagation of an interface in a velocity field are constructed and analyzed the methods are generalizations of the fast interface tracking method proposed in runborg commun math sci 7 365 398 2009 they are based on high order subdivision to make a multiresolution decomposition of the interface instead of tracking marker points on the interface the related wavelet vectors are tracked like the markers they satisfy ordinary differential equations odes but fine scale wavelets can be tracked with longer timesteps than coarse scale wavelets this leads to methods with a computational cost of o log n delta t o log n t rather than o n delta t o n t for n n markers and reference timestep delta t t these methods are proved to still have the same order of accuracy as the underlying direct ode solver under a stability condition in terms of the order of the subdivision the order of the ode solver and the time step ratio between wavelet levels in particular it is shown that with a suitable high order subdivision scheme any explicit runge kutta method can be used numerical examples supporting the theory are also presented

a parareal method for time fractional differential equations in this paper a parareal method is proposed for the parallel in time integration of time fractional differential equations tfdes it is a generalization of the original parareal method proposed for classic differential equations to match the global feature of fractional derivatives the new method has in the correction step embraced the history part of the solution we provide a convergence analysis under the assumption of lipschitz stability conditions we use a multi domain spectral integrator to build the serial solvers and numerical results demonstrate the feasibility of the new approach and confirm the convergence analysis studies also show that both the coarse resolution and the nature of the differential operators can affect the performance

a contoured continuum surface force model for particle methods a surface tension model is essential to simulate multiphase flows with deformed interfaces this study develops a contoured continuum surface force ccsf model for particle methods a color function that varies sharply across the interface to mark different fluid phases is smoothed in the transition region where the local contour curvature can be regarded as the interface curvature the local contour passing through each reference particle in the transition region is extracted from the local profile of the smoothed color function the local contour curvature is calculated based on the taylor series expansion of the smoothed color function whose derivatives are calculated accurately according to the definition of the smoothed color function two schemes are proposed to specify the smooth radius fixed scheme where 2 r e r e particle interaction radius is assigned to all particles in the transition region and varied scheme where r e and 2 r e are assigned to the central and edged particles in the transition region respectively numerical examples including curvature calculation for static circle and ellipse interfaces deformation of square droplet to a circle 2d and 3d droplet deformation in shear flow and droplet coalescence are simulated to verify the ccsf model and compare its performance with those of other methods the ccsf model with the fixed scheme is proven to produce the most accurate curvature and lowest parasitic currents among the tested methods

an asymptotic preserving scheme for the two fluid euler poisson model in the quasineutral limit this paper deals with the modeling of a plasma in the quasineutral limit using the two fluid euler poisson system in this limit explicit numerical schemes suffer from severe numerical constraints related to the small debye length and large plasma frequency here we propose an implicit scheme which reduces to a scheme for the quasineutral euler model in the quasineutral limit such a property is referred to as asymptotic preservation one of the distinctive features of this scheme is that it has a comparable numerical cost to that of an explicit scheme simply the poisson equation is replaced by a different but formally equivalent elliptic problem we present numerical simulations for two different one dimensional test cases they confirm the expected stability of the scheme in the quasineutral limit they also show that this scheme has some accuracy problems in the limit of small electron to ion mass ratio in reproducing the correct electron velocity but this problem is already present in the results of the classical algorithm numerical simulations are also performed for a two dimensional problem of a plasma expansion in vacuum between two electrodes

using hierarchical matrices in the solution of the time fractional heat equation by multigrid waveform relaxation abstract this work deals with the efficient numerical solution of the time fractional heat equation discretized on non uniform temporal meshes non uniform grids are essential to capture the singularities of typical solutions of time fractional problems we propose an efficient space time multigrid method based on the waveform relaxation technique which accounts for the nonlocal character of the fractional differential operator to maintain an optimal complexity which can be obtained for the case of uniform grids we approximate the coefficient matrix corresponding to the temporal discretization by its hierarchical matrix h matrix representation in particular the proposed method has a computational cost of o k n m log m where m is the number of time steps n is the number of spatial grid points and k is a parameter which controls the accuracy of the h matrix approximation the efficiency and the good convergence of the algorithm which can be theoretically justified by a semi algebraic mode analysis are demonstrated through numerical experiments in both one and two dimensional spaces

a lattice boltzmann method for axisymmetric multicomponent flows with high viscosity ratio a color gradient lattice boltzmann method lbm is proposed to simulate axisymmetric multicomponent flows this method uses a collision operator that is a combination of three separate parts namely single component collision operator perturbation operator and recoloring operator a source term is added into the single component collision operator such that in each single component region the axisymmetric continuity and momentum equations can be exactly recovered the interfacial tension effect is realized by the perturbation operator in which an interfacial force of axisymmetric form is derived using the concept of continuum surface force a recoloring operator proposed by latva kokko and rothman is extended to the axisymmetric case for phase segregation and maintenance of the interface to enhance the method s numerical stability for handling binary fluids with high viscosity ratio a multiple relaxation time model is used for the collision operator several numerical examples including static droplet test oscillation of a viscous droplet and breakup of a liquid thread are presented to test the capability and accuracy of the proposed color gradient lbm it is found that the present method is able to accurately capture the phase interface and produce low spurious velocities also the lbm results are all in good agreement with the analytical solutions and or available experimental data for a very broad range of viscosity ratios a color gradient lbm is developed for immiscible axisymmetric multiphase flows the method consists of three separate operators in which axisymmetric effects are considered the method is demonstrated to be accurate for a very wide range of viscosity ratios viscosity ratio is found to affect significantly growth of rayleigh instability but have negligible effect on droplet size

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

towards essential improvement for the parareal tr and parareal gauss4 algorithms parareal is an iterative algorithm and is characterized by two propagators g and f which are respectively associated with large step size t and small step size t where t j t and j 2 is an integer for symmetric positive definite spd system u t a u t g t arising from semi discretizing time dependent pdes if we fix the g propagator to the backward euler method and choose for f some l stable time integrator it can be proven that the convergence factors of the corresponding parareal algorithms satisfy 1 3 j 2 and a 0 where a is the spectrum of the matrix a however this result does not hold when time integrators that lack l stability such as the trapezoidal rule and the 4th order gauss rk method are chosen as the f propagator the parareal algorithms using these two methods for the f propagator are denoted by parareal tr and parareal gauss4 in this paper we propose a strategy to let these two parareal algorithms possess such a uniform convergence property the idea is to choose an l stable propagator f and on each coarse time interval t n t n 1 we perform first two steps of f then followed by j 2 steps of f precisely for the trapezoidal rule we select the 2nd order sdirk method as the f propagator and for the 4th order gauss rk method we select the 4th order lobatto iii c method as the f propagator numerical results are given to support our theoretical conclusions

a multi domain spectral method for time fractional differential equations this paper proposes an approach for high order time integration within a multi domain setting for time fractional differential equations since the kernel is singular or nearly singular two main difficulties arise after the domain decomposition how to properly account for the history memory part and how to perform the integration accurately to address these issues we propose a novel hybrid approach for the numerical integration based on the combination of three term recurrence relations of jacobi polynomials and high order gauss quadrature the different approximations used in the hybrid approach are justified theoretically and through numerical examples based on this we propose a new multi domain spectral method for high order accurate time integrations and study its stability properties by identifying the method as a generalized linear method numerical experiments confirm hp convergence for both time fractional differential equations and time fractional partial differential equations

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

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

parallel in time algorithm with spectral subdomain enhancement for volterra integral equations nsf of china 11201077 11071203 91130002 nsf of fujian province 2012j01007 fuzhou university 0460022456 hong kong research grant council gif grants hong kong baptist university frg grants

level set methods an overview and some recent results the level set method was devised by s osher and j a sethian 1988 j comput phys 79 12 49 as a simple and versatile method for computing and analyzing the motion of an interface in two or three dimensions bounds a possibly multiply connected region the goal is to compute and analyze the subsequent motion of under a velocity field v this velocity can depend on position time the geometry of the interface and the external physics the interface is captured for later time as the zero level set of a smooth at least lipschitz continuous function x t i e t x x t 0 is positive inside negative outside and is zero on t topological merging and breaking are well defined and easily performed in this review article we discuss recent variants and extensions including the motion of curves in three dimensions the dynamic surface extension method fast methods for steady state problems diffusion generated motion and the variational level set approach we also give a user s guide to the level set dictionary and technology and couple the method to a wide variety of problems involving external physics such as compressible and incompressible possibly reacting flow stefan problems kinetic crystal growth epitaxial growth of thin films vortex dominated flows and extensions to multiphase motion we conclude with a discussion of applications to computer vision and image processing

the numerical approximation of a delta function with application to level set methods it is shown that a discrete delta function can be constructed using a technique developed by anita mayo the fast solution of poisson s and the biharmonic equations on irregular regions siam j sci comput 21 1984 285 299 for the numerical solution of elliptic equations with discontinuous source terms this delta function is concentrated on the zero level set of a continuous function in two space dimensions this corresponds to a line and a surface in three space dimensions delta functions that are first and second order accurate are formulated in both two and three dimensions in terms of a level set function the numerical implementation of these delta functions achieves the expected order of accuracy

locally corrected semi lagrangian methods for stokes flow with moving elastic interfaces we present a new method for computing two dimensional stokes flow with moving interfaces that respond elastically to stretching the interface is moved by semi lagrangian contouring a distance function is introduced on a tree of cells near the interface transported by a semi lagrangian time step and then used to contour the new interface the velocity field in a periodic box is calculated as a potential integral resulting from interfacial and body forces using a technique based on ewald summation with analytically derived local corrections the interfacial stretching is found from a surprisingly natural formula a test problem with an exact solution is constructed and used to verify the speed accuracy and robustness of the approach

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

analysis of a new finite difference local discontinuous galerkin method for the fractional diffusion wave equation in this paper a finite difference local discontinuous galerkin method for the fractional diffusion wave equation is presented and analyzed we first propose a new finite difference method to approximate the time fractional derivatives and give a semidiscrete scheme in time further we develop a fully discrete scheme for the fractional diffusion wave equation and prove that the method is unconditionally stable and convergent with order o hk 1 t 3 where k is the degree of piecewise polynomial extensive numerical examples are carried out to confirm the theoretical convergence rates

fast parareal iterations for fractional diffusion equations abstract numerical methods for fractional pdes is a hot topic recently this work is concerned with the parareal algorithm for system of odes u t a u t f that arising from semi discretizations of time dependent fractional diffusion equations with nonsymmetric riemann liouville fractional derivatives the spatial semi discretization of this kind of fractional derivatives often results in a coefficient matrix a with spectrum a satisfying a s c r where 0 is a measure of dissipativity of the differential equations to accelerate the parareal algorithm we propose a scaled model u t 1 a u t f with 0 to serve the coarse grid correction which is an important component of our parareal algorithm given and we derive a sharp bound of the convergence factor of the parareal iterations moreover by minimizing such a bound we get optimized scaling factor opt it is shown that compared to 1 i e the classical implementation pattern of the coarse grid correction the optimized scaling factor significantly improves the convergence rate numerical examples are presented to support the theoretical finding

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

a 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 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 fixed grid sharp interface method for bubble dynamics and phase change abstract a numerical method has been developed for direct simulation of bubble dynamics with large liquid to vapor density ratio and phase change the numerical techniques are based on a fixed grid finite volume method capable of treating the interface as a sharp discontinuity the unsteady axisymmetric navier stokes equations and energy equation in both liquid and vapor phases are computed the mass momentum and energy conditions are explicitly matched at the phase boundary to determine the interface shape and movement the cubic b spline is used in conjunction with a fairing algorithm to yield smooth and accurate information of curvatures nondimensional parameters including reynolds weber and jakob numbers are varied to offer insight into the physical and numerical characteristics of the bubble dynamics based on the present sharp interface approach bubble dynamics for density ratio of 1600 or higher with and without phase change can be successfully computed

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