comparative study on accuracy and conservation properties of two particle regularization schemes and proposal of an optimized particle shifting scheme in isph context abstract the paper provides a comparative investigation on accuracy and conservation properties of two particle regularization schemes namely the dynamic stabilization ds 1 and generalized particle shifting ps 2 schemes in simulations of both internal and free surface flows in isph incompressible sph context the paper also presents an optimized ps ops scheme for accurate and consistent implementation of particle shifting for free surface flows in contrast to ps the ops does not contain any tuning parameters for free surface consistently resulting in perfect elimination of shifting normal to an interface and resolves the unphysical discontinuity beneath the interface seen in ps results

some unconditionally stable time stepping methods for the 3d maxwell s equations almost all the difficulties that arise in the numerical solution of maxwell s equations are due to material interfaces in case that their geometrical features are much smaller than a typical wavelength one would like to use small space steps with large time steps the first time stepping method which combines a very low cost per time step with unconditional stability was the adi fdtd method introduced in 1999 the present discussion starts with this method and with an even more recent crank nicolson based split step method with similar properties we then explore how these methods can be made even more efficient by combining them with techniques that increase their temporal accuracies

regular article a fast spectral algorithm for nonlinear wave equations with linear dispersion spectral algorithms offer very high spatial resolution for a wide range of nonlinear wave equations on periodic domains including well known cases such as the korteweg de vries and nonlinear schrodinger equations for the best computational efficiency one needs also to use high order methods in time while somehow bypassing the usual severe stability restrictions we use linearly implicit multistep methods with the innovation of choosing different methods for different ranges in fourier space high accuracy at low wavenumbers and a stability at high wavenumbers this new approach compares favorably to alternatives such as split step and integrating factor or linearly exact methods

time domain finite difference and finite element methods for maxwell equations in complex media extensions of finite difference time domain fdtd and finite element time domain fetd algorithms are reviewed for solving transient maxwell equations in complex media also provided are a few representative examples to illustrate the modeling capabilities of fdtd and fetd for complex media the term complex media refers here to media with dispersive bi anisotropic inhomogeneous and or nonlinear properties present in the constitutive tensors

analysis of iterated adi fdtd schemes for maxwell curl equations the convergence of the iterative adi fdtd method proposed by wang et al s wang f teixeira j chen an iterative adi fdtd with reduced splitting error ieee microwave wireless comp lett 15 2005 1531 1533 towards the classical implicit crank nicolson scheme when applied to maxwell curl equations and the accuracy stability and dispersion properties of the resulting iterated schemes are investigated the iterated schemes are shown both mathematically and numerically to be unconditionally stable for 2d wave problems in agreement with numerical experiments conducted in s wang f teixeira j chen an iterative adi fdtd with reduced splitting error ieee microwave wireless comp lett 15 2005 1531 1533 however these schemes lose their unconditional stability when applied to full 3d wave problems where te and tm modes do not decouple as illustrated by numerical experiments in a pec box

coupling of smoothed particle hydrodynamics with finite volume method for free surface flows a new algorithm for the solution of free surface flows with large front deformation and fragmentation is presented the algorithm is obtained by coupling a classical finite volume fv approach that discretizes the navier stokes equations on a block structured eulerian grid with an approach based on the smoothed particle hydrodynamics sph method implemented in a lagrangian framework the coupling procedure is formulated in such a way that each solver is applied in the region where its intrinsic characteristics can be exploited in the most efficient and accurate way the fv solver is used to resolve the bulk flow and the wall regions whereas the sph solver is implemented in the free surface region to capture details of the front evolution the reported results clearly prove that the combined use of the two solvers is convenient from the point of view of both accuracy and computing time a new algorithm for coupling meshless lagrangian methods and eulerian grid based methods is proposed a detailed validation using smoothed particle hydrodynamics sph and finite volume fv solvers is provided to our knowledge this is the first time that a coupling like the present one is proposed implemented and validated the intrinsic characteristics of both solvers can be exploited to efficiently and accurately solve complex free surface flows the results prove that the coupling strategy is convenient from the point of view of both accuracy and computing time

finite element time domain solution of the vector wave equation in doubly dispersive media using mobius transformation technique several finite element time domain fetd formulations to model inhomogeneous and electrically magnetically doubly dispersive materials based on the second order vector wave equation discretized by the newmark scheme are developed in contrast to the existing formulations which employ recursive convolution rc approaches we use a mobius transformation method to derive our new formulations hence the obtained equations are not only simpler in form and easier to derive and implement but also do not suffer from the intrinsic limitations of the rc methods in modeling arbitrary high order media to obtain the formulations we first demonstrate that the update equation for the electric field strength e in the mixed crank nicolson cn fetd formulation which is based on expanding the electric and magnetic field in terms of the edge and face elements in space and discretizing the resultant first order differential equations using crank nicolson scheme in time is equivalent to the unconditionally stable us second order vector wave equation for the same variable e discretized by the newmark method with 1 4 in addition we show that the update equation for the magnetic flux density b in cn fetd is the same as the second order vector wave equation for b on the dual grid discretized again by a similar newmark method subsequently thanks to the mixed fetd formulation properties we derive update equations for the constitutive relations using a mobius transformation method separately in addition we use the shown equivalence to derive formulations based on the vector wave equation finally several numerical examples are solved to validate the developed formulations

theoretical analysis and numerical verification of the consistency of viscous smoothed particle hydrodynamics formulations in simulating free surface flows the theoretical formulation of the smoothed particle hydrodynamics sph method deserves great care because of some inconsistencies occurring when considering free surface inviscid flows actually in sph formulations one usually assumes that i surface integral terms on the boundary of the interpolation kernel support are neglected ii free surface conditions are implicitly verified these assumptions are studied in detail in the present work for free surface newtonian viscous flow the consistency of classical viscous weakly compressible sph formulations is investigated in particular the principle of virtual work is used to study the verification of the free surface boundary conditions in a weak sense the latter can be related to the global energy dissipation induced by the viscous term formulations and their consistency numerical verification of this theoretical analysis is provided on three free surface test cases including a standing wave with the three viscous term formulations investigated

a fractional step solution method for the unsteady incompressible navier stokes equations in generalized coordinate systems abstract a fractional step method is developed for solving the time dependent three dimensional incompressible navier stokes equations in generalized coordinate systems the primitive variable formulation uses the pressure defined at the center of the computational cell and the volume fluxes across the faces of the cells as the dependent variables instead of the cartesian components of the velocity this choice is equivalent to using the contravariant velocity components in a staggered grid multiplied by the volume of the computational cell the governing equations are discretized by finite volumes using a staggered mesh system the solution of the continuity equation is decoupled from the momentum equations by a fractional step method which enforces mass conservation by solving a poisson equation this procedure combined with a consistent approximation of the geometric quantities is done to satisfy the discretized mass conservation equation to machine accuracy as well as to gain the favorable convergence properties of the poisson solver the momentum equations are solved by an approximate factorization method and a novel zebra scheme with four color ordering is devised for the efficient solution of the poisson equation several two and three dimensional laminar test cases are computed and compared with other numerical and experimental results to validate the solution method good agreement is obtained in all cases

differential forms galerkin duality and sparse inverse approximations in finite element solutions of maxwell equations we identify primal and dual formulations in the finite element method fem solution of the vector wave equation using a geometric discretization based on differential forms these two formulations entail a mathematical duality denoted as galerkin duality galerkin dual fem formulations yield identical nonzero dynamical eigenvalues up to machine precision but have static zero eigenvalue solution spaces of different dimensions algebraic relationships among the degrees of freedom of primal and dual formulations are explained using a deep rooted connection between the hodge helmholtz decomposition of differential forms and descartes euler polyhedral formula and verified numerically in order to tackle the fullness of dual formulation algebraic and topological thresholdings are proposed to approximate inverse mass matrices by sparse matrices

an efficient method to reduce the numerical dispersion in the lod fdtd method based on the 2 4 stencil a parameter optimized 2 4 stencil based locally one dimensional lod finite difference time domain fdtd is presented with much reduced numerical dispersion errors the method is first proved to be unconditionally stable then by using different optimization schemes the method is optimized to satisfy different accuracy requirements such as minimum dispersion errors in the axial directions in the diagonal direction and in the specified angles performances of the parameter optimized lod fdtd with different time steps and frequencies are also studied it is found that the parameter optimization can significantly reduce numerical dispersion errors bringing them down to the level of the conventional fdtd but with the time step exceeding the cfl limit and without much additional computational cost in addition the optimized parameters are not sensitive to frequencies in particular the optimized parameters obtained at a higher frequency still present low numerical dispersion errors at a lower frequency

homotopy method for a class of nonconvex brouwer fixed point problems abstract in this paper we present a homotopy method for computing fixed points of twice continuously differentiable self mappings in a class of nonconvex subsets in r n the method need not homeomorphically transform the considered set to a closed unit ball and is numerically implementable

a stable fdtd method with embedded reduced order models the computational efficiency of the finite difference time domain fdtd method can be significantly reduced by the presence of complex objects with fine features small geometrical details impose a fine mesh and a reduced time step significantly increasing computational cost model order reduction has been proposed as a systematic way to generate compact models for complex objects by which one can then instantiate into a main fdtd mesh however the stability of fdtd with embedded reduced models remains an open problem we propose a systematic method to generate reduced models for fdtd domains and embed them into a main fdtd mesh with guaranteed stability up to the courant friedrichs lewy cfl limit of the fine mesh with a simple perturbation technique the cfl of the whole scheme can be further extended beyond the fine grid s cfl limit reduced models can be created for arbitrary domains containing inhomogeneous and lossy materials numerical tests confirm the stability of the proposed method and its potential to accelerate multiscale fdtd simulations

new energy analysis of adi fdtd for the two dimensional maxwell equations several new energy identities of the 2d maxwell equations with the perfectly electric conducting boundary conditions are first proposed and proved by the energy methods then the energy identities of the 2d adi fdtd method in the discrete l 2 and h 1 norms are derived by these identities it is proved that the 2d adi fdtd method is unconditionally stable and energy conserved in the discrete l 2 and h 1 norms numerical experiments are carried out and confirm the analysis on stability and energy conservation

generalizations of fixed point theorems and computation as a powerful mechanism fixed point theorems have many applications in mathematical and economic analysis in this paper the well known brouwer fixed point theorem and kakutani fixed point theorem are generalized to a class of nonconvex sets and a globally convergent homotopy method is developed for computing fixed points on this class of nonconvex sets

fixed point theorems and their applications to theory of nash equilibria abstract in this paper we prove fixed point theorems for set valued mappings in products of posets applications to the theory of nash equilibria are presented

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

variable resolution for sph in three dimensions towards optimal splitting and coalescing for dynamic adaptivity abstract as smoothed particle hydrodynamics sph becomes increasingly popular for complex flow analysis the need to improve efficiency particularly for 3 d problems is becoming greater automatic adaptivity with variable particle size is therefore desirable in this paper a novel 3 d splitting and coalescing algorithm is developed which minimizes density error while conserving both mass and momentum using a variational principle accuracy is increased in refined areas unaffected by coarser particle distributions elsewhere for particle splitting the key criteria are the number of split daughter particles their distribution spacing and kernel size four different splitting arrangements are investigated including a cubic stencil with 8 particles a cubic stencil with an additional 6 located at the face centres an icosahedron shaped arrangement with 14 particles and a dodecahedron shaped arrangement with 20 particles where particles are located at the vertices the error analysis also examines whether retaining a particle at the centre of the arrangement is necessary revealing that regardless of the stencil adopted to minimize the density error a daughter particle should be placed at the same position of the original particle the optimum configuration is found to be the icosahedron shaped arrangement while commonly used smoothing kernels such as the cubic and quintic splines and wendland produce similar density errors so that the optimal refinement stencil is effectively independent of the kernel choice a new 3 d coalescing scheme completes the algorithm such that the particle resolution can be either increased or reduced locally the sph splitting and coalescing scheme is tested with poiseuille flow showing negligible loss of convergence accuracy in the refined area and the lid driven cavity for a wide range of reynolds number showing good agreement with reference solutions again with local accuracy defined by particle distribution

examination clarification and simplification of stability and dispersion analysis for adi fdtd and cnss fdtd schemes we describe a rigorous analysis of unconditional stability for the alternating direction implicit finite difference time domain adi fdtd and crank nicholson split step cnss fdtd schemes avoiding use of the von neumann spectral criterion the proof is performed in the spectral domain and uses skew hermitivity of matrix terms in the adi and cnss total amplification matrices a bound for the total adi amplification matrix is provided while the cn and cnss fdtd amplification matrices are unitary the bound on the adi fdtd depends on the courant number importantly we have found that the adi fdtd amplification matrix is not normal i e the unit spectral radius alone cannot be used to prove the adi fdtd unconditional stability the paper also shows that the adi fdtd and cnss fdtd schemes share the same dispersion equation by a similarity of their total amplification matrices and the two schemes have identical numerical dispersion in the frame of plane waves

sph with dynamical smoothing length adjustment based on the local flow kinematics abstract due to the lagrangian nature of smoothed particle hydrodynamics sph the adaptive resolution remains a challenging task in this work we first analyse the influence of the simulation parameters and the smoothing length on solution accuracy in particular in high strain regions based on this analysis we develop a novel approach to dynamically adjust the kernel range for each sph particle separately accounting for the local flow kinematics we use the okubo weiss parameter that distinguishes the strain and vorticity dominated regions in the flow domain the proposed development is relatively simple and implies only a moderate computational overhead we validate the modified sph algorithm for a selection of two dimensional test cases the taylor green flow the vortex spin down the lid driven cavity and the dam break flow against a sharp edged obstacle the simulation results show good agreement with the reference data and improvement of the long term accuracy for unsteady flows for the lid driven cavity case the proposed dynamical adjustment remedies the problem of tensile instability particle clustering

extension of the adi fdtd method to debye media this paper describes an extension of the alternating direction implicit finite difference time domain adi fdtd method to analyze problems involving debye media

general theory of fractal path integrals with applications to many body theories and statistical physics a general scheme of fractal decomposition of exponential operators is presented in any order m namely exp x a b sm x o xm 1 for any positive integer m where sm x et1a et2b et3a et4b etma with finite m depending on m a general recursive scheme of construction of tj is given explicitly it is proven that some of tj should be negative for m 3 and for any finite m nonexistence theorem of positive decomposition general systematic decomposition criterions based on a new type of time ordering are also formulated the decomposition exp x a b sm x n n o xm 1 nm yields a new efficient approach to quantum monte carlo simulations

an accurate sph modeling of viscous flows around bodies at low and moderate reynolds numbers abstract a weakly compressible sph scheme has been used to describe the evolution of viscous flows around blunt bodies at reynolds numbers ranging from 10 to 2400 the simulation of such a wide range rarely addressed to in the sph literature has been possible thanks to the use of a proper ghost fluid technique and to an accurate enforcement of the boundary conditions along the solid boundaries in this context a new numerical technique based on previous works by takeda et al 1994 48 marrone et al 2011 28 and de leffe et al 2011 16 has been proposed along with a new method for the evaluation of the global loads on bodies particular care has been taken to study the influence of the weakly compressibility assumption and of different ghost fluid techniques on the numerical results an in depth validation of the model has been performed by comparing the numerical outcome with experimental data from the literature and other numerical references the influence of the domain size has been discussed in order to avoid wall side effects and at the same time to limit the computational costs the convergence of the numerical solutions has been checked on both global and local quantities by choosing appropriate reynolds cell number

a split step approach for the 3 d maxwell s equations split step procedures have previously been used successfully in a number of situations e g for hamiltonian systems such as certain nonlinear wave equations in this study we note that one particular way to write the 3 d maxwell s equations separates these into two parts requiring only the solution of six uncoupled 1 d wave equations the approach allows arbitrary orders of accuracy in both time and space and features in many cases unconditional stability

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

a cartesian grid method for solving the two dimensional streamfunction vorticity equations in irregular regions we describe a method for solving the two dimensional navier stokes equations in irregular physical domains our method is based on an underlying uniform cartesian grid and second order finite difference finite volume discretizations of the streamfunction vorticity equations geometry representing stationary solid obstacles in the flow domain is embedded in the cartesian grid and special discretizations near the embedded boundary ensure the accuracy of the solution in the cut cells along the embedded boundary we determine a distribution of vorticity sources needed to impose the no slip flow conditions this distribution appears as a right hand side term in the discretized fluid equations and so we can use fast solvers to solve the linear systems that arise to handle the advective terms we use the high resolution algorithms in clawpack we show that our stokes solver is second order accurate for steady state solutions and that our full navier stokes solver is between first and second order accurate and reproduces results from well studied benchmark problems in viscous fluid flow finally we demonstrate the robustness of our code on flow in a complex domain

a stable and efficient direct time integration of the vector wave equation in the finite element time domain method for dispersive media the finite element time domain fetd solution of the vector wave equation vwe is directly extended to doubly dispersive media using the bilinear transform approach the proposed formulation is quite general and flexible in the sense of material dispersion model in contrast to limitations of existing convolutional based approaches in addition it can be implemented in a very straightforward and efficient manner a stability analysis is performed that demonstrates the unconditional stability of the original formulation is preserved in the dispersive case however in order to avoid the well known late time instabilities that arise in this formulation an alternative formulation is considered and extended to the dispersive case with the same approach several numerical examples are simulated to verify the validity and accuracy of the proposed formulations the late time stability of the alternative formulation is tested through a numerical example with 20 million time steps the solution is completely free from late time growth

a particle in cell method for the simulation of plasmas based on an unconditionally stable field solver abstract we propose a new particle in cell pic method for the simulation of plasmas based on a recently developed unconditionally stable solver for the wave equation this method is not subject to a cfl restriction limiting the ratio of the time step size to the spatial step size typical of explicit methods while maintaining computational cost and code complexity comparable to such explicit schemes we describe the implementation in one and two dimensions for both electrostatic and electromagnetic cases and present the results of several standard test problems showing good agreement with theory with time step sizes much larger than allowed by typical cfl restrictions

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

frequency dependent fdtd methods using z transforms the frequency dependent finite difference time domain method fd sup 2 td method has been shown to be capable of correctly calculating electromagnetic propagation through media whose dielectric properties are frequency dependent however as researchers search for more elaborate applications the formulation of the fd sup 2 td methods becomes more complex in this work the mathematics of the fd sup 2 td method is developed using z transform theory this has the advantages of presenting a clearer formulation and allowing researchers to draw on the literature of systems analysis and signal processing disciplines

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

truncation error in mesh free particle methods a truncation error analysis has been developed for the approximation of spatial derivatives in smoothed particle hydrodynamics sph and related first order consistent methods such as the first order form of the reproducing kernel particle method error is shown to depend on both the smoothing length h and the ratio of particle spacing to smoothing length x h for uniformly spaced particles in one dimension analysis shows that as h is reduced while maintaining constant x h error decays as h2 until a limiting discretization error is reached which is independent of h if x h is reduced while maintaining constant h i e if the number of neighbours per particle is increased error decreases at a rate which depends on the kernel function s smoothness when particles are distributed non uniformly error can grow as h is reduced with constant x h first order consistent methods are shown to remove this divergent behaviour numerical experiments confirm the theoretical analysis for one dimension and indicate that the main results are also true in three dimensions this investigation highlights the complexity of error behaviour in sph and shows that the roles of both h and x h must be considered when choosing particle distributions and smoothing lengths copyright 2005 john wiley sons ltd

unconditionally stable fundamental lod fdtd method with second order temporal accuracy and complying divergence an unconditionally stable fundamental locally one dimensional lod finite difference time domain fdtd method with second order temporal accuracy and complying divergence cd denoted as lod2 cd fdtd is presented for three dimensional 3 d maxwell s equations while the conventional lod fdtd method does not have complying divergence the lod2 cd fdtd method has complying divergence in a manner analogous to the conventional explicit fdtd method the update procedures for a family of lod fdtd methods that employ similar splitting matrix operators are presented by extending the previous concept of achieving second order temporal accuracy for the lod2 fdtd method via implicit output processing we hereby propose novel explicit output processing that not only retains second order temporal accuracy but also complying divergence for the lod2 cd fdtd method the current source implementation for the lod2 cd fdtd method involves source incorporation in only the first procedure to further enhance efficiency the lod2 cd fdtd method is formulated into the fundamental lod2 cd fdtd method with efficient matrix operator free right hand sides subsequently detailed implementation for the fundamental lod2 cd fdtd method is presented analytical proof is provided to ascertain the second order temporal accuracy of the lod2 cd fdtd method numerical results and examples are also presented to validate the divergence complying property of the lod2 cd fdtd method

a scalable consistent second order sph solver for unsteady low reynolds number flows abstract smoothed particle hydrodynamics sph has successfully been used to study a variety of cases involving nearly inviscid flows where conservation properties allow for good physical approximation despite poor theoretical approximation properties of differential operators when used to study unsteady low reynolds number flow with large dissipation conservation alone cannot ensure quality of approximation and the traditional approach is inconsistent an alternative formulation has recently become popular making use of an approximate splitting scheme to ensure a divergence free velocity field however this scheme relies on an inconsistent discretization of the laplacian that diverges as particles become disordered under flow we present an incremental pressure correction scheme and combination of existing differential operator renormalizations that are able to achieve second order accuracy in time and space a brief review of sph approximation theory is provided to highlight the necessity of these renormalizations in implementing an approximate factorization scheme we demonstrate that when fast algebraic multigrid preconditioners are used to solve the resulting linear systems the scheme results in a consistent approximation that is scalable and amenable to parallelization several validation cases are presented for which a speedup of several orders of magnitude is achieved over traditional sph approaches finally an interface has been developed between the particle library lammps and the sparse linear algebra libraries in trilinos providing a massively parallel 3d sph capability scaling results for up to 134 million particles on 32 768 cores are presented along with a demonstration of the capability to simulate complex 3d geometries these results show that the added complexity of applying the necessary consistency corrections actually provides a factor of four speed up per linear solver iteration versus the uncorrected case despite the additional cost of constructing the corrections the resulting library provides a method that is consistent efficient and second order in both space and time while maintaining the flexibility of classical sph for single phase flows

sph simulations of flow around a periodic array of cylinders confined in a channel in this paper we present a numerical study on the performance of sph in the case of a very viscous flow of a newtonian liquid around a linear array of cylinders confined in a channel this specific flow problem being characterized by a complex mixing of both shear and extensional behaviour allows to quantify systematically the accuracy of the standard sph in up to now rarely considered complex geometries global accuracy tests based on the estimation of the dimensionless drag force acting on the cylinder as well as the inspection of the local velocity profiles are considered and compared with reference solutions in agreement with previous findings the impact of two numerical parameters namely the smoothing length h and particle spacing x is discussed and found to be crucial for the overall order of convergence of the method in particular accurate results can be obtained which are in very good agreement with standard mesh based methods provided that the number of neighbours is chosen properly the present results being based on a detailed convergence analysis in a complex flow problem justify the applicability of the sph method to more complex wall bounded flows upon critical choice of the model parameters and at the same time can serve as a useful benchmark test for further modelling improvement in the field copyright 2010 john wiley sons ltd

an efficient fluid solid coupling algorithm for single phase flows we present a simple and efficient fluid solid coupling method in two and three spatial dimensions in particular we consider the numerical approximation of the navier stokes equations on irregular domains and propose a novel approach for solving the hodge projection step on arbitrary shaped domains this method is straightforward to implement and leads to a symmetric positive definite linear system for both the projection step and for the implicit treatment of the viscosity we demonstrate the accuracy of our method in the l 1 and l norms and present its removing the errors associated with the conventional rasterization type discretizations we apply this method to the simulation of a flow past a cylinder in two spatial dimensions and show that our method can reproduce the known stable and unstable regimes as well as correct lift and drag forces we also apply this method to the simulation of a flow past a sphere in three spatial dimensions at low and moderate reynolds number to reproduce the known steady axisymmetric and non axisymmetric flow regimes we further apply this algorithm to the coupling of flows with moving rigid bodies

modeling low reynolds number incompressible flows using sph the method of smoothed particle hydrodynamics sph is extended to model incompressible flows of low reynolds number for such flows modification of the standard sph formalism is required to minimize errors associated with the use of a quasi incompressible equation of state treatment of viscosity state equation kernel interpolation and boundary conditions are described simulations using the method show close agreement with series solutions for couette and poiseuille flows furthermore comparison with finite element solutions for flow past a regular lattice of cylinders shows close agreement for the velocity and pressure fields the sph results exhibit small pressure fluctuations near curved boundaries further improvements to the boundary conditions may be possible which will reduce these errors a similar method to that used here may permit the simulation of other flows at low reynolds numbers using sph further development will be needed for cases involving free surfaces or substantially different equations of state

the discrete origin of fetd newmark late time instability and a correction scheme the finite element time domain fetd method is commonly used for transient simulation of electromagnetic wave phenomena most practitioners consider fetd when time integrated using the newmark beta method to be unconditionally stable when s 0 25 unlike the finite difference time domain fdtd courant criterion fetd newmark has no limiting timestep above which the method exhibits exponential growth however herein the stability properties of fetd newmark will be rigorously investigated by deducing the jordan canonical form of the fetd newmark amplification matrix and it will be demonstrated that the method does exhibit linear growth for certain field configurations these modes are none other than the pure gradient fields associated with late time instability though many practical simulations are of short duration and will never observe a linearly growing gradient solution it can be problematic for simulations which require long time periods to be integrated a correction scheme for eliminating this late time instability shall be suggested and numerical results will verify its performance