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

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

on box totally dual integral polyhedra edmonds and giles introduced the class of box totally dual integral polyhedra as a generalization of submodular flow polyhedra in this paper a geometric characterization of these polyhedra is given this geometric result is used to show that each tdi defining system for a box tdi polyhedron is in fact a box tdi system that the class of box tdi polyhedra is in co np and is closed under taking projections and dominants that the class of box perfect graphs is in co np and a result of edmonds and giles which is related to the facets of box tdi polyhdera

transformed multipole theory of the response fields d and h to electric octopole magnetic quadrupole order we consider multipole theory of linear constitutive relations for the macroscopic electromagnetic response fields d and h to electric octopolemagnetic quadrupole order we use a recently developed

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

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

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

on the non existence of linear non reciprocal bi isotropic nrbi media we show that raab and sihvola s theses on the recognizable existence of linear nonreciprocal bi isotropic media are either incorrect or inconsequential to modern electromagnetic theory which has purely microscopic foundations

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

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

constraint on linear homogeneous constitutive relations a constraint on linear homogeneous constitutive relations is presented it does not affect the sources and the primitive fields its effect being solely on the induction fields as the maxwell postulates are satisfied without question its use amounts to a simplification of the description of linear homogeneous magnetoelectric media the constraint is in complete harmony with the covariant character of modern electromagnetic theory

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

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

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

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

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

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

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