fully conservative finite difference scheme in cylindrical coordinates for incompressible flow simulations a new finite difference scheme on a non uniform staggered grid in cylindrical coordinates is proposed for incompressible flow the scheme conserves both momentum and kinetic energy for inviscid flow with the exception of the time marching error provided that the discrete continuity equation is satisfied a novel pole treatment is also introduced where a discrete radial momentum equation with the fully conservative convection scheme is introduced at the pole the pole singularity is removed properly using analytical and numerical techniques the kinetic energy conservation property is tested for the inviscid concentric annular flow for the proposed and existing staggered finite difference schemes in cylindrical coordinates the pole treatment is verified for inviscid pipe flow mixed second and high order finite difference scheme is also proposed and the effect of the order of accuracy is demonstrated for the large eddy simulation of turbulent pipe flow

accurate projection methods for the incompressible navier stokes equations abstract this paper considers the accuracy of projection method approximations to the initial boundary value problem for the incompressible navier stokes equations the issue of how to correctly specify numerical boundary conditions for these methods has been outstanding since the birth of the second order methodology a decade and a half ago it has been observed that while the velocity can be reliably computed to second order accuracy in time and space the pressure is typically only first order accurate in the l norm this paper identifies the source of this problem in the interplay of the global pressure update formula with the numerical boundary conditions and presents an improved projection algorithm which is fully second order accurate as demonstrated by a normal mode analysis and numerical experiments in addition a numerical method based on a gauge variable formulation of the incompressible navier stokes equations which provides another option for obtaining fully second order convergence in both velocity and pressure is discussed the connection between the boundary conditions for projection methods and the gauge method is explained in detail

noncyclic geometric phase and its non abelian generalization we use the theory of dynamical invariants to yield a simple derivation of noncyclic analogues of the abelian and non abelian geometric phases this derivation relies only on the principle of gauge invariance and elucidates the existing definitions of the abelian noncyclic geometric phase we also discuss the adiabatic limit of the noncyclic geometric phase and compute the adiabatic non abelian noncyclic geometric phase for a spin 1 magnetic or electric quadrupole interacting with a precessing magnetic electric field

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

large eddy simulation in complex geometric configurations using boundary body forces anumericalmethodispresentedthatallowslargeeddysimulation les ofturbulente owsincomplexgeometric cone gurations with moving boundaries and that retains the advantages of solving the navier stokes equations on e xed orthogonal grids the boundary conditions are applied independently of the grid by assigning body forces over surfaces that need not coincide with coordinate lines the use of orthogonal nondeforming grids simplie es grid generation facilitates theimplementation of high order nondissipativediscretization schemes andminimizes the spatial and temporal variations in e lter width that complicate unstructured deforming grid les dynamic subgrid scaleturbulence models areparticularly appealing in combination with the body forceprocedure because the dynamic model accounts automatically for the presence of solid walls without requiring damping functions the method is validated by simulations of the turbulent e ow in a motored axisymmetric piston cylinder assembly for which detailed experimental measurements are available computed mean and rms velocity proe les show very good agreement with measured ensemble averages thepresent numerical code runs on small personal computerlike workstations for a comparable level of accuracy computational requirements memory and cpu time are at least a factor of 10 lower compared to published simulations for the same cone guration obtained using an unstructured boundary e tted deforming grid approach

direct simulations of turbulent flow using finite difference schemes abstract this paper presents finite difference solutions to the evolution of small amplitude disturbances and incompressible fully developed turbulent channel flow the main objective of the paper is to provide a comprehensive comparison between the results obtained using finite difference and spectral methods an advantage of finite difference schemes over the highly accurate spectral methods lies in the ease with which they can be applied to complex geometries the finite difference methods used include a kinetic energy conserving type of central difference scheme and a high order accurate upwind difference scheme unlike the central difference scheme the upwind difference scheme was found not to require a kinetic energy conservation property to control aliasing error the dissipative nature of the upwind scheme results in a damping of the higher frequency content as a result very little energy is aliased back the computed data including first and second order statistics for the turbulent channel flow case are found to compare well with experimental data and earlier spectral simulations it appears that the high order accurate upwind scheme is a good candidate for direct simulations of turbulent flows over complex geometries

topological aspects of the non adiabatic berry phase the topology of the non adiabatic parameter space bundle is discussed for evolution of exact cyclic state vectors in berry s original example of split angular momentum eigenstates it turns out that the change in topology occurs at a critical frequency the first chern number that classifies these bundles is proportional to angular momentum the non adiabatic principal bundle over the parameter space is not well defined at the critical frequency

a formulation of navier stokes problem in cylindrical coordinates applied to the 3d entry jet in a duct a pseudospectral formulation of the three dimensional navier stokes equations in the cylindrical system of co ordinates is presented which automatically includes the regularity conditions at the polar axis for the fourier harmonics the mathematical system of equations is numerically implemented using standard methods for spatial discretisation and time advancement the method presented here for incompressible flows can be easily extended to different set of equations and to different numerical schemes of various levels of accuracy the formulation is applied to the solution of incompressible three dimensional entry jets in a circular duct

a fully conservative mimetic discretization of the navier stokes equations in cylindrical coordinates with associated singularity treatment we present a finite difference discretization of the incompressible navier stokes equations in cylindrical coordinates this currently is to the authors knowledge the only scheme available that is demonstrably capable of conserving mass momentum and kinetic energy in the absence of viscosity on both uniform and non uniform grids simultaneously we treat the inherent discretization issues that arise due to the presence of the coordinate singularity at the polar axis we demonstrate the validity of the conservation claims by performing a number of numerical experiments with the proposed scheme and we show that it is second order accurate in space using the method of manufactured solutions

geometric phase bundle classification and group representation the line bundles that arise in the holonomy interpretations of the geometric phase display curious similarities to those encountered in the statement of the borel weil bott theorem of the representation theory the remarkable relationship between the mathematical structure of the geometric phase and the classification theorem for complex line bundles provides the necessary tools for establishing the relevance of the borel weil bott theorem to berry s adiabatic phase this enables one to define a set of topological charges for arbitrary compact connected semisimple dynamical lie groups these charges signify the topological content of the phase they can be explicitly computed in this paper the problem of the determination of the parameter space of the hamiltonian is also addressed it is shown that in general the parameter space is either a flag manifold or one of its submanifolds a simple topological argument is presented to indicate the relation between the riemannian structure on the parameter spa

approximate factorization as a high order splitting for the implicit incompressible flow equations abstract we apply the method of approximate factorization to derive a second order accurate splitting of the incompressible flow equations stokes or navier stokes equations this is novel because the method of approximate factorization was believed inapplicable to this type of equation system we demonstrate the resulting splitting on a second order crank nicolson discretization and point out its intimate relationship to some existing second order accurate splitting projection methods further we use the approximate factorization method to derive entirely new splittings we first develop a new generalized second order accurate splitting which may be specialized to a variety of applications we indicate its application to finite elements checker board free cell centered discretizations and ocean modeling we then generalized the original splitting to an arbitrarily high order scheme

fully conservative higher order finite difference schemes for incompressible flow conservation properties of the mass momentum and kinetic energy equations for incompressible flow are specified as analytical requirements for a proper set of discrete equations existing finite difference schemes in regular and staggered grid systems are checked for violations of the conservation requirements and a few important discrepancies are pointed out in particular it is found that none of the existing higher order schemes for a staggered mesh system simultaneously conserve mass momentum and kinetic energy this deficiency is corrected through the derivation of a general family of fully conservative higher order accurate finite difference schemes for staggered grid systems finite difference schemes in a collocated grid system are also analyzed and a violation of kinetic energy conservation is revealed the predicted conservation properties are demonstrated numerically in simulations of inviscid white noise performed in a two dimensional periodic domain the proposed fourth order schemes in a staggered grid system are generalized for the case of a non uniform mesh and the resulting scheme is used to perform large eddy simulations of turbulent channel flow

an efficient method for temporal integration of the navier stokes equations in confined axisymmetric geometries a method for temporal integration of the navier stokes equations written in cylindrical coordinates is described the objective is to avoid the severe time step limitation usually encountered in confined axisymmetric geometries e g pipe flow caused by a fine azimuthal grid spacing around the centerline and the desire to refine the grid in the radial direction near walls avoiding severe time step limitations usually involves treating all terms with derivatives in the radial and azimuthal directions with an implicit time integration scheme however this leads to a set of coupled nonlinear equations which generally require complex and costly solution procedures the scheme described in this paper decomposes the computational domain into two regions within each region only the derivatives in one coordinate direction is treated implicitly conditions at the interface between the regions are determined to maintain the overall temporal accuracy of the basic time integration schemes results from a direct numerical simulation dns of turbulent pipe flow are validated against computational and experimental results from the literature it is demonstrated that this new scheme allows for larger time steps than other schemes leading to significant cpu savings

a direct method for the computation of hopf bifurcation points we present a method for the numerical computation of a hopf bifurcation point of an evolution equation an augmented time independent system of equations has to be solved for which the hopf bifurcation point is an isolated solution in the case of a system of ordinary differential equations we propose an efficient implementation of newton s method for the solution of the resulting system of algebraic equations if the method is applied directly to a partial differential system with one space variable a two point boundary value problem is obtained we also compare this technique with a related method and results are given for two systems of partial differential equations describing chemical reacting systems

kinetic energy conservation issues associated with the collocated mesh scheme for incompressible flow the collocated mesh scheme is often favored over the staggered mesh scheme for turbulence simulation in complex geometries due to its simpler form in curvilinear coordinates the collocated mesh scheme does not conserve kinetic energy however and few careful checks of the impact of these errors have been made in this work analysis is used to identify two sources of kinetic energy conservation error in the collocated mesh scheme 1 errors arising from the interpolations used to estimate the velocity on the cell faces and 2 errors associated with the slightly inconsistent pressure field used to ensure mass conservation for the cell face volume fluxes it is shown that the interpolation error can be eliminated through the use of first order accurate centered interpolation operators with mesh independent weights the pressure error appears to be intrinsic to the scheme and it is shown to scale as o t2 x2 the effects of the conservation errors are investigated numerically through simulations of inviscid flow over an airfoil and in large eddy simulations of turbulent channel flow neither the interpolation error nor the pressure error appear to lead to significant problems in the channel flow simulations where viscous dissipation is present and where the cartesian mesh is stretched in only one direction the inviscid airfoil simulations performed on a curvilinear mesh show a much greater sensitivity to the interpolation error the standard second order centered interpolation is shown to lead to severe numerical oscillations while the kinetic energy conserving first order centered interpolation produces solutions that are almost as smooth as those obtained with a third order upwind interpolation when compared in channel flow simulations however the first order centered interpolation is shown to be far superior to the third order upwind interpolation the latter being adversely affected by numerical dissipation only slight differences were noted when comparing channel flow simulations using first order and second order centered interpolations these results suggest that numerical oscillations can be controlled in curvilinear coordinates through the use of properly constructed non dissipative centered interpolations

high order pole treatment in cylindrical coordinates for incompressible flow simulations with finite difference collocated schemes abstract a finite difference collocated scheme is proposed for the simulation of unsteady incompressible flows in cylindrical coordinates the rhie chow flux interpolation technique is used to avoid the odd even decoupling of the pressure field it is shown that the calculation of the coriolis and centrifugal acceleration terms based on the cell center values lead to numerical instabilities near the pole in the inviscid regime to avoid this issue a new formulation based on the combination of cell center and cell face velocity components is proposed for the calculation of these terms furthermore a new pole treatment methodology is introduced to calculate the viscous terms resulting single valued properties at the pole as regards the extensions of the present scheme to higher orders of accuracy a fourth order spatial discretization is also introduced and verified moreover it is shown that for higher order extensions the present pole treatment is able to preserve the order of accuracy and the l 2 norm and l norm errors are greatly improved in comparison with the previous schemes the robustness of the present method is assessed via five different numerical tests including laminar flows in a polar cavity vortex wall interaction evolution of a monopole vortex system to a tripole vortex system advection of the lamb dipole and large eddy simulation les of turbulent pipe flows compared to the previous les results for turbulent pipe flows significant improvement is obtained for the mean and fluctuating velocities especially at the core region of the channel similarly at the wall region the fluctuating axial and azimuthal velocities and the skewnesses of the axial and radial velocities are very close to the previous direct numerical simulation and experimental data

spectral methods for the navier stokes equations with one infinite and two periodic directions abstract two numerical methods were designed to solve the time dependent three dimensional incompressible navier stokes equations in boundary layers method a semi infinite domain and mixing layers or wakes method b fully infinite domain their originality lies in the use of rapidly decaying spectral basis functions to approximate the vertical dependence of the solutions combined with one method a or two method b slowly decaying extra functions for each wave vector that exactly represent the irrotational component of the solution at large distances both methods eliminate the pressure term as part of the formulation thus avoiding fractional step time integration they yield rapid convergence and are free of spurious modes in the orr sommerfeld spectra they are also efficient although the operation count is of order n 2 n is the number of modes in the infinite direction these methods have been used for extensive direct numerical simulations of transition and turbulence a new time integration scheme with low storage requirements and good stability properties is also described

on the consistency of the direct forcing method in the fractional step solution of the navier stokes equations in the present work the application of the direct forcing method to the fractional step solution of the navier stokes equations is analyzed in details the central topic of the study is the satisfaction of the boundary conditions in the presence of immersed bodies to this aim simple two dimensional problems with steady forcing and sharp edged surfaces are solved with a standard fractional step method it is shown that the direct forcing scheme is not able to satisfy the impenetrability condition this fact appears to be strictly related to the use of fractional step methods a mathematically based explanation is given suggesting that improvements can be obtained with the iterative solution of the irrotational part of the flow when spectral methods are used and local modification of the discrete differential operators are difficult to be implemented the results are then verified in two dimensional unsteady problems and three dimensional flows with moving smooth boundaries

finite dimensional approximation of nonlinear problems part ii limit points note univ paris 6 f 75230 paris 05 france ecole polytech ctr math appl cnrs equipe rech 747 f 91128 palaiseau france univ pavia cnr ist anal numer i 27100 pavia italy brezzi f univ pavia cnr ist math appl i 27100 pavia italy isi document delivery no lr761times cited 54cited reference count 13 reference asn article 1981 002doi 10 1007 bf01396184 record created on 2006 08 24 modified on 2017 05 12

a co located incompressible navier stokes solver with exact mass momentum and kinetic energy conservation in the inviscid limit the incompressible navier stokes equations conserve mass momentum and kinetic energy in the inviscid limit therefore numerical methods should attempt to mimic these conservation properties as well there exists many well established methods with exact conservation properties based on staggered grids but existing methods based on co located grids introduce numerical dissipation in order to yield smooth pressure fields in the present work a novel method that utilizes null space vectors to yield a smooth pressure field is presented the method exactly preserves mass momentum and kinetic energy on co located grids

highly energy conservative finite difference method for the cylindrical coordinate system a highly energy conservative second order accurate finite difference method for the cylindrical coordinate system is developed it is rigorously proved that energy conservation in discretized space is satisfied when appropriate interpolation schemes are used this argument holds not only for an unequally spaced mesh but also for an equally spaced mesh on cylindrical coordinates but not on cartesian coordinates numerical tests are undertaken for an inviscid flow with various schemes and it turns out that the proposed scheme offers a superior energy conservation property and greater stability than the intuitive and previously proposed methods for both equally spaced and unequally spaced meshes

a fully conservative second order finite difference scheme for incompressible flow on nonuniform grids a second order accurate finite difference discretization of the incompressible navier stokes is presented that discretely conserves mass momentum and kinetic energy in the inviscid limit in space and time the method is thus completely free of numerical dissipation and potentially well suited to the direct numerical simulation or large eddy simulation of turbulent flow the method uses a staggered arrangement of velocity and pressure on a structured cartesian grid and retains its discrete conservation properties for both uniform and nonuniform gird spacing the predicted conservation properties are confirmed by inviscid simulations on both uniform and nonuniform grids the capability of the method to resolve turbulent flow is demonstrated by repeating the turbulent channel flow simulations of h choi and p moin 1994 j comput phys 113 1 where the effect of computational time step on the computed turbulence was investigated the present fully conservative scheme achieved turbulent flow solutions over the entire range of computational time steps investigated t tu2 0 4 to 5 0 little variation in statistical turbulence quantities was observed up to t 1 6 the present results differ significantly from those reported by choi and moin who observed significant discrepancies in the turbulence statistics above t 0 4 and the complete laminarization of the flow at and above t 1 6

an algorithm for the computation of hopf bifurcation points in comparison with other methods we present an algorithm for the computation of a hopf bifurcation point based on a direct method i e an augmented time independent system is solved the algorithm is designed to deal efficiently with problems representing a finite difference discretization of a partial differential system in this case the bandstructure of the jacobian matrix is exploited we also compare this technique with some other methods in regard to its efficiency and reliability

finite dimensional approximation of nonlinear problems in the first two papers of this series 4 5 we have studied a general method of approximation of nonsingular solutions and simple limit points of nonlinear equations in a banach space we derive here general approximation results of the branches of solutions in the neighborhood of a simple bifurcation point the abstract theory is applied to the galerkin approximation of nonlinear variational problems and to a mixed finite element approximation of the von karman equations

skew symmetric form of convective terms and fully conservative finite difference schemes for variable density low mach number flows the form of convective terms for compressible flow equations is discussed in the same way as for an incompressible one by morinishi et al y morinishi t s lund o v vasilyev p moin fully conservative higher order finite difference schemes for incompressible flow j comput phys 124 1998 90 and fully conservative finite difference schemes suitable for shock free unsteady compressible flow simulations are proposed commutable divergence advective and skew symmetric forms of convective terms are defined by including the temporal derivative term for compressible flow these forms are analytically equivalent if the continuity is satisfied and the skew symmetric form is secondary conservative without the aid of the continuity while the divergence form is primary conservative the relations between the present and existing quasi skew symmetric forms are also revealed commutable fully discrete finite difference schemes of convection are then derived in a staggered grid system and they are fully conservative provided that the corresponding discrete continuity is satisfied in addition a semi discrete convection scheme suitable for compact finite difference is presented based on the skew symmetric form the conservation properties of the present schemes are demonstrated numerically in a three dimensional periodic inviscid flow the proposed fully discrete fully conservative second order accurate scheme is also used to perform the dns of compressible isotropic turbulence and the simulation of open cavity flow

numerical approximation of a periodic linear parabolic problem we approximate a periodic linear parabolic problem using a galerkin method for the space variable and a spectral method for the time variable some optimal error estimates are derived

approximation of hopf bifurcation we make several assumptions on a nonlinear evolution problem ensuring the existence of a hopf bifurcation under a fairly general approximation condition we define a discrete problem which retains the bifurcation property and we prove an error estimate between the branches of exact and approximate periodic solutions

high order finite difference schemes on non uniform meshes with good conservation properties numerical simulation of turbulent flows dns or les requires numerical methods that are both stable and free of numerical dissipation one way to achieve this is to enforce additional constraints such as discrete conservation of mass momentum and kinetic energy the objective of this work is to generalize the high order schemes of morinishi et al to non uniform meshes while maintaining conservation properties of the schemes as much as possible this generalization is achieved by preserving symmetries of the uniform mesh case the proposed schemes do not simultaneously conserve mass momentum and kinetic energy however depending on the form of the convective term conservation of either momentum or energy in addition to mass can be achieved it is shown that the conservation properties of the generalized schemes are as good as those of the standard second order finite difference scheme on non uniform meshes while the accuracy of the new schemes is definitely superior the predicted conservation properties are demonstrated numerically in inviscid flow simulations

quantal phase factors accompanying adiabatic changes a quantal system in an eigenstate slowly transported round a circuit c by varying parameters r in its hamiltonian r will acquire a geometrical phase factor exp i c in addition to the familiar dynamical phase factor an explicit general formula for c is derived in terms of the spectrum and eigenstates of r over a surface spanning c if c lies near a degeneracy of c takes a simple form which includes as a special case the sign change of eigenfunctions of real symmetric matrices round a degeneracy as an illustration c is calculated for spinning particles in slowly changing magnetic fields although the sign reversal of spinors on rotation is a special case the effect is predicted to occur for bosons as well as fermions and a method for observing it is proposed it is shown that the aharonov bohm effect can be interpreted as a geometrical phase factor

a finite difference scheme for three dimensional incompressible flows in cylindrical coordinates a finite difference scheme for the direct simulation of the incompressible time dependent three dimensional navier stokes equations in cylindrical coordinates is presented the equations in primitive variables vr v vzandp are solved by a fractional step method together with an approximate factorization technique cylindrical coordinates are singular at the axis the introduction of the radial fluxqr r vron a staggered grid simplifies the treatment of the region atr 0 the method is tested by comparing the evolution of a free vortex ring and its collision with a wall with the theory experiments and other numerical results the formation of a tripolar vortex where the highest vorticity is atr 0 is also considered finally to emphasize the accurate treatment near the axis the motion of a lamb dipole crossing the origin is simulated

finite difference method for incompressible navier stokes equations in arbitrary orthogonal curvilinear coordinates a finite difference method for solving three dimensional time dependent incompressible navier stokes equations in arbitrary curvilinear orthogonal coordinates is presented the method is oriented on turbulent flow simulations and consists of a second order central difference approximation in space and a third order semi implicit runge kutta scheme for time advancement spatial discretization retains some important properties of the navier stokes equations including energy conservation by the nonlinear and pressure gradient terms numerical tests cover cartesian cylindrical polar spherical cylindrical elliptic and cylindrical bipolar coordinate systems both laminar and turbulent flows are considered demonstrating reasonable accuracy and stability of the method

the relation between the berry and the anandan aharonov connections for u n bundles the geometric phase has been defined as the holonomy of two bundles with different base spaces and different connections in this article we establish the relation between the berry simon and the anandan aharonov definitions for a large class of cyclic hamiltonians with n fold degeneracy using the classifying theorem for principal fiber bundles

a pseudospectral approach for polar and spherical geometries the singularities that arise in polar and spherical coordinates have in the past caused significant difficulties in obtaining accurate solutions to convection diffusion type problems in many fields astrophysics geophysics meteorology etc viewing pseudospectral methods as a limiting case of finite difference methods rather than as based on expansions in terms of orthogonal functions leads naturally to very simple yet highly effective fast fourier transform fft based pseudospectral methods in such geometries

comparison of conservative and rotational forms in large eddy simulation of turbulent channel flow abstract fully developed turbulent channel flow is studied numerically using large eddy simulation les with a fourier finite difference method a prominent feature of this paper lies in the use of a conservative form of the arakawa type for the convective terms in the navier stokes equations the results are compared with earlier ones of moin and kim 1 based on the rotational form of the convective terms noticeable differences are found in quantities such as turbulence intensities two point correlations etc the difference is most prominent in the grid scale portion of the turbulent shear stress the present results agree well with the recent direct simulation of a mildly curved channel flow by moser and moin 2 using the fourier chebyshev polynomial expansions an estimate is made of the error inherent in the rotational form combined with the second order central finite difference method the relationship between the energy production mechanism and helicity is pointed out

combined immersed boundary finite difference methods for three dimensional complex flow simulations a second order accurate highly efficient method is developed for simulating unsteady three dimensional incompressible flows in complex geometries this is achieved by using boundary body forces that allow the imposition of the boundary conditions on a given surface not coinciding with the computational grid the governing equations therefore can be discretized and solved on a regular mesh thus retaining the advantages and the efficiency of the standard solution procedures two different forcings are tested showing that while the quality of the results is essentially the same in both cases the efficiency of the calculation strongly depends on the particular expression a major issue is the interpolation of the forcing over the grid that determines the accuracy of the scheme this ranges from zeroth order for the most commonly used interpolations up to second order for an ad hoc velocity interpolation the present scheme has been used to simulate several flows whose results have been validated by experiments and other results available in the literature finally in the last example we show the flow inside an ic piston cylinder assembly at high reynolds number to our knowledge this is the first example in which the immersed boundary technique is applied to a full three dimensional complex flow with moving boundaries and with a reynolds number high enough to require a subgrid scale turbulence model

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