nonlinear system identification using gaussian inputs the paper is concerned with the identification of nonlinear systems represented by volterra expansions and driven by stationary zero mean gaussian inputs with arbitrary spectra that are not necessarily white procedures for the computation of the volterra kernels both in the time as well as in the frequency domain are developed based on cross cumulant information the derived kernels are optimal in the mean squared error sense for noncausal systems order recursive procedures based on minimum mean squared error reduction are derived more general input output representations that result when the volterra kernels are expanded in a given orthogonal base are also considered

modeling a no slip flow boundary with an external force field abstract a novel technique related to peskin s immersed boundary approach is used to introduce solid surfaces into a simulated flow field the navier stokes equations permit the presence of an externally imposed body force that may vary in space and time forces are chosen to lie along a desired surface and to have a magnitude and direction opposing the local flow such that the flow is brought to rest on an element of the surface for unsteady viscous flow the direct calculation of the needed force is facilitated by a feedback scheme in which the velocity is used to iteratively determine the desired value in particular we determine the surface body force from the relation f x 5 t t 0 u x 5 t dt u x 5 t for surface points x 5 velocity u time t and negative constants and examples are presented which include 2d flow around cylinders 3d turbulent channel flow where one boundary is simulated with a force field and turbulent channel flow over a riblet covered surface while the new method may be applied to complex geometries on a non cartesian mesh we have chosen to use a simple cartesian grid all simulations are done with a spectral code in a single computational domain without any mapping of the mesh

determinants and the structure of the integral approximant table abstract the structure of the table of integral approximants based on our minimality definition is studied the key elements are simplices containing only a single linearly independent solution for the integral polynomials we prove some new identities among determinants of the coefficients of the determining equations for integral polynomials of different types relations between the simplices and these determinants are also derived we give determinantal conditions which are both necessary and sufficient for a full simplex to contain just one approximant a nullity lemma is proved limiting the change between contiguous types in the number of linearly independent solutions for integral polynomials virtually all of our results are equally valid for the more general case of the hermite pade approximants of the latin type

ellipticity accuracy and convergence of the discrete navier stokes equations the introduction into the continuity equation of additional terms to recover grid scale ellipticity for the navier stokes equations discretised on a non staggered mesh results in an increase in the discretisation error the introduced error is a combination of the additional truncation error and a false source resulting from the inconsistent construction of the conservation equations used in the finite volume scheme considered the false source error component is removed by constructing the conservation terms consistently while the additional truncation error is shown to be of the same order as the leading order truncation error associated with the unmodified equations a method of reducing the magnitude of the additional terms thereby reducing the additional error is considered it is shown that although this does reduce the magnitude of the error it also reduces the ellipticity of the equations and leads to slower convergence

a reliable method for computing m pade approximants on arbitrary staircases abstract the m pade approximation problem is defined which contains as a special case the hermite pade approximation as well as the newton pade approximation different well known methods for computing m pade approximations are studied they are based on a normal solution table it is shown that the concept of one of them computing bases of sets induced by interpolation conditions can be generalized to the singular case a characterization of special bases leads to a representation of the m pade solution set like in beckermann this journal 1990 a simple efficient and reliable method for computing such bases by so called transfer matrices is derived finally examples of hermite pade and newton pade approximation are given the connection to other well known reliable algorithms for rational interpolation is discussed

application of higher order spectral analysis to cubically nonlinear system identification in this study digital higher order spectral analysis and frequency domain volterra system models are utilized to yield a practical methodology for the identification of weakly nonlinear time invariant systems up to third order the primary focus is on consideration of random excitation of nonlinear systems and thus the approach makes extensive use of higher order spectral analysis to determine the frequency domain volterra kernels which correspond to linear quadratic and cubic transfer functions although the volterra model is nonlinear in terms of its input it is linear in terms of its unknown transfer functions thus a least squares approach is used to determine the optimal in a least squares sense set of linear quadratic and cubic transfer functions of particular practical note is the fact that the approach of this paper is valid for non gaussian as well as gaussian random excitation it may also be utilized for multitone inputs the complexity of the problem addressed in this paper arises from two principal causes 1 the necessity to work in a 3d frequency space to describe cubically nonlinear systems and 2 the necessity to characterize the non gaussian random excitation by computing higher order spectral moments up to sixth order a detailed description of the approach used to determine the nonlinear transfer functions including considerations necessary for digital implementation is presented

an immersed boundary finite volume method for simulations of flow in complex geometries abstract a new immersed boundary method for simulating flows over or inside complex geometries is developed by introducing a mass source sink as well as a momentum forcing the present method is based on a finite volume approach on a staggered mesh together with a fractional step method both momentum forcing and mass source are applied on the body surface or inside the body to satisfy the no slip boundary condition on the immersed boundary and also to satisfy the continuity for the cell containing the immersed boundary in the immersed boundary method the choice of an accurate interpolation scheme satisfying the no slip condition on the immersed boundary is important because the grid lines generally do not coincide with the immersed boundary therefore a stable second order interpolation scheme for evaluating the momentum forcing on the body surface or inside the body is proposed three different flow problems decaying vortices and flows over a cylinder and a sphere are simulated using the immersed boundary method proposed in this study and the results agree very well with previous numerical and experimental results verifying the accuracy of the present method

the structure of the singular solution table of the m pade approximation problem abstract a general interpolation problem is defined which contains as special cases the m pade approximation problem as well as classical interpolation problems e g newton pade approximation to study the structure of the solution table a new concept the minimal solution is introduced statements on the local and global structure of the solution table are obtained as a special case the well known block structure of the pade table is derived finally a characterization of the solution set is given

the discrete continuity equation in primitive variable solutions of incompressible flow abstract the use of a non staggered computational grid for the numerical solutions of the incompressible flow equations has many advantages over the use of a staggered grid a penalty however is inherent in the finite difference approximations of the governing equations on non staggered grids in the primitive variable solutions the penalty is that the discrete continuity equation does not converge to machine accuracy rather it converges to a source term which is proportional to the fourth order derivative of the pressure the time increment and the square of the grid spacing an approach which minimizes the error in the discrete continuity equation is developed numerical results obtained for the driven cavity problem confirm the analytical developments

immersed interface methods for stokes flow with elastic boundaries or surface tension a second order accurate interface tracking method for the solution of incompressible stokes flow problems with moving interfaces on a uniform cartesian grid is presented the interface may consist of an elastic boundary immersed in the fluid or an interface between two different fluids the interface is represented by a cubic spline along which the singularly supported elastic or surface tension force can be computed the stokes equations are then discretized using the second order accurate finite difference methods for elliptic equations with singular sources developed in our previous paper siam j numer anal 31 1994 pp 1019 1044 the resulting velocities are interpolated to the interface to determine the motion of the interface an implicit quasi newton method is developed that allows reasonable time steps to be used

random and pseudorandom inputs for volterra filter identification this paper studies input signals for the identification of nonlinear discrete time systems modeled via a truncated volterra series representation a kronecker product representation of the truncated volterra series is used to study the persistence of excitation pe conditions for this model it is shown that i i d sequences and deterministic pseudorandom multilevel sequences prms s are pe for a truncated volterra series with nonlinearities of polynomial degree n if and only if the sequences take on n 1 or more distinct levels it is well known that polynomial regression models such as the volterra series suffer from severe ill conditioning if the degree of the polynomial is large the condition number of the data matrix corresponding to the truncated volterra series for both prms and i i d inputs is characterized in terms of the system memory length and order of nonlinearity hence the trade off between model complexity and ill conditioning is described mathematically a computationally efficient least squares identification algorithm based on prms or i i d inputs is developed that avoids directly computing the inverse of the correlation matrix in many applications short data records are used in which case it is demonstrated that volterra filter identification is much more accurate using prms inputs rather than gaussian white noise inputs

pressure based residual smoothing operators for multistage pseudocompressibility algorithms implicit residual smoothing operators for accelerating the convergence of explicit multistage artificial compressibility algorithms are developed using ideas from pressure based methods the velocity derivatives in the continuity equation and the pressure gradient terms in the momentum equations are discretized in time implicitly the discrete system of equations is linearized in time producing a block implicit operator which is approximately factorized and diagonalized via a similarity transformation the so derived diagonal operator depends only on the metrics of the geometric transformation and can thus be implemented in an efficient and straightforward manner it is combined with the standard implicit residual smoothing operator and incorporated in a four stage runge kutta algorithm also enhanced with local time stepping and multigrid acceleration linear stability analysis for the three dimensional navier stokes equations and calculations for laminar flows through curved square ducts and pipes demonstrate the damping properties and efficiency of the proposed approach particularly on large aspect ratio highly skewed meshes

unsteady solution of incompressible navier stokes equations abstract a new time accurate finite difference numerical method for solving incompressible navier stokes equations is presented with primitive variables as the unknowns the numerical scheme is a crank nicolson implicit treatment of all terms of the equations with central differencing for space derivatives the pressure and the nonlinearities in convection terms are not lagged to obtain the incompressible solution at the advanced time level a continuous auxiliary system is introduced in pseudo time with artificial compressibility time accurate solutions are presented for two dimensional fluid flows in a square cavity with an impulsively starting lid and with an oscillating lid

generalized inverses of hankel and toeplitz mosaic matrices abstract hankel and toeplitz mosaic matrices are block matrices with hankel or toeplitz blocks respectively it is shown that hankel and toeplitz mosaic matrices possess reflexive generalized inverses which are bezoutians furthermore the bezoutian structure of the moore penrose and group inverses is investigated

subspace identification of bilinear systems subject to white inputs the authors generalize linear subspace identification theory to an analog theory for the subspace identification of bilinear systems a major assumption they make is that the inputs of the system should be white and mutually independent it is shown that in that case most of the properties of linear subspace identification theory can be extended to similar properties for bilinear systems the link between the presented bilinear subspace method and kalman filter theory is made finally the practical relevance of the method is illustrated by making a direct comparison between linear and bilinear subspace identification methods when applied on data from a model of a distillation column

realization of bilinear stochastic systems this note considers the problem of realization of bilinear stochastic systems blsr first an explicit statement for the blsr problem is presented next a realization algorithm is developed in this algorithm the state vector is picked as a basis in the subspace obtained by projecting an appropriately defined past vector onto an appropriately defined future vector also the realization algorithm involves solving a matrix nonlinear equation which is akin to the algebraic riccati equation except for one additional term

a second order projection method for the incompressible navier stokes equations in this paper we describe a second order projection method for the time dependent incom pressible navier stokes equations as in the original projection method developed by chorin we first solve diffusion convection equations to predict intermediate velocities which are then projected onto the space of divergence free vector fields by introducing more coupling between the diffusion onvection step and the projection step we obtain a temporal discretiza tion that is second order accurate our treatment of the diffusion convection step uses a specialized higher order godunov method for differencing the nonlinear convective terms that provides a robust treatment of these terms at high reynolds number the godunov procedure is second order accurate for smooth flow and remains stable for discontinuous initial data even in the zero viscosity limit we approximate the projection directly using a galerkin procedure that uses a local basis for discretely divergence free vector fields numerical results are presented validating the convergence properties of the method we also apply the method to doubly periodic shear layers to assess the performance of the method on more difficult

an adaptive version of the immersed boundary method a computational setting for the immersed boundary method employing an adaptive mesh refinement is presented enhanced accuracy for the method is attained locally by covering an immersed boundary vicinity with a sequence of nested progressively finer rectangular grid patches which dynamically follow the immersed boundary motion the set of equations describing the interaction between a non stationary viscous incompressible fluid and an immersed elastic boundary is solved by coupling a projection method specially designed for locally refined meshes to an implicit formulation of the immersed boundary method the main contributions of this work concern the formulation and the implementation of a multilevel self adaptive version of the immersed boundary method on locally refined meshes this approach is tested for a particular two dimensional model problem for which no significant difference is found between the solutions obtained on a mesh refined locally around the immersed boundary and on the associated uniform mesh built with the resolution of the finest level

a cartesian grid embedded boundary method for poisson s equation on irregular domains we present a numerical method for solving poisson s equation with variable coefficients and dirichlet boundary conditions on two dimensional regions the approach uses a finite volume discretization which embeds the domain in a regular cartesian grid we treat the solution as a cell centered quantity even when those centers are outside the domain cells that contain a portion of the domain boundary use conservative differencing of second order accurate fluxes on each cell volume the calculation of the boundary flux ensures that the conditioning of the matrix is relatively unaffected by small cell volumes this allows us to use multigrid iterations with a simple point relaxation strategy we have combined this with an adaptive mesh refinement amr procedure we provide evidence that the algorithm is second order accurate on various exact solutions and compare the adaptive and nonadaptive calculations

invertibility of higher order moment matrices signal processing algorithms based on volterra filter structures often require that a matrix composed of higher order moments of the underlying process be invertible previously this problem has been studied for uncorrelated random variables the paper establishes conditions under which a wide class of correlated processes have invertible higher order moment matrices

n4sid subspace algorithms for the identification of combined deterministic stochastic systems abstract recently a great deal of attention has been given to numerical algorithms for subspace state space system identification n4sid in this paper we derive two new n4sid algorithms to identify mixed deterministic stochastic systems both algorithms determine state sequences through the projection of input and output data these state sequences are shown to be outputs of non steady state kalman filter banks from these it is easy to determine the state space system matrices the n4sid algorithms are always convergent non iterative and numerically stable since they only make use of qr and singular value decompositions both n4sid algorithms are similar but the second one trades off accuracy for simplicity these new algorithms are compared with existing subspace algorithms in theory and in practice

a cartesian grid projection method for the incompressible euler equations in complex geometries many problems in fluid dynamics require the representation of complicated internal or external boundaries of the flow here we present a method for calculating time dependent incompressible inviscid flow which combines a projection method with a cartesian grid approach for representing geometry in this approach the body is represented as an interface embedded in a regular cartesian mesh the advection step is based on a cartesian grid algorithm for compressible flow in which the discretization of the body near the flow uses a volume of fluid representation a redistribution procedure is used to eliminate time step restrictions due to small cells where the boundary intersects the mesh the projection step uses an approximate projection based on a cartesian grid method for potential flow the method incorporates knowledge of the body through volume and area fractions along with certain other integrals over the mixed cells convergence results are given for the projection itself and for the time dependent algorithm in two dimensions the method is also demonstrated on flow past a half cylinder with vortex shedding

identification of discrete time state affine state space models using cumulants this paper is concerned with the identification of discrete time time invariant state affine state space models driven by an independent identically distributed iid random input and in the presence of process and measurement noise the identification problem is treated using a cumulant based approach it is shown that the input output and input state crosscumulant equations in the time domain have the form of a linear autonomous system an algorithmic procedure is then developed for the computation of the unknown system matrices based on a standard deterministic linear subspace identification algorithm provided the input signal has some persistent excitation properties the special case of gaussian iid input is also examined the proposed method is computationally very efficient and its accuracy is illustrated by simulations

existence of certain sequences of hermite pade approximants abstract we prove the existence of infinite sequences of unique minimal hermite pade polynomials of horizontal near partially diagonal and near diagonal character

a primitive variable method for the solution of three dimensional incompressible viscous flows abstract in this paper we present a new primitive variable method for the solution of the three dimensional incompressible reynolds averaged navier stokes equations in generalized curvilinear coordinates the governing equations are discretized on a non staggered grid and the discrete continuity equation is replaced by a discrete pressure poisson equation the discrete pressure equation is designed in such a way that i the compatibility condition for the poisson neumann problem is automatically satisfied and ii the discrete incompresibility constraint is satisfied to at least truncation error accuracy while the computed pressure is smooth the momentum equations are integrated in time using the four stage runge kutta algorithm while the pressure equation is solved using the point successive relaxation technique the method is applied to calculate the turbulent flow field over a ship model the computed results are in very good agreement with the experimental data

the blob projection method for immersed boundary problems a new finite difference numerical method for modeling the interaction between flexible elastic membranes and an incompressible fluid in a two dimensional domain is presented the method differs from existing methods in the way the forces exerted by the membranes on the fluid are modeled these are described by a collection of regularized point forces and the velocity field they induce is computed directly on a regular cartesian grid via a smoothed dipole potential comparisons between this method and the immersed boundary method of peskin and mcqueen are presented the results show that the method proposed here preserves volumes better and has a higher order of convergence

hermite pade approximation basic notions and theorems abstract our purpose is to give a brief exposition of basic notions and facts on hermite pade approximation theory a hermite pade form hpf is defined here in the same way as a pade approximant is as a consequence in some cases hpf does not exist even in the modified version hpf need not be unique therefore it was worthwhile to choose some hpf as the optimal one all criteria of existence unicity etc are phrased in a unified manner they base on few quantities depending on the power series under consideration and are usable in the theory rather than in the numerical practice

blind identification of bilinear systems this paper is concerned with the blind identification of a class of bilinear systems excited by non gaussian higher order white noise the matrix of coefficients of mixed input output terms of the bilinear system model is assumed to be triangular in this work under the additional assumption that the system output is corrupted by gaussian measurement noise we derive an exact parameter estimation procedure based on the output cumulants of orders up to four results of the simulation experiments presented in the paper demonstrate the validity and usefulness of our approach

regular article an accurate cartesian grid method for viscous incompressible flows with complex immersed boundaries a cartesian grid method has been developed for simulating two dimensional unsteady viscous incompressible flows with complex immersed boundaries a finite volume method based on a second order accurate central difference scheme is used in conjunction with a two step fractional step procedure the key aspects that need to be considered in developing such a solver are imposition of boundary conditions on the immersed boundaries and accurate discretization of the governing equation in cells that are cut by these boundaries a new interpolation procedure is presented which allows systematic development of a spatial discretization scheme that preserves the second order spatial accuracy of the underlying solver the presence of immersed boundaries alters the conditioning of the linear operators and this can slow down the iterative solution of these equations the convergence is accelerated by using a preconditioned conjugate gradient method where the preconditioner takes advantage of the structured nature of the underlying mesh the accuracy and fidelity of the solver is validated by simulating a number of canonical flows and the ability of the solver to simulate flows with very complicated immersed boundaries is demonstrated

gerris a tree based adaptive solver for the incompressible euler equations in complex geometries an adaptive mesh projection method for the time dependent incompressible euler equations is presented the domain is spatially discretised using quad octrees and a multilevel poisson solver is used to obtain the pressure complex solid boundaries are represented using a volume of fluid approach second order convergence in space and time is demonstrated on regular statically and dynamically refined grids the quad octree discretisation proves to be very flexible and allows accurate and efficient tracking of flow features the source code of the method implementation is freely available

the immersed interface method for the navier stokes equations with singular forces abstract peskin s immersed boundary method has been widely used for simulating many fluid mechanics and biology problems one of the essential components of the method is the usage of certain discrete delta functions to deal with singular forces along one or several interfaces in the fluid domain however the immersed boundary method is known to be first order accurate and usually smears out the solutions in this paper we propose an immersed interface method for the incompressible navier stokes equations with singular forces along one or several interfaces in the solution domain the new method is based on a second order projection method with modifications only at grid points near or on the interface from the derivation of the new method we expect fully second order accuracy for the velocity and nearly second order accuracy for the pressure in the maximum norm including those grid points near or on the interface this has been confirmed in our numerical experiments furthermore the computed solutions are sharp across the interface nontrivial numerical results are provided and compared with the immersed boundary method meanwhile a new version of the immersed boundary method using the level set representation of the interface is also proposed in this paper

second order volterra system identification second order volterra system identification is discussed crosscumulant information is converted into a fredholm integral equation special emphasis is focused on inputs obtained at the output of a linear filter driven by higher order white noise

a hybrid cartesian immersed boundary method for simulating flows with 3d geometrically complex moving bodies a numerical method is developed for solving the 3d unsteady incompressible navier stokes equations in cartesian domains containing immersed boundaries of arbitrary geometrical complexity moving with prescribed kinematics the governing equations are discretized on a hybrid staggered non staggered grid layout using second order accurate finite difference formulas the discrete equations are integrated in time via a second order accurate dual time stepping artificial compressibility iteration scheme unstructured triangular meshes are employed to discretize complex immersed boundaries the nodes of the surface mesh constitute a set of lagrangian control points used to track the motion of the flexible body at every instant in time the influence of the body on the flow is accounted for by applying boundary conditions at cartesian grid nodes located in the exterior but in the immediate vicinity of the body by reconstructing the solution along the local normal to the body surface grid convergence tests are carried out for the flow induced by an oscillating sphere in a cubic cavity which show that the method is second order accurate the method is validated by applying it to calculate flow in a cartesian domain containing a rigid sphere rotating at constant angular velocity as well as flow induced by a flapping wing the ability of the method to simulate flows in domains with arbitrarily complex moving bodies is demonstrated by applying to simulate flow past an undulating fish like body and flow past an anatomically realistic planktonic copepod performing an escape like maneuver euver

multiphase dynamics in arbitrary geometries on fixed cartesian grids in this work a mixed eulerian lagrangian algorithm calledelafint eulerian lagrangian algorithm for interface tracking is developed further and applied to compute flows with solid fluid and fluid fluid interfaces the method is capable of handling fluid flows in the presence of both irregularly shaped solid boundaries and moving boundaries on a fixed cartesian grid the field equations are solved on the underlying fixed grid using a collocated variable pressure based formulation the moving boundary is tracked explicitly by the lagrangian translation of marker particles the moving boundary passes through the grid and the immersed boundary technique is used to handle its interaction with the underlying grid the internal solid boundaries are dealt with by using a cut cell technique particular attention is directed toward conservation and consistency in the vicinity of both phase boundaries the complex geometry feature has been tested for a variety of flow problems the performance of the immersed boundary representation is demonstrated in the simulation of newtonian liquid drops the combination of the two features is then employed in the simulation of motion of drops through constricted tubes the capabilities developed here can be useful for solving flow problems involving moving and stationary complex boundaries

recursiveness in matrix rational interpolation problems abstract we consider the problem of computing solutions to a variety of matrix rational interpolation problems these include the partial realization problem for matrix power series and newton pade hermite pade simultaneous pade m pade and multipoint pade approximation problems along with their matrix generalizations a general recurrence relation is given for solving these problems unlike other previous recursive methods our recurrence works along arbitrary computational paths when restricted to specific paths the recurrence relation generalizes previous work of antoulas cabay and labahn beckermann van barel and bultheel and gutknecht along with others our results rely on the concept of extended m pade approximation introduced in this paper this is a natural generalization of the two point pade approximation problem extended to multiple interpolation points including infinity and matrix laurent and newton series by using module theoretic techniques we determine complete parameterizations of all solutions to this problem our recurrence relation then efficiently computes these parameterizations this recursion requires no conditions on the input data we also discuss the concept of duality which was shown to be of particular interest for a stable computation of those approximants finally we show the invariance of our approximation problem under linear transformations of the extended complex plane

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

time and lag recursive computation of cumulants from a state space model time and lag recursive algorithms for the computation of the cumulants of the state vector and the output process of a multiple input multiple output time varying state space model are derived using a kronecker product representation for the cumulants of vector processes the noise processes are not assumed to be stationary symmetry relations for the cumulants of vector processes are discussed computational aspects are examined in detail it is conjectured that the recursive equations derived will be useful in developing state estimators and even optimal controllers based on higher order statistics

efficient algorithms for volterra system identification in this paper nonlinear filtering and identification based on finite support volterra models are considered the volterra kernels are estimated via input output statistics or directly in terms of input output data it is shown that the normal equations for a finite support volterra system excited by zero mean gaussian input have a unique solution if and only if the power spectral process of the input signal is nonzero at least at m distinct frequencies where m is the memory of the system a multichannel embedding approach is introduced a set of primary signals defined in terms of the input signal serve to map efficiently the nonlinear process to an equivalent multichannel format efficient algorithms for the estimation of the volterra parameters are derived for batch as well as for adaptive processing an efficient order recursive method is presented for the determination of the volterra model structure the proposed methods are illustrated by simulations

a stable and accurate convective modelling procedure based on quadratic upstream interpolation a convective modelling procedure is presented which avoids the stability problems of central differencing while remaining free of the inaccuracies of numerical diffusion associated with upstream differencing for combined convection and diffusion the number of operations at each grid point is comparable to that of standard upstream pluscentral differencing however highly accurate solutions can be obtained with a grid spacing much larger than that required by conventional methods for comparable accuracy with obvious practical advantaged in terms of both speed and storage the algorithm is based on a conservative control volume formulation with cell wall values of each field variable written in terms of a quadratic interpolation using in any one coordinate direction the two adjacent nodal values together with the value at the next upstream node this results in a convective differencing scheme with greater formal accuracy than central differencing while retaining the basic stable convective sensitivity property of upstream weighted schemes the consistent treatment of diffusion terms is equivalent to central differencing with careful modelling numerical boundary conditions are not troublesome some idealized problems are studied showing the practical advantages of the method over other schemes in comparison with exact solutions an application to a complex unsteady two dimensional flow is briefly discussed

a representation of curved boundaries for the solution of the navier stokes equations on a staggered three dimensional cartesian grid a method is presented for representing curved boundaries for the solution of the navier stokes equations on a non uniform staggered three dimensional cartesian grid the approach involves truncating the cartesian cells at the boundary surface to create new cells which conform to the shape of the surface we discuss in some detail the problems unique to the development of a cut cell method on a staggered grid methods for calculating the fluxes through the boundary cell faces for representing pressure forces and for calculating the wall shear stress are derived and it is verified that the new scheme retains second order accuracy in space in addition a novel cell linking method is developed which overcomes problems associated with the creation of small cells while avoiding the complexities involved with other cell merging approaches techniques are presented for generating the geometric information required for the scheme based on the representation of the boundaries as quadric surfaces the new method is tested for flow through a channel placed oblique to the grid and flow past a cylinder at re 40 and is shown to give significant improvement over a staircase boundary formulation finally it is used to calculate unsteady flow past a hemispheric protuberance on a plate at a reynolds number of 800 good agreement is obtained with experimental results for this flow