characteristic based time dependent maxwell equation solvers on a general curvilinear frame four cell centered finite volume characteristic based procedures for solving time dependent three dimensional maxwell equations on a general curvilinear frame are developed and implemented on a spherical coordinate system these methods generate simulations or an oscillating electric dipole without wave reflection from the truncated computational domain through a comparative study it is established that an upwind biased third order scheme demonstrates less dispersive and dissipative errors than second order schemes

algebraic splitting for incompressible navier stokes equations fully discretized incompressible navier stokes equations are solved by splitting the algebraic system with an approximate factorization this splitting affects the temporal convergence order of velocity and pressure the splitting error is proportional to the pressure variable and a simple analysis shows that the original convergence order of the time integration scheme can be retained by solving for incremental pressure the combination of splitting and incremental pressure is shown to be equivalent to an error correcting method using the full pressure in numerical experiments employing a third order time integration scheme and various orders for the pressure increment the splitting error is shown to control the convergence order and the full order of the scheme is recaptured for both velocity and pressure the difference between perturbing the momentum or the continuity equation is also explored

implicit technique for three dimensional turbulent magnetoaerodynamics a high resolution numerical procedure designed to simulate three dimensional nonideal magnetogasdynamic mgd phenomena on complex cone gurations is extended to enhance computational efe ciency and physical e delity alooselycoupledapproximatelyfactoredimplicitmethod isdevelopedtoovercometime stepsizelimitations of explicit methods a sub iteration strategy is included to recover up to second order time accuracy verie cation exercises covering wave propagation and diffusion phenomena are presented to demonstrate accuracy and characterize the efe ciency of the numerical procedure because the aerodynamic environment will exhibit relatively small electrical conductivities and large compensatory magnetic e elds a low magnetic reynolds number reae formulation and its solution procedure are described and verie ed by considering mgd control of a compressible laminar e at plate boundary layer at different interaction parameters a two equation k turbulence model with low reynolds number near wall terms is incorporated with additional expressions to reproduce the damping effect of the magnetic e eld the effect of a magnetic dipole on a supersonic turbulent e at plate boundary layer is examined an exploratory study of mgd control of e ow past a classic reentry vehicle cone guration demonstrates the capabilities of the numerical scheme

practical aspects of higher order numerical schemes for wave propagation phenomena this paper examines practical issues related to the use of compact difference based fourth and sixth order schemes for wave propagation phenomena with focus on maxwell s equations of electromagnetics an outline of the formulation and scheme optimization is followed by an assessment of the error accruing from application on stretched meshes with two approaches transformed plane method and physical space differencing in the first technique the truncation error expansion for the sixth order compact scheme confirms that the order of accuracy is preserved if a consistent mesh refinement strategy is followed and further that metrics should be evaluated numerically even if analytic expressions are available physical space differencing formulas are derived for the five point stencil by expressing the coefficients in terms of local spacing ratios the order of accuracy of the reconstruction operator is then verified with a numerical experiment on stretched meshes to ensure stability for a broad range of problems fourier analysis is employed to develop a single parameter family of up to tenth order tridiagonal based spatial filters the implementation of these filters is discussed in terms of their effect on the interior scheme as well as in a 1 d cavity where they are employed to suppress a late time instability the paper concludes after demonstrating the application of the scheme to several 3 d canonical problems utilizing cartesian as well as curvilinear meshes published in 1999 by john wiley sons ltd this article is a u s government work and is in the public domain in the united states

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

uneven order decentered shapiro filters for boundary filtering this paper addresses the use of shapiro filters for boundary filtering a new class of uneven order decentered shapiro filters is proposed and compared to classical shapiro filters and even order decentered shapiro filters the theoretical analysis shows that the proposed boundary filters are more accurate than the centered shapiro filters and more robust than the even order decentered boundary filters usable at the same distance to the boundary the benefit of the new boundary filters is assessed for computations using the compressible euler equations

effects of the computational time step on numerical solutions of turbulent flow effects of large computational time steps on the computed turbulence were investigated using a fully implicit method in turbulent channel flow computations the largest computational time step in wall units which led to accurate prediction of turbulence statistics was determined turbulence fluctuations could not be sustained if the computational time step was near or larger than the kolmogorov time scale

application of a fractional step method to incompressible navier stokes equations a numerical method for computing three dimensional time dependent incompressible flows is presented the method is based on a fractional step or time splitting scheme in conjunction with the approximate factorization technique it is shown that the use of velocity boundary conditions for the intermediate velocity field can lead to inconsistent numerical solutions appropriate boundary conditions for the intermediate velocity field are derived and tested numerical solutions for flows inside a driven cavity and over a backward facing step are presented and compared with experimental data and other numerical results

spatial finite difference approximations for wave type equations the simplest finite difference approximations for spatial derivatives are centered explicit and applied to regular equispaced grids well established generalizations include the use of implicit compact approximations and staggered grids we find here that the combination of these two concepts together with high formal order of accuracy is very effective for approximating the first derivatives in space that occur in many wave type pdes

an r matrix for d 3 4 this letter gives the calculation of a trigonometric r matrix for the twisted affine quantum group of type d 3 4

compact difference scheme applied to simulation of low sweep delta wing flow computational simulations are presented of the flow over a 50 deg sweep delta wing for angles of attack a 5 10 and 15 deg the full navier stokes equations are solved using a sixth order compact differencing scheme coupled with an eighth order low pass spatial filter to provide numerical stability

improving gil werman algorithm for running min and max filters the current best bound on the number of comparison operations needed to compute the running maximum or minimum over a p element sliding data window is approximately three comparisons per output sample this bound is probabilistic for some algorithms and is derived for their complexities on the average for independent identically distributed i i d input signals the worst case complexities of these algorithms are o p the worst case complexity c sub r 3 4 p comparisons per output sample for 1d signals is achieved in the gil werman algorithm 1993 in this correspondence we propose a modification of the gil werman algorithm with the same worst case complexity but with a lower average complexity a theoretical analysis shows that using the proposed modification the complexities of sliding max or min 1d and 2d filters over i i d signals are reduced to c sub 1 2 5 3 5 p 1 p sup 2 and c sub 2 5 7 p 2 p sup 2 comparisons per output sample on the average respectively simulations confirm the theoretical results moreover experiments show that even for highly correlated data namely for real images the behavior of the algorithm remains the same as for i i d signals

an analysis of numerical errors in large eddy simulations of turbulence the reliability of numerical simulations of turbulence depend on our ability to quantify and control discretization errors in the classical literature on error analysis typically simple linear equations are studied estimates of errors derived from such analyses depend on the assumption that each dependent variable can be characterized by a unique amplitude and scale of spatial variation that can be normalized to unity this assumption is not valid for strongly nonlinear problems such as turbulence where nonlinear interactions rapidly redistribute energy resulting in the appearance of a broad continuous spectrum of amplitudes in such situations the numerical error as well as the subgrid model can change with grid spacing in a complicated manner that cannot be inferred from the results of classical error analysis in this paper a formalism for analyzing errors in such nonlinear problems is developed in the context of finite difference approximations for the navier stokes equations when the flow is fully turbulent analytical expressions for the power spectra of these errors are derived by exploiting the joint normal approximation for turbulent velocity fields these results are applied to large eddy simulation of turbulence to obtain quantitative bounds on the magnitude of numerical errors an assessment of the significance of these errors in made by comparing their magnitudes with that of the nonlinear and subgrid terms one method of controlling the errors is suggested and its effectiveness evaluated through quantitative measures although explicit evaluations are presented only for large eddy simulation the expressions derived for the power spectra of errors are applicable to direct numerical simulation as well

high order accurate solution of the incompressible navier stokes equations high order methods are of great interest in the study of turbulent flows in complex geometries by means of direct simulation with this goal in mind the incompressible navier stokes equations are discretized in space by a compact fourth order finite difference method on a staggered grid the equations are integrated in time by a second order semi implicit method stable boundary conditions are implemented and the grid is allowed to be curvilinear in two space dimensions the method is extended to three dimensions by a fourier expansion in every time step a system of linear equations is solved for the velocity and the pressure by an outer and an inner iteration with preconditioning the convergence properties of the iterative method are analyzed the order of accuracy of the method is demonstrated in numerical experiments the method is used to compute the flow in a channel the driven cavity and a constricted channel

fourth order difference methods for hyperbolic ibvps abstract in this paper we consider fourth order difference approximations of initial boundary value problems for hyperbolic partial differential equations we use the method of lines approach with both explicit and compact implicit difference operators in space the explicit operator satisfies an energy estimate leading to strict stability for the implicit operator we develop boundary conditions and give a complete proof of strong stability using the laplace transform technique we also present numerical experiments for the linear advection equation and burgers equation with discontinuities in the solution or in its derivative the first equation is used for modeling contact discontinuities in fluid dynamics the second one is used for modeling shocks and rarefaction waves the time discretization is done with a third order runge kutta tvd method for solutions with discontinuities in the solution itself we add a filter based on second order viscosity in case of the non linear burgers equation we use a flux splitting technique that results in an energy estimate for certain difference approximations in which case also an entropy condition is fulfilled in particular we shall demonstrate that the unsplit conservative form produces a non physical shock instead of the physically correct rarefaction wave in the numerical experiments we compare our fourth order methods with a standard second order one and with a third order tvd method the results show that the fourth order methods are the only ones that give good results for all the considered test problems

toward the construction of a fourth order difference scheme for transient em wave simulation staggered grid approach a compact central difference approximation in conjunction with the yee 1966 grid is used to compute the spatial derivatives in maxwell s equations to advance the semi discrete equations the four stage runge kutta rk integrator is invoked this combination of spatial and temporal differencing leads to a scheme that is fourth order accurate conditionally stable and highly efficient moreover the use of compact differencing allows one to apply the compact operator in the vicinity of a perfect conductor an attribute not found in other higher order methods results are provided that quantify the spectral properties of the method simulations are conducted on problem spaces that span one and three dimensions and whose domains are of the open and closed type results from these simulations are compared with exact closed form solutions the agreement between these results is consistent with numerical analysis

a conservative semi lagrangian multi tracer transport scheme cslam on the cubed sphere grid a conservative multi tracer transport algorithm on the cubed sphere based on the semi lagrangian approach cslam has been developed the scheme relies on backward trajectories and the resulting upstream cells polygons are approximated with great circle arcs biquadratic polynomial functions are used for approximating the density distribution in the cubed sphere grid cells the upstream surface integrals associated with the conservative semi lagrangian scheme are computed as line integrals by employing the gauss green theorem the line integrals are evaluated using a combination of exact integrals and high order gaussian quadrature the upstream cell trajectories information and computation of weights of integrals can be reused for each additional tracer the cslam scheme is extensively tested with various standard benchmark test cases of solid body rotation and deformational flow in both cartesian and spherical geometry and the results are compared with those of other published schemes the cslam scheme is accurate robust and moreover the edges and vertices of the cubed sphere discontinuities do not affect the overall accuracy of the scheme the cslam scheme exhibits excellent convergence properties and has an option for enforcing monotonicity the advantages of introducing cross terms in the fully two dimensional biquadratic density distribution functions are also examined in the context of cartesian as well as the cubed sphere grid which has six local sub domains with discontinuous edges and corners

vertex operators for twisted quantum affine algebras we construct explicitly the q vertex operators intertwining operators for the level one modules v i of the classical quantum affine algebras of twisted types using interacting bosons where i 0 1 for a 2 n 1 i 0 for d 3 i 0 n for d 2 1 and i n for a 2 n a perfect crystal graph for d 3 4 is constructed as a by product

spurious waves in discrete computation of wave phenomena and flow problems in the present work we focus on spurious propagating disturbances q waves to establish the existence of q waves in computations we compare properties of different numerical methods drawn from finite difference finite volume and finite element methods existence and properties of q waves are demonstrated with propagation of wave packets following one dimensional 1d convection equation skewed wave propagation and by solution of linearized rotating shallow water wave equation lrswe specific numerical experiments are performed with parameters that convert a wave packet into a q wave we also show the case where q waves are created additionally to physical disturbances those propagate downstream formation of q waves are shown in the case of a discrete shielded vortex in the uniform flow and incompressible transitional flow past an aerofoil by solving the navier stokes equation in performing this exercise we establish critical wavenumber range beyond which q waves are created relevance of this information for dns and les is discussed we have further discussed the case of spurious caustics in discrete computing

asymptotically optimal algorithms for running max and min filters on random inputs given a d dimensional array of size n d and an integer p the running max or min filter is the set of maximum or minimum elements within a d dimensional sliding window of edge length p inside the array this problem is useful in many signal processing applications such as pattern analysis adaptive signal processing and morphological analysis the current best algorithm for computing the one dimensional 1 d max or min filter due to the work of h yuan and m j atallah running max min filters using 1 o 1 comparisons per sample ieee trans pattern anal mach intell vol 33 no 12 pp 2544 2548 dec 2011 uses 1 o 1 comparisons per sample in the worst case as a direct consequence the d dimensional max or min filter max and min filters respectively can be computed in d o 1 2d o 1 respectively comparisons per sample in this paper we first present an algorithm for computing d dimensional max and min filters simultaneously on i i d inputs that uses 1 5 o 1 expected comparisons per sample this is the first algorithm on i i d inputs that gets rid of the dependence on d in the dominating term with respect to n and p of the expected number of comparisons needed it is also asymptotically optimal when d is a fixed constant as n rightarrow infty and p rightarrow infty we also consider the dynamic version of the problem of d dimensional max and min filters simultaneously on i i d inputs where we want to maintain the filters after changes in the input array we design a linear sized data structure that stores precomputed information for efficient update using o p d 1 log 2 p expected comparisons per update

the cubed sphere a new gridding technique for the solution of partial differential equations in spherical geometry is presented the method is based on a decomposition of the sphere into six identical regions obtained by projecting the sides of a circumscribed cube onto a spherical surface by choosing the coordinate lines on each region to be arcs of great circles one obtains six coordinate systems which are free of any singularity and define the same metric taking full advantage of the symmetry properties of the decomposition a variation of the composite mesh finite difference method can be applied to couple the six grids and obtain with a high degree of efficiency very accurate numerical solutions of partial differential equations on the sphere the advantages of this new technique over both spectral and uniform longitude latitude grid point methods are discussed in the context of applications on serial and parallel architectures we present results of two test cases for numerical approximations to the shallow water equations in spherical geometry the linear advection of a cosine bell and the nonlinear evolution of a rossby haurwitz wave performance analysis for this latter case indicates that the new method can provide with substantial savings in execution times numerical solutions which are as accurate as those obtainable with the spectral transform method

a dispersion relation preserving optimized upwind compact difference scheme for high accuracy flow simulations in this work we have derived an optimized upwind compact difference scheme for achieving excellent spatial resolution the derived numerical scheme adds numerical diffusion which is strictly restricted to a high wavenumber region in order to control numerical instabilities as well as to achieve de aliasing ability more importantly the derived numerical scheme has excellent dispersion relation preserving drp property the applicability of the proposed scheme in simulating real flow problems has been demonstrated by solving flow inside a lid driven cavity a transitional flow past ag24 aerofoil and a two dimensional decaying turbulence flow

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

relative accuracy of several finite difference time domain methods in two and three dimensions a comparison of the accuracy of several orthogonal grid finite difference time domain fdtd schemes is made in both two and three dimensions the relative accuracy is determined from the dispersion error associated with each algorithm and the number of floating point operations required to obtain a desired accuracy level in general in both 2 d and 3 d fourth order algorithms are more efficient than second order schemes in terms of minimizing the number of computations for a given accuracy level in 2 d a second order approach proposed by z chen et al 1991 is much more accurate than the scheme of k s yee 1966 for a given amount of computation and can be as efficient as fourth order algorithms in 3 d yee s algorithm is slightly more efficient than the approach of chen et al in terms of operations but much more efficient in terms of memory requirements

the stability of numerical boundary treatments for compact high order finite difference schemes the stability characteristics of various compact fourth and sixth order spatial operators are assessed with the theory of gustafsson kreiss and sundstrom g k s for the semidiscrete initial boundary value problem these results are generalized to the fully discrete case with a recently developed theory of kreiss and wu in all cases favorable comparisons are obtained between g k s theory eigenvalue determination and numerical simulation the conventional definition of stability then is sharpened to include only those spatial discretizations that are asymptotically stable bounded left half plane eigenvalues many of the higher order schemes that are g k s stable are not asymptotically stable a series of compact fourth and sixth order schemes that are both asymptotically and g k s stable for the scalar case are then developed

optimized compact difference based finite volume schemes for linear wave phenomena high order compact difference based finite volume schemes are developed analyzed and implemented for linear wave propagation phenomena with particular emphasis on computational electromagnetics in the time domain the formulation combines the primitive function approach with five point spatially sixth and fourth order methods optimization in the semi discrete case is achieved by minimizing dispersion and isotropy error the fully discrete scheme is examined by adopting the classical fourth order runge kutta technique stability bounds are established and the coefficients for the spatial discretization are readjusted for optimum performance the scheme is then formally extended to multiple dimensions consistent boundary conditions are presented for the reconstruction operator as well as flux specification several calculations in one and three dimensions confirm the properties of the method

aerodynamic noise prediction for long span bodies abstract a computational methodology is proposed for aerodynamic noise prediction of long span bodies at low mach numbers the three dimensional hydrodynamic field is computed by incompressible large eddy simulation while its two dimensional acoustic field at zero spanwise wavenumber is solved by the linearized perturbed compressible equations lpce a far field acoustic pressure is obtained by extrapolating the pressure fluctuations with kirchhoff method followed by a three dimensional correction with oberai et al s formula the far field sound pressure level for the long span is then estimated by a correction method which is formally derived by revisiting the previous works of kato et al and perot et al along with discussion on finding the spanwise coherence lengths the accuracy of the present method is assessed for broadband noise with a broadened tone from a flow with re d 4 6 10 4 and m 0 21 past a circular cylinder of 30 cylinder diameter span the computed aerodynamic and acoustic results are found in excellent agreement with the experimental measurements

high order upwind compact finite difference lattice boltzmann method for viscous incompressible flows abstract in this work a high order upwind compact finite difference lattice boltzmann method ucdlbm is developed to efficiently solve viscous incompressible flow problems a fifth order upwind compact difference scheme is adopted to discretize the spatial derivatives of the lattice boltzmann equation and the third order total variation diminishing runge kutta scheme is utilized for the discretization of the temporal term compared to the existing central compact finite difference lattice boltzmann method cfdlbm the present ucdlbm can prevent non physical oscillations without filtering due to the natural dissipative property of upwind schemes three benchmark problems involving the taylor green vortex problem the doubly periodic shear layer flow problem and the lid driven square cavity flow problem are numerically solved to demonstrate the accuracy and efficiency of the present method numerical results computed are in good agreement with the analytical solution or other available numerical results and the present ucdlbm is less time consuming than the cfdlbm without degenerating the order of accuracy of the numerical solutions

high order splitting methods for the incompressible navier stokes equations abstract a new pressure formulation for splitting methods is developed that results in high order time accurate schemes for the solution of the incompressible navier stokes equations in particular improved pressure boundary conditions of high order in time are introduced that minimize the effect of erroneous numerical boundary layers induced by splitting methods a new family of stiffly stable schemes is employed in mixed explicit implicit time intgration rules these schemes exhibit much broader stability regions as compared to adams family schemes typically used in splitting methods their stability properties remain almost constant as the accuracy of the integration increases so that robust third or higher order time accurate schemes can readily be constructed that remain stable at relatively large cfl number the new schemes are implemented within the framework of spectral element discretizations in space so that flexibility and accuracy is guaranteed in the numerical experimentation a model stokes problem is studied in detail and several examples of navier stokes solutions of flows in complex geometries are reported comparison is made with the previously used first order in time spectral element splitting and non splitting e g uzawa schemes high order splitting spectral element methods combine accuracy in space and time and flexibility in geometry and thus can be very efficient in direct simulations of turbulent flows in complex geometries

three dimensional elliptic grid generation with fully automatic boundary constraints a new procedure for generating smooth uniformly clustered three dimensional structured elliptic grids is presented here which formulates three dimensional boundary constraints by extending the two dimensional counterpart presented by the author earlier this fully automatic procedure obviates the need for manual specification of decay parameters over the six bounding surfaces of a given volume grid the procedure has been demonstrated here for the mars science laboratory msl geometries such as aeroshell and canopy as well as the inflatable aerodynamic decelerator iad geometry and a 3d analytically defined geometry the new procedure also enables generation of single block grids for such geometries because the automatic boundary constraints permit the decay parameters to evolve as part of the solution to the elliptic grid system of equations these decay parameters are no longer just constants as specified in the conventional approach but functions of generalized coordinate variables over a given bounding surface since these decay functions vary over a given boundary orthogonal grids around any arbitrary simply connected boundary can be clustered automatically without having to break up the boundaries and the corresponding interior or exterior domains into various blocks for grid generation the new boundary constraints are not limited to the simply connected regions only but can also be formulated around multiply connected and isolated regions in the interior the proposed method is superior to other methods of grid generation such as algebraic and hyperbolic techniques in that the grids obtained here are c 2 continuous whereas simple elliptic smoothing of algebraic or hyperbolic grids to enforce c 2 continuity destroys the grid clustering near the boundaries

implementation of a high order compact finite difference lattice boltzmann method in generalized curvilinear coordinates abstract in this work the implementation of a high order compact finite difference lattice boltzmann method cfdlbm is performed in the generalized curvilinear coordinates to improve the computational efficiency of the solution algorithm to handle curved geometries with non uniform grids the incompressible form of the discrete boltzmann equation with the bhatnagar gross krook bgk approximation with the pressure as the independent dynamic variable is transformed into the generalized curvilinear coordinates herein the spatial derivatives in the resulting lattice boltzmann lb equation in the computational plane are discretized by using the fourth order compact finite difference scheme and the temporal term is discretized with the fourth order runge kutta scheme to provide an accurate and efficient incompressible flow solver a high order spectral type low pass compact filter is used to regularize the numerical solution and remove spurious waves generated by boundary conditions flow non linearities and grid non uniformity all boundary conditions are implemented based on the solution of governing equations in the generalized curvilinear coordinates the accuracy and efficiency of the solution methodology presented are demonstrated by computing different benchmark steady and unsteady incompressible flow problems a sensitivity study is also conducted to evaluate the effects of grid size and filtering on the accuracy and convergence rate of the solution four test cases considered herein for validating the present computations and demonstrating the accuracy and robustness of the solution algorithm are unsteady couette flow and steady flow in a 2 d cavity with non uniform grid and steady and unsteady flows over a circular cylinder and the naca0012 hydrofoil at different flow conditions results obtained for the above test cases are in good agreement with the existing numerical and experimental results the study shows the present solution methodology based on the implementation of the high order compact finite difference lattice boltzmann method cfdlbm in the generalized curvilinear coordinates is robust efficient and accurate for solving steady and unsteady incompressible flows over practical geometries

rational r matrices in irreducible representations working directly from the yang baxter equation the author obtains the spectral decomposition of rational r matrices in irreducible representations together with a necessary condition for their existence examples are given and connections with the drinfeld yangian construction are discussed

a high order immersed boundary method for acoustic wave scattering and low mach number flow induced sound in complex geometries a new sharp interface immersed boundary method based approach for the computation of low mach number flow induced sound around complex geometries is described the underlying approach is based on a hydrodynamic acoustic splitting technique where the incompressible flow is first computed using a second order accurate immersed boundary solver this is followed by the computation of sound using the linearized perturbed compressible equations lpce the primary contribution of the current work is the development of a versatile high order accurate immersed boundary method for solving the lpce in complex domains this new method applies the boundary condition on the immersed boundary to a high order by combining the ghost cell approach with a weighted least squares error method based on a high order approximating polynomial the method is validated for canonical acoustic wave scattering and flow induced noise problems applications of this technique to relatively complex cases of practical interest are also presented

accurate finite difference methods for time harmonic wave propagation finite difference methods for solving problems of time harmonic acoustics are developed and analyzed multi dimensional inhomogeneous problems with variable possibly discontinuous coefficients are considered accounting for the effects of employing non uniform grids a weighted average representation is less sensitive to transition in wave resolution due to variable wave numbers or non uniform grids than the standard pointwise representation further enhancement in method performance is obtained by basing the stencils on generalizations of pade approximation or generalized definitions of the derivative reducing spurious dispersion anisotropy and reflection and by improving the representation of source terms the resulting schemes have fourth order accurate local truncation error on uniform grids and third order in the non uniform case guidelines for discretization pertaining to grid orientation and resolution are presented

an analysis of the fractional step method the fractional step method for solving the incompressible navier stokes equations in primitive variables is analyzed as a block lu decomposition in this formulation the issues involving boundary conditions for the intermediate velocity variables and the pressure are clearly resolved in addition it is shown that poor temporal accuracy first order is not due to boundary conditions but due to the method itself a generalized block lu decomposition that overcomes this difficulty is presented allowing arbitrarily high temporal order of accuracy the generalized decomposition is shown to be useful for a wide range of problems including steady problems technical issues such as stability and the appropriate pressure update scheme are also addressed numerical simulations of the steady incompressible navier stokes equations in a square domain confirm the theoretical results 18 refs 4 figs

running max min filters using 1 o 1 comparisons per sample a running max or min filter asks for the maximum or minimum elements within a fixed length sliding window the previous best deterministic algorithm developed by gil and kimmel and refined by coltuc can compute the 1d max filter using 1 5 o 1 comparisons per sample in the worst case the best known algorithm for independent and identically distributed input uses 1 25 o 1 expected comparisons per sample by gil and kimmel in this work we show that the number of comparisons can be reduced to 1 o 1 comparisons per sample in the worst case as a consequence of the new max min filters the opening or closing filter can also be computed using 1 o 1 comparisons per sample in the worst case where the previous best work requires 1 5 o 1 comparisons per sample by gil and kimmel and computing the max and min filters simultaneously can be done in 2 o 1 comparisons per sample in the worst case where the previous best work by lemire requires three comparisons per sample our improvements over the previous work are asymptotic that is the number of comparisons is reduced only when the window size is large

computing 2 d min median and max filters fast algorithms for computing min median max or any other order statistic filter transforms are described the algorithms take constant time per pixel to compute min or max filters and polylog time per pixel in the size of the filter to compute the median filter a logarithmic time per pixel lower bound for the computation of the median filter is shown

an efficient quadrature rule on the cubed sphere abstract a new quadrature rule for functions defined on the sphere is introduced the nodes are defined as the points of the cubed sphere the associated weights are defined in analogy to the trapezoidal rule on each panel of the cubed sphere the formula enjoys a symmetry property ensuring that a proportion of 7 8 of all spherical harmonics is integrated exactly based on the remaining spherical harmonics it is possible to define modified weights giving an enhanced quadrature rule numerical results show that the new quadrature is competitive with classical rules of the literature this second quadrature rule is believed to be of interest for applied mathematicians physicists and engineers dealing with data located at the points of the cubed sphere

implicit high order compact algorithm for computational acoustics accurate solution of the linearized multidimensional euler equations for aeroacoustics as a system of simple wave equations is demonstrated if organized this system has unambiguous easily implemented boundary conditions allowing waves of same group speeds to pass through numerical boundaries or comply with wall conditions thus the task of designing a complex multidimensional scheme with approximate boundary conditions reduces to the design of accurate schemes for the simple wave equation in particular an implicit compact finite difference scheme and a characteristically exact but numerically nth order accurate boundary condition are used this low dispersion scheme has a third order spatial accuracy for various types of nonuniform meshes fourth order accuracy on uniform meshes and by choice a temporal accuracy of second order for algorithmic simplicity as the crank nicolson scheme the robustness and accuracy of the scheme and the validity of the system decoupling are demonstrated through a series of numerical experiments and comparisons with published results including the recent institute for computer applications in science and engineering nasa langley research center benchmark problems of acoustic and convective wave propagation in cartesian and cylindrical domains and reflection at stationary and or moving boundaries

mathematical complexity of running filters on semi groups and related problems this paper proves that the mathematical complexity of running filters on semi groups is c p 3 6 p 1 operations per sample where p is the filter window on other algebraic structures the mathematical complexity of the filtering can be lower two such cases are investigated the running filtering on max min lattice and on additions group they correspond to max min and moving average filters it is shown that the algorithms developed for semi groups are of interest in such cases too thus the fastest deterministic algorithm for max min filtering known so far is based on an algorithm for running filtering on semi groups first an optimized version is proposed in this paper then further improvement for data dependent max min algorithms is proposed finally the case of moving average and exponential smoothing is investigated their implementation by using the algorithms for semi groups is of lower complexity than the classical recursive implementation for the particular case of small size windows p 3 and p 4

fast algorithms for finding nearest common ancestors we consider the following problem given a collection of rooted trees answer on line queries of the form what is the nearest common ancester of vertices x and y we show that any pointer machine that solves this problem requires omega log log n time per query in the worst case where n is the total number of vertices in the trees on the other hand we present an algorithm for a random access machine with uniform cost measure and a bound of omega log n on the number of bits per word that requires o 1 time per query and o n preprocessing time assuming that the collection of trees is static for a version of the problem in which the trees can change between queries we obtain an almost linear time and linear space algorithm

a class of deformational flow test cases for linear transport problems on the sphere a class of new benchmark deformational flow test cases for the two dimensional horizontal linear transport problems on the sphere is proposed the scalar field follows complex trajectories and undergoes severe deformation during the simulation however the flow reverses its course at half time and the scalar field returns to its initial position and shape this process makes the exact solution available at the end of the simulation and facilitates assessment of the accuracy of the underlying transport scheme a procedure to eliminate possible cancellations of errors when the flow reverses is proposed the test suite consists of four cases three are based on non divergent flow fields and one on a divergent flow the initial conditions are prescribed in terms of regular latitude longitude spherical coordinates and are easy to implement the divergent flow is specifically aimed for conservative global transport schemes to test for conservation consistency and monotonicity or positivity of limiters filters in a challenging flow environment in the context of semi lagrangian schemes the time varying flow fields can be used to test trajectory algorithms where the exact trajectories do not follow great circle arcs the characteristics of the test cases are demonstrated with two different transport schemes

hermitian approximation of the spherical divergence on the cubed sphere previous work croisille 2013 showed that the cubed sphere grid offers a suitable discrete framework for extending hermitian compact operators collatz 1960 to the spherical setup in this paper we further investigate the design of high order accurate approximations of spherical differential operators on the cubed sphere with an emphasis on the spherical divergence of a tangent vector field the basic principle of this approximation relies on evaluating pointwise hermitian derivatives along a series of great circles covering the sphere several test cases demonstrate the very good accuracy of the approximate spherical divergence calculated with the new scheme

a proof that the discrete singular convolution dsc lagrange distributed approximating function ldaf method is inferior to high order finite differences finite differences approximate the mth derivative of a function u x by a series j n nd j m u x j where the x j are the grid points the closely related discrete singular convolution dsc and lagrange distributed approximating function ldaf methods treated here as a single algorithm approximate derivatives in the same way as finite differences but with different numerical weights that depend upon a free parameter a by means of fourier analysis and error theorems we show that the dsc is worse than the standard finite differences in differentiating exp ikx for all k when a a f d where a f d 1 n 1 with n as the stencil width is the value of the dsc parameter that makes its weights most closely resemble those of finite differences for a

development of a wavenumber preserving scheme for solving maxwell s equations in curvilinear non staggered grids abstract in this paper a compact finite difference solver for solving the maxwell s equations in curvilinear coordinates is presented the scheme formulated in time domain can theoretically preserve zero divergence condition and scaled wavenumber characteristics in non staggered grids the inherent local conservation laws are also retained discretely all the time the space and time derivative terms are approximated to yield an equal fourth order spatial and temporal accuracy in irregular physical domain maxwell s equations are recast in terms of the contravariant and covariant field variables so that the developed dual preserving solver can be directly implemented in addition in curvilinear coordinates the four components in the metric tensor have been calculated under the guideline that the determinant of the transformation matrix is computed exactly through the computational exercises it is demonstrated that the newly proposed solver with a fairly small numerical scaled wavenumber error in curvilinear coordinates is computationally efficient for use to get the long time accurate maxwell s solutions in irregular physical domain

finite volume compact schemes on staggered grids compact finite difference schemes have been recently used in several direct numerical simulations of turbulent flows since they can achieve high order accuracy and high resolution without exceedingly increasing the size of the computational stencil the development of compact finite volume schemes is more revolved due to the appearance of surface and volume integrals while pereira et al j comput phys 167 2001 and smirnov et al aiaa paper 2546 2001 focused on collocated grids in this paper we use the staggered grid arrangement compact schemes can be tuned to achieve very high resolution for a given formal order of accuracy we develop and test high resolution schemes by following a procedure proposed by lele j comput phys 103 1992 which to the best of our knowledge has not yet been applied to compact finite volume methods on staggered grids results from several one and two dimensional simulations for the scalar transport and navier stokes equations are presented showing that the proposed method is capable to accurately reproduce complex steady and unsteady flows

on the use of higher order finite difference schemes on curvilinear and deforming meshes this study enables the use of very high order finite difference schemes for the solution of conservation laws on stretched curvilinear and deforming meshes to illustrate these procedures we focus on up to 6th order pade type spatial discretizations coupled with up to 10th order low pass filters these are combined with explicit and implicit time integration methods to examine wave propagation and wall bounded flows described by the navier stokes equations it is shown that without the incorporation of the filter application of the high order compact scheme to nonsmooth meshes results in spurious oscillations which inhibit their applicability inclusion of the discriminating low pass high order filter restores the advantages of high order approach even in the presence of large grid discontinuities when three dimensional curvilinear meshes are employed the use of standard metric evaluation procedures significantly degrades accuracy since freestream preservation is violated to overcome this problem a simple technique is adopted which ensures metric cancellation and thus ensures freestream preservation even on highly distorted curvilinear meshes for dynamically deforming grids an effective numerical treatment is described to evaluate expressions containing the time varying transformation metrics with these techniques metric cancellation is guaranteed regardless of the manner in which grid speeds are defined the efficacy of the new procedures is demonstrated by solving several model problems as well as by application to flow past a rapidly pitching airfoil and past a flexible panel

hyperbolic conservation laws on the sphere a geometry compatible finite volume scheme we consider entropy solutions to the initial value problem associated with scalar nonlinear hyperbolic conservation laws posed on the two dimensional sphere we propose a finite volume scheme which relies on a web like mesh made of segments of longitude and latitude lines the structure of the mesh allows for a discrete version of a natural geometric compatibility condition which arose earlier in the well posedness theory established by ben artzi and lefloch we study here several classes of flux vectors which define the conservation law under consideration they are based on prescribing a suitable vector field in the euclidean three dimensional space and then suitably projecting it on the sphere s tangent plane even when the flux vector in the ambient space is constant the corresponding flux vector is a non trivial vector field on the sphere in particular we construct here equatorial periodic solutions analogous to one dimensional periodic solutions to one dimensional conservation laws as well as a wide variety of stationary steady state solutions we also construct confined solutions which are time dependent solutions supported in an arbitrarily specified subdomain of the sphere finally representative numerical examples and test cases are presented

application of compact finite difference schemes to simulations of stably stratified fluid flows abstract this paper presents a comparison of the results of numerical simulations obtained by two different numerical methods for one specific case of stably stratified incompressible flow the focus in this paper is on the numerical results obtained using some of the compact finite difference discretizations introduced in the paper 1 the numerical scheme itself follows the principle of semi discretisation with high order compact discretisation in space while the time integration is carried out by the strong stability preserving runge kutta scheme results are compared against the reference solution obtained by the ausm finite volume method the test case used to demonstrate the capabilities of selected numerical methods represents the flow of stably stratified fluid over low smooth hill like wall mounted obstacle

chebyshev like generalized shapiro filters for high accuracy flow computations this paper presents chebyshev like generalized shapiro cs filters with improved spectral like resolution compared to existing generalized shapiro filters these new filters combine the advantages of shapiro filters i e arbitrary accuracy order no dispersion full damping of 2 waves and the advantages of chebyshev filters i e purely dissipative response function with equal ripples satisfying an arbitrary chebyshev criterion in passband thanks to the formalism of generalized shapiro filters general formulas are derived for arbitrary accuracy orders and arbitrary chebyshev criterion a python script is provided in appendix to compute cs filter coefficients computations based on the euler equations assess the benefit of cs filters compared to the standard shapiro filters since cs filters differ from shapiro filters only by their coefficients they can easily and advantageously be implemented in computational solvers already making use of generalized shapiro filters