differentiability of multivalued functions on time scales and applications to multivalued dynamic equations abstract in this paper a class of new derivatives of multivalued functions on a time scale called the hukuhara hilger derivative suited to our study of multivalued dynamic equations is developed moreover some corresponding properties of the hukuhara hilger derivative are discussed the proposed approach forms the appropriate environment within which the study of multivalued dynamic inclusions on time scales can be developed a first example of multivalued dynamic equations is included

implicit schemes and lu decompositions implicit methods for hyperbolic equations are analyzed by constructing lu factorizations it is shown that the solution of the resulting tridiagonal systems in one dimension is well conditioned if and only if the lu factors are diagonally dominant stable implicit methods that have diagonally dominant factors are constructed for hyperbolic equations in n space dimesnions only two factors are required even in three space dimensions acceleration to a steady state is analyzed when the multidimensional backward euler method is used with large time steps it is shown that the scheme approximates a newton raphson iteration procedure

three dimensional incompressible navier stokes solver using lower upper symmetric gauss seidel algorithm a numerical method based on the pseudocompressibility concept is developed for solving the three dimensional incompressible navier stokes equations using the lower upper symmetric gauss seidel implicit scheme very high efficiency is achieved in a new flow solver ins3d lu code by accomplishing the complete vectorizability of the algorithm on obiique planes of sweep in three dimensions

space time block codes from orthogonal designs we introduce space time block coding a new paradigm for communication over rayleigh fading channels using multiple transmit antennas data is encoded using a space time block code and the encoded data is split into n streams which are simultaneously transmitted using n transmit antennas the received signal at each receive antenna is a linear superposition of the n transmitted signals perturbed by noise maximum likelihood decoding is achieved in a simple way through decoupling of the signals transmitted from different antennas rather than joint detection this uses the orthogonal structure of the space time block code and gives a maximum likelihood decoding algorithm which is based only on linear processing at the receiver space time block codes are designed to achieve the maximum diversity order for a given number of transmit and receive antennas subject to the constraint of having a simple decoding algorithm the classical mathematical framework of orthogonal designs is applied to construct space time block codes it is shown that space time block codes constructed in this way only exist for few sporadic values of n subsequently a generalization of orthogonal designs is shown to provide space time block codes for both real and complex constellations for any number of transmit antennas these codes achieve the maximum possible transmission rate for any number of transmit antennas using any arbitrary real constellation such as pam for an arbitrary complex constellation such as psk and qam space time block codes are designed that achieve 1 2 of the maximum possible transmission rate for any number of transmit antennas for the specific cases of two three and four transmit antennas space time block codes are designed that achieve respectively all 3 4 and 3 4 of maximum possible transmission rate using arbitrary complex constellations the best tradeoff between the decoding delay and the number of transmit antennas is also computed and it is shown that many of the codes presented here are optimal in this sense as well

set valued functions in frechet spaces continuity hukuhara differentiability and applications to set differential equations abstract the set k c f of compact convex subsets of a frechet space f is studied in detail and is realized as a projective limit of metric spaces the notion of hausdorff metric on it is replaced by a family of corresponding semi metrics which provide the necessary background for the support of continuity and lipschitz continuity finally the notion of hukuhara derivative suited to our study is developed the proposed approach forms the appropriate environment within which the study of set differential equations for frechet spaces can be developed a first example on r is included

multigrid solution of the euler equations using implicit schemes on utilise une methode multigrille du type factorisation approchee couplee a un schema de direction alternee implicite pour resoudre les equations d euler pour l ecoulement transsonique sur un profil aerodynamique on obtient une convergence tres rapide

hukuhara differentiability of interval valued functions and interval differential equations on time scales abstract using the concept of the generalized hukuhara difference in this paper we introduce and study the differentiability and the integrability for the interval valued functions on time scales some illustrative examples to interval differential equations on time scales are presented

space time codes for high data rate wireless communication performance criteria in the presence of channel estimation errors mobility and multiple paths space time coding is a bandwidth and power efficient method of communication over fading channels that realizes the benefits of multiple transmit antennas specific codes have been constructed using design criteria derived for quasi static flat rayleigh or rician fading where channel state information is available at the receiver it is evident that the practicality of space time codes will be greatly enhanced if the derived design criteria remain valid in the absence of perfect channel state information it is even more desirable that the design criteria not be unduly sensitive to frequency selectivity and to the doppler spread this paper presents a theoretical study of these issues beginning with the effect of channel estimation error here it is assumed that a channel estimator extracts fade coefficients at the receiver and for constellations with constant energy it is proved that in the absence of ideal channel state information the design criteria for space time codes is still valid the analysis also demonstrates that standard channel estimation techniques can be used in conjunction with space time codes provided that the number of transmit antennas is small we also derive the maximum likelihood detection metric in the presence of channel estimation errors next the effect of multiple paths on the performance of space time codes is studied for a slowly changing rayleigh channel it is proved that the presence of multiple paths does not decrease the diversity order guaranteed by the design criteria used to construct the space time codes similar results hold for rapid fading channels with or without multiple paths the conclusion is that the diversity order promised by space time coding is achieved under a variety of mobility conditions and environmental effects

interconnection between set and fuzzy differential equations abstract the original formulation of fuzzy differential equations suffers from the disadvantage since the solutions increases as time increases in this paper employing the results of set differential equations obtained in v laksmikantham s leela a s vatsala setvalued hybrid differential equations and stability in terms of two measures j hybrid systems 2 2 2002 169 188 a new approach is suggested in order to capture the vagueness and the rich properties of solutions without fuzziness

application of simultaneous perturbation stochastic approximation method for aerodynamic shape design optimization aerodynamic shape design optimization problems such as inverse and constrained airfoil design and axisymmetric nozzle design are investigated by applying the simultaneous perturbation stochastic approximation spsa method to objective functions that are estimated during each design iteration using a finite volume computational fluid dynamics technique for solving the compressible navier stokes equations the spsa method has been demonstrated in the literature as having significant advantages over stochastic global optimization methods such as the simulated annealing sa method in this work the spsa is compared with sa method for a class of twodimensional and axisymmetric aerodynamic design optimization problems the numerical studies show that the spsa method is robust in reaching optimal aerodynamic shapes is easy to implement and is highly efficient the spsa method can also decrease the computational costs significantly compared with the sa method

a hybrid cartesian grid and gridless method for compressible flows a hybrid cartesian grid and gridless method is presented to compute unsteady compressible flows for complex geometries in this method a cartesian grid is used as baseline mesh to cover the computational domain while the boundary surfaces are addressed using a gridless method this hybrid method combines the efficiency of a cartesian grid method and the flexibility of a gridless method for the complex geometries the developed method is used to compute a number of test cases to validate the accuracy and efficiency of the method the numerical results obtained indicate that the use of this hybrid method leads to a significant improvement in performance over its unstructured grid counterpart for the time accurate solution of the compressible euler equations an overall speed up factor of about eight and a saving in storage requirements about one order of magnitude for a typical three dimensional problem in comparison with the unstructured grid method are demonstrated

square matrix embeddable space time block codes for complex signal constellations space time block codes for providing transmit diversity in wireless communication systems are considered based on the principles of linearity and unitarity a complete classification of linear codes is given in the case when the symbol constellations are complex and the code is based on a square matrix or restriction of such by deleting columns antennas maximal rate delay optimal codes are constructed within this category the maximal rates allowed by linearity and unitarity fall off exponentially with the number of transmit antennas

a multidimensional gas kinetic bgk scheme for hypersonic viscous flow this paper concerns the development and application of a gas kinetic scheme based on the bhatnagar gross krook bgk model for the navier stokes equations in the study of hypersonic viscous flow firstly we extend the gas kinetic navier stokes solver k xu a gas kinetic bgk scheme for the navier stokes equations and its connection with artificial dissipation and godunov method j comput phys 171 2001 289 335 by implementing a multidimensional particle propagation mechanism in the flux evaluation where the gradients of flow variables in both normal and tangential directions of a cell interface are explicitly included with the construction of a time averaged flux function an implicit bgk scheme with lu sgs method is constructed the main purpose of the current research is to pave the way to extend the current approach directly to the flow computation with unstructured mesh where the flow gradients in both parallel and perpendicular directions around a cell interface can be explicitly taken into account in a viscous flow computation in the numerical parts we concentrate on the computation of heat flux in laminar hypersonic viscous flows where complicated flow phenomena i e shock boundary layer interaction flow separation and viscous inviscid interaction will be encountered the cases studied include the type iv shock shock interaction around a circular cylinder and hypersonic flow passing through a double cone geometry in the hypersonic viscous flow in comparison with the capturing of velocity and pressure fields the accurate computation of stress and heat flux bears large difficulties in all cases studied here the heat fluxes obtained across body surfaces have good agreement with the experimental measurements

aerodynamic shape optimization using computational fluid dynamics and parallel simulated annealing algorithms aerodynamic shape design using stochastic optimization methods such as simulated annealing method to optimize objective functions evaluated by modern state of the art computational fluid dynamics solvers normally requires enormous computation time to search for the global optimal design aerodynamic shape optimization of internal flow systems is studied using euler navier stokes solvers and parallel simulated annealing algorithm which is implemented on parallel computing platforms a variety of inverse and direct design of internal flow systems are carried out to examine the efficiency and speedup of the parallel simulated annealing algorithms

stability of moving invariant sets and uncertain dynamic systems on time scales abstract in this paper we study the stability of moving invariant sets and uncertain dynamic systems on time scale a control application is considered

stability for time varying linear dynamic systems on time scales we study conditions under which the solutions of a time varying linear dynamic system of the form x t a t x t are stable on certain time scales we give sufficient conditions for various types of stability including lyapunov type stability criteria and eigenvalue conditions on slowly varying systems that ensure exponential stability finally perturbations of the unforced system are investigated and an instability criterion is also developed

almost periodicity of set valued functions and set dynamic equations on time scales in this paper we first propose the concept of the almost periodicity of set valued functions on almost periodic time scales then based on the exponential dichotomy we discuss the existence and uniqueness of almost periodic solutions of set dynamic equations on time scales as an application several examples are presented to exhibit that one can obtain the existence of almost periodic solutions to interval valued dynamic equations or fuzzy dynamic equations and their discrete counterparts in a united means

linear and non linear high order accurate residual distribution schemes for the discretization of the steady compressible navier stokes equations a robust and high order accurate residual distribution rd scheme for the discretization of the steady navier stokes equations is presented the proposed method is very flexible it is formulated for unstructured grids regardless the shape of the elements and the number of spatial dimensions a continuous approximation of the solution is adopted and standard lagrangian shape functions are used to construct the discrete space as in finite element methods the traditional technique for designing rd schemes is adopted evaluate for any element a total residual split it into nodal residuals sent to the degrees of freedom of the element solve the non linear system that has been assembled and then iterate up to convergence the main issue addressed by the paper is that the technique relies in depth on the continuity of the normal flux across the element boundaries this is no longer true since the gradient of the state solution appears in the flux hence continuity is lost when using standard finite element approximations naive solution methods lead to very poor accuracy to cope with the fact that the normal component of the gradient of the numerical solution is discontinuous across the faces of the elements a continuous approximation of the gradient of the numerical solution is recovered at each degree of freedom of the grid and then interpolated with the same shape functions used for the solution preserving the optimal accuracy of the method linear and non linear schemes are constructed and their accuracy is tested with the method of the manufactured solutions the numerical method is also used for the discretization of smooth and shocked laminar flows in two and three spatial dimensions we propose a very high order accurate methods for the approximation of the compressible navier stokes equations with residual distribution schemes the memory footprint is lower than for discontinuous galerkin like methods we show uniform accuracy for the whole range of reynolds numbers the solution technique is described in details and we show how to reach excellent convergence

novel constructions of improved square complex orthogonal designs for eight transmit antennas constructions of square maximum rate complex orthogonal space time block codes co stbcs are well known however codes constructed via the known methods include numerous zeros which impede their practical implementation by modifying the williamson and wallis whiteman arrays to apply to complex matrices we propose two methods of construction of square order 4n co stbcs from square order n codes which satisfy certain properties applying the proposed methods we construct square maximum rate order 8 co stbcs with no zeros such that the transmitted symbols are equally dispersed through transmit antennas those codes referred to as the improved square co stbcs have the advantages that the power is equally transmitted via each transmit antenna during every symbol time slot and that a lower peak to average power ratio papr is required to achieve the same bit error rates as the conventional co stbcs with zeros

upwind differencing and lu factorization for chemical non equilibrium navier stokes equations abstract an efficient and robust upwind method for solving the chemical non equilibrium navier stokes equations has been developed the method uses either the roe or van leer flux splitting for inviscid terms and central differencing for viscous terms in the explicit operator residual and the steger warming sw splitting and lower upper lu approximate factorization for the implicit operator this approach is efficient since the sw lu combination requires the inversion of only block diagonal matrices as opposed to the block tridiagonal inversion of the widely used adi method and is fully vectorizable the lu method is particularly advantageous for systems with large number of equations such as for chemical and thermal nonequilibrium flow formulas of the numerical method are presented for the finite volume discretization of the navier stokes equations in general coordinates numerical tests in hypersonic blunt body ramped duct shock wave boundary layer interaction and divergent nozzle flows demonstrate the efficiency and robustness of the present method

overrelaxation applied to lower upper symmetric gauss seidel method for hypersonic flow an implicit time marching method for acceleration of the convergence of solution for the compressible navier stokes equations is presented this is based on the lower upper symmetric gauss seidel lu sgs method proposed by yoon and jameson a very simple overrelaxation is additionally executed in the lu sgs method coupled with diagonal flux splitting then an overrelaxation parameter w a parameter similar to that in the well known successive overrelaxation method is introduced the calculated results for a hypersonic viscous flows around a cylinder and through a compression corner indicate that the convergence is accelerated by a proper value of 1 2 this method is also applied to a hypersonic thermochemical nonequilibrium flow around a sphere

aerodynamic optimization of supersonic transport wing using unstructured adjoint method in the application of gradient based methods to practical aerodynamic design problems one of the major concerns is an accurate and efficient calculation of sensitivity derivatives of an aerodynamic objective function sensitivity derivatives can be evaluated robustly and efficiently by using a sensitivity analysis code based either on a direct method or on an adjoint method an adjoint method is preferable in aerodynamic designs because it is more economical when the number of design variables is larger than the total number of an objective function and constraints

a p multigrid discontinuous galerkin method for the euler equations on unstructured grids a p multigrid p polynomial degree discontinuous galerkin method is presented for the solution of the compressible euler equations on unstructured grids the method operates on a sequence of solution approximations of different polynomial orders a distinct feature of this p multigrid method is to use different time integration schemes on different approximation levels resulting in an accurate fast and low memory method that can be used to accelerate the convergence of the euler equations to a steady state for discontinuous galerkin methods the developed method is used to compute the compressible flows for a variety of test problems on unstructured grids the numerical results obtained strongly indicate the order independent property of this p multigrid method an overall speed up factor more than one order of magnitude for both second and third order solutions of all test cases in comparison with the explicit method is demonstrated

calculus of fuzzy vector valued functions and almost periodic fuzzy vector valued functions on time scales abstract in this paper we establish an embedding theorem for the fuzzy multidimensional space and introduce the new types of multiplications of fuzzy vectors determined by the determinant algorithm then some fundamental results of calculus of fuzzy vector valued functions on time scales are established based on these results we introduce the concept of shift almost periodic fuzzy vector valued functions and develop a theory of almost periodic fuzzy functions on time scales this function theory can be used to study almost periodic fuzzy dynamic equations on time scales including a new type of fuzzy dynamic equations called fuzzy q dynamic equation i e quantum fuzzy dynamic equation

wavenumber optimized immersed boundary method for aeroacoustic analysis based on cartesian mesh an immersed boundary method ibm suitable for aeroacoustic analysis is developed using the block structured cartesian mesh method called the building cube method the ibm using a ghost cell approach in conjunction with an image point is employed a hybrid interpolation scheme combining the wavenumber based method and inverse distance weighting method is introduced to the ibm this method is evaluated using four test cases the results of interpolation at an image point indicate that the wavenumber based method provides more accurate results than standard interpolation methods for aeroacoustic problems the results of acoustic scattering around a sphere show that the proposed ibm achieves better than second order accuracy in the case of noise propagation from a generic inlet the proposed ibm is shown to yield more accurate predictions for the far field sound pressure level than the inverse distance weighting based ibm in a different application involving the jt15d nacelle the far field sound pressure

multigrid convergence of an implicit symmetric relaxation scheme the multigrid method has been applied to an existing three dimensional compressible euler solver to accelerate the convergence of the implicit symmetric relaxation scheme this lower upper symmetric gauss seidel implicit scheme is shown to be an effective multigrid driver in three dimensions a grid refinement study is performed including the effects of large cell aspect ratio meshes performance figures of the present multigrid code on cray computers including the new c90 are presented a reduction of three orders of magnitude in the residual for a three dimensional transonic inviscid flow using 920 k grid points is obtained in less than 4 min on a cray c90 23 refs

orthogonal designs with maximal rates orthogonal designs have been used as space time block codes for wireless communications with multiple transmit antennas which can achieve full transmit diversity and have a very simple decoupled maximum likelihood decoding algorithm the rate of an orthogonal design is defined as the ratio of the number of transmitted information symbols in a block of channel uses to the length of the given block which reflects the bandwidth efficiency of the employed space time block code constructed from the orthogonal design this paper focuses on the analysis and synthesis of orthogonal designs with the maximum possible rates which may be real or complex and square or rectangular matrices we first provide several representations of orthogonal designs and their characterizations in terms of hurwitz radon matrix equations next we observe that the real orthogonal designs square or rectangular and the complex square orthogonal designs with maximal rates have been well understood from the existing results in the mathematics literature which can be dated back to 1890s however unfortunately it is not the case for the complex rectangular orthogonal designs with rates as high as possible we then construct a class of complex orthogonal designs for any number of transmit antennas the proposed complex orthogonal designs for the number of transmit antennas n 2m 1 and 2m have the same rate m 1 and 2m where m is any natural number finally we demonstrate that for n 2m 1 and 2m with any given natural number m the value m 1 and 2m is the maximum possible rate that the complex orthogonal designs square or rectangular with n transmit antennas can achieve

lower upper implicit scheme for high speed inlet analysis on developpe une methode numerique d analyse du champ d ecoulement non visqueux d une entree a grande vitesse par resolution des equations d euler le schema se revele efficace et robuste aussi bien pour les faibles nombres de mach que pour les ecoulements transsoniques

novel classes of minimal delay and low papr rate 1 over 2 complex orthogonal designs complex orthogonal designs cods of rate 1 2 have been considered recently for use in analog transmissions and as an alternative to maximum rate cods due to the savings in decoding delay as the number of antennas increases while algorithms have been developed to show that an upper bound on the minimum decoding delay for rate 1 2 cods with n 2m 1 or n 2m columns is n 2m 1 or n 2m depending on the parity of n modulo 8 it remains open to determine the exact minimum delay this paper shows that this bound n is also a lower bound on minimum decoding delay for a major class of rate 1 2 cods named balanced complex orthogonal designs bcods and that this is the exact minimum decoding delay for most bcods these rate 1 2 codes are conjugation separated and thus permit a linearized description of the transceiver signal bcods also display other combinatorial properties that are expected to be useful in implementation such as having no linear processing an elegant construction is provided for a class of rate 1 2 cods that have no zero entries effectively no irrational coefficients no linear processing and have each variable appearing exactly twice per column the resulting codes meet the aforementioned bound on decoding delay in most cases this class of cods will be useful in practice due to their low peak to average power ratio papr and other desirable properties

lower upper implicit schemes with multiple grids for the euler equations on montre qu une methode de surrelaxation successive pour la resolution du schema implicite non factorise est equivalente a une forme modifiee du schema implicite inferieur superieur

lower upper symmetric gauss seidel method for the euler and navier stokes equations on developpe un schema de relaxation multigrille application a des ecoulements transsoniques

efficient real gas upwinded navier stokes computations of high speed flows an efficient method to account for the chemically frozen thermodynamic and transport properties of air in three dimensional navier stokes calculations has been demonstrated this approach uses an explicitly specified equation of state eos so that the fluid pressure temperature and transport properties are directly related to the flow variables the method is efficient since no subiterations are required to deduce the pressure and temperature from the flux variables and is modular by allowing different equations of state to be easily supplied to the code the flexibility of the eos approach is shown by its implementation into a high order total variation diminishing upwinding scheme as well as a standard central differencing scheme the eos approach is then demonstrated by computing the hypersonic flow through the corner region of two mutually perpendicular flat plates using both the upwind and central differencing schemes he capability to efficiently compute chemically frozen single stream flows using an explicitly specified equation of state eos has been added to a three dimensional navier stokes solver this flow solver is based upon the parc codes whose origin can be traced to the air2d 3d solvers by pul liam and steger 1 which used the block alternating direction implicit adi algorithm presented by beam and warming 2 to increase the computational efficiency and to reduce storage requirements pulliam3 diagonalized the block implicit opera tors of the original beam warming adi algorithm resulting in the arc2d 3d codes cooper4 further modified the arc codes to be used in a production environment for solving the propulsion oriented applications at the arnold engineering development center resulting in the parc codes coirier5 replaced the implicit operator with the lu sgs lower upper symmetric gauss seidel algorithm and demonstrated this scheme for hypersonic corner and gap seal problems this scheme is based on an lu decomposition method proposed by jameson and turkel6 and demonstrated by jameson and yoon7 for the euler equations in addition shuen and yoon8 and yu et al 9 with the rplus series of codes have shown the efficiency and robustness of this algorithm for solving the navier stokes equations fully coupled to the chemical trans port equations for computing finite rate chemically reacting flowfields for flows where the dissociation and recombination rates are much slower than the fluid residence time i e in the limit as the damkohler number approaches zero the fluid can be modeled as a mixture of inert chemically frozen gases when the converse is true i e the damkohler number approaches infinity the fluid can be modeled as if it were in chemical equilibrium if either of these limitations holds for the flow field to be considered great simplifications can be made and the resulting computational work reduced the present re search demonstrates the capability to efficiently model gen eral nonmixing chemically frozen flows using a method based on a generalized equation of state an eos for chemi cally frozen air is generated and its ease in implementation is shown for both a high order total variation diminishing tvd upwinding scheme based upon flux differencing10 and van leer s flux vector splitting11 as well as a standard central differencing scheme with added first and third difference dissi pation the upwinding scheme is then compared favorably to experimental data for the hypersonic flow through the corner region of two mutually perpendicular flat plates corner flow to demonstrate the eos a similar corner flowfield is com puted at a higher freestream stagnation enthalpy and detailed comparisons between the central difference and upwinding schemes are made for both 7 const and the chemically frozen air eos

partially implicit scheme for chemically reacting flows at all mach numbers chemical reactions make computations of chemically reacting e ows stiff the degree of stiffness increases as the mach number decreases because the e ow timescale increases while the reaction timescales remain constant thus the computation of reacting e ows at low mach numbers is more dife cult than that in high mach number in the present study a new implicit scheme that employs partially implicit treatment of chemical source terms at mixed time levels has been developed the chemical jacobian is reduced to a partial form of the full chemical jacobian a lower triangular matrix and thus saves timein matrix inversion in addition robust calculation of the reacting e ows is made possible because a negative real eigenvalue of the partial chemical jacobian allows larger time step sizes than the full chemical jacobian for applications at all mach numbers a preconditioned lower upper symmetric gauss seidel scheme employing an approximate e ux jacobian splitting is incorporated for high mach number e ows the partially implicit scheme maintains similar convergence rates to the fully implicit one therefore it enhances computational efe ciency by reducing computing time per iteration for low machnumber reacting e ows it also enables robust calculation of reactions as well as the fully implicit one however its convergence rate is rather slow furthermore more stable and efe cient computations are possible when the fully implicit scheme is coupled with the partially implicit one

implicit solution method for incompressible navier stokes equations including two layer k tau turbulence model the two dimensional incompressible navier stokes equations including a low reynolds number two layer k turbulence model are solved by an implicit time stepping routine using the method of artificial compressibility the two layer model uses a transport equation for the turbulent kinetic energy k and a new algebraic relationship for the turbulent time scale near the wall but reverts to the two equation k turbulence model in the bulk of the flow away from the wall the algebraic relationship for the turbulent time scale and the eddy viscosity damping function f are validated by direct numerical simulation data and asymptotic analysis of near wall turbulence a fifth order upwind biased differencing scheme is used to discretize the convective and pressure terms and second order central differences are employed for other spatial derivatives the nonlinear equations are solved using the preconditioned generalized minimal residual technique in conjunction with numerical linearization a ld 1 u factorization of the approximate jacobian matrix is used as preconditioning matrix

an implicit scheme for nonideal magnetohydrodynamics a new implicit algorithm is developed for solving the time dependent nonideal magnetohydrodynamic equations it can also be used as an efficient relaxation scheme for steady state solutions the algorithm is a finite volume scheme that uses an approximate riemann solver for the hyperbolic fluxes and central differencing applied on nested control volumes for the parabolic fluxes that arise from the non ideal terms i e resistivity and viscosity in one dimension the scheme is second order accurate in space and time in two or three dimensions the accuracy is between first and second order for the class of problems considered the implicit formulation is stable for any size time step thus allowing efficient tracking of slower transients the implicit operator is inverted using a lower upper symmetric gauss seidel iteration results from several test cases are presented that show good agreement with analytical solutions and illustrate the advantages of the scheme

parallelization of rotorcraft aerodynamics navier stokes codes the modie cation of unsteady three dimensional navier stokes codes for application on massively parallel and distributed computing environments is investigated previously theeulermode of thenavier stokescode turns hasbeenparallelized fortheefe cientimplementation ofthenavier stokesmodeofturns onparallelcomputing systems several algorithmic changes should be made the main modie cation is done on the implicit operator lower upper symmetric gauss seidel two new implicit operators are used because of convergence problems of traditional operators with high cell aspect ratio grids needed for viscous calculations results for navier stokes cases are presented for various operators the message passing interface protocol is used because of its portability to various parallel architectures nomenclature a speed of sound e total energy p pressure pr prandtl number re reynolds number u v w cartesian velocities x y z cartesian coordinates specie c heat ratio dynamic viscosity generalized coordinates density 9 rotor azimuth angle

complex orthogonal designs with forbidden 2 times 2 submatrices complex orthogonal designs cods are used to construct space time block codes cod oz with parameter p n k is a p n matrix where nonzero entries are filled zi by zi i 1 2 k or such that ozhoz z1 2 z2 2 zk 2 in n define oz a first type cod if and only if oz does not contain submatrix zj 0 0 zj or zj 0 0 zj it is already known that all cods with maximal rate i e maximal k p are of the first type in this paper we will determine all achievable parameters p n k of first type cod as well as all their possible structures the existence of parameters is proved by explicit form constructions new cods with parameters p n k n w 1 n w 1 n n w for 0 w n are constructed which demonstrate the possibility of sacrificing code rate to reduce decoding delay it is worth mentioning that all maximal rate minimal delay cods are contained in our constructions and their uniqueness under equivalence operation is proved

stability criteria for set dynamic equations on time scales very recently a new theory known as set dynamic equations on time scales has been built in this paper notions of stability for the solutions of set dynamic equations on time scales using lyapunov like functions are considered criteria for the equistability equiasymptotic stability uniform and uniform asymptotic stability are developed

local solution acceleration method for the euler and navier stokes equations the solution of the compressible euler and navier stokes equations via an upwind finite volume scheme is obtained for the inviscid fluxes the monotone upstream centered scheme for conservation laws muscl has been incorporated into a riemann solver the muscl scheme is used for the unfactored implicit equations that are solved by a newton form and relaxation is performed via gauss seidel relaxation technique the solution on the fine grid is obtained by iterating first on a sequence of coarser grids and then interpolating the solution up to the next refined grid since the distribution of the numerical error is nonuniform the local solution of the equations can be obtained in regions where the numerical errors are large the construction of the partial meshes in which the iterations will be continued is determined by an adaptive procedure taking into account some convergence criteria reduction of the computational work units for two dimensional problems is obtained via the local adaptive mesh solution which is expected to be more effective in three dimensional complex flow computations

convergence acceleration of a navier stokes solver for efficient static aeroelastic computations new capabilities have been developed for a navier stokes solver to perform steady state simulations more efficiently the flow solver for solving the navier stokes equations is based on a combination of the lower upper factored symmetric gauss seidel implicit method and the modified harten lax van leer einfeldt upwind scheme a numerically stable and efficient pseudo time marching method is also developed for computing steady flows over flexible wings results are demonstrated for transonic flows over rigid and flexible wings

comparison of nonequilibrium solution algorithms applied to chemically stiff hypersonic flows three solution algorithms explicit under relaxation point implicit and lower upper symmetric gauss seidel are used to compute nonequilibrium flow around the apollo 4 return capsule at the 62 km altitude point in its descent trajectory by varying the mach number the efficiency and robustness of the solution algorithms were tested for different levels of chemical stiffness the performance of the solution algorithms degraded as the mach number and stiffness of the flow increased at mach 15 and 30 the lower upper symmetric gauss seidel method produces an eight order of magnitude drop in the energy residual in one third to one half the cray c 90 computer time as compared to the point implicit and explicit under relaxation methods the explicit under relaxation algorithm experienced convergence difficulties at mach 30 and above at mach 40 the performance of the lower upper symmetric gauss seidel algorithm deteriorates to the point that it is out performed by the point implicit method the effects of the viscous terms are investigated grid dependency questions are explored

an implicit lu scheme for the euler equations applied to arbitrary cascades a new implicit scheme for solving the euler equations has been implemented and tested derivation of the scheme initially follows that of the popular alternating direction implicit scheme the principal difference between the two schemes lies in the form of the approximate factoring of the implicit operator the new scheme results in only two factors independent of the spatial dimension of the problem each factor represents an algebraic system that is either a lower l or upper u block diagonal hence the name lu inversion of such systems is relatively simple and efficient implementation of the lu scheme is in a finite volume form that permits the calculation of realistic problems by allowing the use of arbitrary grids also the conservation property of this form allows the capture of weak solutions the present application of the scheme is for flows through two dimensional cascades results are given for subsonic and transonic flows with varying degrees of geometrical complexity comparisons with other numerical and analytical solutions show good agreement execution times are compared with other methods and it is verified that the lu scheme is an attractive method for computing solutions to the euler equations i introduction a new scheme for solving the euler equations has been jfjlimplemented and tested for the problems of subsonic and transonic flow through two dimensional cascades efficiency has been the motivation for the scheme and is achieved primarily in three ways 1 the finite difference equations are in a finite volume formulation this permits the calculation of realistic problems by allowing the use of arbitrary grids these grids are usually generated numerically and can have the advantages of being boundary conforming and efficiently refined in regions of large flow gradients figure 1 shows an example of such a grid the figure also shows the periodic h type grid topology for which the code is written 2 the numerical scheme is an implicit one which remains stable as the courant number proportional to the ratio of the time step to the mesh spacing becomes arbitrarily large this allows the use of a larger time step than is permitted by an explicit method for problems that are slowly time varying or in which convergence to steady state is desired 3 numerical efficiency is achieved by the particular form of the factoring of the implicit operator proposed by jameson and turkel 1 the scheme always has two factors independent of the dimension of the problem the use of one sided difference operators in each factor results in matrices that are either lower l or upper u block diagonal hence the name lu the blocks arise because of the system of coupled differential equations and are 4x4 for twodimensional problems or 5 x 5 for three dimensional problems inversion of such systems is very simple and efficient since for each factor only a point by point sweep through the domain is required at each point the local diagonal block is inverted

the use of domain decomposition in accelerating the convergence of quasihyperbolic systems this paper proposes an alternate form of the active domain method k nakahashi and e saitoh aiaa j 35 1280 1997 that is applicable to streamwise separated flows named the marching window the algorithm consists of performing pseudo time iterations on a minimal width subdomain composed of a sequence of cross stream planes of nodes the upstream boundary of the subdomain is positioned such that all nodes upstream exhibit a residual smaller than the user specified convergence threshold the advancement of the downstream boundary follows the advancement of the upstream boundary except in zones of significant streamwise ellipticity where a streamwise ellipticity sensor ensures its continuous progress compared to the standard pseudo time marching approach the marching window decreases the work required for convergence by up to 24 times for flows with little streamwise ellipticity and by up to eight times for flows with large streamwise separated regions storage is reduced by up to six times by not allocating memory to the nodes not included in the computational subdomain the marching window satisfies the same convergence criterion as the standard pseudo time stepping methods hence resulting in the same converged solution within the tolerance of the user specified convergence threshold the algorithm is not restricted to a discretization stencil and pseudo time stepping scheme in particular and is used here with the yee roe scheme and block implicit approximate factorization solving the favre averaged navier stokes fans equations closed by the wilcox k turbulence model the eigenstructure of the fans equations is also presented

approximate factorization with source terms a comparative evaluation is made of three methodologies with a view to that which offers the best approximate factorization error while two of these methods are found to lead to more efficient algorithms in cases where factors which do not contain source terms can be diagonalized the third method used generates the lowest approximate factorization error this method may be preferred when the norms of source terms are large and transient solutions are of interest

convergence characteristics of preconditioned euler equations the convergence characteristics of the preconditioned euler equations were studied a perturbation analysis was conducted to search for the relationships between the convergence characteristics and the flow mach numbers also the influence of cancellation errors on the convergence characteristics was investigated the governing equations were the preconditioned two dimensional euler equations flows in a two dimensional channel with a 10 circular bump in the middle of the channel were calculated at different speeds roe s fds scheme was used for spatial discretization and the lu sgs lower upper symmetric gauss seidel scheme was used for time integration it was shown that the convergence characteristics of continuity and momentum equations were maintained regardless of the mach numbers but the convergence characteristics of energy equation were strongly dependant on the mach numbers and worsened as the mach number decreased the convergence characteristics were well explained by the perturbation analysis the convergence characteristics were strongly dependant on the characteristics of the preconditioning matrix cancellation errors caused a serious convergence problem especially in the calculation of the energy equation at very low mach numbers the relative treatments and a higher precision of floating point variables alleviated cancellation problems to some extent however the convergence rate was not affected by the relative treatments or by the precision of floating point variables

optimizing a boundary layer ingestion offset inlet by discrete adjoint approach a large amount of low momentum boundary layer flow ingesting into a flush mounted inlet can cause significant total pressure loss and distortion to the extent beyond operability of a fan compressor to improve the quality of incoming flow into the engine shape optimization of the surface geometry at the inlet entrance has been carried out using the discrete adjoint method the inlet floor shape is parameterized by the use of control points on b spline surface patches to resolve the complicated geometry flexibly and wall bounded turbulent flow accurately an overset mesh system is well suited for integrating the flow analysis code sensitivity analysis code and grid modification tools to enhance the convergence characteristics of the sensitivity analysis code additional numerical dissipation for the discrete adjoint formulation is introduced after using this optimization procedure the new inlet yields a significant improvement in performance a more than 50 reduction in flow distortion and a 3 increase in total pressure recovery high performance at off design conditions is also realized with only slight degradation confirming the capability of the adjoint method for a practical design problem finally the physical meaning and implication of the performance improvement are elaborated upon in relation to the flow characteristics resulting from the new design

nonlinear variation of parameters formula for set differential equations in a metric space nonlinear variation of parameters formula for set differential equations in a metric space is developed investigating necessary tools such as differentiability of solutions relative to initial values other needed results are also proven

fully implicit chebyshev time spectral method for general unsteady flows an efficient fully implicit chebyshev time spectral method tsm is developed to solve general unsteady flows with or without periodicity high accuracy of the chebyshev time spectral operator is d

on the multidimensional gas kinetic bgk scheme this paper concerns the performance difference among the multidimensional md gas kinetic bgk scheme the corresponding quasi one dimensional q1d extension and the directional splitting ds scheme with kinetic boundary conditions the md scheme includes tangential slopes in the flux calculation which are absent in a q1d or ds method in spite of taking more computational time the md scheme is found to be able to capture the characteristics of rarefied flow having a boundary with curvature or a nonuniform temperature such as the inverted velocity distribution in rarefied cylindrical couette flow and the weak flow field induced by the temperature gradient of a body where the q1d fails the md scheme can also yield clearly better results in high speed microchannel flow and power law fluid flow between concentric rotating cylinders when compared with direct simulation monte carlo studies and analytic solutions in the low reynolds number flow around a naca0012 airfoil case the md scheme and the q1d method predict wall heat flux distribution with obvious difference the ds method predicts results nearly identical to those from q1d in these steady flow cases except that it can hardly give reasonable solutions in power law fluid case with viscous exponential factor away from unity correct prediction of the stress and the wall temperature gradient is considered responsible for this better performance in simulations of the scalar convection diffusion equation it is found that the inclusion of tangential slopes in the flux computation can clearly improve the temporal accuracy of the scheme in this case the ds scheme also shows good performance the present study suggests caution in adopting of the q1d extension or ds method in multidimensional flow when it is sensitive to the accuracy of stress or wall variable gradient calculations it is better to use the md scheme for high performance simulation

a counterexample for the open problem on the minimal delays of orthogonal designs with maximal rates x liang systematically investigated orthogonal designs with maximal rates gave the maximal rates of complex orthogonal designs and a concrete construction procedure for complex orthogonal designs with the maximal rates he also posed an open problem on the minimal decoding delays of complex orthogonal designs with maximal rates and proved that the problem is correct for less than or equal to six transmit antennas in this correspondence we give a counterexample for the open problem for n 8 and prove that the minimal delay for complex orthogonal designs with eight columns is 56 hence we give a negative answer for the open problem

on the nonexistence of rate one generalized complex orthogonal designs orthogonal space time block coding proposed recently by alamouti 1998 and tarokh et al 1999 is a promising scheme for information transmission over rayleigh fading channels using multiple transmit antennas due to its favorable characteristics of having full transmit diversity and a decoupled maximum likelihood ml decoding algorithm tarokh et al extended the theory of classical orthogonal designs to the theory of generalized real or complex linear processing orthogonal designs and then applied the theory of generalized orthogonal designs to construct space time block codes stbc with the maximum possible diversity order while having a simple decoding algorithm for any given number of transmit and receive antennas it has been known that the stbc constructed in this way can achieve the maximum possible rate of one for every number of transmit antennas using any arbitrary real constellation and for two transmit antennas using any arbitrary complex constellation contrary to this in this correspondence we prove that there does not exist rate one stbc from generalized complex linear processing orthogonal designs for more than two transmit antennas using any arbitrary complex constellation

exponential stability for set dynamic equations on time scales abstract a new theory known as set dynamic equations on time scales has been built the criteria for the equistability equiasymptotic stability uniform and uniformly asymptotic stability were developed in hong 2010 1 in this paper we consider the exponential stability exponentially asymptotic stability uniform and uniformly exponentially asymptotic stability for the trivial solution of set dynamic equations on time scales by using lyapunov like functions

simulation of vortex breakdown using adaptive grid refinement with vortex center identification a topological feature adaptation method is proposed to compute vortical flows around a delta wing at high incidence vortex center identification based on the locally applied critical point method is utilized as an indicator of the grid refinement using rivara s bisection algorithm the three dimensional navier stokes equations are solved using the hybrid unstructured grid the computed results show that the refinement at the vortex core is effective to improve the numerical accuracy of the flow around a delta wing the present feature adaptive refinement is especially effective to improve the prediction of the vortex breakdown positions at high incidence

on modified block ssor iteration methods for linear systems from steady incompressible viscous flow problems abstract in order to solve the large sparse systems of linear equations arising from numerical solutions of two dimensional steady incompressible viscous flow problems in primitive variable formulation we present block ssor and modified block ssor iteration methods based on the special structures of the coefficient matrices in each step of the block ssor iteration we employ the block lu factorization to solve the sub systems of linear equations we show that the block lu factorization is existent and stable when the coefficient matrices are block diagonally dominant of type ii by columns under suitable conditions we establish convergence theorems for both block ssor and modified block ssor iteration methods in addition the block ssor iteration and af adi method are considered as preconditioners for the nonsymmetric systems of linear equations numerical experiments show that both block ssor and modified block ssor iterations are feasible iterative solvers and they are also effective for preconditioning krylov subspace methods such as gmres and bicgstab when used to solve this class of systems of linear equations

the monotone iterative technique for impulsive hybrid set valued integro differential equations abstract we develop the monotone method for impulsive hybrid set integro differential equations in all its generality some interesting observations are presented

stability criteria for set control differential equations abstract the existence and comparison results on solutions of set control differential equation were studied in n d phu t t tung some results on sheaf solutions of sheaf set control problems nonlinear analysis 67 2007 1309 1315 in this paper we present the stability criteria for solutions of set control differential equation

on green s functions and positive solutions for boundary value problems on time scales in this paper we offer a form of self adjoint differential equations on time scales so that the associated green s function is found symmetric in the usual sense for this purpose together with the delta derivative we employ the nabla derivative as well we introduce the concepts of lebesgue delta and nabla integrals on time scales next sign properties of the green s function are investigated and existence results for positive solutions of nonlinear boundary value problems are established upper and lower bounds for these positive solutions also are given

phase spaces and periodic solutions of set functional dynamic equations with infinite delay abstract very recently a new theory known as set dynamic equations on time scales has been built in this paper a phase space is built for set functional dynamic equations with infinite delay on time scales and sufficient criteria are established for the existence of periodic solutions of such equations which generalize and incorporate as special cases some known results for set differential equations and for set difference equations when the time scale is the real number set or the integer set respectively moreover for differential inclusions and difference inclusions if the variable under consideration is a single valued mapping our results show that one can unify the study of some continuous or discrete problems in the sense of set dynamic equations on general time scales

analysis and prediction of thin airfoil stall phenomena with hybrid turbulence methodology analysis and prediction of thin airfoil stall phenomena of a naca 64a006 airfoil are numerically investigated using large eddy simulation les reynolds averaged navier stokes rans hybrid methodology with a high order compact differencing scheme subsonic flow of m 0 17 with the high reynolds number of re 5 8 x 10 6 is considered and the angle of attack is varied from 4 0 to 11 0 deg

a reconstructed discontinuous galerkin method for incompressible flows on arbitrary grids abstract the discontinuous galerkin dg methods have attained increasing popularity for solving the incompressible navier stokes ins equations in recent years however the dg methods have their own weakness due to the high computational costs and storage requirements in this work we develop a high order hybrid reconstructed dg rdg method for solving the ins equations on arbitrary grids to be specific the inviscid term of the ins equations is discretized by applying the third order hybrid rdg p 1 p 2 method with a simplified artificial compressibility flux while the viscous term of the ins equations is discretized by using the simple direct dg ddg method a number of incompressible flow problems in both steady and unsteady forms for a variety flow conditions are computed to numerically assess the performance of the hybrid rdg p 1 p 2 method which confirm its ability to achieve the optimal third order of accuracy at a significantly reduced computational costs furthermore a detailed comparison of a variety of different reconstructed strategies is performed and presented numerical results demonstrate that the hybrid rdg p 1 p 2 method outperforms the rdg p 1 p 2 method based on either the original least squares reconstruction or the green gauss reconstruction for solving the ins equations

parallel processing scheme for the navier stokes equations part 2 parallel implementation parallel performance of two implicit schemes for solving the compressible navier stokes equations on two parallel computational platforms using the standard portable message passing interface is studied these two schemes are a lower upper cycle independent scheme developed by the authors and the symmetric successive overrelaxation scheme representative of cycle dependent schemes the parallel computational platforms used here are the lewis advanced cluster environment which is an example of a network of workstations and the ohio supercomputer cray t3d massive parallel computing environment two versions of the lower upper cycleindependent scheme are studied version i where one processor per block is used and version ii where two processors per block are used however only version i is possible with the symmetric successive overrelaxation scheme thecompetitivenessoftheworkstationclustertothecrayt3disdemonstrated moreover parallelperformance results indicate that version i of the lower upper cycle independent scheme is superior to version ii in the range of a moderate number of processors however in the future as the number of processors increases and the communication cost decreases this scheme will provide a means for using larger computational power relative to version i that would otherwise be idle

implicit boundary equations for conservative navier stokes equations abstract co existence of the physical and numerical boundary conditions makes implicit boundary treatment a particularly difficult problem in modern cfd simulations previous studies adopted space time extrapolation or specially designed partial differential equations on the boundaries that are different from those of interior points they are often formulated in terms of primitive variables and are very challenging for complicated boundary types to be converted to and implemented in the conservative variables that are preferred in numerical simulations more importantly different boundary equations or different extrapolation techniques may compromise the stability accuracy or convergence rate of the a stable schemes that are developed for interior points a new methodology for implicit boundary treatment is proposed in this study by introducing a simple correction matrix t a set of generalized equations q t i t r are developed in terms of conservative variables it is applicable for both the interior domain t 0 and the boundaries t 0 it is in a partial differential equation form satisfies the boundary conditions accurately independent of the time and spatial discretizations any one sided schemes can be used on the boundaries but still maintain the upwind property implicit solution techniques are made significantly easy to implement using for example the data parallel lower upper relation method and the newton method combined with the gmres method for subsidiary iterations numerical experiments show that the proposed methodology produces stable simulations for very large cfl numbers and preserve the imposed boundary values accurately

implicit unified gas kinetic scheme for steady state solutions in all flow regimes this paper presents an implicit unified gas kinetic scheme ugks for non equilibrium steady state flow computation the ugks is a direct modeling method for flow simulation in all regimes with the updates of both macroscopic flow variables and microscopic gas distribution function by solving the macroscopic equations implicitly a predicted equilibrium state can be obtained first through iterations with the newly predicted equilibrium state the evolution equation of the gas distribution function and the corresponding collision term can be discretized in a fully implicit way for fast convergence through iterations as well the lower upper symmetric gauss seidel lu sgs factorization method is implemented to solve both macroscopic and microscopic equations which improves the efficiency of the scheme since the ugks is a direct modeling method and its physical solution depends on the mesh resolution and the local time step a physical time step needs to be fixed before using an implicit iterative technique with a pseudo time marching step therefore the physical time step in the current implicit scheme is determined by the same way as that in the explicit ugks for capturing the physical solution in all flow regimes but the convergence to a steady state speeds up through the adoption of a numerical time step with large cfl number many numerical test cases in different flow regimes from low speed to hypersonic ones such as the couette flow cavity flow and the flow passing over a cylinder are computed to validate the current implicit method the overall efficiency of the implicit ugks can be improved by one or two orders of magnitude in comparison with the explicit one

an accelerated fully coupled parallel 3d hybrid finite volume fluid structure interaction scheme abstract in this paper we propose a fast parallel 3d fully coupled partitioned hybrid unstructured finite volume fluid structure interaction fsi scheme spatial discretisation is effected via a vertex centred finite volume method where a hybrid nodal elemental strain procedure is employed for the solid in the interest of accuracy for the incompressible fluid a split step algorithm is presented which allows the entire fluid solid system to be solved in a fully implicit yet matrix free manner the algorithm combines a preconditioned gmres solver for implicit integration of pressures with dual timestepping on the momentum equations thereby allowing strong coupling of the system to occur through the inner solver iterations further acceleration is provided at little additional cost by applying lu sgs relaxation to the viscous and advective terms the solver is parallelised for distributed memory systems using mpi and its scaling efficiency evaluated the developed modelling technology is evaluated by application to two 3d fsi problems the advanced matrix free solvers achieve reductions in overall cpu time of up to 50 times while preserving close to linear parallel computing scaling using up to 128 cpus for the problems considered

the development of a free surface capturing approach for multidimensional free surface flows in closed containers a new surface capturing method is developed for numerically simulating viscous free surface flows in partially filled containers the method is based on the idea that the flow of two immiscible fluids within a closed container is governed by the equations of motion for an incompressible viscous nonhomogeneous variable density fluid by computing the flow fields in both the liquid and gas regions in a consistent manner the free surface can be captured as a discontinuity in the density field thereby eliminating the need for special free surface tracking procedures the numerical algorithm is developed using a conservative implicit finite volume discretization of the equations of motion the algorithm incorporates the artificial compressibility method in conjunction with a dual time stepping strategy to maintain a divergence free velocity field a slope limited high order muscl scheme is adopted for approximating the inviscid flux terms while the viscous fluxes are centrally differenced the capabilities of the surface capturing method are demonstrated by calculating solutions to several two and three dimensional problems

decoupled implicit method for aerothermodynamics and reacting flows we propose a new implicit computational fluid dynamics method for steady state compressible reacting flows the concept is to decouple the total mass momentum and energy conservation equations from the species mass and internal energy equations and to solve the two equation sets sequentially with certain approximations to the implicit system it is possible to dramatically reduce the cost of the solution with little to no penalty on the convergence properties importantly the cost of the decoupled implicit problem scales linearly with the number of species as opposed to the quadratic scaling for the conventional fully coupled method furthermore the new approach reduces the memory requirements by a significant factor the decoupled implicit method shows promise for the application to aerothermodynamics problems and reacting flows

implicit navier stokes solver for three dimensional compressible flows a three dimensional numerical method based on the lower upper symmetric gauss seidel implicit scheme in conjunction with the flux limited dissipation model is developed for solving the compressible navier stokes equations a new computer code based on this method requires only 9 s per grid point per iteration on a single processor of a cray ymp computer and executes at the sustained rate of 175 mflops a reduction of three orders of magnitude in the residual for a high reynolds number flow using 636k grid points is obtained in 38 min

stability of set differential equations and applications abstract the paper introduces some results on stability of sheaf solutions exponential stability of solutions and sheaf solutions of set differential equations and their applications to set control differential equations

on preconditioned iterative methods for unsteady incompressible navier stokes equations when the implicit finite difference scheme and linearization technique in conjunction with the artificial compressibility method are employed to discretize the unsteady incompressible navier stokes equations in each pseudo time step a structured system of linear equations is obtained and needs to be solved numerically in this paper preconditioning techniques are applied to solve such linear systems numerical example is given to illustrate the effectiveness of the proposed method we also find that a combination of the linearization technique with the preconditioned gmres method is quite efficient for the implicit finite difference discretization of the incompressible navier stokes equations

data parallel line relaxation method for the navier stokes equations the gauss seidel line relaxation method is modie ed for the simulation of viscous e ows on massively parallel computers the resulting data parallel line relaxation method is shown to have good convergence properties for a seriesoftestcases thenewmethodrequiressignie cantlymorememorythanthepreviouslydevelopeddata parallel relaxation methods but it reaches a steady state solution in much less time for all cases tested to date in addition the data parallel line relaxation method shows good convergence properties even on the high cell aspect ratio grids required to simulate high reynolds number e ows the new method is implemented using message passing on the cray t3e and the parallel performance of the method on this machine is discussed the data parallel line relaxation method combines the fast convergence of the gauss seidel line relaxation method with a high parallel efe ciency and thus shows promise for large scale simulation of viscous e ows

dynamics and stability of impulsive hybrid setvalued integro differential equations with delay abstract we study the dynamics and stability theory for impulsive hybrid set integro differential equations with delay sufficient conditions for the stability of the null solution of impulsive hybrid set integro differential equations with delay are presented

implicit treatment of diffusion terms in lower upper algorithms a method is presented which allows diffusion terms to be treated implicitly in the lower upper lu algorithm which is a commonly used method for solving compressible euler and navier stokes equations so that the algorithm s good stability properties will not be impaired the new method generalizes the concept of lu factorization from that associated with the sign of eigenvalues to that associated with backward and forward difference operators without regard to eigenvalues the method is verified in a turbulent boundary layer study

the theory of quaternion orthogonal designs over the past several years there has been a renewed interest in complex orthogonal designs for their application in space time block coding motivated by the success of this application this paper generalizes the definition of complex orthogonal designs by introducing orthogonal designs over the quaternion domain this paper builds a theory of these novel quaternion orthogonal designs offers examples and provides several construction techniques these theoretical results along with the results of preliminary simulations lay the foundation for developing applications of these designs as orthogonal space time polarization block codes

geometric multigrid with applications to computational fluid dynamics an overview is given of the development of the geometric multigrid method with emphasis on applications in computational fluid dynamics over the last ten years both compressible and incompressible flow problems and their corresponding multigrid solution methods are discussed the state of the art is described with respect to methods employed in industry as well as the multigrid efficiency obtained in academic applications

set differential equations versus fuzzy differential equations the study of fuzzy differential equations fdes forms a suitable setting for a mathematical modeling of real world problems in which uncertainties or vagueness pervades in recent years the theory of fdes has been investigated extensively in the original formulation as well as in an alternative framework which leads to ordinary multivalued differential inclusions it has recently been realized that initiating the study of set differential equations in a metric space has several advantages in addition to providing a natural setting for considering fdes in this paper we present some interesting results in this direction with the necessary background material