fixed points and approximate solutions for nonlinear operator equations we study a nonlinear operator equation and obtain a sequence of approximate solutions by extending the monotone iterative technique to new situations some examples and applications are presented

importance of convection and damping on rates of convergence for the lax wendroff method it is well known that in solving steady state problems using hyperbolic time stepping methods the intent is to drive the transients to zero as quickly as possible in this paper the convergence to steady state of the lax wendroff method applied to solving the equations of gas dynamics is analyzed for the laval nozzle problem by comparing the relative rates of damping and convection using a linearized eigenmode analysis this analysis is developed for the simpler isenthalpic system and then extended to the full euler equations finally this allows a comparison between these systems for both models useful analytical information can be gleaned about the transient behavior of these systems especially in regard to quantifying the competitive factors affecting the removal of unsteady waves

an unstructured finite elements method for solving the compressible rans equations and the spalart allmaras turbulence model this paper deals with a stabilized finite element method for solving the compressible navier stokes equations combined with the spalart allmaras turbulence model the aim is to assess the ability of this formulation to solve high reynolds number turbulent flows over anisotropic meshes this formulation lies in the framework of the stream line upwind petrove galerkin method we propose a simple and efficient formulation for the stabilization matrix and develop a shock capturing operator numerical tests on the 3d boundary layer over a flat plate and on the onera m6 wing show the stability and robustness of the proposed method

periodic boundary value problems for a class of functional differential equations in this paper we show that the method of upper and lower solutions coupled with the monotone iterative technique is valid to obtain constructive proofs of existence of solutions for nonlinear periodic boundary value problems of functional differential equations without assuming properties of monotonicity in the nonlinear part

multigrid solution of the two dimensional euler equations on unstructured triangular meshes a multigrid algorithm has been developed to accelerate the convergence of the euler equations to a steady state on unstructured triangular meshes the method operates on a sequence of coarse and fine unstructured meshes and assumes no relation exists between the various meshes a tree search algorithm is used to efficiently identify regions of overlap between coarse and fine grid cells the multigrid method is applied to two different discretizations of the euler equations and results about multi element airfoils are presented for both discretization schemes convergence is accelerated by an order of magnitude resulting in convergence rates comparable to those obtained with structured multigrid algorithms

implicit second order cusp gridless method for unsteady moving boundary simulations efficient first order and second order gridless method is presented for calculation of unsteady compressible flows the convective upwind split pressure cusp gridless scheme is applied for solving unsteady fluid flow equations in the arbitrary lagrangianeulerian ale formulation in order to manage dynamic cloud and nodes movement the nodes are moved based on the boundary movements using the segment spring analogy discretization of spatial derivatives are done by using the taylor series least squares at each node for increasing the accuracy second order taylor series sots expansion is also used on the cusp gridless method for time advancement implicit dual time and explicit schemes are used the accuracy of the methods is compared with the agard experimental data and finite volume results for some test cases in steady and unsteady flows results show that the cusp gridless scheme is accurate in steady and unsteady flows and using the second order discretization increases the accuracy a little bit and also the gridless schemes reduce the computational time as compared with finite volume method numerical results are in good agreement with the experimental data

implicit flux split euler schemes for unsteady aerodynamic analysis involving unstructured dynamic meshes improved algorithms for the solution of the time dependent euler equations are presented for unsteady aerodynamic analysis involving unstructured dynamic meshes the improvements have been developed recently to the spatial and temporal discretizations used by unstructured grid flow solvers the spatial discretization involves a flux split approach which is naturally dissipative and captures shock waves sharply with at most one grid point within the shock structure the temporal discretization involves an implicit time integration shceme using a gauss seidel relaxation procedure which is computationally efficient for either steady or unsteady flow problems for example very large time steps may be used for rapid convergence to steady state and the step size for unsteady cases may be selected for temporal accuracy rather than for numerical stability steady and unsteady flow results are presented for the naca 0012 airfoil to demonstrate applications of the new euler solvers the unsteady results were obtained for the airfoil pitching harmonically about the quarter chord the resulting instantaneous pressure distributions and lift and moment coefficients during a cycle of motion compare well with experimental data the paper presents a description of the euler solvers along with results and comparisons which assess the capability

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

dynamic hebbian learning in adaptive frequency oscillators nonlinear oscillators are widely used in biology physics and engineering for modeling and control they are interesting because of their synchronization properties when coupled to other dynamical systems in this paper we propose a learning rule for oscillators which adapts their frequency to the frequency of any periodic or pseudo periodic input signal learning is done in a dynamic way it is part of the dynamical system and not an offline process an interesting property of our model is that it is easily generalizable to a large class of oscillators from phase oscillators to relaxation oscillators and strange attractors with a generic learning rule one major feature of our learning rule is that the oscillators constructed can adapt their frequency without any signal processing or the need to specify a time window or similar free parameters all the processing is embedded in the dynamics of the adaptive oscillator the convergence of the learning is proved for the hopf oscillator then numerical experiments are carried out to explore the learning capabilities of the system finally we generalize the learning rule to non harmonic oscillators like relaxation oscillators and strange attractors

periodic boundary value problem for first order impulsive functional differential equations this paper discusses the periodic boundary value problem for a class of first order impulsive functional differential equations we establish several existence results under weaker hypotheses by using the leray schauder alternative the lower and upper solution method and the monotone iterative technique the corresponding results in the literature are improved or extended some examples are also given to illustrate the advantage of the results

implicit fully mesh less method for compressible viscous flow calculations a dual time implicit mesh less scheme is developed for solution of governing viscous flow equations the computational efficiency of the method is enhanced by adopting accelerating techniques such as local time stepping and residual smoothing the taylor series least square method is used for approximation of derivatives at each node which leads to a central difference spatial discretization the capabilities of the method are demonstrated by flow computations about standard cases at subsonic and transonic laminar flow conditions results are presented which indicate good agreements with the alternative numerical and experimental data the computational time is considerably reduced when using the proposed mesh less method compared with the explicit mesh less and finite volume counterparts using the same distribution of points

high order flux correction finite difference schemes for strand grids a novel high order method combining unstructured flux correction along body surfaces and high order finite differences normal to surfaces is formulated for unsteady viscous flows on strand grids the flux correction algorithm is applied in each unstructured layer of the strand grid and the layers are then coupled together via a source term containing derivatives in the strand direction strand direction derivatives are approximated to high order via summation by parts operators for first derivatives and second derivatives with variable coefficients we show how this procedure allows for the proper truncation error canceling properties required for the flux correction scheme the resulting scheme possesses third order design accuracy but often exhibits fourth order accuracy when higher order derivatives are employed in the strand direction especially for highly viscous flows we prove discrete conservation for the new scheme and time stability in the absence of the flux correction terms results in two dimensions are presented that demonstrate improvements in accuracy with minimal computational and algorithmic overhead over traditional second order algorithms

further results on periodic boundary value problems for nonlinear first order impulsive functional differential equations abstract this paper is concerned with the solvability of periodic boundary value problems for nonlinear impulsive functional differential equations x t a t x t f t x t x 1 t x n t t j t 1 t p x t k x t k i k x t k k 1 2 p x 0 x t we obtain sufficient conditions for the existence of at least one solution of problem at resonance and nonresonance cases respectively examples are presented to illustrate the main results

implicit multiple grid solution of the compressible navier stokes equations using k epsilon turbulence closure in the present work an algorithm for the numerical solution of the two dimensional mass weighted ensemble averaged compressible navier stokes equations is presented turbulence closure for the reynolds stresses is obtained using a low reynolds n umber two equation k s model which includes near wall effects the same algorithm is used for the integration of both the navier stokes and the turbulence transport equations the algorithm consists of a basic explicit finite volume scheme whose convergence is accelerated using local time step ping and multiple grid techniques convergence is further enhanced by the use of an implicit residual smoothing technique applied both in the fine and the coarser grids the application of the numerical scheme to the solution of the k s equations is examined in detail comparisons of computations with experimental data are presented for three shock wave turbulent boundary layer interaction flows algorithm convergence rate and cpu time require ments are discussed he numerical solution of the navier stokes equations for the simulation of turbulent flowfields is a subject of intense research and code development work 1 interest is focused both on code applicability to variegated config urations and on computational rapidity although direct simulation of turbulent flows2 or large eddy numerical sim ulations using subgrid turbulence modeling 3 4 have appeared in the literature current status of algorithm development and computer power indicate that for practical applications the ensemble averaged navier stokes equations should be used in conjunction with transport equations for turbulence closure 5 7 algebraic or mixing length models may provide satisfactory results for relatively simple flow geometries8 but require the determination of the shear layer thickness and of the distance of each grid point from the solid boundary thus they lack both geometric invariance and locality which are highly desirable properties from a computational viewpoint when addressing complex flowfields with many interacting solid boundaries although research on reynolds stre ss transport closure appears quite promising 9 10 its extension to three dimensions involves considerable increase of the number of transport equations to be solved also further research con cerning wall effects is required the more so since the use of wall functions is considered inadequate 11 on the other hand the use of two equation closures such as a 12 14 is quite widespread notwithstanding the fact that the use of the boussinesq hypothesis15 introduces a question able simplification of the flow physics 16 the major drawback of the k s model is probably the near wall formulation which fails to reproduce correctly the effects of the solid boundary on turbulence several variants of the original jones launder model12 have been developed in an attempt to improve upon near wall modeling some ten such models have been thor oughly examined in a critical review article by patel et al 17 who concluded that the models of launder and sharma 14

solution of the euler equations for two dimensional transonic flow by a multigrid method the assumption of potential o w implies that the o w is irrotational this is not strictly correct when shock waves are present an exact description of transonic inviscid o w requires the solution of the euler equations the numerical solution of the euler equations for steady transonic o ws is therefore a problem of great interest to the aeronautical community it also presents a testing challenge to applied mathematicians and numerical analysts

locally implicit total variation diminishing schemes on unstructuredtriangular meshes a numerical solution procedure that includes locally implicit total variation diminishing schemes and adaptive mesh generation techniques has been developed in this work in a cartesian coordinate system the euler equations are solved by using a cell centered finite volume algorithm a new construction of symmetric total variation diminishing schemes on unstructured triangular meshes is presented the validation of the present solution adaptive methods is confirmed by comparison with related numerical results for inviscid flows around an isolated naca 0012 airfoil and passing through a channel with a circular arc bump in transonic and supersonic flow regimes to further prove the feasibility of this approach a two element airfoil flow is also investigated furthermore one unsteady transonic channel flow is studied to demonstrate the reliability and capability of the present solution procedure for a time accurate calculation

asymptotic stability of competitive systems with delays and impulsive perturbations abstract a general impulsive nonautonomous lotka volterra system of integro differential equations with infinite delay is considered the impulses are realized at fixed moments of time sufficient conditions for uniform stability and asymptotic stability of solutions are investigated the main results are obtained by using the comparison principle and the lyapunov method

an hourglass control algorithm for lagrangian smooth particle hydrodynamics abstract this paper presents a stabilization scheme which addresses the rank deficiency problem in meshless collocation methods for solid mechanics specifically smooth particle hydrodynamics sph in the total lagrangian formalism is considered this method is rank deficient in the sense that the sph approximation of the deformation gradient is not unique with respect to the positions of the integration points the non uniqueness can result in the formation of zero energy modes if undetected these modes can grow and completely dominate the solution here an algorithm is introduced which effectively suppresses these modes in a fashion similar to hour glass control mechanisms in finite element methods simulations utilizing this control algorithm exhibit much improved stability accuracy and error convergence properties in contrast to an alternative method which eliminates zero energy modes namely the use of additional integration points the here presented algorithm is easy to implement and computationally very efficient

oscillatory associative memory network with perfect retrieval abstract inspired by the discovery of possible roles of synchronization of oscillations in the brain networks of coupled phase oscillators have been proposed before as models of associative memory based on the concept of temporal coding of information here we show however that error free retrieval states of such networks turn out to be typically unstable regardless of the network size in contrast to the classical hopfield model we propose a remedy for this undesirable property and provide a systematic study of the improved model in particular we show that the error free capacity of the network is at least 2 e 2 log n patterns per neuron where n is the number of oscillators neurons and e the strength of the second order mode in the coupling function

unsteady transonic two dimensional euler solutions using finite elements a finite element solution of the unsteady euler equations is presented and demonstrated for two dimensional airfoil configurations oscillating in transonic flows computations are performed by spatially discretizing the conservation equations using the galerkin weighted residual method and then employing a multistage rungekutta scheme to march forward in time triangular finite elements are employed in an unstructured o mesh computational grid surrounding the airfoil grid points are fixed in space at the far field boundary and are constrained to move with the airfoil surface to form the near field boundary a mesh deformation scheme has been developed to efficiently move interior points in a smooth fashion as the airfoil undergoes rigid body pitch and plunge motion both steady and unsteady results are presented and a comparison is made with solutions obtained using finite volume techniques the effects of using either a lumped or consistent mass matrix were studied and are presented results show the finite element method provides an accurate solution for unsteady transonic flows about isolated airfoils he accurate determination of the unsteady flowfield surrounding an oscillating airfoil or wing in transonic flow is of paramount importance in the prediction of the flutter characteristics of the body transonic flutter remains an active research topic because of the continued interest by both the military and commercial sectors to operate in these flight regimes with vehicles that are ever lighter and as a result more flexible typically analysis of fluid structure interaction in flight vehicles involves describing the vehicle structure using finite elements whereas finite difference methods are used to model the surrounding fluid coupling of the two dissimilar models then presents problems because of the disparity between the two solution techniques additional complexities arise because of phase mismatching between the fluid pressures and the displacements of the structure it seems a natural progression to use finite element methods to describe the behavior of both the fluid and structure thus bringing more commonality into the analysis of the two media early research efforts concentrated on using the transonic small disturbance equation or the nonlinear full potential equation as the model for the gas dynamic behavior in transonic flows unfortunately this idealization leads to errors when strong shocks are present because of their inability to account for the production of entropy and vorticity to properly account for these effects within the framework of the conservation laws the euler equations must be used these equations although they neglect fluid viscosity have become the standard when unsteady transonic solutions are desired the absence of a viscosity representation is an important limitation of the present formulation and must be considered

euler solution using cartesian grid with a gridless least squares boundary treatment an approach that uses gridless or meshless methods to address the problem of boundary implementation associated with the use of cartesian grid is discussed this method applies the gridless concept only at the interface whereas a standard structured grid method is used everywhere else the cartesian grid is used to specify and distribute the computational points on the boundary surface but not to define the geometrical properties euler fluxes for the neighbors of cut cells are computed using the gridless method involving a local least squares curve fit of a cloud of grid points the boundary conditions implemented on the surface points are automatically satisfied in the process of evaluating the surface values in a similar least squares fashion the present method does not require the use of halo points subsonic transonic and supersonic flows are computed for the naca 0012 and rae 2822 airfoils and the results compare well with solutions obtained by a standard euler solver on body fitted grids the method is also used to calculate the flow over a three element airfoil configuration and the result is compared with the exact solution for this configuration obtained by conformal mapping

periodic boundary value problem for first order impulsive functional differential equations in this paper by means of the method of upper and lower solutions and the monotone iterative technique the existence of minimal and maximal solutions of the periodic boundary value problem for first order impulsive functional differential equations is considered

nonlinear boundary problem of first order impulsive integro differential equations this paper focuses on first order impulsive integro differential equations with nonlinear boundary the lower and upper solutions combined with monotone iterative techniques are used to obtain the existence of extremal solutions of the problem numerical examples are given to prove its validity

a general family of morphed nonlinear phase oscillators with arbitrary limit cycle shape we present a general family of nonlinear phase oscillators which can exhibit arbitrary limit cycle shapes and infinitely large basins of attraction this general family is the superset of familiar control methods like pd control over a periodic reference and rhythmic dynamical movement primitives the general methodology is based on morphing the limit cycle of an existing phase oscillator with phase based scaling functions to obtain a desired limit cycle behavior the introduced methodology can be represented as first second or n th order dynamical systems the elegance of the formulation provides the possibility to define explicit arbitrary convergence behavior for simple cases we analyze the stability properties of the methodology with the poincare bendixson theorem and the contraction theory and use numerical simulations to show the properties of some oscillators that are a subset of this general family c 2013 elsevier b v all rights reserved

hebbian learning and spiking neurons a correlation based hebbian learning rule at a spike level with millisecond resolution is formulated mathematically analyzed and compared with learning in a firing rate description the relative timing of presynaptic and postsynaptic spikes influences synaptic weights via an asymmetric learning window a differential equation for the learning dynamics is derived under the assumption that the time scales of learning and neuronal spike dynamics can be separated the differential equation is solved for a poissonian neuron model with stochastic spike arrival it is shown that correlations between input and output spikes tend to stabilize structure formation with an appropriate choice of parameters learning leads to an intrinsic normalization of the average weight and the output firing rate noise generates diffusion like spreading of synaptic weights s1063 651x 99 02804 4

a numerical study of the arc roof and the one sided roof enclosures based on the entropy generation minimization this paper describes an enhanced finite volume method for solving the arc roof and the one sided roof enclosures enclosures were assumed like two dimensional cavities with the natural convection of air inside them various boundary conditions such as the greenhouse boundary conditions were considered in order to estimate exergy destruction inside enclosures the volumetric entropy generation in flow due to the heat transfer and the fluid friction was calculated using an enhanced scheme for finding the first derivative terms in provided fortran code an explicit fourth order runge kutta integration algorithm was applied to find the steady state solutions next the results were evaluated with other cited works also performance of the one sided roof enclosure was compared with the performance of the arc roof enclosure based on their exergy destruction results showed that the entropy generation into the one sided roof type is less than the other

compact higher order characteristic based euler solver for unstructured grids two new methods are presented for solving the euler equations using a compact higher order polynomial reconstruction technique on unstructured grids the methods use a characteristic based approach with a cell centered finite volume method for transonic ringleb flow computations are performed for first order to fourth order accuracy and are compared with the hodograph solution results for a 10 deg ramp case are also presented an analysis is performed that demonstrates that the higher order method is an order of magnitude more efficient than the lower order method in modeling the flow for moderate to fine error tolerances accuracy speed and memory requirements are evaluated in the efficiency study compact higher order polynomial reconstruction technique is developed that allows for higher order char acteristic based numerical solutions to the euler equations on unstructured grids this reconstruction requires an extended set of euler equations that includes as dependent variables not only mass momentum and energy but also their spatial derivatives these additional dependent variables are used in a compact polynomial reconstruction process within a finite volume framework the development presented follows some of the ideas in the computational fluid dynamics cfd litera ture using continuous and discontinuous piecewise polynomial approximations continuous piecewise linear polynomials have been used in several finite volume and finite element unstructured grid methods jameson and mavriplis 1 lohner et al 2 and others have developed continuous piecewise linear elements using an added artificial dissipation and or flux corrected transport terms more recently oden3 has extended the linear elements by the use of higher order elements oden s work represents a compact higher order approximation of the continuous ele ment type discontinuous piecewise linear polynomials have similarly been used on unstructured grids with a characteristic based approach thareja et al 4 batina 5 frink 6 and others have developed discontinuous piecewise linear schemes with ap proximate riemann solvers on unstructured grids earth and frederickson7 developed a technique where polynomials of degree k are reconstructed for each cell by maintaining aver age dependent variable properties over a neighboring set of cells in a least squares formulation these polynomials are reconstructed using a large number of neighboring cells there fore the representation is not compact this paper describes two methods that compactly reconstruct higher order polyno mials over each cell in a discontinuous piecewise polynomial procedure two methods are presented for extending the euler equa tion set the first method solves the spatial derivatives of the governing integral equations the second method follows the work of allmaras 8 where the spatial moments of the govern ing equations are solved allmaras developed an approach

frequency analysis with coupled nonlinear oscillators we present a method to obtain the frequency spectrum of a signal with a nonlinear dynamical system the dynamical system is composed of a pool of adaptive frequency oscillators with negative mean field coupling for the frequency analysis the synchronization and adaptation properties of the component oscillators are exploited the frequency spectrum of the signal is reflected in the statistics of the intrinsic frequencies of the oscillators the frequency analysis is completely embedded in the dynamics of the system thus no pre processing or additional parameters such as time windows are needed representative results of the numerical integration of the system are presented it is shown that the oscillators tune to the correct frequencies for both discrete and continuous spectra due to its dynamic nature the system is also capable to track non stationary spectra further we show that the system can be modeled in a probabilistic manner by means of a nonlinear fokker planck equation the probabilistic treatment is in good agreement with the numerical results and provides a useful tool to understand the underlying mechanisms leading to convergence

on monotone method for first and second order periodic boundary value problems and periodic solutions of functional differential equations abstract in this paper we show that the method of monotone iterative technique is valid to obtain two monotone sequences that converge uniformly to extremal solutions of first and second order periodic boundary value problems and periodic solutions of functional differential equations we obtain some new results relative to the lower solution and upper solution with

dynamical movement primitives learning attractor models for motor behaviors nonlinear dynamical systems have been used in many disciplines to model complex behaviors including biological motor control robotics perception economics traffic prediction and neuroscience while often the unexpected emergent behavior of nonlinear systems is the focus of investigations it is of equal importance to create goal directed behavior e g stable locomotion from a system of coupled oscillators under perceptual guidance modeling goal directed behavior with nonlinear systems is however rather difficult due to the parameter sensitivity of these systems their complex phase transitions in response to subtle parameter changes and the difficulty of analyzing and predicting their long term behavior intuition and time consuming parameter tuning play a major role this letter presents and reviews dynamical movement primitives a line of research for modeling attractor behaviors of autonomous nonlinear dynamical systems with the help of statistical learning techniques the essence of our approach is to start with a simple dynamical system such as a set of linear differential equations and transform those into a weakly nonlinear system with prescribed attractor dynamics by means of a learnable autonomous forcing term both point attractors and limit cycle attractors of almost arbitrary complexity can be generated we explain the design principle of our approach and evaluate its properties in several example applications in motor control and robotics

finite volume solution of the two dimensional euler equations on a regular triangular mesh the two dimensional euler equations have been solved on a triangular grid by a multigrid scheme using the finite volume approach by careful construction of the dissipative terms the scheme is designed to be secondorder accurate in space provided the grid is smooth except in the vicinity of shocks where it behaves as firstorder accurate in its present form the accuracy and convergence rate of the triangle code are comparable to that of the quadrilateral mesh code of jameson

high order finite volume methods for viscoelastic flow problems in this paper accurate and stable finite volume schemes for solving viscoelastic flow problems are presented two contrasting finite volume schemes are described a hybrid cell vertex scheme and a pure cell centred counterpart both schemes employ a time splitting algorithm to evolve the solution through time towards steady state in the case of the hybrid scheme a semi implicit formulation is employed in the momentum equation based on the taylor galerkin approach with a pressure correction step to enforce incompressibility the basis of the pure finite volume approach is a backward euler scheme with a semi lagrangian step to treat the convection terms in the momentum and constitutive equations two distinct finite volume schemes are presented for solving the systems of partial differential equations describing the flow of viscoelastic fluids the schemes are constructed to be second order accurate in space the issue of stability is also addressed with respect to the treatment of convection numerical examples are presented illustrating the performance of these schemes on some steady and transient problems that possess analytical solutions

locally implicit hybrid algorithm for steady and unsteady viscous flows a locally implicit hybrid finite volume algorithm on mixed type of triangular and quadrilateral meshes for the two dimensional steady and unsteady viscous flows has been developed the unsteady full navier stokes equations are solved in the cartesian coordinate system a new construction of a total variation diminishing formulation on triangles is used to obtain high resolution results in the convective dominated flow region in the viscous dominated part a second and fourth order dissipative model on quadrilateral grids is employed to minimize the numerical dissipation

distributed implicit stepping with unstructured finite volumes for 2d transport a detailed description of transport phenomena in real life complex geometries is important in several areas of reservoir and environmental engineering this paper presents numerical issues related to the application of high performance computing in this field the specific example treated comes from reservoir engineering a distributed parallel environment is developed based upon domain decomposition we discuss both the iterative properties and the parallel performance on an ibm sp2 it will be shown that the numerical approach leads to an attractive tool for treating real life large scale problems

an accurate moving boundary formulation in cut cell methods a cut cell method for cartesian meshes to simulate viscous compressible flows with moving boundaries is presented we focus on eliminating unphysical oscillations occurring in cartesian grid methods extended to moving boundary problems in these methods cells either lie completely in the fluid or solid region or are intersected by the boundary for the latter cells the time dependent volume fraction lying in the fluid region can be so small that explicit time integration schemes become unstable and a special treatment of these cells is necessary when the boundary moves a fluid cell may become a cut cell or a solid cell may become a small cell at the next time level this causes an abrupt change in the discretization operator and a suddenly modified truncation error of the numerical scheme this temporally discontinuous alteration is shown to act like an unphysical source term which deteriorates the numerical solution i e it generates unphysical oscillations in the hydrodynamic forces exerted on the moving boundary we develop an accurate moving boundary formulation based on the varying discretization operators yielding a cut cell method which avoids these discontinuities results for canonical two and three dimensional test cases evidence the accuracy and robustness of the newly developed scheme

unsteady euler algorithm with unstructured dynamic mesh for complex aircraft aerodynamic analysis an euler solution algorithm is presented for unsteady aerodynamic analysis of complex aircr aft configurations the flow solver involves a multistage runge kutta time stepping scheme that uses a finite volume spatial discretization on an unstructured grid made up of tetrahedra a significant contribution of the research is the development and implementation of a moving mesh algorithm that is employed for problems involving static or dynamic deformation of the aircraft the mesh algorithm is a general procedure that can treat realistic motions and deformations of complex aircraft configurations steady and unsteady results are presented for a supersonic fighter configuration to demonstrate applications of the euler solver and dynamic mesh algorithm the unsteady flow results were obtained for the aircraft oscillating harmonically in a complete vehicle bending mode effects of angle of attack and reduced frequency on instantaneous pressures and force responses were investigated the paper presents descriptions of the euler solver and dynamic mesh algorithm along with results that assess the capability

new comparison results for impulsive integro differential equations and applications we prove some new maximum principles for ordinary integro differential equations this allows us to introduce a new definition of lower and upper solutions which leads to the development of the monotone iterative technique for a periodic boundary value problem related to a nonlinear first order impulsive integro differential equation

periodic boundary value problems for the first order impulsive functional differential equations this paper is concerned with the existence of extreme solutions of the periodic boundary value problems for a class of first order functional differential equations we introduce new concept of lower and upper solutions and present that the method of lower and upper solutions coupled with monotone iterative technique is still valid meanwhile we extend previous results

impulsive periodic boundary value problems of first order differential equations in this paper by using schaeffer s theorem we prove new existence theorems for a nonlinear periodic boundary value problem of first order differential equations with impulses our results improve and generalize some known results

a high resolution characteristics based implicit dual time stepping vof method for free surface flow simulation on unstructured grids in this paper a new unstructured grid finite volume incompressible navier stokes solver based on a high order characteristics based method the artificial compressibility method and a matrix free implicit dual time stepping scheme has been developed to study unsteady free surface flows the free surface effects are calculated using the volume of fluid vof method and continuum surface force the transport equation for the vof is numerically solved using exactly the same method for the flow solver a number of test cases have been studied to validate the proposed method and demonstrate its capability by comparison with other schemes and published results