linearly implicit imex runge kutta methods for a class of degenerate convection diffusion problems multispecies kinematic flow models with strongly degenerate diffusive corrections give rise to systems of nonlinear convection diffusion equations of arbitrary size applications of these systems include models of polydisperse sedimentation and multiclass traffic flow implicit explicit imex runge kutta rk methods are suitable for the solution of these convection diffusion problems since the stability restrictions coming from the explicitly treated convective part are much less severe than those that would be deduced from an explicit treatment of the diffusive term these schemes usually combine an explicit rk scheme for the time integration of the convective part with a diagonally implicit one for the diffusive part in r burger p mulet and l m villada siam j sci comput 35 2013 pp b751 b777 a scheme of this type is proposed where the nonlinear and nonsmooth systems of algebraic equations arising in the implicit treatment of the degenerate diffusive part are solved by smoothing o

a semi implicit numerical scheme for reacting flow an additive semi implicit projection scheme for the simulation of unsteady combustion in two dimensions is constructed the scheme relies on a zero mach number formulation of the compressible conservation equations with detailed chemistry the governing equations are discretized in space using second order differences and integrated in time using a semi implicit approach time integration of the evolution equations for species mass fraction thermodynamic pressure and density is performed using a semi implicit nonsplit scheme that combines a second order predictor corrector treatment of convection and diffusion terms and a stiff integrator for the reaction source terms meanwhile the momentum equations are integrated using a second order projection scheme the projection scheme is based on a predictor corrector approach that couples the evolution of the velocity and density fields in order to stabilize computations of reacting flows with large density variations a pressure poisson equation is inverted following both the predictor and corrector steps using a fast solver the advantages of the stiff integration of reaction source terms are analyzed by comparing the performance of the scheme to that of a predictor corrector scheme in which reaction and diffusion are integrated in a similar nonstiff fashion the comparison in based on both one dimensional 1d unsteady tests of a premixed methane air flame and unsteady two dimensional tests of the same flame interacting with a counterrotating vortex pair in both cases the grimech1 2 reaction mechanism with 32 species and 177 elementary reactions is used computed results show that the stiff reaction scheme enables selection of larger time steps and thus leads to substantial improvement in the performance of the computations for the present reaction mechanism and flame conditions speedup factors of about 10 are achieved in the 1d tests and about five in two dimensions possible extensions of the present scheme to further improve efficiency are also discussed

stability and error estimates of local discontinuous galerkin methods with implicit explicit time marching for advection diffusion problems the main purpose of this paper is to analyze the stability and error estimates of the local discontinuous galerkin ldg methods coupled with carefully chosen implicit explicit imex runge kutta time discretization up to third order accuracy for solving one dimensional linear advection diffusion equations in the time discretization the advection term is treated explicitly and the diffusion term implicitly there are three highlights of this work the first is that we establish an important relationship between the gradient and interface jump of the numerical solution with the independent numerical solution of the gradient in the ldg methods the second is that by aid of the aforementioned relationship and the energy method we show that the imex ldg schemes are unconditionally stable for the linear problems in the sense that the time step tau is only required to be upper bounded by a constant which depends on the ratio of the diffusion and the square of the advection coefficients and is independent

criteria for asymptotic stability of linear time delay systems several sufficient conditions which guarantee stability of linear time delay systems are derived each of these results is expressed by a succinct scalar inequality and corresponds to a certain extent to the tradeoff between simplicity and sharpness

high order asymptotic preserving methods for fully nonlinear relaxation problems we study solutions to nonlinear hyperbolic systems with fully nonlinear relaxation terms in the limit of both infinitely stiff relaxation and arbitrary late time in this limit the dynamics is governed by effective systems of parabolic type which may contain degenerate and or fully nonlinear diffusion terms for this class of problems we develop an implicit explicit method based on runge kutta discretization in time and we apply this method to the investigation of several examples of interest in fluid dynamics importantly we impose here a realistic stability condition on the time step and we demonstrate that solutions in the hyperbolic to parabolic regime can be computed numerically with high robustness and accuracy even in the presence of fully nonlinear relaxation

a high order semi implicit imex weno scheme for the all mach isentropic euler system abstract in this paper new high order schemes are constructed and analyzed for the numerical solution of euler equations of isentropic gas dynamics material waves are treated explicitly while acoustic waves are treated implicitly thus avoiding severe cfl restrictions for low mach flows high order accuracy in space is obtained by finite difference weno schemes while high order in time is obtained by imex methods with semi implicit linearization treatment the schemes are proven to be asymptotic preserving and asymptotic accurate as the mach number vanishes several tests in one and two space dimensions illustrate the effectiveness of the proposed schemes

high order semi implicit schemes for unsteady compressible flow simulations direct numerical simulation of stability and transition of compressible boundary layers requires high orderaccurate and computationally efe cient numerical methods to resolve a wide range of time and length scales associated with wave e elds in the boundary layers explicit methods have been used mainly in such simulations to advance the compressible navier stokes equations in time however the small wall normal grid sizes for viscous e ow simulations impose a severe stability restriction on the allowable time steps in simulations using the explicit method this requires implicit treatment to our numerical method although fully implicit methods are often used in steady e ow calculations to remove the stability restriction on time steps they are seldom used in transient e ow simulations because the time steps used in time accurate calculations are often not large enough to offset high computational cost of using fully implicit methods a high order accurate semi implicit scheme is presented for the direct numerical simulation of the stability and transition of compressible wall bounded e ows the efe ciency and accuracy of the semi implicit scheme are evaluated by applying the method to transient e ow simulations of several supersonic and hypersonic wall bounded e ow stability problems

an improved lmi based approach for stability of piecewise affine time delay systems with uncertainty the stability problem for uncertain piecewise affine pwa time delay systems is investigated in this article it is assumed that there exists a known constant time delay in the system and the uncertainly is norm bounded sufficient conditions for the stability of nominal systems and the stability of systems subject to uncertainty are derived using the lyapunov krasovskii functional with a triple integration term this approach handles switching based on the delayed states in addition to the states for a pwa time delay system considers structured as well as unstructured uncertainty and reduces the conservativeness of previous approaches the effectiveness of the proposed approach is demonstrated by comparing with the existing methods through numerical examples

an adaptive implicit explicit scheme for the dns and les of compressible flows on unstructured grids an adaptive implicit explicit scheme for direct numerical simulation dns and large eddy simulation les of compressible turbulent flows on unstructured grids is developed the method uses a node based finite volume discretization with summation by parts sbp property which in conjunction with simultaneous approximation terms sat for imposing boundary conditions leads to a linearly stable semi discrete scheme the solution is marched in time using an implicit explicit runge kutta imex rk time advancement scheme a novel adaptive algorithm for splitting the system into implicit and explicit sets is developed the method is validated using several canonical laminar and turbulent flows load balance for the new scheme is achieved by a dual constraint domain decomposition algorithm the scalability and computational efficiency of the method is investigated and memory savings compared with a fully implicit method is demonstrated a notable reduction of computational costs compared to both fully implicit and fully explicit schemes is observed

delay dependent stability for uncertain stochastic neural networks with time varying delay abstract this paper is concerned with the robust stability analysis problem for uncertain stochastic neural networks with time varying delay the parameter uncertainties are assumed to be norm bounded by defining a new lyapunov krasovskii functional the restrictions such as the time varying delay was required to be differentiable and its derivative was strictly smaller than one are removed based on the linear matrix inequality approach delay dependent stability criteria are obtained such that for all admissible uncertainties the stochastic neural network is globally asymptotically stable in the mean square two slack variables are introduced into the obtained stability criteria to reduce the conservatism finally a numerical example is given to illustrate the effectiveness of the developed method

regular article a semi implicit numerical scheme for reacting flow a stiff 1 operator split projection scheme is constructed for the simulation of unsteady two dimensional reacting flow with detailed kinetics the scheme is based on the compressible conservation equations for an ideal gas mixture in the zero mach number limit the equations of motion are spatially discretized using second order centered differences and are advanced in time using a new stiff predictor corrector approach the new scheme is a modified version of the additive stiff scheme introduced in a previous effort by h n najm p s wyckoff and o m knio 1998 j comput phys 143 381 the predictor updates the scalar fields using a strang type operator split integration step which combines several explicit diffusion sub steps with a single stiff step for the reaction terms such that the global time step may significantly exceed the critical diffusion stability limit convection terms are explicitly handled using a second order multi step scheme the velocity field is advanced using a projection scheme which consists of a partial convection diffusion update followed by a pressure correction step a split approach is also adopted for the convection diffusion step in the momentum update this splitting combines an explicit treatment of the convective terms at the global time step with several explicit fractional steps for diffusion finally a corrector step is implemented in order to couple the evolution of the density and velocity fields and to stabilize the computations the corrector acts only on the convective terms and the pressure field while the predicted updates due to diffusion and reaction are left unchanged the correction of the scalar fields is implemented using a single step non split non stiff second order time integration a similar procedure is used for the velocity field which is followed by a pressure projection step the performance and behavior of the operator split scheme are first analyzed based on tests for a nonlinear reaction diffusion equation in one space dimension followed by computations with a detailed c 1c 2 methane air mechanism in one and two dimensions the tests are used to verify that the scheme is effectively second order in time and to suggest guidelines for selecting integration parameters including the number of fractional diffusion steps and tolerance levels in the stiff integration for two dimensional simulations with the present reaction mechanism flame conditions and resolution parameters speedup factors of about 5 are achieved over the previous additive scheme and about 25 over the original explicit scheme

robust exponential stability of uncertain systems with time varying delays focuses on the problem of robust exponential stability of a class of uncertain systems described by functional differential equations with time varying delays the uncertainties are assumed to be continuous time varying nonlinear and norm bounded sufficient conditions for robust exponential stability are given for both single and multiple delays cases

stability analysis of linear systems with two delays of overlapping ranges in this paper a delay dependent stability criterion is derived for linear time delay systems with two constant delays having overlapping ranges this overlapping feature of the delays is exploited in delay dependent analysis of the system using lyapunov krasovskii approach the developed treatment of the delays reduces conservatism in analysis compared to the approaches treating the delays individually numerical examples are used to demonstrate the less conservativeness of the derived criterion

robust sliding mode control of nonlinear systems with delay a design via polytopic formulation this paper outlines the possibility to control nonlinear uncertain systems with single possibly time varying state delay these systems are submitted to additive perturbations possibly nonvanishing the control is of sliding mode type and the sliding surface is designed so to maximize the calculable set of delays which do not destabilize the system the way to deal with the nonlinear parts of the model relies on a polytopic formulation the conditions for the existence of the sliding regime are studied by using both a lyapunov krasovskii functionnal and a lyapunov razumikhin function the optmization precedure for the choice of the sliding surface is expressed in terms of lmis an example illustrates the proposed method

new exponential estimates for time delay systems this note considers the problem of exponential stability for time delay systems in terms of linear matrix inequalities a new sufficient condition for exponential stability is obtained based on this an improved upper bound of the decay rate can be easily calculated when time varying norm bounded parameter uncertainties appear a new sufficient condition for robust exponential stability of uncertain time delay systems is also provided the reduced conservatism of the proposed conditions is illustrated via two numerical examples

stability of imex runge kutta methods for delay differential equations stability of imex implicit explicit runge kutta methods applied to delay differential equations ddes is studied on the basis of the scalar test equation du dt lu t mu t t where t is a constant delay and l m are complex parameters more specifically p stability regions of the methods are defined and analyzed in the same way as in the case of the standard runge kutta methods a new imex method which possesses a superior stability property for ddes is proposed some numerical examples which confirm the results of our analysis are presented

observer design for nonlinear systems under unknown time varying delays the design of observers for nonlinear systems with unknown time varying bounded delays on both state and input still constitutes an open problem in this technical note we show how to solve it for a class of nonlinear systems by combining the high gain observer approach with a lyapunov krasovskii functional suitable choice sufficient conditions are provided to prove the practical stability of the observer it is shown that the observation error is bounded and depends on the size of two parameters the known upper bound delay of the unknown time varying function delay and the instantaneous state dynamic variation furthermore for the particular case of constant known time delay the convergence of the proposed observer becomes exponential the feasibility of the proposed strategy is illustrated by a numerical example

construction of infinite dimensional interacting diffusion processes through dirichlet forms by the theory of quasi regular dirichletforms and the associated special standard processes the existence of symmetric diffusion processes taking values in the space of non negative integer valued radon measures on mbox boldmath r nu and having gibbs invariant measures associated with some given pair potentials is considered the existence of such diffusions can be shown for a wide class of potentials involving some singular ones also as a consequence of an application of stochastic calculus a representation for the diffusion by means of a stochastic differential equation is derived

on exponential stabilization for a class of neutral type systems with parameter uncertainties an integral sliding mode approach this paper is focused on integral sliding mode control ismc for a class of parameter uncertain neutral type systems with time varying delays ntstd an integral sliding surface functional is firstly constructed for the ntstd then a delay dependent robust stability criterion is established for all admissible uncertainties which can guarantee the sliding mode dynamic system to be robustly exponentially stable under a certain decay rate in addition by solving the generalized eigenvalue problem gevp presented in the subsequent work the global maximal value of the decay rate as well as the condition of exponential stability for the sliding mode system are derived furthermore a sliding mode control smc law is then synthesised to ensure the stability of the closed loop system and the proposed smc law can drive the state of controlled dynamic system into the predefined sliding surface in finite time finally a numerical example is provided to demonstrate the effectiveness of the obtained results

semi implicit runge kutta schemes development and application to compressible channel flow time stepconstraintdueto thefine meshnear thewall the explicitsubschemeis asix stage fourth order low storage runge kutta scheme based on analysis in fourier space and results obtained for propagation test cases the semiimplicitschemesareshowntobeoforder3and forwavesdiscretizedbyanumberofpointsperperiodbetween4and 16 tobeasaccurateas ormoreaccuratethan thestandardexplicitfourth orderrunge kuttaalgorithmintermsof dissipationanddispersion thelarge eddysimulationofacompressibleturbulentchannelflowatafrictionreynolds numberof360andamachnumberof0 1isthencarriedoutwithoneoftheproposedalgorithms thecomputational time is reduced by a factor 1 33 with respect to a large eddy simulation using the explicit subscheme in all directions wall pressure and velocity spectra from the large eddy simulation are presented to give insights into the flow turbulent structures in particular wave number frequency spectra are calculated acoustic components appear to be identified in these spectra

krylov implicit integration factor methods for spatial discretization on high dimensional unstructured meshes application to discontinuous galerkin methods abstract integration factor methods are a class of exactly linear part time discretization methods in q nie y t zhang r zhao efficient semi implicit schemes for stiff systems journal of computational physics 214 2006 521 537 a class of efficient implicit integration factor iif methods were developed for solving systems with both stiff linear and nonlinear terms arising from spatial discretization of time dependent partial differential equations pdes with linear high order terms and stiff lower order nonlinear terms the tremendous challenge in applying iif temporal discretization for pdes on high spatial dimensions is how to evaluate the matrix exponential operator efficiently for spatial discretization on unstructured meshes to solve pdes on complex geometrical domains how to efficiently apply the iif temporal discretization was open in this paper we solve this problem by applying the krylov subspace approximations to the matrix exponential operator then we apply this novel time discretization technique to discontinuous galerkin dg methods on unstructured meshes for solving reaction diffusion equations numerical examples are shown to demonstrate the accuracy efficiency and robustness of the method in resolving the stiffness of the dg spatial operator for reaction diffusion pdes application of the method to a mathematical model in pattern formation during zebrafish embryo development shall be shown

some new additive runge kutta methods and their applications we propose some new additive runge kutta methods of orders ranging from 2 to 4 that may be used for solving some nonlinear system of odes especially for the temporal discretization of some nonlinear systems of pdes with constraints only linear odes or pdes need to be solved at each time step with these new methods

on the asymptotic properties of imex runge kutta schemes for hyperbolic balance laws implicit explicit imex schemes are a powerful tool in the development of numerical methods for hyperbolic systems with stiff sources here we focus our attention on the asymptotic properties of such schemes like the preservation of steady states well balanced property and the behavior in presence of small space time scales asymptotic preservation property we analyze conditions under which the standard additive approach based on taking the fluxes explicitly and the sources implicitly yields a well balanced behavior in addition we consider a partitioned strategy which possesses better well balanced properties the behavior of the additive and partitioned approaches under classical scaling limits is then studied in the context of asymptotic preserving schemes additional order conditions that guarantee the correct behavior of the schemes in the navier stokes regime are derived several examples illustrate these asymptotic behaviors and the performance of the new methods

third order conservative sign preserving and steady state preserving time integrations and applications in stiff multispecies and multireaction detonations abstract in this paper we develop third order conservative sign preserving and steady state preserving time integrations and seek their applications in multispecies and multireaction chemical reactive flows in this problem the density and pressure are nonnegative and the mass fraction for the ith species denoted as z i 1 i m should be between 0 and 1 where m is the total number of species there are four main difficulties in constructing high order bound preserving techniques for multispecies and multireaction detonations first of all most of the bound preserving techniques available are based on euler forward time integration therefore for problems with stiff source the time step will be significantly limited secondly the mass fraction does not satisfy a maximum principle and hence it is not easy to preserve the upper bound 1 thirdly in most of the previous works for gaseous denotation the algorithm relies on second order strang splitting methods where the flux and stiff source terms can be solved separately and the extension to high order time discretization seems to be complicated finally most of the previous ode solvers for stiff problems cannot preserve the total mass and the positivity of the numerical approximations at the same time in this paper we will construct third order conservative sign preserving rugne kutta and multistep methods to overcome all these difficulties the time integrations do not depend on the strang splitting i e we do not split the flux and the stiff source terms moreover the time discretization can handle the stiff source with large time step and preserves the steady state numerical experiments will be given to demonstrate the good performance of the bound preserving technique and the stability of the scheme for problems with stiff source terms

observer based adaptive control for uncertain time delay systems in this paper we will focus on investigating the observer based controlling problem of time delay systems first we investigate a class of simple time delay systems the corresponding adaptive observer and controller are designed which are both independent of the time delays based on lyapunov stability theory we prove that the closed loop system is asymptotically stable next we further consider the interconnected time delay system case the corresponding adaptive observer and controller are designed we prove that the resulting closed loop system is also asymptotically stable simulations on controlling time delay systems and interconnected systems are investigated and the results show that the designed controllers are feasible and efficient

design and implementation of predictors for additive semi implicit runge kutta methods space discretization of some time dependent partial differential equations gives rise to stiff systems of ordinary differential equations in this case implicit methods should be used and therefore in general nonlinear systems must be solved the solutions to these systems are approximated by iterative schemes and in order to obtain an efficient code good initializers should be used recently a parallel code based on some runge kutta and additive runge kutta methods has been constructed focusing especially on additive semi implicit runge kutta asirk methods the aim of the present paper is to develop efficient initializers for these methods

additive semi implicit runge kutta methods for computing high speed nonequilibrium reactive flows this paper is concerned with time stepping numerical methods for computing stiff semi discrete systems of ordinary differential equations for transient hypersonic flows with thermo chemical nonequilibrium the stiffness of the equations is mainly caused by the viscous flux terms across the boundary layers and by the source terms modeling finite rate thermo chemical processes implicit methods are needed to treat the stiff terms while more efficient explicit methods can still be used for the nonstiff terms in the equations this paper studies three different semi implicit runge kutta methods for additively split differential equations in the form ofu f u g u wherefis treated by explicit runge kutta methods andgis simultaneously treated by three implicit runge kutta methods a diagonally implicit runge kutta method and two linearized implicit runge kutta methods the coefficients of up to third order accurate additive semi implicit runge kutta methods have been derived such that the methods are both high order accurate and strongly a stable for the implicit terms the results of two numerical tests on the stability and accuracy properties of these methods are also presented in the paper

stability criteria for linear systems with uncertain delays new delay independent and delay dependent stability criteria for linear systems with multiple uncertain delays are established by using both the time domain and the frequency domain methods the results are derived based on the established new preliminary lemmas and by using new type stability theorems for general retarded dynamical systems and new analysis techniques in the time domain and the frequency domain all the established stability criteria depend only on the eigenvalues related to the coefficient matrices of the systems and do not involve any free tuning parameters in addition some remarks are given to explain in detail the obtained results and to point out the limitations of the existing results in the literature

improved exponential stability for time varying systems with nonlinear delayed perturbations in this paper a new sufficient delay dependent exponential stability condition for a class of linear time varying systems with nonlinear delayed perturbations is derived by using an improved lyapunov krasovskii functional the proposed exponential stability conditions are formulated in terms of the solution of lyapunov differential equations the approach allows for computation of the bounds that characterize the exponential stability rate of convergence of the solution compared with existing results our conditions are shown to be less conservative numerical examples are given to illustrate the effectiveness of the obtained conditions

robust stabilization of uncertain t s fuzzy time delay systems with exponential estimates this paper deals with the problem of robust stabilization for uncertain takagi sugeno t s fuzzy systems with constant time delays the purpose is to design a state feedback fuzzy controller such that the closed loop system is robustly exponentially stable with a prescribed decay rate sufficient conditions for the solvability of this problem are presented in terms of linear matrix inequalities lmis by using feasible solutions of these lmis desired fuzzy controllers are designed and their corresponding exponential estimates are given in addition the main results of this paper are explicitly dependent on the decay rate this enables one to design fuzzy controllers by freely selecting decay rates according to different practical conditions two numerical examples are provided finally to demonstrate the effectiveness of the proposed design methods

stability analysis of time delay systems with incommensurate delays using positive polynomials we present a new stability condition for linear time delay systems tds with multiple incommensurate delays based on the rekasius substitution and positive polynomials the condition is checked by testing the positivity of multivariate polynomials in certain domains for this purpose we propose two alternative algorithms based on linear programming and sum of squares methods respectively the efficiency and accuracy of the algorithms is compared in an example to alternative stability conditions taken from the literature

stabilization of uncertain dynamic systems including state delay the authors consider a class of time varying systems with time varying state delay and uncertain input and parameters they present sufficient conditions on the open loop to obtain an arbitrary degree closed loop stability they construct a min max controller from knowledge of the upper bound of the delay

memoryless stabilization of uncertain linear systems including time varying state delays the problem of stabilizing a class of uncertain time delay systems via memoryless linear feedback is examined the systems under consideration are linear systems with time varying state delays they also contain uncertain parameters possibly time varying whose values are known only to within a prescribed compact bounding set the main contribution given is to enlarge the class of time delay systems for which one can construct a stabilizing memoryless linear feedback controller within this framework a novel notion of robust memoryless stabilizability is first introduced via the method of lyapunov functionals then a sufficient condition for the stabilizability is proposed it is shown that solvability of a parameterized riccati equation can be used to determine whether the time delay system satisfies the sufficient condition if there exists a positive definite symmetric solution satisfying the riccati equation a suitable memoryless linear feedback law can be derived

efficient semi implicit schemes for stiff systems when explicit time discretization schemes are applied to stiff reaction diffusion equations the stability constraint on the time step depends on two terms the diffusion and the reaction the part of the stability constraint due to diffusion can be totally removed if the linear diffusions are treated exactly using integration factor if or exponential time differencing etd methods for systems with severely stiff reactions those methods are not efficient because the reaction terms in if or etd are still approximated with explicit schemes in this paper we introduce a new class of semi implicit schemes which treats the linear diffusions exactly and explicitly and the nonlinear reactions implicitly a distinctive feature of the scheme is the decoupling between the exact evaluation of the diffusion terms and implicit treatment of the nonlinear reaction terms as a result the size of the nonlinear system arising from the implicit treatment of the reactions is independent of the number of spatial grid points it only depends on the number of original equations unlike the case in which standard implicit temporal schemes are directly applied to the reaction diffusion system the stability region for this class of methods is much larger than existing methods using an explicit treatment of reaction terms in particular the one with second order accuracy is unconditionally linearly stable with respect to both diffusion and reaction direct numerical simulations on test equations as well as morphogen systems from developmental biology show the new semi implicit schemes are efficient robust and accurate

new hybrid runge kutta methods for unsteady reactive flow simulation in the numerical simulation of transient reacting flow standard explicit calculation is prohibitively expensive because of the small time steps needed to address the stiffness of a governing differential system to circumvent this new hybrid implicit explicit methods proposed treat the stiffness whereas the underlying time step control is governed by the courant stability criterion because the coefficients of both explicit and implicit operations are entirely determined by solving the necessary conditions of accuracy and l stability without any extra assumptions the methods are more generalized than other similar methods in the literature two families of semi implicit runge kutta schemes are developed for split differential equations in the form of u f t u g t u where f is treated explicitly and g is simultaneously treated implicitly like the rest of all the developed schemes a low storage family of semi implicit schemes is also derived to be globally high order accurate and l stable for implicit calculations in a companion paper yoh j j and zhong x new hybrid runge kutta methods for unsteady reactive flow simulation applications aiaa journal v ol 42 no 8 2004 pp 1601 1611 the new schemes are tested to solve a wide range of applications in high speed flow physics involving combustion

technical communique d stability for linear continuous time systems with multiple time delays this paper addresses the d stability problem of linear continuous time systems with multiple time delays a sufficient condition to guarantee all poles of a given linear time delay system located in the specified region is proposed this condition can be solved using lmi toolbox the result is also extended to the robust d stability problem of perturbed linear time delay systems the illustrative example shows that this method is effective to check the d stability of linear time delay systems

numerical solution of the reaction advection diffusion equation on the sphere a finite volume algorithm for the solution of the reaction advection diffusion equation on the sphere is derived and evaluated using analytical solutions the proposed approach is based on the principle of semidiscretization the convective and diffusive fluxes are approximated first and then the resulting set of the ordinary differential equations odes is solved using the appropriate time stepping algorithm in the first part of the paper solutions to both the linear advection and the advection diffusion problems for a single conservative scalar are discussed the monotonicity of the scheme is achieved with the explicit adaptive dissipation the development as well as the selected applications of the method are illustrated using a finite volume mesh constructed on the basis of geodesic icosahedral grid which in the past 40 years has been frequently applied in different models of geophysical fluid dynamics the performance of the solver is assessed using a suite of standard tests based on solid body rotation for different initial conditions after analysis of the advection diffusion problem the extension of the method for the equations with reactive terms is presented the performance of the solver is assessed by comparing the results to the analytical solution of the linearized reaction diffusion system in the final part of the paper the application of the solver for studies of nonlinear reactions on the sphere is illustrated the main intended application of the proposed method includes the simulation of transport of chemical constituents in the earth s atmosphere as well as the forecasting of moisture and cloud water fields in numerical weather prediction and climate models

robust stabilization of a class of nonlinear time delay systems the problem of robust stabilization for a class of uncertain dynamic systems with multiple delayed state perturbations is considered it is assumed that perturbations of the time delayed sections are not bounded by first order linear functions but bounded by high order functions with unknown gains and the time delay considered is time varying two classes of controllers are proposed when the time derivative of each time varying time delay is less than 1 a class of adaptive state feedback controllers are proposed based on lyapunov krasovskii method which can render the closed loop systems uniformly ultimately bounded stable novel nonlinear feedback controllers are developed by employing razumikhin lemma and the controller also can render the closed loop systems stable in the sense of uniform ultimate boundedness finally several examples are given to show the potential of the proposed techniques

robust control of delay systems a sliding mode control design via lmi this paper considers the sliding mode control of uncertain systems with single or multiple constant or time varying state delays submitted to additive perturbations the sliding surface is designed so to maximize the calculable set of admissible delays the conditions for the existence of the sliding regime are studied by using lyapunov krasovskii functionals and lyapunov razumikhin functions lmis are used for the optimization procedure two examples illustrate the proposed method

steady state and sign preserving semi implicit runge kutta methods for odes with stiff damping term in this paper we develop a family of second order semi implicit time integration methods for systems of ordinary differential equations odes with stiff damping term the important feature of the new methods resides in the fact that they are capable of exactly preserving the steady states as well as maintaining the sign of the computed solution under the time step restriction determined by the nonstiff part of the system only the new semi implicit methods are based on the modification of explicit strong stability preserving runge kutta ssp rk methods and are proven to have a formal second order of accuracy a alpha stability and stiff decay we illustrate the performance of the proposed ssp rk based semi implicit methods on both a scalar ode example and a system of odes arising from the semi discretization of the shallow water equations with stiff friction term the obtained numerical results clearly demonstrate that the ability of the introduced ode solver to exactly preserve equilibria plays

technical communique robust h control of linear neutral systems this paper investigates the problems of robust stability and robust h control for a class of uncertain neutral systems the class describes linear state models with norm bounded uncertain system parameters and unknown constant state delay first we develop a sufficient condition for robust stability independent of delay then we provide sufficient conditions for designing a memoryless state feedback controller which stabilizes the uncertain neutral system under consideration and guarantees an h norm bound constraint on the disturbance attenuation for all admissible uncertainties and unknown state delay in both problems the results are expressed in the form of linear matrix inequalities it has been established that several earlier results are special cases of the developed theory

derivation of high order compact finite difference schemes for non uniform grid using polynomial interpolation in this paper simple polynomial interpolation is used to derive arbitrarily high order compact schemes for the first derivative and tridiagonal compact schemes for the second derivative consisting of three second derivative nodes in the interior and two on the boundary on non uniform grids boundary and near boundary schemes of the same order as the interior are also developed using polynomial interpolation and for a general compact scheme on a non uniform grid it is shown that polynomial interpolation is more efficient than the conventional method of undetermined coefficients for finding coefficients of the scheme the high order non uniform schemes along with boundary closure of up to 14th order thus obtained are shown to be stable on a non uniform grid with appropriate stretching so that more grid points are clustered near the boundary the stability and resolution properties of the high order non uniform grid schemes are studied and the results of three numerical tests on stability and accuracy properties are also presented

robust stability of delay dependence for linear uncertain systems a sufficient condition for the stability of the linear uncertain time delay systems is presented the result obtained can include information on the size of the delay and therefore can be a delay dependent stability condition the lyapunov method is employed to investigate the problem the result is demonstrated by an illustrative example

delay independent stability conditions and decay estimates for time varying functional differential equations this paper presents sufficient delay independent conditions that guarantee stability of nonlinear time varying functional differential equations fde s estimates on the rate of decay of solutions are also obtained

sharp bounds for lyapunov exponents and stability conditions for uncertain systems with delays stability of a set of systems with norm bounded nonlinear terms and arbitrary time varying as well as distributed delays is studied a novel approach to this problem based on deriving bounds for the norms of system solutions is developed a sharp estimate for the maximal lyapunov exponent of the solutions expressed in the bounds for the uncertain parameters is found the subsystems for which the obtained estimate is attained are indicated using these results a delay independent necessary and sufficient stability condition for the considered set of systems is derived for a system with prescribed parameters sufficient conditions for exponential stability and upper bound for the maximal lyapunov exponent are obtained the proposed approach is applied to illustrative examples which contrast its efficiency

stability and stabilization of switched linear dynamic systems with time delay and uncertainties this paper considers the problem of exponential stability and stabilization of switched linear time delay systems the system parameter uncertainties are time varying and unknown but norm bounded the delay in the system states is also time varying by using an improved lyapunov krasovskii functional a switching rule for the exponential stability and stabilization is designed in terms of the solution of riccati type equations the approach allows for computation of the bounds that characterize the exponential stability rate of the solution numerical examples are given to illustrate the results

a computationally efficient semi implicit iterative method for the time integration of reacting flows with stiff chemistry a semi implicit preconditioned iterative method is proposed for the time integration of the stiff chemistry in simulations of unsteady reacting flows such as turbulent flames using detailed chemical kinetic mechanisms emphasis is placed on the simultaneous treatment of convection diffusion and chemistry without using operator splitting techniques the preconditioner corresponds to an approximation of the diagonal of the chemical jacobian upon convergence of the sub iterations the fully implicit second order time accurate crank nicolson formulation is recovered performance of the proposed method is tested theoretically and numerically on one dimensional laminar and three dimensional high karlovitz turbulent premixed n heptane air flames the species lifetimes contained in the diagonal preconditioner are found to capture all critical small chemical timescales such that the largest stable time step size for the simulation of the turbulent flame with the proposed method is limited by the convective cfl rather than chemistry the theoretical and numerical stability limits are in good agreement and are independent of the number of sub iterations the results indicate that the overall procedure is second order accurate in time free of lagging errors and the cost per iteration is similar to that of an explicit time integration the theoretical analysis is extended to a wide range of flames premixed and non premixed unburnt conditions fuels and chemical mechanisms in all cases the proposed method is found theoretically to be stable and to provide good convergence rate for the sub iterations up to a time step size larger than 1 s this makes the proposed method ideal for the simulation of turbulent flames

a collocated method for the incompressible navier stokes equations inspired by the box scheme we present a new finite difference numerical method to solve the incompressible navier stokes equations using a collocated discretization in space on a logically cartesian grid the method shares some common aspects with and it was inspired by the box scheme it uses centered second order accurate finite difference approximations for the spatial derivatives combined with semi implicit time integration the proposed method is constructed to ensure discrete conservation of mass and momentum by discretizing the primitive velocity pressure form of the equations the continuity equation is enforced exactly to machine accuracy at the collocated locations whereas the momentum equations are evaluated in a staggered manner this formulation preempts the appearance of spurious pressure modes in the embedded elliptic problem associated with the pressure the method shows uniform order of accuracy both in space and time for velocity and pressure in addition the skew symmetric form of the non linear advection term of the navier stokes equations improves discrete conservation of kinetic energy in the inviscid limit to within the order of the truncation error of the time integrator the method has been formulated to accommodate different types of boundary conditions fully periodic periodic channel inflow outflow and lid driven cavity always ensuring global mass conservation a novel aspect of this finite difference formulation is the derivation of the discretization near boundaries using the weak form of the equations as in the finite element method the method of manufactured solutions is utilized to perform accuracy analysis and verification of the solver to assess the applicability of the new method presented in this paper four realistic flow problems have been simulated and results are compared with those in the literature these cases include a lid driven cavity backward facing step kovasznay flow and fully developed turbulent channel