on partial information optimal singular control problem for mean field stochastic differential equations driven by teugels martingales measures abstractthis paper is concerned with partial information mixed optimal stochastic continuous singular control problem for mean field stochastic differential equation driven by teugels martingales and an independent brownian motion where the teugels martingales are a family of pairwise strongly orthonormal martingales associated with levy processes the control variable has two components the first being absolutely continuous and the second singular partial information necessary and sufficient conditions of optimal continuous singular control for these mean field models are investigated as an illustration this paper studies a partial information linear quadratic control problem of mean field type involving continuous singular control

reduced aliasing formulations of the convective terms within the navier stokes equations for a compressible fluid the effect on aliasing errors of different formulations describing the cubically nonlinear convective terms within the discretized navier stokes equations is examined in the presence of a non trivial density spectrum fourier analysis shows that the existing skew symmetric forms of the convective term result in reduced aliasing errors relative to the conservation form several formulations of the convective term including a new formulation proposed for cubically nonlinear terms are tested in direct numerical simulation dns of decaying compressible isotropic turbulence both in chemically inert small density fluctuations and reactive cases large density fluctuations and for different degrees of resolution in the dns of reactive turbulent flow the new cubic skew symmetric form gives the most accurate results consistent with the spectral error analysis and at the lowest cost in marginally resolved dns and les poorly resolved by definition the new cubic skew symmetric form represents a robust convective formulation which minimizes both aliasing and computational cost while also allowing a reduction in the use of computationally expensive high order dissipative filters

brief paper stochastic maximum principle in the mean field controls in buckdahn djehiche li and peng 2009 the authors obtained mean field backward stochastic differential equations bsdes in a natural way as a limit of some highly dimensional system of forward and backward sdes corresponding to a great number of particles or agents the objective of the present paper is to deepen the investigation of such mean field bsdes by studying their stochastic maximum principle this paper studies the stochastic maximum principle smp for mean field controls which is different from the classical ones this paper deduces an smp in integral form and it also gets under additional assumptions necessary conditions as well as sufficient conditions for the optimality of a control as an application this paper studies a linear quadratic stochastic control problem of mean field type

analysis of numerical errors in large eddy simulation using statistical closure theory this paper develops a dynamic error analysis procedure for the numerical errors arising from spatial discretization in large eddy simulation the analysis is based on edqnm closure theory and is applied to the les of decaying isotropic turbulence first the effects of finite differencing truncation error aliasing error and the dynamic smagorinsky model are independently considered the time evolution of kinetic energy and spectra predicted by the analysis are compared to actual les using the navier stokes equations and good agreement is obtained the analysis is then extended to simultaneously consider all sources of error in a second order discretely energy conserving central difference les solver good agreement between the analysis and actual les is obtained the analysis is used to compare the contribution of the subgrid model to that of numerical errors and it is shown that the contribution of the subgrid scale model is much higher than the numerical errors the proposed one dimensional edqnm les model shows potential as a more general tool for the analysis of numerical error and sgs model in simulations of turbulent flow

probabilistic analysis of mean field games the purpose of this paper is to provide a complete probabilistic analysis of a large class of stochastic differential games with mean field interactions we implement the mean field game strategy developed analytically by lasry and lions in a purely probabilistic framework relying on tailor made forms of the stochastic maximum principle while we assume that the state dynamics are affine in the states and the controls and the costs are convex our assumptions on the nature of the dependence of all the coefficients upon the statistical distribution of the states of the individual players remains of a rather general nature our probabilistic approach calls for the solution of systems of forward backward stochastic differential equations of a mckean vlasov type for which no existence result is known and for which we prove existence and regularity of the corresponding value function finally we prove that a solution of the mean field game problem as formulated by lasry and lions does indeed provide appr

on the effect of numerical errors in large eddy simulations of turbulent flows aliased and dealiased numerical simulations of a turbulent channel flow are performed using spectral and finite difference methods analytical and numerical studies show that aliasing errors are more destructive for spectral and high order finite difference calculations than for low order finite difference simulations numerical errors have different effects for different forms of the nonlinear terms in the navier stokes equations for divergence and convective forms spectral methods are energy conserving only if dealiasing is performed for skew symmetric and rotational forms both spectral and finite difference methods are energy conserving even in the presence of aliasing errors it is shown that discrepancies between the results of dealiased spectral and standard nondialiased finite difference methods are due to both aliasing and truncation errors with the latter being the leading source of differences the relative importance of aliasing and truncation errors as compared to subgrid scale model terms in large eddy simulations is analyzed and discussed for low order finite difference simulations truncation errors can exceed the magnitude of the subgrid scale term

indefinite mean field stochastic linear quadratic optimal control this paper is concerned with the discrete time indefinite mean field linear quadratic optimal control problem the so called mean field type stochastic control problems refer to the problem of incorporating the means of the state variables into the state equations and cost functionals such as the mean variance portfolio selection problems a dynamic optimization problem is called to be nonseparable in the sense of dynamic programming if it is not decomposable by a stage wise backward recursion the classical dynamic programming based optimal stochastic control methods would fail in such nonseparable situations as the principle of optimality no longer applies in this paper we show that both the well posedness and the solvability of the indefinite mean field linear quadratic problem are equivalent to the solvability of two coupled constrained generalized difference riccati equations and a constrained linear recursive equation we characterize the optimal control set completely and obtain a set of necessary and sufficient conditions on the mean variance portfolio selection problem the results established in this paper offer a more accurate solution scheme in tackling directly the issue of nonseparability and deriving the optimal policies analytically for the mean variance type portfolio selection problems

a high order low dispersion symmetry preserving finite volume method for compressible flow on curvilinear grids a new high order finite volume method is presented that preserves the skew symmetry of convection for the compressible flow equations the method is intended for large eddy simulations les of compressible turbulent flows in particular in the context of hybrid rans les computations the method is fourth order accurate and has low numerical dissipation and dispersion due to the finite volume approach mass momentum and total energy are locally conserved furthermore the skew symmetry preservation implies that kinetic energy sound velocity and internal energy are all locally conserved by convection as well the method is unique in that all these properties hold on non uniform curvilinear structured grids due to the conservation of kinetic energy there is no spurious production or dissipation of kinetic energy stemming from the discretization of convection this enhances the numerical stability and reduces the possible interference of numerical errors with the subgrid scale model by minimizing the numerical dispersion the numerical errors are reduced by an order of magnitude compared to a standard fourth order finite volume method

linear quadratic optimal control problems for mean field stochastic differential equations linear quadratic optimal control problems are considered for mean field stochastic differential equations with deterministic coefficients by a variational method the optimality system is derived which is a linear mean field forward backward stochastic differential equation using a decoupling technique two riccati differential equations are obtained which are uniquely solvable under certain conditions then a feedback representation is obtained for the optimal control

dynamic mean variance portfolio selection with no shorting constraints this paper is concerned with mean variance portfolio selection problems in continuous time under the constraint that short selling of stocks is prohibited the problem is formulated as a stochastic optimal linear quadratic lq control problem however this lq problem is not a conventional one in that the control portfolio is constrained to take nonnegative values due to the no shorting restriction and thereby the usual riccati equation approach involving a completion of squares does not apply directly in addition the corresponding hamilton jacobi bellman hjb equation inherently has no smooth solution to tackle these difficulties a continuous function is constructed via two riccati equations and then it is shown that this function is a viscosity solution to the hjb equation solving these riccati equations enables one to explicitly obtain the efficient frontier and efficient investment strategies for the original mean variance problem an example illustrating these results is also presented

a closed loop saddle point for zero sum linear quadratic stochastic differential games with mean field type abstract this paper is concerned with a linear quadratic zero sum differential game with mean field type the notions of explicit and implicit strategy laws are proposed based on them a closed loop formulation for saddle points in the mixed strategy law form is established in order to construct the saddle point the classical entire completion of square argument is developed to a four step completion of square argument and a pair of optimality conditions is proposed

indefinite mean field stochastic linear quadratic optimal control from finite horizon to infinite horizon in this paper the finite horizon and the infinite horizon indefinite mean field stochastic linear quadratic optimal control problems are studied firstly the open loop optimal control and the closed loop optimal strategy for the finite horizon problem are introduced and their characterizations difference and relationship are thoroughly investigated the open loop optimal control can be defined for a fixed initial state whose existence is characterized via the solvability of a linear mean field forward backward stochastic difference equation with stationary conditions and a convexity condition on the other hand the existence of a closed loop optimal strategy is shown to be equivalent to any one of the following conditions the solvability of a couple of generalized difference riccati equations the finiteness of the value function for all the initial pairs and the existence of the open loop optimal control for all the initial pairs it is then proved that the solution of the generalized difference riccati equations converges to a solution of a couple of generalized algebraic riccati equations by studying another generalized algebraic riccati equation the existence of the maximal solution of the original ones is obtained together with the fact that the stabilizing solution is the maximal solution finally we show that the maximal solution is employed to express the optimal value of the infinite horizon indefinite mean field linear quadratic optimal control furthermore for the question whether the maximal solution is the stabilizing solution the necessary and the sufficient conditions are presented for several cases

fully conservative higher order finite difference schemes for incompressible flow conservation properties of the mass momentum and kinetic energy equations for incompressible flow are specified as analytical requirements for a proper set of discrete equations existing finite difference schemes in regular and staggered grid systems are checked for violations of the conservation requirements and a few important discrepancies are pointed out in particular it is found that none of the existing higher order schemes for a staggered mesh system simultaneously conserve mass momentum and kinetic energy this deficiency is corrected through the derivation of a general family of fully conservative higher order accurate finite difference schemes for staggered grid systems finite difference schemes in a collocated grid system are also analyzed and a violation of kinetic energy conservation is revealed the predicted conservation properties are demonstrated numerically in simulations of inviscid white noise performed in a two dimensional periodic domain the proposed fourth order schemes in a staggered grid system are generalized for the case of a non uniform mesh and the resulting scheme is used to perform large eddy simulations of turbulent channel flow

on the use of kinetic energy preserving dg schemes for large eddy simulation abstract recently element based high order methods such as discontinuous galerkin dg methods and the closely related flux reconstruction fr schemes have become popular for compressible large eddy simulation les element based high order methods with riemann solver based interface numerical flux functions offer an interesting dispersion dissipation behavior for multi scale problems dispersion errors are very low for a broad range of scales while dissipation errors are very low for well resolved scales and are very high for scales close to the nyquist cutoff in some sense the inherent numerical dissipation caused by the interface riemann solver acts as a filter of high frequency solution components this observation motivates the trend that element based high order methods with riemann solvers are used without an explicit les model added only the high frequency type inherent dissipation caused by the riemann solver at the element interfaces is used to account for the missing sub grid scale dissipation due to under resolution of vortical dominated structures typical for les type setups element based high order methods suffer from stability issues caused by aliasing errors of the non linear flux terms a very common strategy to fight these aliasing issues and instabilities is so called polynomial de aliasing where interpolation is exchanged with projection based on an increased number of quadrature points in this paper we start with this common no model or implicit les iles dg approach with polynomial de aliasing and riemann solver dissipation and review its capabilities and limitations we find that the strategy gives excellent results but only when the resolution is such that about 40 of the dissipation is resolved for more realistic coarser resolutions used in classical les e g of industrial applications the iles dg strategy becomes quite inaccurate we show that there is no obvious fix to this strategy as adding for instance a sub grid scale models on top doesn t change much or in worst case decreases the fidelity even more finally the core of this work is a novel les strategy based on split form dg methods that are kinetic energy preserving the scheme offers excellent stability with full control over the amount and shape of the added artificial dissipation this premise is the main idea of the work and we will assess the les capabilities of the novel split form dg approach when applied to shock free moderate mach number turbulence we will demonstrate that the novel dg les strategy offers similar accuracy as the iles methodology for well resolved cases but strongly increases fidelity in case of more realistic coarse resolutions

higher entropy conservation and numerical stability of compressible turbulence simulations we present a numerical formulation for the treatment of nonlinear instabilities in shock free compressible turbulence simulations the formulation is high order and contains no artificial dissipation numerical stability is enhanced through semi discrete satisfaction of global conservation properties stemming from the second law of thermodynamics and the entropy equation the numerical implementation is achieved using a conservative skew symmetric splitting of the nonlinear terms the robustness of the method is demonstrated by performing unresolved numerical simulations and large eddy simulations of compressible isotropic turbulence at a very high reynolds number results show the scheme is capable of capturing the statistical equilibrium of low mach number compressible turbulent fluctuations at infinite reynolds number comparisons with the entropy splitting technique j comput phys 162 2000 33 j comput phys 178 2002 307 staggered method j comput phys 191 2 2003 392 and skew symmetric like schemes j comput phys 161 2000 114 confirm the superiority of the current approach we also discuss a flaw in the skew symmetric splitting implemented in the literature very good results are obtained based on the proper splitting

discrete time mean field stochastic linear quadratic optimal control problems this paper firstly presents necessary and sufficient conditions for the solvability of discrete time mean field stochastic linear quadratic optimal control problems secondly the optimal control within a class of linear feedback controls is investigated using a matrix dynamical optimization method thirdly by introducing several sequences of bounded linear operators the problem is formulated as an operator stochastic linear quadratic optimal control problem by the kernel range decomposition representation of the expectation operator and its pseudo inverse the optimal control is derived using solutions to two algebraic riccati difference equations finally by completing the square the two riccati equations and the optimal control are also obtained

stability analysis for different formulations of the nonlinear term in p n p n 2 spectral element discretizations of the navier stokes equations we show that for the pn pn 2 spectral element method in which velocity and pressure are approximated by polynomials of order n and n 2 respectively numerical instabilities can occur in the spatially discretized navier stokes equations both a staggered and nonstaggered arrangement of the n 2 pressure points are considered these instabilities can be masked by viscous damping at low reynolds numbers we demonstrate that the instabilities depend on the formulation of the nonlinear term the numerical discretization is stable for the convective form but unstable for the divergence and the skew symmetric form further numerical analysis indicates that this instability is not caused by nonlinear effects since it occurs for linearized systems as well an eigenvalue analysis of the fully discretized system shows that an instability is introduced by the formulation of the nonlinear term we demonstrate that the instability is related to the divergence error of the computed solution at those velocity points at which the continuity equation is not enforced

a well balanced and entropy conservative discontinuous galerkin spectral element method for the shallow water equations in this work we design an arbitrary high order accurate nodal discontinuous galerkin spectral element type method for the one dimensional shallow water equations the novel method uses a skew symmetric formulation of the continuous problem we prove that this discretisation exactly preserves the local mass and momentum furthermore we show that combined with a special numerical interface flux function the method exactly preserves the entropy which is also the total energy for the shallow water equations finally we prove that the surface fluxes the skew symmetric volume integrals and the source term are well balanced numerical tests are performed to demonstrate the theoretical findings

generalized conservative approximations of split convective derivative operators we propose a strategy to design locally conservative finite difference approximations of convective derivatives for shock free compressible flows with arbitrary order of accuracy that generalizes the approach of ducros et al 2000 1 and that can be applied as a building block of low dissipative hybrid shock capturing methods the approximations stem from application of standard central difference formulas to split forms of the convective terms in the compressible euler equations which guarantee strong numerical stability and near energy preservation in the inviscid limit a convenient implementation of the high order fluxes is suggested which guarantees improved computational efficiency over existing methods numerical tests performed for isotropic turbulence at zero viscosity show stability of schemes with order of accuracy up to ten and effectiveness of convective splitting of kennedy and gruber 2008 2 in providing extra stability in the presence of strong density variations numerical simulations of compressible turbulent boundary layer flow indicate suitability of the method for non uniform grids and overall support superior computational efficiency of high order schemes

split form nodal discontinuous galerkin schemes with summation by parts property for the compressible euler equations fisher and carpenter 2013 12 found a remarkable equivalence of general diagonal norm high order summation by parts operators to a subcell based high order finite volume formulation this equivalence enables the construction of provably entropy stable schemes by a specific choice of the subcell finite volume flux we show that besides the construction of entropy stable high order schemes a careful choice of subcell finite volume fluxes generates split formulations of quadratic or cubic terms thus by changing the subcell finite volume flux to a specific choice we are able to generate in a systematic way all common split forms of the compressible euler advection terms such as the ducros splitting and the kennedy and gruber splitting although these split forms are not entropy stable we present a systematic way to prove which of those split forms are at least kinetic energy preserving with this we construct a unified high order split form dg framework we investigate with three dimensional numerical simulations of the inviscid taylorgreen vortex and show that the new split forms enhance the robustness of high order simulations in comparison to the standard scheme when solving turbulent vortex dominated flows in fact we show that for certain test cases the novel split form discontinuous galerkin schemes are more robust than the discontinuous galerkin scheme with over integration

linear quadratic mean field stochastic zero sum differential games abstract in this paper we consider the two player linear quadratic mean field stochastic differential game lq mf szsdg where the expected values of state and players control variables are included in the corresponding mean field stochastic system and the objective functional we characterize the explicit condition under which the feedback saddle point equilibrium for the lq mf szsdg exists the results are obtained by using the completion of squares method and the ordered interchangeability property of multiple saddle points we show that the corresponding saddle point equilibrium is linear in state which is characterized by the two coupled riccati differential equations crdes we also discuss the solvability conditions of the crdes numerical results are presented to verify the theoretical results of the paper

asymptotically optimal decentralized control for large population stochastic multiagent systems the interaction of interest coupled decision makers and the uncertainty of individual behavior are prominent characteristics of multiagent systems mas how to break through the framework of conventional control theory which aims at single decision maker and single decision objective and to extend the methodology and tools in the stochastic adaptive control theory to analyze mas are of great significance in this paper a preliminary exploration is made in this direction and the decentralized control problem is considered for large population stochastic mas with coupled cost functions different from the deterministic discounted costs in the existing differential game models a time averaged stochastic cost function is adopted for each agent the decentralized control law is constructed based on the state aggregation method and tracking like quadratic optimal control by using probability limit theory the stability and optimality of the closed loop system are analyzed the main contributions of this paper include the following points 1 the concepts of asymptotic nash equilibrium in probability and almost surely respectively are introduced and the relationship between these concepts is illuminated which provide necessary tools for analyzing the optimality of the decentralized control laws 2 the closed loop system is shown to be almost surely uniformly stable and bounded independently of the number of agents n 3 the population state average psa is shown to converge to the infinite population mean ipm trajectory in the sense of both l2 norm and time average almost surely as n increases to infinity 4 the decentralized control law is designed and shown to be almost surely asymptotically optimal the cost of each agent based on local measurements converges to that based on global measurements almost surely as n increases to infinity

further improvement and analysis of ccd scheme dissipation discretization and de aliasing properties in this paper we further analyze a combined compact difference ccd scheme proposed recently t k sengupta v lakshmanan v v s n vijay a new combined stable and dispersion relation preserving compact scheme for non periodic problems j comput phys 228 8 2009 3048 3071 for its dissipation discretization properties to show that its superiority also helps in controlling aliasing error for a benchmark internal flow however application of the same ccd method to study the receptivity of a boundary layer experiencing adverse pressure gradient is not successful this is traced to the nature of the equilibrium flow where the better dissipation property is not helpful in the inviscid part of the flow where the aliasing problems continue to persist a further modification is proposed to the ccd method here to solve complex physical problems requiring information on higher order disturbance quantities as in problems of flow receptivity and instability

group velocity in finite difference schemes the relevance of group velocity to the behavior of finite difference models of time dependent partial differential equations is surveyed and illustrated applications involve the propagation of wave packets in one and two dimensions numerical dispersion the behavior of parasitic waves and the stability analysis of initial boundary value problems

discretely conservative finite difference formulations for nonlinear conservation laws in split form theory and boundary conditions the lax wendroff theorem stipulates that a discretely conservative operator is necessary to accurately capture discontinuities the discrete operator however need not be derived from the divergence form of the continuous equations indeed conservation law equations that are split into linear combinations of the divergence and product rule form and then discretized using any diagonal norm skew symmetric summation by parts sbp spatial operator yield discrete operators that are conservative furthermore split form discretely conservation operators can be derived for periodic or finite domain sbp spatial operators of any order examples are presented of a fourth order sbp finite difference operator with second order boundary closures sixth and eighth order constructions are derived and are supplied in an accompanying text file

symmetry preserving discretization of turbulent flow we propose to perform turbulent flow simulations in such manner that the difference operators do have the same symmetry properties as the underlying differential operators i e the convective operator is represented by a skew symmetric coefficient matrix and the diffusive operator is approximated by a symmetric positive definite matrix mimicking crucial properties of differential operators forms in itself a motivation for discretizing them in a certain manner we give it a concrete form by noting that a symmetry preserving discretization of the navier stokes equations is stable on any grid and conserves the total mass momentum and kinetic energy for the latter the physical dissipation is to be turned off of coarse being stable on any grid the choice of the grid may be based on the required accuracy solely and the main question becomes how accurate is a symmetry preserving discretization its accuracy is tested for a turbulent flow in a channel by comparing the results to those of physical experiments and previous numerical studies the comparison is carried out for a reynolds number of 5600 which is based on the channel width and the mean bulk velocity based on the channel half width and wall shear velocity the reynolds number becomes 180 the comparison shows that with a fourth order symmetry preserving method a 64 64 32 grid suffices to perform an accurate numerical simulation

social optima in mean field lqg control centralized and decentralized strategies we study a class of linear quadratic gaussian lqg control problems with n decision makers where the basic objective is to minimize a social cost as the sum of n individual costs containing mean field coupling the exact socially optimal solution determining a particular pareto optimum requires centralized information for each agent and has high implementational complexity as an alternative we subsequently exploit a mean field structure in the centralized optimal control problem to develop decentralized cooperative optimization so that each agent only uses its own state and a function which may be computed offline the resulting set of strategies asymptotically achieves the social optimum as n a key feature in this scheme is to let each agent optimize a new cost as the sum of its own cost and another component capturing its social impact on all other agents we also discuss the relationship between the decentralized cooperative solution and the so called nash certainty equivalence based solution presented in previous work on mean field lqg games

kinetic energy and entropy preserving schemes for compressible flows by split convective forms abstract this study proposes a kinetic energy and entropy preserving scheme to achieve stable and non dissipative compressible flow simulations the proposed scheme is built in such a way that the numerical formulations satisfy the analytical relations among the governing equations at the discrete level the mass and momentum convective terms are recast into split convective forms once the mass and momentum equations are discretized the constraints given by the analytical relations subsequently determine the formulations of the numerical fluxes solved in the total energy equation an analysis reveals that satisfying the analytical relations at the discrete level is essential for solving the energy exchange between the kinetic energy and internal energy correctly in the total energy equation and therefore important for entropy conservation taylor green vortex and euler isotropic turbulence simulations at infinite reynolds number are conducted to verify the analysis given in this paper the proposed scheme achieves both kinetic energy conservation in the incompressible limit and entropy conservation as well as convergences of thermodynamic variable fluctuations whereas existing kinetic energy preserving schemes fail entropy conservation and the thermodynamic variable fluctuations diverge

using high order methods on adaptively refined block structured meshes derivatives interpolations and filters block structured adaptive mesh refinement amr is used for efficient resolution of partial differential equations pdes solved on large computational domains by clustering mesh points only where required by large gradients previous work has indicated that fourth order convergence can be achieved on such meshes by using a suitable combination of high order derivative interpolation and filter stencils and can deliver significant computational savings over conventional second order methods at engineering error tolerances in this paper we explore the interactions between the errors introduced by the discretized operators for derivatives interpolations and filters we develop general expressions for high order derivative interpolation and filter stencils applicable in multiple dimensions using a fourier approach to facilitate high order block structured amr implementations these stencils are derived under the assumption that the fields that they are applied to are smooth for a given derivative stencil and thus a given order of accuracy the necessary interpolation order is found to be dependent on the highest spatial derivative in the pde being solved this is demonstrated empirically using one and two dimensional model equations by observing the increase in delivered accuracy as the order of accuracy of the interpolation stencil is increased we also examine the empirically observed order of convergence as the effective resolution of the mesh is increased by successively adding levels of refinement with different orders of derivative interpolation and filter stencils the procedure devised here is modular and its various pieces i e the derivative interpolation and filter stencils can be extended independently to higher orders and dimensions in the case of interpolation stencils the application of these methods often requires nontrivial logic especially near domain boundaries this logic along with the stencils used in this study are available as a freely downloadable software library

revisiting numerical errors in direct and large eddy simulations of turbulence physical and spectral spaces analysis abstract some recent studies on the effects of truncation and aliasing errors on the large eddy simulation les of turbulent flows via the concept of modified wave number are revisited it is shown that all the results obtained for nonlinear partial differential equations projected and advanced in time in spectral space are not straightforwardly applicable to physical space calculations due to the nonequivalence by fourier transform of spectral aliasing errors and numerical errors on a set of grid points in physical space the consequences of spectral static aliasing errors on a set of grid points are analyzed in one dimension of space for quadratic products and their derivatives the dynamical process that results through time stepping is illustrated on the burgers equation a method based on midpoint interpolation is proposed to remove in physical space the static grid point errors involved in divergence forms it is compared to the sharp filtering technique on finer grids suggested by previous authors global performances resulting from combination of static aliasing errors and truncation errors are then discussed for all classical forms of the convective terms in navier stokes equations some analytical results previously obtained on the relative magnitude of subgrid scale terms and numerical errors are confirmed with 3d realistic random fields the physical space dynamical behavior and the stability of typical associations of numerical schemes and forms of nonlinear terms are finally evaluated on the les of self decaying homogeneous isotropic turbulence it is shown that the convective form if conservative properties are not strictly required associated with highly resolving compact finite difference schemes provides the best compromise which is nearly equivalent to dealiased pseudo spectral calculations

indefinite stochastic linear quadratic control and generalized differential riccati equation a stochastic linear quadratic lq control problem is indefinite when the cost weighting matrices for the state and the control are allowed to be indefinite indefinite stochastic lq theory has been extensively developed and has found interesting applications in finance however there remains an outstanding open problem which is to identify an appropriate riccati type equation whose solvability is it equivalent to the solvability of the indefinite stochastic lq problem this paper solves this open problem for lq control in a finite time horizon a new type of differential riccati equation called the generalized differential riccati equation is introduced which involves algebraic equality inequality constraints and a matrix pseudoinverse it is then shown that the solvability of the generalized riccati equation is not only sufficient but also necessary for the well posedness of the indefinite lq problem and the existence of optimal feedback open loop controls moreover all of the optimal controls can be identified via the solution to the riccati equation an example is presented to illustrate the theory developed

skew symmetric form of convective terms and fully conservative finite difference schemes for variable density low mach number flows the form of convective terms for compressible flow equations is discussed in the same way as for an incompressible one by morinishi et al y morinishi t s lund o v vasilyev p moin fully conservative higher order finite difference schemes for incompressible flow j comput phys 124 1998 90 and fully conservative finite difference schemes suitable for shock free unsteady compressible flow simulations are proposed commutable divergence advective and skew symmetric forms of convective terms are defined by including the temporal derivative term for compressible flow these forms are analytically equivalent if the continuity is satisfied and the skew symmetric form is secondary conservative without the aid of the continuity while the divergence form is primary conservative the relations between the present and existing quasi skew symmetric forms are also revealed commutable fully discrete finite difference schemes of convection are then derived in a staggered grid system and they are fully conservative provided that the corresponding discrete continuity is satisfied in addition a semi discrete convection scheme suitable for compact finite difference is presented based on the skew symmetric form the conservation properties of the present schemes are demonstrated numerically in a three dimensional periodic inviscid flow the proposed fully discrete fully conservative second order accurate scheme is also used to perform the dns of compressible isotropic turbulence and the simulation of open cavity flow

theoretical characteristics of the vibration of sandwich plates with in plane negative poisson s ratio values abstract this paper is concerned with re entrant cell honeycombs which show in plane negative poisson s ratio values in which their anisotropic mechanical properties are described using the cellular material theory out of plane shear moduli are affected by the unit cell geometric parameters and for some ranges of the latter it is possible to obtain higher values of the shear moduli compared to those of a regular hexagonal honeycomb in particular for cell geometries with a negative poisson s ratio a first order sandwich plate theory is applied in order to obtain the fundamental frequencies of sandwich laminates in cylindrical bending and for the simply supported case sensitivities of the frequencies per unit mass versus the geometric cell parameters are also calculated the results suggest that the dynamic performance of a sandwich structure could be significantly improved with a proper design of the unit cell shape of the honeycomb in particular re entrant cell cores offer improvements in bending stiffness capabilities for particular cell parameter ranges

on the orthogonal wavelet transform for model reduction synthesis of structures model reduction techniques are widely used in numerical structural dynamics to synthesize large matrix systems and perform fast computations of natural frequencies and mode shapes several new model reduction techniques have been proposed in recent years methods such as the guyan or static reduction dynamic condensation the improved reduced system irs approach or the system equivalent reduction expansion serep may be used with good results especially over low frequency ranges 1 5 while the guyan is based solely on the sti ness matrix reduction the serep has been shown to map exactly the mass and sti ness matrices for a desired set of modes at an arbitrary set of d o f using a dynamic condensation technique with the full modal basis of the system on the other hand the irs uses guyan reduction as an estimate of the reduction system and then makes adjustments to compensate for the inertia e ects that were ignored in the guyan process without the penalty of requiring a full eigensolution advantages of using these techniques are their relative e ciency and cost e ectiveness when compared with analysis on the full system model a disadvantage however is the approximate system descriptions that result from their use sometimes leading to serious error such methods also require skilled selection of the number and location of the reduced degrees of freedom that can make up the reduced system if the degrees of freedom that represent the reduced system are chosen improperly poor solution results will follow 4 moreover classical model reduction techniques are not appropriate for synthesizing the dynamic behaviour of structures in the middleand high frequency range or with high modal densities this fact leads the structural analyst to prepare large numerical fem models with high computational costs or to use statistical energy analysis sea methods to predict the dynamic behaviour of the structure for high frequency ranges on the other hand large nite element models are already prepared for static analysis purposes their lack of use for dynamic analysis leads to an increase of the global pre processing time which greatly consumes manpower resources the existence of a reliable condensation technique for structural middle and high frequencies would also speed up the evaluation of novel materials and structures concepts for aerospace and naval applications 6 the aim of this paper is to explore the orthogonal wavelet transform for model synthesis of structures in order to preserve the middleand high frequency spectra components only a new technique is illustrated using two simple simulated examples namely a simply supported beam and a framework structure the technique is intended as an initial step

numerically stable formulations of convective terms for turbulent compressible flows abstract a systematic analysis of the discrete conservation properties of non dissipative central difference approximations of the compressible navier stokes equations is reported a generalized splitting of the nonlinear convective terms is considered and energy preserving formulations are fully characterized by deriving a two parameter family of split forms previously developed formulations reported in literature are shown to be particular members of this family novel splittings are introduced and discussed as well furthermore the conservation properties yielded by different choices for the energy equation i e total and internal energy entropy are analyzed thoroughly it is shown that additional preserved quantities can be obtained through a suitable adaptive selection of the split form within the derived family local conservation of primary invariants which is a fundamental property to build high fidelity shock capturing methods is also discussed in the paper numerical tests performed for the taylor green vortex at zero viscosity fully confirm the theoretical findings and show that a careful choice of both the splitting and the energy formulation can provide remarkably robust and accurate results

compressible large eddy simulation of separation control on a wall mounted hump compressible large eddy simulations of turbulent flow over a wall mounted hump with active flow control are performed and compared with previous experiments the flow is characterized by the unsteady separation before the steep trailing edge which naturally reattaches downstream of the hump to form an unsteady turbulent separation bubble the low mach number large eddy simulation demonstrated a good prediction of surface pressure coefficient separation bubble length and velocity profiles compared with experiments the effect of compressibility on the baseline flow is documented and analyzed and is found to increase the separation bubble size due to a reduced growth rate control is applied just before the natural separation point via steady suction and zero net mass flux oscillatory forcing and steady suction is shown to be more effective in decreasing the size of the separation bubble and pressure drag for the control parameters investigated controlled flow at a compressible subsonic mach number is applied and found to be slightly less effective than the same control parameters at low mach numbers

stabilized non dissipative approximations of euler equations in generalized curvilinear coordinates we discuss stabilization strategies for finite difference approximations of the compressible euler equations in generalized curvilinear coordinates that do not rely on explicit upwinding or filtering of the physical variables our approach rather relies on a skew symmetric like splitting of the convective derivatives that guarantees preservation of kinetic energy in the semi discrete low mach number limit a locally conservative formulation allows efficient implementation and easy incorporation into existing compressible flow solvers the validity of the approach is tested for benchmark flow cases including the propagation of a cylindrical vortex and the head on collision of two vortex dipoles the tests support high accuracy and superior stability over conventional central discretization of the convective derivatives the potential use for dns les of turbulent compressible flows in complex geometries is discussed

generalized hypergeometric function solutions for transverse vibration of a class of non uniform annular plates free vibration analysis of thin annular plate with thickness varying monotonically in arbitrary power form is presented transformation of variable is introduced to translate the governing equation for the free vibration of thin annular plate into a fourth order generalized hypergeometric equation the analytical solutions in terms of generalized hypergeometric function taking either logarithmic or non logarithmic forms are proposed which encompass existing published solutions as special cases to illustrate the use of the closed form solutions presented free vibration analyses of a thin annular ultra high molecular weight polyethylene and a steel plate with linear and nonlinear thickness variation are performed the results are compared with those from fe analysis based on kirchhoff thin plate theory and 3d elasticity theory indicating good agreement

stochastic linear quadratic regulators with indefinite control weight costs ii in part i of this paper s chen x li and x zhou siam j control optim 36 1998 pp 1685 1702 an optimization model of stochastic linear quadratic regulators lqrs with indefinite control cost weighting matrices is proposed and studied in this sequel the problem of solving lqr models with system diffusions dependent on both state and control variables which is left open in part i is tackled first the solvability of the associated stochastic riccati equations sres is studied in the normal case namely all the state and control weighting matrices and the terminal matrix in the cost functional are nonnegative definite with at least one positive definite which in turn leads to an optimal state feedback control of the lqr problem in the general indefinite case the problem is decomposed into two optimal lqr problems one with a forward dynamics and the other with a backward dynamics the well posedness and solvability of the original lqr problem are then obtained by solving these two subproblems and an optimal control is explicitly constructed examples are presented to illustrate the results

truncation error analysis of the rotational form for the convective terms in the navier stokes equation the truncation error of the rotational form for the convective terms in the navier stokes equation is examined in the direct numerical simulation dns of the fully developed turbulent channel flow in which the low order finite difference method was used for the partial derivatives in the wall normal direction an estimate of the truncation error using the taylor expansion revealed that this truncation error term is comparable to the rotational stress generation term represented by the nonlineark model in the reynolds averaged turbulence models in the governing equations for the reynolds shear stress and the normal stress due to the coriolis force term acting in a channel flow rotating about the spanwise axis the effective angular velocity due to the truncation error term was dependent on the distance from the wall and the turbulence was reduced on both sides of the walls analogously to the laminarization of turbulence on the suction side of the conventional rotating channel flow this analogy was further assessed in the dns of the channel flow rotating with this effective angular velocity the time development of the wall friction velocity was similar to that obtained using the rotational form

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

stochastic linear quadratic regulators with indefinite control weight costs this paper considers optimal minimizing control of stochastic linear quadratic regulators lqrs the assumption that the control weight costs must be positive definite inherited from the determ

stochastic maximum principle for mean field type optimal control under partial information this technical note is concerned with a partially observed optimal control problem whose novel feature is that the cost functional is of mean field type hence determining the optimal control is time inconsistent in the sense that bellman s dynamic programming principle does not hold a maximum principle is established using girsanov s theorem and convex variation some nonlinear filtering results for backward stochastic differential equations bsdes are developed by expressing the solutions of the bsdes as some ito s processes an illustrative example is demonstrated in terms of the maximum principle and the filtering

high order fluxes for conservative skew symmetric like schemes in structured meshes developing high order non dissipative schemes is an important research task for both steady and unsteady flow computations we take as a starting point the built in de aliasing property of the discretized skew symmetric form for the non linear terms of the navier stokes equations recalled in kravchenko and moin 1 two families of high order locally conservative schemes matching this discretized skew symmetric form are considered and rewritten in terms of telescopic fluxes for both finite difference and finite volume approximations in the context of compressible flows the jameson s scheme 2 is shown to be the second order member of larger families of skew symmetric like centered schemes the fourth order finite volume and finite difference and the sixth order finite difference schemes which belong to this family are provided the proposed schemes are extended to shock capturing schemes either by modifying the jameson s artificial viscosity or by hybriding the centered flux with weno 3 fluxes an adapted interpolation is proposed to extend the use of the proposed schemes to non regular grids several tests are provided showing that the conjectured order is properly recovered even with irregular meshes and that the shock capturing properties allow us to improve the second order results for standard test cases the improvement due to fourth order is then confirmed for the estimation of the growth of two ts waves and three crow instability dimensional unstable modes for both confined and free shear flows the last application concerns the steady computation using the spalart allmaras model of a separated boundary layer it confirms that the use of a high order scheme improves the results even in this type of steady applications

an entropy stable nodal discontinuous galerkin method for the two dimensional shallow water equations on unstructured curvilinear meshes with discontinuous bathymetry we design an arbitrary high order accurate nodal discontinuous galerkin spectral element approximation for the non linear two dimensional shallow water equations with non constant possibly discontinuous bathymetry on unstructured possibly curved quadrilateral meshes the scheme is derived from an equivalent flux differencing formulation of the split form of the equations we prove that this discretization exactly preserves the local mass and momentum furthermore combined with a special numerical interface flux function the method exactly preserves the mathematical entropy which is the total energy for the shallow water equations by adding a specific form of interface dissipation to the baseline entropy conserving scheme we create a provably entropy stable scheme that is the numerical scheme discretely satisfies the second law of thermodynamics finally with a particular discretization of the bathymetry source term we prove that the numerical approximation is well balanced we provide numerical examples that verify the theoretical findings and furthermore provide an application of the scheme for a partial break of a curved dam test problem

a further study of numerical errors in large eddy simulations numerical errors in large eddy simulations les arise from aliasing and discretization errors and errors in the subfilter scale sfs turbulence model using a direct numerical simulation dns dataset of stably stratified shear flow to perform a priori tests we compare the numerical error from several finite difference schemes to the magnitude of the sfs force this is an extension of ghosal s analysis j comput phys 125 1996 187 to realistic flow fields by evaluating different grid resolutions as well as different filter grid ratios we provide guidelines for les for a second order finite difference scheme a filter grid ratio of at least four is desired for a sixth order pade scheme a filter grid ratio of two is sufficient

large population cost coupled lqg problems with nonuniform agents individual mass behavior and decentralized varepsilon nash equilibria we consider linear quadratic gaussian lqg games in large population systems where the agents evolve according to nonuniform dynamics and are coupled via their individual costs a state aggregation technique is developed to obtain a set of decentralized control laws for the individuals which possesses an epsiv nash equilibrium property a stability property of the mass behavior is established and the effect of inaccurate population statistics on an isolated agent is also analyzed by variational techniques

an entropy stable discontinuous galerkin approximation for the incompressible navier stokes equations with variable density and artificial compressibility abstract we present a provably stable discontinuous galerkin spectral element method for the incompressible navier stokes equations with artificial compressibility and variable density stability proofs which include boundary conditions that follow a continuous entropy analysis are provided we define a mathematical entropy function that combines the traditional kinetic energy and an additional energy term for the artificial compressibility and derive its associated entropy conservation law the latter allows us to construct a provably stable split form nodal discontinuous galerkin dg approximation that satisfies the summation by parts simultaneous approximation term sbp sat property the scheme and the stability proof are presented for general curvilinear three dimensional hexahedral meshes we use the exact riemann solver and the bassi rebay 1 br1 scheme at the inter element boundaries for inviscid and viscous fluxes respectively and an explicit low storage runge kutta rk3 scheme to integrate in time we assess the accuracy and robustness of the method by solving a manufactured solution the kovasznay flow a lid driven cavity the inviscid taylor green vortex and the rayleigh taylor instability

linear exponential quadratic control for mean field stochastic systems in this technical note we consider linear exponential quadratic leq control for mean field stochastic differential equations mfsdes the mfsde includes the expectation value of state and control and the objective functional is exponential of a quadratic functional in state control and their expectations we obtain the explicit optimal solution as well as the optimal cost the corresponding optimal solution is linear in state and its expectation which is characterized by the riccati differential equations rdes the results are obtained by showing that after applying the completion of squares method the remaining exponentiated stochastic integral and additional rde terms can be eliminated together by taking expectation since they constitute the associated radon nikodym derivative as an extension of the problem the leq zero sum differential game is considered for which we obtain the explicit optimal solution saddle point equilibrium as well as the optimal cost