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Orthogonal Decomposition (orthogonal + decomposition)

Distribution by Scientific Domains
Engineering83%

Kinds of Orthogonal Decomposition

  • proper orthogonal decomposition
    		•

    Selected Abstracts

    The flow-field downstream of a collapsible tube during oscillation onset

    INTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN BIOMEDICAL ENGINEERING, Issue 5 2009
    N. K. Truong
    Abstract The flow-field immediately downstream of a collapsible tube during oscillation onset starting from the collapsed state was measured using two-dimensional high-speed particle image velocimetry. Both tube and fluid were chosen to produce oscillation at the lowest possible Reynolds number, of just over 300. The flow was examined in the plane formed by the tube axis extended into the downstream pipe and the major axis of the tube collapse cross-section. The resulting time-series of spatial fields of 2D velocity vectors was analysed by frequency content and by proper orthogonal decomposition. Areas of the flow where oscillation initially occurs were identified. Flow disturbances centred at various frequencies were identified, some associated with the growing oscillation arising from the instability of the fluid,structure interaction between the main flow and the tube and others associated with the instability of the confined twin jets emanating from the collapsed-tube throat. Copyright © 2009 John Wiley & Sons, Ltd. [source]

    On the stability and convergence of a Galerkin reduced order model (ROM) of compressible flow with solid wall and far-field boundary treatment,

    INTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN ENGINEERING, Issue 10 2010
    I. Kalashnikova
    Abstract A reduced order model (ROM) based on the proper orthogonal decomposition (POD)/Galerkin projection method is proposed as an alternative discretization of the linearized compressible Euler equations. It is shown that the numerical stability of the ROM is intimately tied to the choice of inner product used to define the Galerkin projection. For the linearized compressible Euler equations, a symmetry transformation motivates the construction of a weighted L2 inner product that guarantees certain stability bounds satisfied by the ROM. Sufficient conditions for well-posedness and stability of the present Galerkin projection method applied to a general linear hyperbolic initial boundary value problem (IBVP) are stated and proven. Well-posed and stable far-field and solid wall boundary conditions are formulated for the linearized compressible Euler ROM using these more general results. A convergence analysis employing a stable penalty-like formulation of the boundary conditions reveals that the ROM solution converges to the exact solution with refinement of both the numerical solution used to generate the ROM and of the POD basis. An a priori error estimate for the computed ROM solution is derived, and examined using a numerical test case. Published in 2010 by John Wiley & Sons, Ltd. [source]

    A reduced-order simulated annealing approach for four-dimensional variational data assimilation in meteorology and oceanography

    INTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN FLUIDS, Issue 11 2008
    I. Hoteit
    Abstract Four-dimensional variational data assimilation in meteorology and oceanography suffers from the presence of local minima in the cost function. These local minima arise when the system under study is strongly nonlinear. The number of local minima further dramatically increases with the length of the assimilation period and often renders the solution to the problem intractable. Global optimization methods are therefore needed to resolve this problem. However, the huge computational burden makes the application of these sophisticated techniques unfeasible for large variational data assimilation systems. In this study, a Simulated Annealing (SA) algorithm, complemented with an order-reduction of the control vector, is used to tackle this problem. SA is a very powerful tool of combinatorial minimization in the presence of several local minima at the cost of increasing the execution time. Order-reduction is then used to reduce the dimension of the search space in order to speed up the convergence rate of the SA algorithm. This is achieved through a proper orthogonal decomposition. The new approach was implemented with a realistic eddy-permitting configuration of the Massachusetts Institute of Technology general circulation model (MITgcm) of the tropical Pacific Ocean. Numerical results indicate that the reduced-order SA approach was able to efficiently reduce the cost function with a reasonable number of function evaluations. Copyright © 2008 John Wiley & Sons, Ltd. [source]

    Reduced-order controllers for control of flow past an airfoil

    INTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN FLUIDS, Issue 5 2006
    S. S. Ravindran
    Abstract Reduced-order controller design by means of reduced-order model for control of a wake flow is presented. Reduced-order model is derived by combining the Galerkin projection with proper orthogonal decomposition (POD) or with other related reduced-order approaches such as singular value decomposition or reduced-basis method. In the present investigation, we discuss the applicability of the reduced-order approaches for fast computation of the optimal control for control of vortex shedding behind a thin airfoil through unsteady blowing on the airfoil surface. Accuracy of the reduced-order model is quantified by comparing flow fields obtained from the reduced-order models with those from the full-order simulations under the same free-stream conditions. A control of vortex shedding is demonstrated for Reynolds number 100. It is found that downstream directed blowing on the upper surface of the airfoil near the leading edge is more efficient in mitigating flow separation and suppressing the vortex shedding. Copyright © 2005 John Wiley & Sons, Ltd. [source]

    Reduced-order suboptimal control design for a class of nonlinear distributed parameter systems using POD and ,,D techniques

    OPTIMAL CONTROL APPLICATIONS AND METHODS, Issue 3 2008
    Radhakant Padhi
    Abstract A new computational tool is presented in this paper for suboptimal control design of a class of nonlinear distributed parameter systems (DPSs). In this systematic methodology, first proper orthogonal decomposition-based problem-oriented basis functions are designed, which are then used in a Galerkin projection to come up with a low-order lumped parameter approximation. This technique has evolved as a powerful model reduction technique for DPSs. Next, a suboptimal controller is designed using the emerging ,,D technique for lumped parameter systems. This time domain control solution is then mapped back to the distributed domain using the same basis functions, which essentially leads to a closed form solution for the controller in a state-feedback form. We present this technique for the class of nonlinear DPSs that are affine in control. Numerical results for a benchmark problem as well as for a more challenging representative real-life nonlinear temperature control problem indicate that the proposed method holds promise as a good optimal control design technique for the class of DPSs under consideration. Copyright © 2007 John Wiley & Sons, Ltd. [source]

    Adaptive ensemble reduction and inflation

    THE QUARTERLY JOURNAL OF THE ROYAL METEOROLOGICAL SOCIETY, Issue 626 2007
    B. Uzunoglu
    Abstract In this paper we address the question of whether it is possible consistently to reduce the number of ensemble members at a late stage in the assimilation cycle. As an extension, we consider the question: given this reduction, is it possible to reintroduce ensemble members at a later time, if the accuracy is decreasing significantly? To address these questions, we present an adaptive methodology for reducing and inflating an ensemble by projecting the ensemble onto a limited number of its leading empirical orthogonal functions, through a proper orthogonal decomposition. We then apply this methodology with a global shallow-water-equations model on the sphere in conjunction with an ensemble filter developed at Florida State University and the Cooperative Institute for Research in the Atmosphere at Colorado State University. An adaptive methodology for reducing and inflating ensembles is successfully applied in two contrasting test cases with the shallow-water-equations model. It typically results in a reduction in the number of ensemble members required for successful implementation, by a factor of up to two. Copyright © 2007 Royal Meteorological Society [source]