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Adjoint Method (adjoint + method)
Selected AbstractsA new approach to avoid excessive numerical diffusion in Eulerian,Lagrangian methodsINTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN BIOMEDICAL ENGINEERING, Issue 11 2008A. Younes Abstract Lumping is often used to avoid non-physical oscillations for advection,dispersion equations but is known to add numerical diffusion. A new approach is detailed in order to avoid excessive numerical diffusion in Eulerian,Lagrangian methods when several time steps are used. The basic idea of this approach is to keep the same characteristics during all time steps and to interpolate only the concentration variations due to the dispersion process. In this way, numerical diffusion due to the lumping is removed at the end of each time step. The method is combined with the Eulerian,Lagrangian localized adjoint method (ELLAM) which is a mass conservative characteristic method for solving the advection,dispersion equation. Two test problems are modelled to compare the proposed method to the consistent, the full and the selective lumping approaches for linear and non-linear transport equations. Copyright © 2007 John Wiley & Sons, Ltd. [source] Data assimilation and inverse problem for fluid traffic flow models and algorithmsINTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN ENGINEERING, Issue 6 2008P. Jaisson Abstract This article deals with traffic data assimilation and algorithms that are able to predict the traffic flow on a road section. The traffic flow is modellized by the Aw,Rascle hyperbolic system. We have to minimize a functional whose optimization variables are initial condition. We use the Roe method to compute the solution to the traffic flow modelling system. Then we compute the gradient of the functional by an adjoint method. This gradient will be used to optimize the functional. Copyright © 2008 John Wiley & Sons, Ltd. [source] Aerodynamic shape optimization on overset grids using the adjoint methodINTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN FLUIDS, Issue 12 2010Wei Liao Abstract This paper deals with the use of the continuous adjoint equation for aerodynamic shape optimization of complex configurations with overset grids methods. While the use of overset grid eases the grid generation process, the non-trivial task of ensuring communication between overlapping grids needs careful attention. This need is effectively addressed by using a practically useful technique known as the implicit hole cutting (IHC) method. The method depends on a simple cell selection process based on the criterion of cell size, and all grid points including interior points and fringe points are treated indiscriminately in the computation of the flow field. This paper demonstrates the simplicity of the IHC method for the adjoint equation. Similar to the flow solver, the adjoint equations are solved on conventional point-matched and overlapped grids within a multi-block framework. Parallel computing with message passing interface is also used to improve the overall efficiency of the optimization process. The method is successfully demonstrated in several two- and a three-dimensional shape optimization cases for both external and internal flow problems. Copyright © 2009 John Wiley & Sons, Ltd. [source] Numerical solution of steady free-surface flows by the adjoint optimal shape design methodINTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN FLUIDS, Issue 1 2003E. H. van Brummelen Abstract Numerical solution of flows that are partially bounded by a freely moving boundary is of great importance in practical applications such as ship hydrodynamics. Free-boundary problems can be reformulated into optimal shape design problems, which can in principle be solved efficiently by the adjoint method. In this work we investigate the suitability of the adjoint shape optimization method for solving steady free-surface flows. The asymptotic convergence behaviour of the method is determined for free-surface flows in 2D and 3D. It is shown that the convergence behaviour depends sensitively on the occurrence of critical modes. The convergence behaviour is moreover shown to be mesh-width independent, provided that proper preconditioning is applied. Numerical results are presented for 2D flow over an obstacle in a channel. The observed convergence behaviour is indeed mesh-width independent and conform the derived asymptotic estimates. Copyright © 2003 John Wiley & Sons, Ltd. [source] On the use of large time steps with ELLAM for transport with kinetic reactions over heterogeneous domainsAICHE JOURNAL, Issue 5 2009Marwan Fahs Abstract An Eulerian Lagrangian localized adjoint method (ELLAM) is considered for the resolution of advection-dominated transport problems in porous media. Contrary to standard Eulerian methods, ELLAM can use large time steps because the advection term is approximated accurately without any CFL restriction. However, it is shown in this article that special care must be taken for the approximation of the dispersive and reactive terms when large time steps are used over heterogeneous domains. An alternative procedure is proposed. It is based on an equivalent dispersion coefficient or an equivalent reaction rate when different zones are encountered during the tracking. Numerical experiments are performed with variable dispersion or variable reaction rates over space (including nonlinearity). When classical ELLAM require numerous time steps to handle heterogeneity, the alternative procedure is shown to perform with the same accuracy in a single time step. © 2009 American Institute of Chemical Engineers AIChE J, 2009 [source] Characteristic-mixed covolume methods for advection-dominated diffusion problemsNUMERICAL LINEAR ALGEBRA WITH APPLICATIONS, Issue 9 2006Zhangxin Chen Abstract Characteristic-mixed covolume methods for time-dependent advection-dominated diffusion problems are developed and studied. The diffusion term in these problems is discretized using covolume methods applied to the mixed formulation of the problems on quadrilaterals, and the temporal differentiation and advection terms are treated by characteristic tracking schemes. Three characteristic tracking schemes are studied in the context of mixed covolume methods: the modified method of characteristics, the modified method of characteristics with adjusted advection, and the Eulerian,Lagrangian localized adjoint method. The proposed methods preserve the conceptual and computational merits of both characteristics-based schemes and the mixed covolume methods. Existence and uniqueness of a solution to the discrete problem arising from the methods is shown. Stability and convergence properties of these methods are also obtained; unconditionally stable results and error estimates of optimal order are established. Copyright © 2006 John Wiley & Sons, Ltd. [source] Robust estimation of the normal to a curve using optimal controlOPTIMAL CONTROL APPLICATIONS AND METHODS, Issue 4 2008J. Fehrenbach Abstract We propose an optimal control problem whose optimal command approximates the normal vector field to a given curve. This problem is obtained by studying a partial differential equation satisfied by a map that jumps across the given curve. The gradient of the cost function is then estimated by an adjoint method, and an explicit algorithm is proposed to obtain the optimal command. Examples show that this numerical estimation of the normal is robust, in the sense that when the curve is not a simple closed curve, or when it is incomplete (dashed), the solution is still a good approximation of the normal. As applications, we show how the optimal state can help closing discontinuous curves and improve image restoration; it also provides a coloring of simple planar maps. Copyright © 2007 John Wiley & Sons, Ltd. [source] Estimating observation impact without adjoint model in an ensemble Kalman filterTHE QUARTERLY JOURNAL OF THE ROYAL METEOROLOGICAL SOCIETY, Issue 634 2008Junjie Liu Abstract We propose an ensemble sensitivity method to calculate observation impacts similar to Langland and Baker (2004) but without the need for an adjoint model, which is not always available for numerical weather prediction models. The formulation is tested on the Lorenz 40-variable model, and the results show that the observation impact estimated from the ensemble sensitivity method is similar to that from the adjoint method. Like the adjoint method, the ensemble sensitivity method is able to detect observations that have large random errors or biases. This sensitivity could be routinely calculated in an ensemble Kalman filter, thus providing a powerful tool to monitor the quality of observations and give quantitative estimations of observation impact on the forecasts. Copyright © 2008 Royal Meteorological Society [source] A review on the use of the adjoint method in four-dimensional atmospheric-chemistry data assimilationTHE QUARTERLY JOURNAL OF THE ROYAL METEOROLOGICAL SOCIETY, Issue 576 2001K.-Y. Wang Abstract In this paper we review a theoretical formulation of the adjoint method to be used in four-dimensional (4D) chemistry data assimilation. The goal of the chemistry data assimilation is to combine an atmospheric-chemistry model and actual observations to produce the best estimate of the chemistry of the atmosphere. The observational dataset collected during the past decades is an unprecedented expansion of our knowledge of the atmosphere. The exploitation of these data is the best way to advance our understanding of atmospheric chemistry, and to develop chemistry models for chemistry-climate prediction. The assimilation focuses on estimating the state of the chemistry in a chemically and dynamically consistent manner (if the model allows online interactions between chemistry and dynamics). In so doing, we can: produce simultaneous and chemically consistent estimates of all species (including model parameters), observed and unobserved; fill in data voids; test the photochemical theories used in the chemistry models. In this paper, the Hilbert space is first formulated from the geometric structure of the Banach space, followed by the development of the adjoint operator in Hilbert space. The principle of the adjoint method is described, followed by two examples which show the relationship of the gradient of the cost function with respect to the output vector and the gradient of the cost function with respect to the input vector. Applications to chemistry data assimilation are presented for both continuous and discrete cases. The 4D data variational adjoint method is then tested in the assimilation of stratospheric chemistry using a simple catalytic ozone-destruction mechanism, and the test results indicate that the performance of the assimilation method is good. [source] | ||||||||||