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  • 1
    Electronic Resource
    Electronic Resource
    A postprocessed error estimate and an adaptive procedure for the semidiscrete finite element method in dynamic analysis (1994)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 37 (1994), S. 3585-3603 
    Details
    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: In the paper we present a postprocessed type of a posteriori error estimate and a h-version adaptive procedure for the semidiscrete finite element method in dynamic analysis. In space the super-convergent patch recovery technique is used for determining higher-order accurate stresses and, thus, a spatial error estimate. In time a postprocessing technique is developed for obtaining a local error estimate for one step time integration schemes (the HHT-α method). Coupling the error estimate with a mesh generator, a h-version adaptive finite element procedure is presented for two-dimensional dynamic analysis. It updates the spatial mesh and time step automatically so that the discretization errors are controlled within specified tolerances. Numerical studies on different problems are presented for demonstrating the performances of the proposed adaptive procedure.
    Additional Material: 19 Ill.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/nme.1620372102
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    Paper (German National Licenses)
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  • 2
    Electronic Resource
    Electronic Resource
    FINITE ELEMENT METHOD FOR GRADIENT PLASTICITY AT LARGE STRAINS (1996)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 39 (1996), S. 619-633 
    Details
    ISSN: 0029-5981
    Keywords: gradient plasticity ; strain localization ; mixed strain element method ; large strain ; consistent algorithm ; Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: A finite element method for gradient elasto-plastic continuum in which the yield strength of strain hardening/softening materials not only depends on the effective plastic strain but also on its Laplacian is presented. The consistent integration algorithm to update the stress and the internal state variable at integration points and the consistent compliance matrix for the gradient plasticity are formulated in the non-local sense.The methodology to derive the finite element formulation for the gradient plasticity at large strains presented in this paper is applicable to general finite element analysis; the formulation in the context of the two-dimensional four-noded mixed finite element with one integration point and mean von Mises yield criterion is particularly derived.Numerical examples are tested to demonstrate the capability and performance of the present finite element method at large strain in solving for the strain localization problem.
    Additional Material: 2 Ill.
    Type of Medium: Electronic Resource
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    Paper (German National Licenses)
  • 3
    Electronic Resource
    Electronic Resource
    STRUCTURAL DYNAMIC ANALYSIS BY A TIME-DISCONTINUOUS GALERKIN FINITE ELEMENT METHOD (1996)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 39 (1996), S. 2131-2152 
    Details
    ISSN: 0029-5981
    Keywords: discontinuous Galerkin finite element method ; predictor-multicorrector ; adaptive time integration ; structural dynamics ; Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: This paper studies a time-discontinuous Galerkin finite element method for structural dynamic problems, by which both displacements and velocities are approximated as piecewise linear functions in the time domain and may be discontinuous at the discrete time levels. A new iterative solution algorithm which involves only one factorization for each fixed time step size and a few iterations at each step is presented for solving the resulted system of coupled equations. By using the jumps of the displacements and the velocities in the total energy norm as error indicators, an adaptive time-stepping procedure for selecting the proper time step size is described. Numerical examples including both single-DOF and multi-DOF problems are used to illustrate the performance of these algorithms. Comparisons with the exact results and/or the results by the Newmark integration scheme are given. It is shown that the time-discontinuous Galerkin finite element method discussed in this study possesses good accuracy (third order) and stability properties, its numerical implementation is not difficult, and the higher computational cost needed in each time step is compensated by use of a larger time step size.
    Additional Material: 20 Ill.
    Type of Medium: Electronic Resource
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  • 4
    Electronic Resource
    Electronic Resource
    A simple local error estimator and an adaptive time-stepping procedure for direct integration method in dynamic analysis (1993)
    Chichester : Wiley-Blackwell
    Communications in Numerical Methods in Engineering 9 (1993), S. 273-292 
    Details
    ISSN: 1069-8299
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: A simple a posteriori local error estimator for time discretization in structural dynamic analysis is presented. It is derived from the difference of the solutions between an ordinary integration method (the Newmark scheme) and another higher-order one which assumes that the derivatives of accelerations vary linearly within each time step. It may be obtained directly without resolving new equations, so the additional computational cost is small and the implementation is convenient. Furthermore, it is shown that this error estimator may also be obtained by Taylor expansion or by a post-processing technique. Accordingly, an adaptive time-stepping procedure, which automatically adjusts the time-step size so that the local error at each time step is within a prescribed accuracy, is described. Numerical examples, including two single-DOF problems, a two-DOF problem and a multi-DOF model, are presented. The results show that the presented local error estimator is simple, reliable and accurate.
    Additional Material: 9 Ill.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/cnm.1640090402
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  • 5
    Electronic Resource
    Electronic Resource
    Superconvergent patch recovery of finite-element solution and a posteriori L2 norm error estimate (1994)
    Chichester : Wiley-Blackwell
    Communications in Numerical Methods in Engineering 10 (1994), S. 313-320 
    Details
    ISSN: 1069-8299
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: In the paper we present a superconvergent patch recovery technique for obtaining higher-order-accurate finite-element solutions and thus a postprocessed type of L2 norm error estimate. Two modifications make our procedure different from the one proposed by Zienkiewicz and Zhu (1992), in which higher-order-accurate derivatives of the finite-element solution at nodes are determined. Firstly, the recovery process is made for element, not for nodes. An ‘element patch’, which represents the union of an element under consideration and the surrounding elements, is introduced. Secondly, the local error estimate is calculated directly from the improved solution for this element. Numerical tests on both 1D and 2D model problems show that this method can provide an asymptotically exact a posteriori L2 norm error estimate if the used element possesses superconvergent points for the solutions.
    Additional Material: 7 Ill.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/cnm.1640100406
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  • 6
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    The Role of Atmospheric Aerosol Concentration on Deep Convective Precipitation: Cloud-resolving Model Simulations (2007)
    In:  CASI
    Details
    Publication Date: 2018-06-06
    Description: Aerosols and especially their effect on clouds are one of the key components of the climate system and the hydrological cycle [Ramanathan et al., 20011. Yet, the aerosol effect on clouds remains largely unknown and the processes involved not well understood. A recent report published by the National Academy of Science states "The greatest uncertainty about the aerosol climate forcing - indeed, the largest of all the uncertainties about global climate forcing - is probably the indirect effect of aerosols on clouds NRC [2001]." The aerosol effect on clouds is often categorized into the traditional "first indirect (i.e., Twomey)" effect on the cloud droplet sizes for a constant liquid water path and the "semi-direct" effect on cloud coverage. The aerosol effect on precipitation processes, also known as the second type of aerosol indirect effect, is even more complex, especially for mixed-phase convective clouds. ln this paper, a cloud-resolving model (CRM) with detailed spectral-bin microphysics was used to examine the effect of aerosols on three different deep convective cloud systems that developed in different geographic locations: South Florida, Oklahoma and the Central Pacific. In all three cases, rain reaches the ground earlier for the low CCN (clean) case. Rain suppression is also evident in all three cases with high CCN (dirty) case. However, this suppression only occurs during the first hour of the simulations. During the mature stages of the simulations, the effects of increasing aerosol concentration range from rain suppression in the Oklahoma case, to almost no effect in the Florida case, to rain enhancement in the Pacific case. These results show the complexity of aerosol interactions with convection.
    Keywords: Meteorology and Climatology
    Format: application/pdf
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  • 7
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    Cloud-Resolving Model and GPM (2003)
    In:  Other Sources
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    Publication Date: 2019-07-18
    Description: Over the past twenty years, rainfall retrieval algorithms have been developed to retrieve rainfall and vertical hydrometeor structures from passive microwave observations by making use of the fact that weighting functions for various frequencies peak at different levels within a rainy atmosphere. GPROF is one of two TMI rainfall algorithms. It is physically based retrieval that finds the vertical hydrometeor profile that best fits the brightness temperatures in the available passive radiometer channels. Matching is achieved using a library of hydrometeor profiles generated by cloud-resolving models (CRMs). The hydrometeor profiles have a corresponding surface precipitation rate. The algorithm retrieves the hydrometeor profiles and associated surface rainfall using a Bayesian approach that gives the estimated expected values. The ability of CRMs to produce cloud structures that are reliable and representative of observed storms is crucial for the success of GPROF. The cloud mycrophysics are one of the keys to achieving this. In addition, CRMs have been a very useful tool for GPM-algorithm developers through Cloud-Radiation Simulations (CRS), one of the nine GPM disciplinary research themes. This paper will discuss how to generate consistent and comprehensive 4D cloud datasets from an improved (i.e., in regard to bulk and multi-moment microphysics) CRM for TRMM and GPM rainfall retrieval algorithm developers. These cloud datasets include CRM-simulated clouds and cloud systems from different geographic locations in the tropics and midlatitudes. By linking the CRM with a passive microwave radiative-transfer model and using satellite and airborne data, the performance of the "cloud physics" can be assessed and in turn modified and improved. This paper will also address how to assess and improve the performance of various latent and diabatic heating algorithms and develop an algorithm to retrieve the vertical structure of apparent moistening (Q2). Considering that the GPM will produce high (temporal and spatial) resolution heating and rainfall data, these algorithms will be used to obtain the temporal and spatial distributions of surface rainfall and the associated vertical heating and moistening profiles throughout the subtropical and midlatitudes.
    Keywords: Meteorology and Climatology
    Type: 3rd Global Precipation Mission Workshop; Jun 24, 2003 - Jun 26, 2003; Noordwijk; Netherlands
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  • 8
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    The Role of Aerosols on Precipitation Processes (2006)
    In:  Other Sources
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    Publication Date: 2019-07-18
    Description: Cloud physics is inevitably affected by the smoke particle (CCN, cloud condensation nuclei) size distribution below the clouds. Therefore, the size distributions parameterized as spectral bin microphysics are needed to explicitly study the effects of atmospheric aerosol concentration on cloud development, rainfall production, and rainfall rates for convective clouds. Recently, a detailed spectral--bin microphysical scheme was implemented into the Goddard Cumulus Ensemble (GCE) model. The formulation for the explicit spectral-bin microphysical processes is based on solving stochastic kinetic equations for the size distribution functions of water droplets (i.e., cloud droplets and raindrops), and several types of ice particles [i.e., pristine ice crystals (columnar and plate-like), snow (dendrites and aggregates), graupel and frozen drops/hail]. Each type is described by a special size distribution function containing many categories (i.e., 33 bins). Atmospheric aerosols are also described using number density size-distribution functions.
    Keywords: Meteorology and Climatology
    Type: 2006 Joint Assembly; May 23, 2006 - May 26, 2006; Baltimore, MD; United States
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  • 9
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    The Impact of Aerosols on Cloud and Precipitation Processes: Cloud-Resolving Model Simulations (2005)
    In:  Other Sources
    Details
    Publication Date: 2019-07-18
    Description: Cloud microphysics are inevitable affected by the smoke particle (CCN, cloud condensation nuclei) size distributions below the clouds, Therefore, size distributions parameterized as spectral bin microphysics are needed to explicitly study the effect of atmospheric aerosol concentration on cloud development, rainfall production, and rainfall rates for convective clouds. Recently, a detailed spectral-bin microphysical scheme was implemented into the the Goddard Cumulus Ensemble (GCE) model. The formulation for the explicit spectral-bim microphysical processes is based on solving stochastic kinetic equations for the size distribution functions of water droplets (i.e., cloud droplets and raindrops), and several types of ice particles [i.e., pristine ice crystals (columnar and plate-like), snow (dendrites and aggregates), graupel and frozen drops/hail]. Each type is described by a special size distribution function containing many categories (i.e., 33 bins). Atmospheric aerosols are also described using number density size-distribution functions.
    Keywords: Meteorology and Climatology
    Type: IAMAS 2005; Aug 02, 2005 - Aug 12, 2005; Beijing; China
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  • 10
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    The Impact of Aerosols on Cloud and Precipitation Processes: Cloud-Resolving Model Simulations (2004)
    In:  Other Sources
    Details
    Publication Date: 2019-07-18
    Description: Cloud microphysics is inevitably affected by the smoke particle (CCN, cloud condensation nuclei) size distributions below the clouds. Therefore, size distributions parameterized as spectral bin microphysics are needed to explicitly study the effects of atmospheric aerosol concentration on cloud development, rainfall production, and rainfall rates for convective clouds. Recently, two detailed spectral-bin microphysical schemes were implemented into the Goddard Cumulus Ensembel (GCE) model. The formulation for the explicit spectral-bin microphysical processes is based on solving stochastic kinetic equations for the size distribution functions of water droplets (i.e., cloud droplets and raindrops), and several types of ice particles [i.e. pristine ice crystals (columnar and plate-like), snow (dendrites and aggregates), graupel and frozen drops/hail]. Each type is described by a special size distribution function containing many categories (i.e. 33 bins). Atmospheric aerosols are also described using number density size distribution functions. A spectral-bin microphysical model is very expensive from a computational point of view and has only been implemented into the 2D version of the GCE at the present time. The model is tested by studying the evolution of deep tropical clouds in the west Pacific warm pool region and in the mid-latitude continent with different concentrations of CCN: a low "c1ean"concentration and a high "dirty" concentration. In addition, differences and similarities between bulk microphysics and spectral-bin microphysical schemes will be examined and discussed.
    Keywords: Meteorology and Climatology
    Type: 2nd International Workshop on NWP Model; May 17, 2004 - May 20, 2004; Seoul; Korea, Republic of
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