scholarly journals Testing of the new JOREK stellarator-capable model in the tokamak limit

2021 ◽  
Vol 87 (3) ◽  
Author(s):  
Nikita Nikulsin ◽  
Matthias Hoelzl ◽  
Alessandro Zocco ◽  
Karl Lackner ◽  
Sibylle Günter ◽  
...  
Keyword(s):  
Alternative Model ◽  
Momentum Conservation ◽  
Momentum Equation ◽  
Original Model ◽  
Reduced Model ◽  
Projection Operators ◽  
Reduced Models ◽  
Mhd Model

In preparation for extending the JOREK nonlinear magnetohydrodynamics (MHD) code to stellarators, a hierarchy of stellarator-capable reduced and full MHD models has been derived and tested. The derivation was presented at the EFTC 2019 conference. Continuing this line of work, we have implemented the reduced MHD model (Nikulsin et al., Phys. Plasmas, vol. 26, 2019, 102109) as well as an alternative model which was newly derived using a different set of projection operators for obtaining the scalar momentum equations from the full MHD vector momentum equation. With the new operators, the reduced model matches the standard JOREK reduced models for tokamaks in the tokamak limit and conserves energy exactly, while momentum conservation is less accurate than in the original model whenever field-aligned flow is present.

Hybrid Reduced Model of Rotor

2013 ◽  
Vol 60 (3) ◽  
pp. 319-333
Author(s):  
Rafał Hein ◽  
Cezary Orlikowski
Keyword(s):  
Finite Element Method ◽  
Finite Element ◽  
Hybrid Model ◽  
Rotor System ◽  
Reduced Model ◽  
Order Model ◽  
Gyroscopic Effect ◽  
Reduced Models ◽  
Rigid Finite Element Method ◽  
Low Order

Abstract In the paper, the authors describe the method of reduction of a model of rotor system. The proposed approach makes it possible to obtain a low order model including e.g. non-proportional damping or the gyroscopic effect. This method is illustrated using an example of a rotor system. First, a model of the system is built without gyroscopic and damping effects by using the rigid finite element method. Next, this model is reduced. Finally, two identical, low order, reduced models in two perpendicular planes are coupled together by means of gyroscopic and damping interaction to form one model of the system. Thus a hybrid model is obtained. The advantage of the presented method is that the number of gyroscopic and damping interactions does not affect the model range

SIRE BY HERD INTERACTIONS FOR MILK YIELD AND COMPOSITION TRAITS

1977 ◽  
Vol 57 (3) ◽  
pp. 383-388 ◽  
Author(s):  
A. K. W. TONG ◽  
B. W. KENNEDY ◽  
J. E. MOXLEY
Keyword(s):  
Milk Yield ◽  
Milk Fat ◽  
Genetic Parameter ◽  
Genetic Correlations ◽  
Dairy Herd ◽  
Protein Yield ◽  
Reduced Model ◽  
Parameter Estimates ◽  
Full Model ◽  
Reduced Models

A total of 13,561 Holstein 305-day lactation records from 779 Quebec and Maritime herds enrolled on the Dairy Herd Analysis Service were used to evaluate the importance of sire × herd interactions for milk yield and composition traits. Sire × herd interaction accounted for 4.1, 1.1, 0.3, 2.6 and 5.6% of the total variation of milk, fat and protein yield and fat and protein percent, respectively. Genetic parameter estimates obtained under two different models, a full model that accounted for sire × herd interaction and a reduced model that ignored it, were examined. Heritabilities of milk, fat and protein yield and fat and protein percent were, respectively: for the full model, 0.36, 0.47, 0.45, 0.59 and 0.31 and for the reduced model, 0.49, 0.50, 0.46, 0.66 and 0.46. Phenotypic correlations between the traits were not appreciably different when estimated under the full and reduced models. Genetic correlations between the yield traits were also similar when estimated under the full and reduced models, but genetic correlations between yield and percentage traits were more stongly positive, or less negative, when sire × herd interaction was accounted for. The genetic correlation between fat and protein percent was larger under the reduced model than under the full model.

Preserving Stability Properties in Reduced Models of Time-Periodic Systems Using Proper Orthogonal Decomposition

2011 ◽  
Author(s):  
Thomas Pumhoessel ◽  
Peter Hehenberger ◽  
Klaus Zeman
Keyword(s):  
Proper Orthogonal Decomposition ◽  
Orthogonal Decomposition ◽  
Stability Parameter ◽  
Reduced Model ◽  
Periodic Coefficients ◽  
Reduced Models ◽  
Model Based ◽  
Wide Range ◽  
Proper Orthogonal ◽  
Time Periodic

The necessity of providing reduced models of dynamical systems is growing continuously. Model-based control and model-based design are exemplary fields of applications. In this contribution, the reduction of a controlled drivetrain of a rolling mill using the method of Proper Orthogonal Decomposition is investigated, where the specific choice of the control law leads to equations of motion with time-periodic coefficients. Depending on amplitudes and frequency parameters of the time-periodic coefficients, artificial damping is introduced, referred to as parametric control. The maximum damping effect depends on these parameters in a nonlinear manner, as it is shown by means of a stability-parameter from Floquet theory. The reduced model set-up approximates the stability-parameter of the full model in an appropriate way within a wide range of the parameters. A measure based on the linear time-invariant system is developed that gives insight into the effect of the simulated timeseries on the properties of the reduced model.

Mechanisms of Thin-Film Evaporation Considering Momentum and Energy Conservation

2013 ◽  
Author(s):  
Chunji Yan ◽  
Xinxiang Pan ◽  
Xiaowei Lu
Keyword(s):  
Thin Film ◽  
Heat Transfer ◽  
Fluid Flow ◽  
Mathematic Model ◽  
Momentum Conservation ◽  
Momentum Equation ◽  
Maximum Heat ◽  
Thin Film Evaporation ◽  
Film Evaporation ◽  
Phase Change Heat Transfer

A mathematic model, which can be used to predict the evaporation and fluid flow in thin film region, is developed based on momentum and energy conservations and the augmented Young-Laplace equation in this paper. In the model the variations of the enthalpy and kinetics energy of the thin-film along the evaporating region are considered. By theoretical analysis, we have obtained the governing equation for thin film profile. The fluid flow and phase-change heat transfer in an evaporating extended meniscus are numerically studied. The differences between the model considering momentum conservation only and including both momentum and energy conservations are compared. It is found that the maximum heat flux of the thin-film evaporation by using two mathematical models obtained has no change, but when considering the momentum and energy conservations the total heat transfer rate unit width along the thin-film evaporation region is greater than that of only including momentum equation.

Modal Based Geometric Stiffening Formulation for Dynamics Simulation of Multibody Systems

2011 ◽  
Author(s):  
Fengxia Wang
Keyword(s):  
Finite Element ◽  
Finite Element Model ◽  
Element Model ◽  
Dynamics Simulation ◽  
Reduced Model ◽  
Reduced Models ◽  
Modal Reduction ◽  
Body Dynamics ◽  
Geometric Stiffening ◽  
Multi Body

This work concerns the implementation of nonlinear modal reduction to flexible multi-body dynamics. Linear elastic theory will lead to instability issues with rotating beamlike structures, due to the neglecting of the membrane-bending coupling on the beam cross-section. During the past decade, considerable efforts have been focused on the derivation of geometric nonlinear formulation based on nodal coordinates. In this work, in order to improve the convergence characteristic and also to reduce the computation time in flexible multi-body dynamics, which is extremely important for complicated large systems, a standard modal reduction procedure based on matrix operation is developed with essential geometric stiffening nonlinearities retained in the equation of motion. The example used in this work is a rotating Euler-Bernoulli beam, two nonlinear reduced models were established based on modal coordinates, the first reduced model created from theoretical bending and axial mode shapes by Galerkin method; the second reduced model is derived by the standard matrix operator from a full finite element model. Transient simulation results of lower degrees of freedom from above two reduced models are compared with those obtained from full nonlinear finite element model.

MODEL REDUCTION WITH GEOMETRIC STIFFENING NONLINEARITIES FOR DYNAMIC SIMULATIONS OF MULTIBODY SYSTEMS

2013 ◽  
Vol 13 (08) ◽  
pp. 1350046 ◽  
Author(s):  
FENGXIA WANG
Keyword(s):  
Finite Element ◽  
Finite Element Model ◽  
Model Reduction ◽  
Reduction Process ◽  
Flexible Multibody Dynamics ◽  
Element Model ◽  
Reduced Model ◽  
Matrix Operation ◽  
Reduced Models ◽  
Geometric Stiffening

This work investigates the implementation of nonlinear model reduction to flexible multibody dynamics. Linear elastic theory will lead to instability issues with rotating beam-like structures, due to the neglecting of the membrane-bending coupling on the beam cross-section. During the past decade, considerable efforts have been focused on the derivation of geometric nonlinear formulation based on nodal coordinates. In order to reduce the computation cost in flexible multibody dynamics, which is extremely important for complex large system simulations, modal reduction is usually implemented to a rotating flexible structure with geometric nonlinearities retained in the model. In this work, a standard model reduction process based on matrix operation is developed, and the essential geometric stiffening nonlinearities are retained in the reduced model. The time responses of a tip point on a rotating Euler–Bernoulli blade are calculated based on two nonlinear reduced models. The first reduced model is derived by the standard matrix operation from a full finite element model and the second reduced model is obtained via the Galerkin method. The matrix operation model reduction process is validated through the comparison of the simulation results obtained from these two different reduced models. An interesting phenomenon is observed in this work: In the nonlinear model, if only quadratic geometric stiffing term is retained, the two reduced models converge to the full finite element model with only one bending mode and two axial modes. While if both quadratic and cubic geometric stiffing terms are retained in the nonlinear equation, the modal-based reduced model will not converge to the finite element model unless all eigenmodes are retained, that is the reduced model has no degree of freedom reduction at all.

scholarly journals Model-Reduced Variational Data Assimilation

2006 ◽  
Vol 134 (10) ◽  
pp. 2888-2899 ◽  
Author(s):  
P. T. M. Vermeulen ◽  
A. W. Heemink
Keyword(s):  
Diffusion Coefficient ◽  
Data Assimilation ◽  
Original Model ◽  
Variational Data Assimilation ◽  
Reduced Model ◽  
New Approach ◽  
Model Simulations ◽  
Computational Costs ◽  
Recent Estimate ◽  
Reduced Space

Abstract This paper describes a new approach to variational data assimilation that with a comparable computational efficiency does not require implementation of the adjoint of the tangent linear approximation of the original model. In classical variational data assimilation, the adjoint implementation is used to efficiently compute the gradient of the criterion to be minimized. Our approach is based on model reduction. Using an ensemble of forward model simulations, the leading EOFs are determined to define a subspace. The reduced model is created by projecting the original model onto this subspace. Once this reduced model is available, its adjoint can be implemented very easily and can be used to approximate the gradient of the criterion. The minimization process can now be solved completely in reduced space with negligible computational costs. If necessary, the procedure can be repeated a few times by generating new ensembles closer to the most recent estimate of the parameters. The reduced-model-based method has been tested on several nonlinear synthetic cases for which a diffusion coefficient was estimated.

On the formation of geophysical and planetary zonal flows by near-resonant wave interactions

2007 ◽  
Vol 576 ◽  
pp. 405-424 ◽  
Author(s):  
YOUNGSUK LEE ◽  
LESLIE M. SMITH
Keyword(s):  
Large Scale ◽  
Reduced Model ◽  
Small Scale ◽  
Full System ◽  
Time Asymmetry ◽  
Zonal Flows ◽  
Reduced Models ◽  
Random Forcing ◽  
Resonant Triads ◽  
Triad Interactions

Numerical simulations on a β-plane are used to further understand the formation of zonal flows from small-scale fluctuations. The dynamics of ‘reduced models’ are computed by restricting the nonlinear term to include a subset of triad interactions in Fourier space. Reduced models of near-resonant triads are considered, as well as the complement set of non-resonant triads. At moderately small values of the Rhines number, near-resonant triad interactions are shown to be responsible for the generation of large-scale zonal flows from small-scale random forcing. Without large-scale drag, both the full system and the reduced model of near resonances produce asymmetry between eastward and westward jets, in favour of stronger westward jets. When large-scale drag is included, the long-time asymmetry is reversed in the full system, with eastward jets that are thinner and stronger than westward jets. Then the reduced model of near resonances exhibits a weaker asymmetry, but there are nevertheless more eastward jets stronger than a threshold value.

Improved Bilinear Routh Approximation Method for Discrete-Time Systems

2000 ◽  
Vol 123 (1) ◽  
pp. 125-127 ◽  
Author(s):  
Younseok Choo
Keyword(s):  
Impulse Response ◽  
Discrete Time ◽  
Approximation Method ◽  
Original Model ◽  
Reduced Model ◽  
Discrete Time Systems ◽  
The Stability ◽  
Time Systems

Hwang and Shieh proposed a bilinear Routh approximation method for reducing the order of discrete-time systems. A reduced model derived by the method is not only stable whenever an original model is stable, but also fits the first few time-moments of the original one. This paper addresses the possibility of improving the method by letting the impulse response energy of the original model also be conserved in the reduced model without destroying the stability preserving and time-moments matching properties.

scholarly journals Researches regarding scale reduced models for the optimisation of the aerodynamic coefficient

2019 ◽  
Vol 290 ◽  
pp. 04011
Author(s):  
Alexandru Lucian Stanciu ◽  
Nicoleta Pascu ◽  
Constantin Dogariu ◽  
Cristina Mohora
Keyword(s):  
Computer Aided Design ◽  
Original System ◽  
Vehicle Body ◽  
Reduced Model ◽  
Small Scale ◽  
Reduced Models ◽  
Simulation And Optimization ◽  
Optimization Stage ◽  
Computer Aided ◽  
Scale Modelling

Within the lifecycle of the product, the reduced models are very important for the experimental validation of the prototype. The modelling, simulation and optimization stage precedes the prototype realization, being part of the computer aided design (CAD), computer aided engineering (CAE). The physical model is a physical layout or test setup that reproduces, on a small scale, the features of the original system, in our case the vehicle body layout. The paper presents an automobile reduced model, with the aim to study the aerodynamic theory. The paper presents the algorithms of conceptual design of the scale reduced model, namely: 3D modelling, small scale modelling technology and geometric shape optimization solutions using different CAD-CAE programs.

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