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Second-Order MaxEnt Predictive Modelling Methodology. II: Probabilistically Incorporated Computational Model (2nd-BERRU-PMP)
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作者 Dan Gabriel Cacuci 《American Journal of Computational Mathematics》 2023年第2期267-294,共28页
This work presents a comprehensive second-order predictive modeling (PM) methodology based on the maximum entropy (MaxEnt) principle for obtaining best-estimate mean values and correlations for model responses and par... This work presents a comprehensive second-order predictive modeling (PM) methodology based on the maximum entropy (MaxEnt) principle for obtaining best-estimate mean values and correlations for model responses and parameters. This methodology is designated by the acronym 2<sup>nd</sup>-BERRU-PMP, where the attribute “2<sup>nd</sup>” indicates that this methodology incorporates second- order uncertainties (means and covariances) and second (and higher) order sensitivities of computed model responses to model parameters. The acronym BERRU stands for “Best-Estimate Results with Reduced Uncertainties” and the last letter (“P”) in the acronym indicates “probabilistic,” referring to the MaxEnt probabilistic inclusion of the computational model responses. This is in contradistinction to the 2<sup>nd</sup>-BERRU-PMD methodology, which deterministically combines the computed model responses with the experimental information, as presented in the accompanying work (Part I). Although both the 2<sup>nd</sup>-BERRU-PMP and the 2<sup>nd</sup>-BERRU-PMD methodologies yield expressions that include second (and higher) order sensitivities of responses to model parameters, the respective expressions for the predicted responses, for the calibrated predicted parameters and for their predicted uncertainties (covariances), are not identical to each other. Nevertheless, the results predicted by both the 2<sup>nd</sup>-BERRU-PMP and the 2<sup>nd</sup>-BERRU-PMD methodologies encompass, as particular cases, the results produced by the extant data assimilation and data adjustment procedures, which rely on the minimization, in a least-square sense, of a user-defined functional meant to represent the discrepancies between measured and computed model responses. 展开更多
关键词 second-order Predictive modeling Data Assimilation Data Adjustment Uncertainty Quantification Reduced Predicted Uncertainties
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Second-Order MaxEnt Predictive Modelling Methodology. I: Deterministically Incorporated Computational Model (2nd-BERRU-PMD)
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作者 Dan Gabriel Cacuci 《American Journal of Computational Mathematics》 2023年第2期236-266,共31页
This work presents a comprehensive second-order predictive modeling (PM) methodology designated by the acronym 2<sup>nd</sup>-BERRU-PMD. The attribute “2<sup>nd</sup>” indicates that this met... This work presents a comprehensive second-order predictive modeling (PM) methodology designated by the acronym 2<sup>nd</sup>-BERRU-PMD. The attribute “2<sup>nd</sup>” indicates that this methodology incorporates second-order uncertainties (means and covariances) and second-order sensitivities of computed model responses to model parameters. The acronym BERRU stands for “Best- Estimate Results with Reduced Uncertainties” and the last letter (“D”) in the acronym indicates “deterministic,” referring to the deterministic inclusion of the computational model responses. The 2<sup>nd</sup>-BERRU-PMD methodology is fundamentally based on the maximum entropy (MaxEnt) principle. This principle is in contradistinction to the fundamental principle that underlies the extant data assimilation and/or adjustment procedures which minimize in a least-square sense a subjective user-defined functional which is meant to represent the discrepancies between measured and computed model responses. It is shown that the 2<sup>nd</sup>-BERRU-PMD methodology generalizes and extends current data assimilation and/or data adjustment procedures while overcoming the fundamental limitations of these procedures. In the accompanying work (Part II), the alternative framework for developing the “second- order MaxEnt predictive modelling methodology” is presented by incorporating probabilistically (as opposed to “deterministically”) the computed model responses. 展开更多
关键词 second-order Predictive modeling Data Assimilation Data Adjustment Uncertainty Quantification Reduced Predicted Uncertainties
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Second-Order MaxEnt Predictive Modelling Methodology. III: Illustrative Application to a Reactor Physics Benchmark
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作者 Ruixian Fang Dan Gabriel Cacuci 《American Journal of Computational Mathematics》 2023年第2期295-322,共28页
This work illustrates the innovative results obtained by applying the recently developed the 2<sup>nd</sup>-order predictive modeling methodology called “2<sup>nd</sup>- BERRU-PM”, where the ... This work illustrates the innovative results obtained by applying the recently developed the 2<sup>nd</sup>-order predictive modeling methodology called “2<sup>nd</sup>- BERRU-PM”, where the acronym BERRU denotes “best-estimate results with reduced uncertainties” and “PM” denotes “predictive modeling.” The physical system selected for this illustrative application is a polyethylene-reflected plutonium (acronym: PERP) OECD/NEA reactor physics benchmark. This benchmark is modeled using the neutron transport Boltzmann equation (involving 21,976 uncertain parameters), the solution of which is representative of “large-scale computations.” The results obtained in this work confirm the fact that the 2<sup>nd</sup>-BERRU-PM methodology predicts best-estimate results that fall in between the corresponding computed and measured values, while reducing the predicted standard deviations of the predicted results to values smaller than either the experimentally measured or the computed values of the respective standard deviations. The obtained results also indicate that 2<sup>nd</sup>-order response sensitivities must always be included to quantify the need for including (or not) the 3<sup>rd</sup>- and/or 4<sup>th</sup>-order sensitivities. When the parameters are known with high precision, the contributions of the higher-order sensitivities diminish with increasing order, so that the inclusion of the 1<sup>st</sup>- and 2<sup>nd</sup>-order sensitivities may suffice for obtaining accurate predicted best- estimate response values and best-estimate standard deviations. On the other hand, when the parameters’ standard deviations are sufficiently large to approach (or be outside of) the radius of convergence of the multivariate Taylor-series which represents the response in the phase-space of model parameters, the contributions stemming from the 3<sup>rd</sup>- and even 4<sup>th</sup>-order sensitivities are necessary to ensure consistency between the computed and measured response. In such cases, the use of only the 1<sup>st</sup>-order sensitivities erroneously indicates that the computed results are inconsistent with the respective measured response. Ongoing research aims at extending the 2<sup>nd</sup>-BERRU-PM methodology to fourth-order, thus enabling the computation of third-order response correlations (skewness) and fourth-order response correlations (kurtosis). 展开更多
关键词 second-order Predictive modeling OECD/NEA Reactor Physics Benchmark Data Assimilation Best-Estimate Results Uncertainty Quantification Reduced Predicted Uncertainties
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NUMERICAL SIMULATION OF METHANE-AIR TURBULENT JET FLAME USING A NEW SECOND-ORDER MOMENT MODEL 被引量:4
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作者 陈兴隆 周力行 张健 《Acta Mechanica Sinica》 SCIE EI CAS CSCD 2000年第1期41-47,共7页
A new second-order moment model for turbulent combustion is applied in the simulation of methane-air turbulent jet flame. The predicted results are compared with the experimental results and with those predicted using... A new second-order moment model for turbulent combustion is applied in the simulation of methane-air turbulent jet flame. The predicted results are compared with the experimental results and with those predicted using the well-known EBU-Arrhenius model and the original second-order moment model. The comparison shows the advantage of the new model that it requires almost the same computational storage and time as that of the original second-order moment model, but its modeling results are in better agreement with experiments than those using other models. Hence, the new second-order moment model is promising in modeling turbulent combustion with NOx formation with finite reaction rate for engineering application. 展开更多
关键词 turbulent combustion second-order moment model numerical simulation
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Comparison of a Full Second-Order Moment Model and an Algebraic Stress Two-Phase Turbulence Model for Simulating Bubble-Liquid Flows in a Bubble Column 被引量:3
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作者 周力行 杨玟 +2 位作者 廉春英 L.S.Fan D.J.Lee 《Chinese Journal of Chemical Engineering》 SCIE EI CAS CSCD 2002年第2期142-148,共7页
A full second-order moment (FSM) model and an algebraic stress (ASM) two-phase turbulence modelare proposed and applied to predict turbulent bubble-liquid flows in a 2D rectangular bubble column. Predictiongives the b... A full second-order moment (FSM) model and an algebraic stress (ASM) two-phase turbulence modelare proposed and applied to predict turbulent bubble-liquid flows in a 2D rectangular bubble column. Predictiongives the bubble and liquid velocities, bubble volume fraction, bubble and liquid Reynolds stresses and bubble-liquidvelocity correlation. For predicted two-phase velocities and bubble volume fraction there is only slight differencebetween these two models, and the simulation results using both two models are in good agreement with the particleimage velocimetry (PIV) measurements. Although the predicted two-phase Reynolds stresses using the FSM are insomewhat better agreement with the PIV measurements than those predicted using the ASM, the Reynolds stressespredicted using both two models are in general agreement with the experiments. Therefore, it is suggested to usethe ASM two-phase turbulence model in engineering application for saving the computation time. 展开更多
关键词 second-order moment model two-phase turbulence bubble-liquid flow bubble column
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Closed-form steady-state solutions for forced vibration of second-order axially moving systems
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作者 Jingming FAN Bo CHEN Yinghui LI 《Applied Mathematics and Mechanics(English Edition)》 SCIE EI CSCD 2023年第10期1701-1720,共20页
Second-order axially moving systems are common models in the field of dynamics, such as axially moving strings, cables, and belts. In the traditional research work, it is difficult to obtain closed-form solutions for ... Second-order axially moving systems are common models in the field of dynamics, such as axially moving strings, cables, and belts. In the traditional research work, it is difficult to obtain closed-form solutions for the forced vibration when the damping effect and the coupling effect of multiple second-order models are considered.In this paper, Green's function method based on the Laplace transform is used to obtain closed-form solutions for the forced vibration of second-order axially moving systems. By taking the axially moving damping string system and multi-string system connected by springs as examples, the detailed solution methods and the analytical Green's functions of these second-order systems are given. The mode functions and frequency equations are also obtained by the obtained Green's functions. The reliability and convenience of the results are verified by several examples. This paper provides a systematic analytical method for the dynamic analysis of second-order axially moving systems, and the obtained Green's functions are applicable to different second-order systems rather than just string systems. In addition, the work of this paper also has positive significance for the study on the forced vibration of high-order systems. 展开更多
关键词 Green's function axially moving system closed-form solution second-order model forced vibration Laplace transform
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A two-scale second-order moment two-phase turbulence model for simulating dense gas-particle flows 被引量:4
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作者 Zhuoxiong Zeng Lixing Zhou Jian Zhang 《Acta Mechanica Sinica》 SCIE EI CAS CSCD 2005年第5期425-429,共5页
A two-scale second-order moment two-phase turbulence model accounting for inter-particle collision is developed, based on the concepts of particle large-scale fluctuation due to turbulence and particle small-scale flu... A two-scale second-order moment two-phase turbulence model accounting for inter-particle collision is developed, based on the concepts of particle large-scale fluctuation due to turbulence and particle small-scale fluctuation due to collision and through a unified treatment of these two kinds of fluctuations. The proposed model is used to simulate gas-particle flows in a channel and in a downer. Simulation results are in agreement with the experimental results reported in references and are near the results obtained using the sin- gle-scale second-order moment two-phase turbulence model superposed with a particle collision model (USM-θ model) in most regions. 展开更多
关键词 Gas-particle flows .second-order moment model . Two-scale fluctuation
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Static output feedback stabilization for second-order singular systems using model reduction methods 被引量:1
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作者 Zheng WANG Yuhao CONG Xiulin HU 《Applied Mathematics and Mechanics(English Edition)》 SCIE EI CSCD 2021年第3期457-466,共10页
In this paper,the static output feedback stabilization for large-scale unstable second-order singular systems is investigated.First,the upper bound of all unstable eigenvalues of second-order singular systems is deriv... In this paper,the static output feedback stabilization for large-scale unstable second-order singular systems is investigated.First,the upper bound of all unstable eigenvalues of second-order singular systems is derived.Then,by using the argument principle,a computable stability criterion is proposed to check the stability of secondorder singular systems.Furthermore,by applying model reduction methods to original systems,a static output feedback design algorithm for stabilizing second-order singular systems is presented.A simulation example is provided to illustrate the effectiveness of the design algorithm. 展开更多
关键词 second-order singular system static output feedback model reduction method argument principle
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Comparisons of Wave Force Model Effects on the Structural Responses and Fatigue Loads of a Semi-Submersible Floating Wind Turbine
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作者 HAN Yanqing LE Conghuan +1 位作者 ZHANG Puyang XU Shengnan 《Journal of Ocean University of China》 CAS CSCD 2024年第1期69-79,共11页
The selection of wave force models will significantly impact the structural responses of floating wind turbines.In this study,comparisons of wave force model effects on the structural responses and fatigue loads of a ... The selection of wave force models will significantly impact the structural responses of floating wind turbines.In this study,comparisons of wave force model effects on the structural responses and fatigue loads of a semi-submersible floating wind turbine(SFWT)were conducted.Simulations were performed by employing the Morison equation(ME)with linear or second-order wave kinematics and potential flow theory(PFT)with first-or second-order wave forces.A comparison of regular waves,irregular waves,and coupled wind/waves analyses with the experimental data showed that many of the simulation results and experimental data are relatively consistent.However,notable discrepancies are found in the response amplitude operators for platform heave,tower base bending moment,and tension in mooring lines.PFT models give more satisfactory results of heave but more significant discrepan-cies in tower base bending moment than the ME models.In irregular wave analyses,low-frequency resonances were captured by PFT models with second-order difference-frequency terms,and high-frequency resonances were captured by the ME models or PFT models with second-order sum-frequency terms.These force models capture the response frequencies but do not reasonably predict the response amplitudes.The coupled wind/waves analyses showed more satisfactory results than the wave-only analyses.However,an important detail to note is that this satisfactory result is based on the overprediction of wind-induced responses. 展开更多
关键词 floating wind turbine wave force model potential flow theory Morison equation second-order wave forces
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Derivation of a second-order model for Reynolds stress using renormalization group analysis and the two-scale expansion technique
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作者 Xiao-Hong Wang Zheng-Feng Liu Xiao-Xia Lu 《Acta Mechanica Sinica》 SCIE EI CAS CSCD 2011年第5期649-659,共11页
With the two-scale expansion technique proposed by Yoshizawa,the turbulent fluctuating field is expanded around the isotropic field.At a low-order two-scale expansion,applying the mode coupling approximation in the Ya... With the two-scale expansion technique proposed by Yoshizawa,the turbulent fluctuating field is expanded around the isotropic field.At a low-order two-scale expansion,applying the mode coupling approximation in the Yakhot-Orszag renormalization group method to analyze the fluctuating field,the Reynolds-average terms in the Reynolds stress transport equation,such as the convective term,the pressure-gradient-velocity correlation term and the dissipation term,are modeled.Two numerical examples:turbulent flow past a backward-facing step and the fully developed flow in a rotating channel,are presented for testing the efficiency of the proposed second-order model.For these two numerical examples,the proposed model performs as well as the Gibson-Launder (GL) model,giving better prediction than the standard k-ε model,especially in the abilities to calculate the secondary flow in the backward-facing step flow and to capture the asymmetric turbulent structure caused by frame rotation. 展开更多
关键词 Turbulent modeling Renormalization group Two-scale expansion Reynolds stress transport equation second-order model
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Second-order modeling of non-premixed turbulent methane-air combustion
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作者 Ali ERSHADI Mehran RAJABI ZARGARABADI 《Journal of Central South University》 SCIE EI CAS CSCD 2021年第11期3545-3555,共11页
The main purpose of this research is the second-order modeling of flow and turbulent heat flux in nonpremixed methane-air combustion.A turbulent stream of non-premixed combustion in a stoichiometric condition,is numer... The main purpose of this research is the second-order modeling of flow and turbulent heat flux in nonpremixed methane-air combustion.A turbulent stream of non-premixed combustion in a stoichiometric condition,is numerically analyzed through the Reynolds averaged Navier-Stokes(RANS) equations.For modeling radiation and combustion,the discrete ordinates(DO) and eddy dissipation concept model have been applied.The Reynolds stress transport model(RSM) also was used for turbulence modeling.For THF in the energy equation,the GGDH model and high order algebraic model of HOGGDH with simple eddy diffusivity model have been applied.Comparing the numerical results of the SED model(with the turbulent Prandtl 0.85) and the second-order heat flux models with available experimental data follows that applying the second-order models significantly led to the modification of predicting temperature distribution and species mass fraction distribution in the combustion chamber.Calculation of turbulent Prandtl number in the combustion chamber shows that the assumption of Pr_(t) of 0.85 is far from reality and Pr_(t) in different areas varies from 0.4 to 1.2. 展开更多
关键词 combustion modeling turbulent Prandtl number second-order models Reynolds stress transport model
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EFFECT OF EMPIRICAL COEFFICIENTS ON SIMULATION IN TWO-SCALE SECOND-ORDER MOMENT PARTICLE-PHASE TURBULENCE MODEL
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作者 胡春波 曾卓雄 《Applied Mathematics and Mechanics(English Edition)》 SCIE EI 2006年第11期1491-1497,共7页
A two-scale second-order moment two-phase turbulence model accounting for inter-particle collision is developed, based on the concept of particle large-scale fluctuation due to turbulence and particle small-scale fluc... A two-scale second-order moment two-phase turbulence model accounting for inter-particle collision is developed, based on the concept of particle large-scale fluctuation due to turbulence and particle small-scale fluctuation due to collision. The proposed model is used to simulate gas-particle downer reactor flows. The computational results of both particle volume fraction and mean velocity are in agreement with the experimental results. After analyzing effects of empirical coefficient on prediction results, we can come to a conclusion that, inside the limit range of empirical coefficient, the predictions do not reveal a large sensitivity to the empirical coefficient in the downer reactor, but a relatively great change of the constants has important effect on the prediction. 展开更多
关键词 two-phase flow second-order moment model two-scale fluctuation empirical coefficients
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SECOND-ORDER MOMENT MODEL FOR DENSE TWO-PHASE TURBULENT FLOW OF BINGHAM FLUID WITH PARTICLES
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作者 曾卓雄 周力行 刘志和 《Applied Mathematics and Mechanics(English Edition)》 SCIE EI 2006年第10期1373-1381,共9页
The USM-θ model of Bingham fluid for dense two-phase turbulent flow was developed, which combines the second-order moment model for two-phase turbulence with the particle kinetic theory for the inter-particle collisi... The USM-θ model of Bingham fluid for dense two-phase turbulent flow was developed, which combines the second-order moment model for two-phase turbulence with the particle kinetic theory for the inter-particle collision. In this model, phases interaction and the extra term of Bingham fluid yield stress are taken into account. An algorithm for USM-θ model in dense two-phase flow was proposed, in which the influence of particle volume fraction is accounted for. This model was used to simulate turbulent flow of Bingham fluid single-phase and dense liquid-particle two-phase in pipe. It is shown USM-θ model has better prediction result than the five-equation model, in which the particle-particle collision is modeled by the particle kinetic theory, while the turbulence of both phase is simulated by the two-equation turbulence model. The USM-θ model was then used to simulate the dense two-phase turbulent up flow of Bingham fluid with particles. With the increasing of the yield stress, the velocities of Bingham and particle decrease near the pipe centre. Comparing the two-phase flow of Bingham-particle with that of liquid-particle, it is found the source term of yield stress has significant effect on flow. 展开更多
关键词 Bingham fluid two-phase flow yield stress second-order moment model
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Dynamics of Rabi model under second-order Born Oppenheimer approximation
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作者 王治海 周端陆 《Chinese Physics B》 SCIE EI CAS CSCD 2013年第11期311-314,共4页
We apply the second-order Born-Oppenheimer (BO) approximation to investigate the dynamics of the Rabi model, which describes the interaction between a two-level system and a single bosonic mode beyond the rotating w... We apply the second-order Born-Oppenheimer (BO) approximation to investigate the dynamics of the Rabi model, which describes the interaction between a two-level system and a single bosonic mode beyond the rotating wave approxi- mation. By comparing with the numerical results, we find that our approach works well when the frequency of the two-level system is much smaller than that of the bosonic mode. 展开更多
关键词 Rabi model second-order Born-Oppenheimer approximation
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Second-Order Adjoint Sensitivity Analysis Methodology for Computing Exactly Response Sensitivities to Uncertain Parameters and Boundaries of Linear Systems: Mathematical Framework 被引量:3
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作者 Dan Gabriel Cacuci 《American Journal of Computational Mathematics》 2020年第3期329-354,共26页
This work presents the “Second-Order Comprehensive Adjoint Sensitivity Analysis Methodology (2<sup>nd</sup>-CASAM)” for the efficient and exact computation of 1<sup>st</sup>- and 2<sup>... This work presents the “Second-Order Comprehensive Adjoint Sensitivity Analysis Methodology (2<sup>nd</sup>-CASAM)” for the efficient and exact computation of 1<sup>st</sup>- and 2<sup>nd</sup>-order response sensitivities to uncertain parameters and domain boundaries of linear systems. The model’s response (<em>i.e.</em>, model result of interest) is a generic nonlinear function of the model’s forward and adjoint state functions, and also depends on the imprecisely known boundaries and model parameters. In the practically important particular case when the response is a scalar-valued functional of the forward and adjoint state functions characterizing a model comprising N parameters, the 2<sup>nd</sup>-CASAM requires a single large-scale computation using the First-Level Adjoint Sensitivity System (1<sup>st</sup>-LASS) for obtaining all of the first-order response sensitivities, and at most N large-scale computations using the Second-Level Adjoint Sensitivity System (2<sup>nd</sup>-LASS) for obtaining exactly all of the second-order response sensitivities. In contradistinction, forward other methods would require (<em>N</em>2/2 + 3 <em>N</em>/2) large-scale computations for obtaining all of the first- and second-order sensitivities. This work also shows that constructing and solving the 2<sup>nd</sup>-LASS requires very little additional effort beyond the construction of the 1<sup>st</sup>-LASS needed for computing the first-order sensitivities. Solving the equations underlying the 1<sup>st</sup>-LASS and 2<sup>nd</sup>-LASS requires the same computational solvers as needed for solving (<em>i.e.</em>, “inverting”) either the forward or the adjoint linear operators underlying the initial model. Therefore, the same computer software and “solvers” used for solving the original system of equations can also be used for solving the 1<sup>st</sup>-LASS and the 2<sup>nd</sup>-LASS. Since neither the 1<sup>st</sup>-LASS nor the 2<sup>nd</sup>-LASS involves any differentials of the operators underlying the original system, the 1<sup>st</sup>-LASS is designated as a “<u>first-level</u>” (as opposed to a “first-order”) adjoint sensitivity system, while the 2<sup>nd</sup>-LASS is designated as a “<u>second-level</u>” (rather than a “second-order”) adjoint sensitivity system. Mixed second-order response sensitivities involving boundary parameters may arise from all source terms of the 2<sup>nd</sup>-LASS that involve the imprecisely known boundary parameters. Notably, the 2<sup>nd</sup>-LASS encompasses an automatic, inherent, and independent “solution verification” mechanism of the correctness and accuracy of the 2nd-level adjoint functions needed for the efficient and exact computation of the second-order sensitivities. 展开更多
关键词 second-order Comprehensive Adjoint Sensitivity Analysis Methodology (2nd-CASAM) First-Level Adjoint Sensitivity System (1st-LASS) Second-Level Adjoint Sensitivity System (2nd-LASS) Operator-Type Response second-order Sensitivities to Uncertain model Boundaries second-order Sensitivities to Uncertain model Parameters
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A nonlinear k_p-ε_p particle two-scale turbulence model and its application 被引量:3
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作者 Zhuoxiong Zeng Zhuozhi Zeng Yihua Xu 《Acta Mechanica Sinica》 SCIE EI CAS CSCD 2007年第6期621-625,共5页
A particle nonlinear two-scale kp-εp turbulence model is proposed for simulating the anisotropic turbulent two-phase flow. The particle kinetic energy equation for two-scale fluctuation, particle energy transfer rate... A particle nonlinear two-scale kp-εp turbulence model is proposed for simulating the anisotropic turbulent two-phase flow. The particle kinetic energy equation for two-scale fluctuation, particle energy transfer rate equation for large-scale fluctuation, and particle turbulent kinetic energy dissipation rate equation for small-scale fluctuation are derived and closed. This model is used to simulate gas-particle flows in a sudden-expansion chamber. The simulation is com- pared with the experiment and with those obtained by using another two kinds of tow-phase turbulence model, such as the single-scale k-ε two-phase turbulence model and the particle two-scale second-order moment (USM) two-phase turbulence model. It is shown that the present model gives simulation in much better agreement with the experiment than the single-scale k-ε two-phase turbulence model does and is almost as good as the particle two-scale USM turbu-lence model. 展开更多
关键词 Gas-particle flows second-order moment model Two-scale fluctuation
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Adiabatic Shear Localization for Steels Based on Johnson-Cook Model and Second-and Fourth-Order Gradient Plasticity Models 被引量:2
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作者 WANG Xue-bin 《Journal of Iron and Steel Research International》 SCIE EI CAS CSCD 2007年第5期56-61,共6页
To consider the effects of the interactions and interplay among microstructures, gradient-dependent models of second- and fourth-order are included in the widely used phenomenological Johnson-Cook model where the effe... To consider the effects of the interactions and interplay among microstructures, gradient-dependent models of second- and fourth-order are included in the widely used phenomenological Johnson-Cook model where the effects of strain-hardening, strain rate sensitivity, and thermal-softening are successfully described. The various parameters for 1006 steel, 4340 steel and S-7 tool steel are assigned. The distributions and evolutions of the local plastic shear strain and deformation in adiabatic shear band (ASB) are predicted. The calculated results of the second- and fourth- order gradient plasticity models are compared. S-7 tool steel possesses the steepest profile of local plastic shear strain in ASB, whereas 1006 steel has the least profile. The peak local plastic shear strain in ASB for S-7 tool steel is slightly higher than that for 4340 steel and is higher than that for 1006 steel. The extent of the nonlinear distribution of the local plastic shear deformation in ASB is more apparent for the S-7 tool steel, whereas it is the least apparent for 1006 steel. In fourth-order gradient plasticity model, the profile of the local plastic shear strain in the middle of ASB has a pronounced plateau whose width decreases with increasing average plastic shear strain, leading to a shrink of the portion of linear distribution of the profile of the local plastic shear deformation. When compared with the sec- ond-order gradient plasticity model, the fourth-order gradient plasticity model shows a lower peak local plastic shear strain in ASB and a higher magnitude of plastic shear deformation at the top or base of ASB, which is due to wider ASB. The present numerical results of the second- and fourth-order gradient plasticity models are consistent with the previous numerical and experimental results at least qualitatively. 展开更多
关键词 adiabatic shear band steel gradient-dependent plasticity Johnson-Cook model second-order gradient fourth-order gradient
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Validation of the RANS-SOM Combustion Model Using Direct Numerical Simulation of Incompressible Turbulent Reacting Flows 被引量:1
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作者 王方 许春晓 周力行 《Chinese Journal of Chemical Engineering》 SCIE EI CAS CSCD 2008年第5期679-685,共7页
The second-order moment combustion model, proposed by the authors is validated using the direct numerical simulation (DNS) of incompressible turbulent reacting channel flows. The instantaneous DNS results show the n... The second-order moment combustion model, proposed by the authors is validated using the direct numerical simulation (DNS) of incompressible turbulent reacting channel flows. The instantaneous DNS results show the near-wall strip structures of concentration and temperature fluctuations. The DNS statistical results give the budget of the terms in the correlation equations, showing that the production and dissipation terms are most important. The DNS statistical data are used to validate the closure model in RANS second-order moment (SOM) combustion model. It is found that the simulated diffusion and production terms are in agreement with the DNS data in most flow regions, except in the near-wall region, where the near-wall modification should be made, and the closure model for the dissipation term needs further improvement. The algebraic second-order moment (ASOM) combustion model is well validated by DNS. 展开更多
关键词 second-order moment combustion model direct numerical simulation incompressible reacting flows
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Illustrative Application of the 2<sup>nd</sup>-Order Adjoint Sensitivity Analysis Methodology to a Paradigm Linear Evolution/Transmission Model: Reaction-Rate Detector Response 被引量:2
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作者 Dan Gabriel Cacuci 《American Journal of Computational Mathematics》 2020年第3期382-397,共16页
This work continues the illustrative application of the “Second Order Comprehensive Adjoint Sensitivity Analysis Methodology” (2<sup>nd</sup>-CASAM) to a benchmark mathematical model that can simulate th... This work continues the illustrative application of the “Second Order Comprehensive Adjoint Sensitivity Analysis Methodology” (2<sup>nd</sup>-CASAM) to a benchmark mathematical model that can simulate the evolution and/or transmission of particles in a heterogeneous medium. The model response considered in this work is a reaction-rate detector response, which provides the average interactions of particles with the respective detector or, alternatively, the time-average of the concentration of a mixture of substances in a medium. The definition of this model response includes both uncertain boundary points of the benchmark, thereby providing both direct and indirect contributions to the response sensitivities stemming from the boundaries. The exact expressions for the 1<sup>st</sup>- and 2<sup>nd</sup>-order response sensitivities to the boundary and model parameters obtained in this work can serve as stringent benchmarks for inter-comparing the performances of all (deterministic and statistical) sensitivity analysis methods. 展开更多
关键词 second-order Adjoint Comprehensive Sensitivity Analysis Methodology (2nd-CASAM) Evolution Benchmark model Exact and Efficient Computation of First- and second-order Response Sensitivities
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Illustrative Application of the 2<sup>nd</sup>-Order Adjoint Sensitivity Analysis Methodology to a Paradigm Linear Evolution/Transmission Model: Point-Detector Response 被引量:2
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作者 Dan Gabriel Cacuci 《American Journal of Computational Mathematics》 2020年第3期355-381,共27页
This work illustrates the application of the “Second Order Comprehensive Adjoint Sensitivity Analysis Methodology” (2<sup>nd</sup>-CASAM) to a mathematical model that can simulate the evolution and/or tr... This work illustrates the application of the “Second Order Comprehensive Adjoint Sensitivity Analysis Methodology” (2<sup>nd</sup>-CASAM) to a mathematical model that can simulate the evolution and/or transmission of particles in a heterogeneous medium. The model response is the value of the model’s state function (particle concentration or particle flux) at a point in phase-space, which would simulate a pointwise measurement of the respective state function. This paradigm model admits exact closed-form expressions for all of the 1<sup>st</sup>- and 2<sup>nd</sup>-order response sensitivities to the model’s uncertain parameters and domain boundaries. These closed-form expressions can be used to verify the numerical results of production and/or commercial software, e.g., particle transport codes. Furthermore, this paradigm model comprises many uncertain parameters which have relative sensitivities of identical magnitudes. Therefore, this paradigm model could serve as a stringent benchmark for inter-comparing the performances of all deterministic and statistical sensitivity analysis methods, including the 2<sup>nd</sup>-CASAM. 展开更多
关键词 second-order Adjoint Comprehensive Sensitivity Analysis Methodology (2nd-CASAM) Evolution Benchmark model Exact and Efficient Computation of First- and second-order Response Sensitivities
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