第1章緒論
1.1研究背景和意義
1.2國內外研究現狀
1.2.1高溫堆耦合繫統求解的研究現狀
1.2.2JFNK求解耦合繫統研究現狀
1.2.3節塊法的研究現狀
1.3研究內容
1.3.1研究思路
1.3.2主要工作
第2章節塊展開法和JFNK求解耦合繫統的核心問題分析
2.1耦合繫統的特殊性分析
2.1.1多物理場多回路相互耦合
2.1.2時間多尺度空間多尺度求解變量多尺度耦合
2.1.3多區域多種耦合類型並存
2.1.4高溫堆耦合繫統特殊性
2.2耦合繫統求解的挑戰和關鍵問題
2.2.1收斂性問題
2.2.2計算精度和效率問題
2.2.3時間空間離散格式問題
2.3耦合繫統求解方法
2.3.1傳統耦合方法及其存在問題
2.3.2JFNK耦合方法及其關鍵技術
2.4開發基於節塊展開法的JFNK耦合方法的關鍵問題
2.4.1節塊展開法統一求解耦合繫統的關鍵問題
2.4.2基於節塊展開法的JFNK的關鍵問題
2.5本章小結
第3章耦合模型的通用節塊展開法研究
3.1耦合模型通用節塊展開法的初步開發
3.1.1基本思路
3.1.2模型推導
3.2通用節塊展開法求解含空腔區域中子擴散方程問題
3.3通用節塊展開法求解對流擴散方程的數值特性分析
3.3.1穩定性理論分析
3.3.2耗散特性理論分析
3.3.3數值驗證和分析
3.3.4特性總結和存在問題分析
3.4廣義節塊展開法的開發與驗證
3.4.1基本思路
3.4.2模型推導和理論分析
3.4.3方法特點
3.4.4數值特性分析
3.5一種新高階矩陣節塊展開法模型開發
3.5.1基本思路
3.5.2求解框架
3.5.3方法特點
3.5.4數值振蕩問題分析
3.5.5精度和計算效率分析
3.5.6橫向洩漏項處理精度分析
3.6本章小結
第4章節塊展開法統一求解耦合繫統的關鍵技術研究
4.1耦合模型分析
4.2模型離散格式的統一
4.2.1耦合源項處理和高階信息的傳遞
4.2.2非線性項處理和物性參數的離散
4.2.3多孔介質模型壓力場與速度場之間耦合處理
4.3瞬態問題的求解
4.3.1時間項橫向積分思路推廣
4.3.2瞬態中子擴散方程的時間空間全橫向積分處理
4.4含有多區域耦合、多類型耦合問題的統一求解
4.5計算流程和特點
4.6數值實驗和分析
4.6.1多孔介質熱工耦合問題
4.6.2穩態物理熱工耦合問題
4.6.3瞬態物理熱工耦合問題
4.6.4多種結構、多種耦合類型並存的復雜耦合問題
4.7本章小結
第5章基於節塊展開法的JFNK聯立求解耦合繫統方法研究
5.1殘差方程的建立
5.1.1基本思路和形式
5.1.2穩態中子場的特殊性
5.2局部消去技術研究
5.2.1基本思路
5.2.2耦合源項和橫向洩漏項消去處理
5.2.3展開繫數消去處理
5.2.4終殘差方程建立方案
5.3預處理技術研究
5.3.1線性預處理
5.3.2非線性預處理
5.3.3線性預處理與非線性預處理對比
5.4全局收斂技術研究
5.5計算框架
5.6數值實驗和分析
5.6.1單根燃料棒耦合模型
5.6.2多維多群中子場模型
5.6.3多維多物理場耦合模型
本章小結
第6章總結與展望
6.1工作總結
6.2主要創新點
6.3工作展望
參考文獻
附錄ATWIGL、IAEA2D各個材料和空腔區域群常數
附錄B物理熱工耦合問題網格劃分和截面溫度繫數
附錄C二維4群中子場模型群常數
在學期間發表的學術論文
致謝
Contents
Chapter 1Introduction
1.1Background and Significance
1.2Research Actuality
1.2.1Coupled Methods for HTR Multiphysics Systems
1.2.2JFNK for Reactor Coupled Problems
1.2.3Nodal Method
1.3Research Work
1.3.1Research Method
1.3.2Research Framework
Chapter 2Analysis of Key Problems of NEM and JFNK
for Reactor Coupled Systems
2.1Particularity Analysis of Reactor Coupled Systems
2.1.1Multiphysics and Multiloop Coupling
2.1.2Multiscale Temperal, Spatial and Variable
Coupling
2.1.3MutiDomain Coupling and MultiType
Coupling Coexistence
2.1.4Charateristics of HTR Coupled Systems
2.2Challenge and Key Problems of Reactor Coupled Systems
2.2.1Convergence
2.2.2Accuracy and Efficiency
2.2.3Temperal and Spatial Discrete Scheme
2.3Coupled Methods of Reactor Systems
2.3.1Traditonal Coupled Method and Analysis of
Existing Problems
2.3.2JFNK Method and Key Technologies
2.4Key Ideas of JacobianFree NewtonKrylov Nodal
Expansion Method
2.4.1Nodal Expansion Method for Coupled Problems
2.4.2JacobianFree NewtonKrylov Nodal Expansion
Method for Coupled Problems
2.5Brief Summary
Chapter 3Nodal Expansion Method for Neutron and
Thermohaudraulic Model
3.1Formulation of Nodal Expansion Method
3.1.1Basic Framework
3.1.2Model Derivation
3.2Nodal Expansion Method for Neutron Prolems With
Void Regions
3.3Nodal Expansion Method for ConvectionDiffusion
Equations
3.3.1Stability Analysis
3.3.2Dissipation Analysis
3.3.3Numerical Results and Analysis
3.3.4Conclusions and Analysis of Existing Problems
3.4General Nodal Expansion Method
3.4.1Basic Framework
3.4.2Model Derivation and Theoretical Analysis
3.4.3Charateristics
3.4.4Numerical Results and Analysis
3.5A New Nodal Expansion Method With HighOrder
Moments
3.5.1Basic Ideas
3.5.2Computational Framework
3.5.3Charateristics
3.5.4Numerical Oscillation Analysis
3.5.5Numerical Accuracy and Efficiency
3.5.6Analysis of Transverse Leakage Terms
3.6Brief Summary
Chapter 4Nodal Expansion Method for Reactor
Coupled Systems
4.1Analysis of Coupled Model
4.2Unified Discrete Schemes of Coupled Model
4.2.1Special Treatments of Coupled Source Terms and
Higher Order Information Transfer
4.2.2Treatment of Nonlinear Terms and Discretization of
Property Parameter
4.2.3Coupled Problems Between Pressure and Velocity
for Porous Medium Model
4.3Transient Models
4.3.1TransverseIntegrated Techniques for Temperal
Terms
4.3.2SpaceTime Fully TransverseIntegrated Methods
for Transient Neutron Equations
4.4Gobal Solutions of MutiDomain and MultiType
Coupling Problems
4.5Calculation Process and Characteristics
4.6Numerical Results and Analysis
4.6.1Thermohydraulic Coupled Problem for Porous
Media Model
4.6.2Steady N/TH Coupled Problem for Pebble
Bed Core Systems
4.6.3Transient N/TH Coupled Problems
4.6.4Complicated MutiDomain and MultiType
Coupled Problems
4.7Brief Summary
Chapter 5JacobianFree NewtonKrylov Nodal Expansion
Method for Reactor Coupled Problems
5.1Residual Equation Construction
5.1.1Basic Ideas and Formulation
5.1.2Particularity Analysis of KEigenvalue Problems
5.2Local Elimination Method
5.2.1Basic Ideas
5.2.2Elimination Method for Coupled Terms
and Transverse Leakage Terms
5.2.3Elimination Method for Nodal Expansion
Coeffcients
5.2.4Establishion of Final Residuals
5.3Preconditioning Method
5.3.1Linear Preconditioning
5.3.2Nonlinear Preconditioning
5.3.3Comparision of Linear Preconditioning and
Nonlinear Preconditioning
5.4Global Convergence Method
5.5Calculation Framework
5.6Numerical Results and Analysis
5.6.1Coupled Model for Single Fuel Rods
5.6.2Mutidimensional and Mutigroup Neutron Model
5.6.3Mutidimensional and Mutiphysics Coupled Model
5.7Brief Summary
Chapter 6Conclusions and Suggestions
6.1Conclusions
6.2Innovations
6.3Suggestions
References
Appendices AMaterial Contants of TWIGL and IAEA2D
Problems
Appendices BMesh Size and Temperature Coefficient of
N/TH Coupled Problems
Appendices CMaterial Constants of 2D4g Neutron
Problems
Published Academic Papers
Acknowledgements