《数值传热学》研究生课程教学资源（课件讲稿）Chapter 2 Discretization of Computational Domain and Governing Equations

热流科学与工程西步文源大学E教育部重点实验室Numerical Heat Transfer（数值传热学）Chapter2Discretizationof ComputationalDomainandGoverningEquationsInstructorTao,Wen-QuanKeyLaboratoryofThermo-FluidScience&EngineeringInt.JointResearchLaboratoryofThermal Science&EngineeringXi'an Jiaotong UniversityInnovativeHarborofWestChina,Xian2022-Sept-18CFD-NHT-EHTΦCENTER

Instructor Tao, Wen-Quan Numerical Heat Transfer (数值传热学) Chapter 2 Discretization of Computational Domain and Governing Equations Key Laboratory of Thermo-Fluid Science & Engineering Int. Joint Research Laboratory of Thermal Science & Engineering Xi’an Jiaotong University Innovative Harbor of West China, Xian 2022-Sept-18

热流科学与工程西步文源大堂E教育部重点实验室Contents(Domain2.1GridGeneration（网格生成）Discretization)2.2 Taylor Expansion and PolynomialFitting（多项式拟合）forEquationDiscretization（控制容积）2.3Control Volumeand HeatBalance Methods for EquationDiscretization2/46CFD-NHT-EHTΦCENTER

2/46 2.1 Grid Generation (网格生成)（Domain Discretization） 2.2 Taylor Expansion and Polynomial Fitting (多项式拟合)for Equation Discretization 2.3 Control Volume （控制容积）and Heat Balance Methods for Equation Discretization Contents

热流科学与工程西步文通大堂G教育部重点实验室2.1 Grid Generation (Domain Discretization)2.1.1 Task, method and classification of domaindiscretization2.1.2Expressionofgridlayout（布置）2.1.3 Introduction to different methods of gridgeneration2.1.4 Comparison between Practices A and B2.1.5Grid-independent（网格独立解）solutionCFD-NHT-EHTΦ3/46CENTER

3/46 2.1 Grid Generation (Domain Discretization) 2.1.1 Task, method and classification of domain discretization 2.1.3 Introduction to different methods of grid generation 2.1.4 Comparison between Practices A and B 2.1.2 Expression of grid layout (布置） 2.1.5 Grid-independent （网格独立解）solution

热流科学与工程西步文源大堂E教育部重点实验室2.1 Grid Generation2.1.1 Task, method and classification1.Task of domain discretizationDiscretizing the computational domain into anumberof sub-domainswhicharenotoverlapped(重叠andcancompletelycoverthecomputationaldomainFour kinds of information can be obtained:(1) Node （节点） :the position at which the values ofdependent variables are solved:e（CV,控制容积）：theminimum(2)Control volumevolume to which the conservation law is applied:(3)Interface (界面):boundary of two neighboringCVs.(相邻的)中CFD-NHT-EHT4/46CENTER

4/46 2.1 Grid Generation 2.1.1 Task, method and classification 1. Task of domain discretization Discretizing the computational domain into a number of sub-domains which are not overlapped(重叠) and can completely cover the computational domain. Four kinds of information can be obtained: (1) Node（节点） :the position at which the values of dependent variables are solved; (2) Control volume （ CV, 控制容积） : the minimum volume to which the conservation law is applied; (3) Interface（界面） :boundary of two neighboring （相邻的） CVs

热流科学与工程西步文源大堂G教育部重点实验（网格线）：Curves formed by connecting(4) Grid linestwo neighboring nodes.The spatial relationship between two neighboring nodes.the influencing coefficients, will be decided in the procedureof the equation discretization.2.Classification of domain discretization method(1)Accordingtonoderelationship:structured(结构化）vs.unstructured（非结构化）(2) According to node position: inner node vs. outernode2.1.2Expressionofgrid system（网格系统表示）Grid line-solid line;Interface-dashed line（虚线）;Distance between two nodes - SxDistance between two interfaces- AxΦCFD-NHT-EH5/46CENTER

5/46 (4) Grid lines（网格线） : Curves formed by connecting two neighboring nodes. 2. Classification of domain discretization method (1)According to node relationship: structured (结构化） vs. unstructured（非结构化） (2) According to node position：inner node vs. outer node 2.1.2 Expression of grid system (网格系统表示) Grid line－solid line；Interface-dashed line（虚线）； Distance between two nodes－  x The spatial relationship between two neighboring nodes, the influencing coefficients, will be decided in the procedure of the equation discretization. Distance between two interfaces－ x

热流科学与工程西步文通大堂E教育部重点实验室Interfacesbylowercases(小写字母）wande(x)w(ax)Distance between nodes?1)(i+(i-GridlineEPVATInterfaceDistance between interfacesW2.1.3 Introduction to different types of grid systemand generation method(1）Structuredgrid（结构化网格）：Nodepositionlayout（布置）is in order（有序的），and fixedfortheentire domain.CFD-NHT-EHTΦ6/46CENTER

6/46 2.1.3 Introduction to different types of grid system and generation method （1） Structured grid (结构化网格)：Node position layout（布置）is in order (有序的）, and fixed for the entire domain. Interface Gridline Distance between nodes Distance between interfaces Interfaces by lower cases(小写字母) w and e

热流科学与工程亚步文源大堂E教育部重点实验室(2)Unstructuredgrid（非结构化网格）：Nodepositionlayout(布置) is in disorder, and may change from node tonode.The generation and storage of the relationship ofneighboring nodes are the major work of grid generationStructured (b)Structured (a)5elementsUn-structured6neighboringelementsCFD-NHT-EHTG7/46CENTER

7/46 （2） Unstructured grid (非结构化网格)：Node position layout(布置) is in disorder, and may change from node to node. The generation and storage of the relationship of neighboring nodes are the major work of grid generation. Structured（a) Structured（b) Un-structured 5 elements 6 neighboring elements

热流科学与工程亚步文源大堂E教育部重点实验室Both structured and unstructured grid layout(（节点布置)have two practices: outer node and inner node(3)Outer nodeand inner nodeforstructured grid(a) Outer node method: Node is positioned at thevertexofasub-domain(子区域的角顶）；Theinterfaceisbetween two nodes; Generating procedure: Node firstandinterfacesecond---calledPracticeA(byPatankar)orcell-vertexmethod（单元顶点法）Sub-D极坐标个孤度(radian)直角坐标6CV|Cylindrical (2D)PolarCartesianCFD-NHT-EHTΦ8/46CENTER

8/46 Both structured and unstructured grid layout (节点布置) have two practices：outer node and inner node. （3）Outer node and inner node for structured grid (a) Outer node method：Node is positioned at the vertex of a sub-domain(子区域的角顶)；The interface is between two nodes；Generating procedure：Node first and interface second-called Practice A (by Patankar) ， or cell-vertex method (单元顶点法). Sub-D Cartesian CV Cylindrical（2D） Polar (radian)

热流科学与工程西步文通大学C教育部重点实验室(b)Innernode method:Node is positioned at thecenter of sub-domain,Sub-domain is identical to controlvolume; Generating procedure: Interface first and nodesecond, called Practice B(by Patankar), or cell-1（单元中心法）centered methodAxe(斧头)1radian(1弧度）Sub-domainisthecontrol volumeCFD-NHT-EHTG9/46CENTER

9/46 (b) Inner node method：Node is positioned at the center of sub-domain; Sub-domain is identical to control volume; Generating procedure: Interface first and node second, called Practice B (by Patankar) , or cell￾centered method（单元中心法）. Sub-domain is the control volume 1 radian （1弧度） Axe (斧头)

热流科学与工程西步文通大堂E教育部重点实验室Generating procedure of Practice BCFD-NHT-EHTG10/46CENTER

10/46                                                                         Generating procedure of Practice B