Moukalled F., Mangani L., Darwish M. The finite volume method in computational fluid dynamics. An advanced introduction with OpenFOAM and Matlab (Moukalled F., Mangani L., Darwish M. The finite volume method in computational fluid dynamics. An advanced introduction with OpenFOAM and Matlab.pdf), страница 2
Описание файла
PDF-файл из архива "Moukalled F., Mangani L., Darwish M. The finite volume method in computational fluid dynamics. An advanced introduction with OpenFOAM and Matlab.pdf", который расположен в категории "". Всё это находится в предмете "компьютерный практикум по специальности" из 11 семестр (3 семестр магистратуры), которые можно найти в файловом архиве МГУ им. Ломоносова. Не смотря на прямую связь этого архива с МГУ им. Ломоносова, его также можно найти и в других разделах. .
Просмотр PDF-файла онлайн
Текст 2 страницы из PDF
. . . . . . . . . . . . .3.6.1Conservation of Energy in Terms of SpecificInternal Energy . . . . . . . . . . . . . . . . . . . . .3.6.2Conservation of Energy in Terms of SpecificEnthalpy. . . . . . . . . . . . . . . . . . . . . . . . . .3.6.3Conservation of Energy in Terms of SpecificTotal Enthalpy . . .
. . . . . . . . . . . . . . . . . .3.6.4Conservation of Energy in Termsof Temperature . . . . . . . . . . . . . . . . . . . . .3.7General Conservation Equation . . . . . . . . . . . . . . . . .3.8Non-dimensionalization Procedure . . . .
. . . . . . . . . . .3.9Dimensionless Numbers . . . . . . . . . . . . . . . . . . . . . .3.9.1Reynolds Number . . . . . . . . . . . . . . . . . . .3.9.2Grashof Number . . . . . . . . . . . . . . . . . . . .3.9.3Prandtl Number. . . . . . . . . . . . . . . . . . . . .3.9.4Péclet Number . . . . . . . . . . . . . .
. . . . . . .3.9.5Schmidt Number . . . . . . . . . . . . . . . . . . . ..................................2829323233343537383941...............434344..................454647485051525254..........5557.....60.....61.....61.........626567727273737575.....................................................................................Contents3.9.6Nusselt Number3.9.7Mach Number. .3.9.8Eckert Number .3.9.9Froude Number .3.9.10Weber Number .3.10 Closure . . .
. . . . . . . . . .3.11 Exercises . . . . . . . . . . . .References. . . . . . . . . . . . . . . . .xi........................................................................................................................................................................................................77777879798080824The Discretization Process. . . . . . .
. . . . . . . . . . . . . . . . . . .4.1The Discretization Process . . . . . . . . . . . . . . . . . . . . .4.1.1Step I: Geometric and Physical Modeling . . . .4.1.2Step II: Domain Discretization . . . . . . . . . . .4.1.3Mesh Topology. . . . . . . . . . . .
. . . . . . . . . .4.1.4Step III: Equation Discretization . . . . . . . . . .4.1.5Step IV: Solution of the Discretized Equations4.1.6Other Types of Fields . . . . . . . . . . . . . . . . .4.2Closure . . . . . . . . . . . . . . . . . . . . . . . . . .
. . . . . . . .....................................858587889093981001015The Finite Volume Method . . . . . . . . . . . . . . . . . . . . . . . . . .5.1Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .5.2The Semi-Discretized Equation . . . . . . . . . . . . . . .
. . . .5.2.1Flux Integration Over Element Faces . . . . . . . .5.2.2Source Term Volume Integration. . . . . . . . . . .5.2.3The Discrete Conservation Equationfor One Integration Point . . . . . . . . . . . . . . . .5.2.4Flux Linearization . . . . . . .
. . . . . . . . . . . . . .5.3Boundary Conditions . . . . . . . . . . . . . . . . . . . . . . . . . .5.3.1Value Specified (Dirichlet Boundary Condition)5.3.2Flux Specified (Neumann Boundary Condition).5.4Order of Accuracy. . . . . . . . . . . . . . . . . . . . . . . . . . . .5.4.1Spatial Variation Approximation . . . . . . . .
. . .5.4.2Mean Value Approximation . . . . . . . . . . . . . .5.5Transient Semi-Discretized Equation . . . . . . . . . . . . . . .5.6Properties of the Discretized Equations . . . . . . . . . . . . .5.6.1Conservation. . . . . . . . . . . . .
. . . . . . . . . . . .5.6.2Accuracy . . . . . . . . . . . . . . . . . . . . . . . . . . .5.6.3Convergence . . . . . . . . . . . . . . . . . . . . . . . . .5.6.4Consistency . . . . . . . . . . . . . . . . . . . . . . . . .5.6.5Stability . . . . . . . . . . . . . . . . . . .
. . . . . . . . .5.6.6Economy . . . . . . . . . . . . . . . . . . . . . . . . . . .5.6.7Transportiveness . . . . . . . . . . . . . . . . . . . . . .5.6.8Boundedness of the Interpolation Profile . . . . ................103103104105107......................................................108109111111112113113114117118118119119120120120120121xiiContents5.7Variable Arrangement . . . . . . . . . . . .
. . . .5.7.1Vertex-Centered FVM . . . . . . . . .5.7.2Cell-Centered FVM . . . . . . . . . . .5.8Implicit Versus Explicit Numerical Methods .5.9The Mesh Support. . . . . . . . . . . . . . . . . . .5.10 Computational Pointers . . . . . . . . . .
. . . . .5.10.1uFVM . . . . . . . . . . . . . . . . . . . .5.10.2OpenFOAM® . . . . . . . . . . . . . . .5.11 Closure . . . . . . . . . . . . . . . . . . . . . . . . . .5.12 Exercises . . . . . . . . . . . . . . . . . . . . . . . . .References. . . . . . .
. . . . . . . . . . . . . . . . . . . . . . .67....................................................................................................................................122123124126127128128129133133134The Finite Volume Mesh . . . . . . . . . . . . . . . . . . . . . . .6.1Domain Discretization . . . . . .
. . . . . . . . . . . . . .6.2The Finite Volume Mesh . . . . . . . . . . . . . . . . . .6.2.1Mesh Support for Gradient Computation6.3Structured Grids . . . . . . . . . . . . . . . . . . . . . . . .6.3.1Topological Information . . . . . . . . . . . .6.3.2Geometric Information . . . .
. . . . . . . . .6.3.3Accessing the Element Field . . . . . . . . .6.4Unstructured Grids . . . . . . . . . . . . . . . . . . . . . .6.4.1Topological Information (Connectivities)6.5Geometric Quantities . . . . . . . . . . . . . . . .
. . . . .6.5.1Element Types . . . . . . . . . . . . . . . . . .6.5.2Computing Surface Area and Centroidof Faces . . . . . . . . . . . . . . . . . . . . . . .6.6Computational Pointers . . . . . . . . . . . . . . . . . . .6.6.1uFVM . . . . . . . . . . . . . . . . . . . . . . . .6.6.2OpenFOAM® . . . . . . .
. . . . . . . . . . . .6.7Closure . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .6.8Exercises . . . . . . . . . . . . . . . . . . . . . . . . . . . . .References. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .................................................................................................137137138139142142144145146147152153........................................................154162162164170170170The Finite Volume Mesh in OpenFOAM® and uFVM7.1uFVM . . . . . .
. . . . . . . . . . . . . . . . . . . . . . . .7.1.1An OpenFOAM® Test Case . . . . . . . .7.1.2The polyMesh Folder. . . . . . . . . . . . .7.1.3The uFVM Mesh. . . . . . . . . . . . . . . .7.1.4uFVM Geometric Fields. . . . . . .
. . . .7.1.5Working with the uFVM Mesh . . . . . .7.1.6Computing the Gauss Gradient . . . . . .7.2OpenFOAM® . . . . . . . . . . . . . . . . . . . . . . . . .7.2.1Fields and Memory . . . . . . . . . . . . . .7.2.2InternalField Data . . . . . . . . .
. . . . . .........................................................................................173173173175178183187188191197199...........Contentsxiii7.2.3BoundaryField Data . . . .7.2.4lduAddressing . . . . . . . .7.2.5Computing the Gradient .7.3Mesh Conversion Tools . . . . . . . .7.4Closure . . . . . . . . . . . . . . . .
. . .7.5Exercises . . . . . . . . . . . . . . . . . .References. . . . . . . . . . . . . . . . . . . . . . .............................200200202204205205207Spatial Discretization: The Diffusion Term. . . . . . . . . . . . . . .8.1Two-Dimensional Diffusion in a Rectangular Domain . . .8.2Comments on the Discretized Equation . . . . . . . . . . . . .8.2.1The Zero Sum Rule . .
. . . . . . . . . . . . . . . . . .8.2.2The Opposite Signs Rule . . . . . . . . . . . . . . . .8.3Boundary Conditions . . . . . . . . . . . . . . . . . . . . . . . . . .8.3.1Dirichlet Boundary Condition . . . . . . . . . . . . .8.3.2Von Neumann Boundary Condition . . . . . . . . .8.3.3Mixed Boundary Condition . . . . .
. . . . . . . . .8.3.4Symmetry Boundary Condition . . . . . . . . . . . .8.4The Interface Diffusivity . . . . . . . . . . . . . . . . . . . . . . .8.5Non-Cartesian Orthogonal Grids . . . . . . . . . . . . . . . . . .8.6Non-orthogonal Unstructured Grid. . . . . . . . . . . . . . . . .8.6.1Non-orthogonality . . . . . . . . .
