Visualization of Fields and Applications in Engineering (eBook)

Stephen Tou, National University, San Diego, USA Dr Stephen Tou joined the National University in San Diego, USA as an Adjunct Professor in 2006, having previously been with the Department of Mechanical and Aerospace Engineering at Nanyang Technological University, Singapore as an associate professor for 20 years. He teaches a graduate course in transport phenomena and undergraduate courses in fluid mechanics, energy systems & heat transfer, environmental fluid mechanics, energy conversion systems and machinery, and engineering mathematics. He has published circa 60 refereed journal papers and 20 conference papers.

Preface.

1 Introduction.

1.1 A General View.

1.2 Historical Development and Progress in Visual Science.

1.3 Scientific Visualization Philosophy, Techniques andChallenges.

2 Field Descriptions and Kinematics.

2.1 Lagrangian/Eulerian Description and Transformation.

2.2 Curvilinear Coordinates.

2.3 Field Kinematics and Visual Attributes.

3 Field Model, Representation and Visualization.

3.1 Field Models and Concepts.

3.2 Scalar Fields and Representation.

3.3 Vector Fields and Representation.

3.4 Vector Icons and Classifications.

3.5 Scalar Potential.

3.6 Vector Potential.

3.7 Vector Field Specification.

3.8 Tensor Contraction and Transport Process Visualization.

3.9 Multiple Fields.

4 Complex Analysis and Complex Potentials.

4.1 Complex Variables/Functions and Applications.

4.2 Complex Analysis and Cauchy-Riemann Equation.

4.3 Differentiation of Complex Function.

4.4 Integration of Complex Functions.

4.5 Visualization of Complex Potentials.

4.6 Example 4.1a Visualization of Heat and Fluid Transport in aCorner.

5 Field Mapping and Applications.

5.1 Introduction.

5.2 Mapping of Euclidean Geometry.

5.3 Inversion Mapping.

5.4 Mapping with Complex Functions.

5.5 Conformal Mapping and Applications.

5.6 Hodograph Method and Mapping.

5.7 Hodograph Representations and Applications.

5.8 Example 4.1b Mapping of Field Patterns and ImageWarping.

6 Tensor Representation, Contraction andVisualization.

6.1 Introduction.

6.2 Development of Tensor Visualization Techniques.

6.3 Tensor Description and Representation.

6.4 Tensor Decomposition and Tensor Rank Reduction.

6.5 Visualization of Symmetric Tensors.

6.6 Visualization of Antisymmetric Tensors.

6.7 Example: 4.1c Convective Momentum Flux TensorVisualization.

7 Critical Point Topology, Classification andVisualization.

7.1 Introduction.

7.2 Complex Analysis of Critical Point.

7.3 Critical Point Theory and Classification.

7.4 Example 4.1d Critical Point Topology.

7.5 Singular Point Visualization and Mapping.

7.6 Example 7.1 Mapping of a Point Source.

8 Engineering Application Examples.

8.1 Example 8.1: Torsion of a Square Beam.

8.2 Example 8.2: Bending of a Cantilever Beam Subject to a PointLoad.

8.3 Example 8.3: Squeezing Flow and Vorticity Transport.

8.4 Example 8.4: Groundwater Flows in an Anisotropic PorousMedium.

References.

Index.