1 A Brief Review of Previous Work on Viscous Flow Simulation.- 1.1 Introduction.- 1.2 Review of Work on Boundary Elements.- References.- 2 Boundary Element Formulation for Viscous Compressible Flow.- 2.1 Introduction.- 2.1.1 Finite Differences.- 2.1.2 Finite Elements.- 2.1.3 Finite Volume.- 2.1.4 Boundary Elements.- 2.2 Proposed Approach.- 2.3 Statement of the Problems—Governing Equations for Compressible Fluid Flow.- 2.3.1 The Navier Stokes Equations.- 2.3.2 Turbulent Flow Equations.- 2.4 State of the Art in Boundary Elements for Fluids.- 2.4.1 Basic Integral Equations—Two-Dimensional Case.- 2.4.2 Procedure for Incompressible Flow.- 2.4.3 Integral Formulation—Three-Dimensional Case.- 2.4.4 Procedure for Compressible Flow.- References.- 3 A Generalized Formulation for Unsteady Viscous Flow Problems.- 3.1 Introduction.- 3.2 Mathematical Formulation.- 3.2.1 Coordinate Transformation.- 3.2.2 Simplifications in the Boundary Layer Region.- 3.2.3 Surface Vorticity Determination.- 3.3 Numerical Formulation.- 3.4 Results and Discussions.- 3.5 Concluding Remarks.- Acknowledgement.- References.- 4 Natural and Forced Convection Simulation Using the Velocity-Vorticity Approach.- 4.1 Introduction.- 4.2 Governing Equations.- 4.3 Vector Potential.- 4.4 Boundary Integral Equation for Flow Kinematics.- 4.4.1 BIE for Stream Function.- 4.4.2 Vector Elliptic Equation.- 4.4.3 BIE for Vector Potential.- 4.4.4 BIE for External Flows.- 4.4.5 Plane Flow.- 4.5 Discretisation of the BIE for Flow Kinematics.- 4.5.1 Discretised BIE of Plane Flow Kinematics.- 4.5.2 Discretised BIE fo the Kinematics for the 3D Flow.- 4.6 Boundary Integral Equation for the Flow Kinetics.- 4.6.1 BIE for Kinetics of Plane Flows.- 4.6.2 BIE for Kinetics of 3D Flows.- 4.7 Discretised BIE for the Kinetics of Flow.- 4.7.1 Discretised BIE for Kinetics of Plane Flows.- 4.7.2 Discretised BIE of the Kinetics for 3D Flow.- 4.8 Boundary Integral Equation for Energy Transport.- 4.9 Discretised Energy Transport Equation.- 4.10 Computational Scheme.- 4.11 Boundary Conditions.- 4.12 Numerical Examples.- 4.12.1 Thermally Driven Cavity Flow.- 4.12.2 Channel Flow over a Square Obstacle.- 4.12.3 Natural Convection from a Cylinder in a Closed Cavity.- 4.12.4 Natural Convection form a Cylinder in an Open Space.- 4.13 Conclusion.- References.- 5 A Boundary Element Analysis for Thermal Convection Problems.- 5.1 Introduction.- 5.2 Theory.- 5.2.1 Basic Equations.- 5.2.2 Boundary Integral Formulations.- 5.2.3 Evaluation of Convective Terms.- 5.3 Numerical Implementation.- 5.3.1 Boundary-Domain Element Discretization.- 5.3.2 Self-adaptive Coordinate Transformation Technique.- 5.3.3 Iterative Technique.- 5.4 Numerical Results.- 5.4.1 Evaluation of Quasi-singular Boundary Integrals.- 5.4.2 Square Cavity Flow Problem.- 5.4.3 Evaluation of Pressure Field.- 5.5 Conclusion.- Acknowledgement.- References.- 6 Calculation of the Potential Flow with Consideration of the Boundary Layer.- 6.1 Introduction.- 6.2 Potential Flow.- 6.3 Boundary Layer.- 6.4 Example.- 6.5 Conclusions.- References.- 7 Applications in Non-Newtonian Fluid Mechanics.- 7.1 Introduction.- 7.2 The Behaviour of Non-Newtonian Liquids.- 7.3 Governing Equations.- 7.4 Boundary Integral Formulations and Solution Methods.- 7.5 Applications.- 7.6 Conclusions.- References.- 8 Viscous Fluid Mechanics.- Abstract.- 8.1 Introduction.- 8.2 Governing Equations.- 8.3 Integral Formulations.- 8.3.1 Reciprocal Theorem.- 8.3.2 Integral Representation of ?.- 8.3.3 Boundary Equations for Stokes Flow.- 8.4 Numerical Procedure.- 8.4.1 Boundary Integrals.- 8.4.2 Surface Integrals.- 8.5 Numerical Examples for Stokes Flows.- 8.5.1 Flow Around a Steady Infinitely Long Cylinder.- 8.5.2 “Stick-slip” Problem Related to the Motion of a Free Jet.- 8.6 Numerical Examples for Convective Flows.- 8.6.1 Numerical Methods for the Solution of Non-linear Equations.- 8.6.2 Flow Around a Steady Cylinder Between Two Moving Infinite Planes for Reynolds Numbers up to 40.- 8.7 Conclusion.- References.
