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Full Description
The Boundary Element Method has now become a powerful tool of engineering analysis and is routinely applied for the solution of elastostatics and potential problems. More recently research has concentrated on solving a large variety of non-linear and time dependent applications and in particular the method has been developed for viscous fluid flow problems. This book presents the state of the art on the solution of viscous flow using boundary elements and discusses different current approaches which have been validated by numerical experiments. . Chapter 1 of the book presents a brief review of previous work on viscous flow simulation and in particular gives an up-to-date list of the most important BEM references in the field. Chapter 2 reviews the governing equations for general viscous flow, including compressibility. The authors present a compre hensive treatment of the different cases and their formulation in terms of boundary integral equations. This work has been the result of collaboration between Computational Mechanics Institute of Southampton and Massa chusetts Institute of Technology researchers. Chapter 3 describes the gen eralized formulation for unsteady viscous flow problems developed over many years at Georgia Institute of Technology. This formulation has been extensively applied to solve aer09ynamic problems.
Contents
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.- 2.2 Proposed Approach.- 2.3 Statement of the Problems—Governing Equations for Compressible Fluid Flow.- 2.4 State of the Art in Boundary Elements for Fluids.- References.- 3 A Generalized Formulation for Unsteady Viscous Flow Problems.- 3.1 Introduction.- 3.2 Mathematical Formulation.- 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.- 4.5 Discretisation of the BIE for Flow Kinematics.- 4.6 Boundary Integral Equation for the Flow Kinetics.- 4.7 Discretised BIE for the Kinetics of 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.- 4.13 Conclusion.- References.- 5 A Boundary Element Analysis for Thermal Convection Problems.- 5.1 Introduction.- 5.2 Theory.- 5.3 Numerical Implementation.- 5.4 Numerical Results.- 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.- 7.6Conclusions.- References.- 8 Viscous Fluid Mechanics.- Abstract.- 8.1 Introduction.- 8.2 Governing Equations.- 8.3 Integral Formulations.- 8.4 Numerical Procedure.- 8.5 Numerical Examples for Stokes Flows.- 8.6 Numerical Examples for Convective Flows.- 8.7 Conclusion.- References.
