Viscous Flow Applications

ISBN-13: 9783642836855 / Angielski / Miękka / 2011 / 183 str.

Carlos A. Brebbia

Opis

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."

Spis treści

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.