Computational Methods in Viscous Aerodynamics

Most problems in viscous aerodynamics are concerned with the computation of the characteristics and effects of the boundary layer caused by viscosity manifested in the form of drag, turbulence, separation, vorticity and general unsteady flow. All these problems involve the solution of highly non-linear Navier-Stokes equations and progress is only possible by developing suitable computational methods. There are four main methods of numerical solution of the Navier-Stokes equations, namely: Integral equations; Finite differences; Finite volume; and Finite elements. In addition there are so-called spectral methods which fall beyond the scope of this book as they are highly specialized. The choice of a particular method depends to a large extent on the flow region in question. Detailed illustrations of the four main methodologies are included in this volume. Containing contributions by some of the world's leading experts, this book is the definitive reference source for anyone interested in the the latest trends in Computational Methods.

Table of Contents:
1. Three Dimensional Boundary Layers. Introduction. Sample of three dimensional boundary layers. Properties of three dimensional boundary layers. Boundary layers. Equations in surface oriented coordinate systems. Numerical solution for two dimensional boundary layers. Numerical solution for three dimensional boundary layers. Three dimensional, steady, laminar, compressible boundary layer along the line of symmetry of an inclined ellipsoid. Closing remarks. 2. Calculation of Three-Dimensional Boundary Layers. Introduction. Boundary layer equations. Integral methods. Singularities in boundary layer calculations. Solution of local equations. Appendix: Close relationships used in the integral method. 3. Computation of Unsteady Laminar Incompressible Viscous Flows using the Vorticity Stream Function Formulation. Introduction. The differential equations and the problems to be considered. Numerical methods for the vorticity stream function formulation. Numerical results. Superimposed motions of circular cylinders. 4. The Finite Volume Approach for the Navier-Stokes Equations. Navier-Stokes equations. Finite volume discretization. Viscous terms evaluation. Spatial accuracy. Viscous grid. Artificial dissipation. An explicit node-based finite volume scheme. 5. Navier-Stokes Computations for Aerodynamics Configurations at High Angle of Attack. Governing equations. Numerical algorithm. Computational results. 6. Adaptation Methods for Viscous Flows. Adaptive algorithms. Adaptation strategies. Feature detection. An algebraic turbulence model with unstructured grid. Coding with unstructured meshes. Example of adaptive calculations. Adaptation evaluation. 7. Finite Element Vorticity Based Methods for the Solution of the Compressible Navier-Stokes Equations. The stream function - vorticity/method. Transonic viscous/inviscis interaction. The velocity-vorticity approach. 8. Experiences with Finite Element Methods for the Velocity-Vorticity Formulation of Three Dimensional Viscous Incompressible Flows. Mathematical models: Differential equations and boundary conditions. Mathematical models: Weak formulations and boundary conditions. Finite element discretization. The accuracy of finite element approximations. Iterative methods for the discrete equations. Examples of the convergence histories of the various iterative methods. Each chapter includes an introduction and reference section. 9. Navier-Stokes Code Development for Transonic Flow Simulations. Governing equation and numerical algorithm. some of the application example. Code development for unsteady transonic flows. Supporting computer system. Final remarks. 10. A Fast Viscous Convection Method for Transonic Aerodynamics. Shock-wave/boundary-layer interaction. Numerical procedures. Viscous convection of full-potential flows. Viscous convection of unsteady small-disturbance solutions. Conclusions. 11. Two-Dimensional Incompressible Aerofoil Design and Analysis. Performance prediction.