1 Introduction to the equations of fluid dynamics and the finite element
1.1 General remarks and classification of fluid dynamics problems discussed in this book
1.2 The governing equations of fluid dynamics
1.3 Inviscid, incompressible flow
1.4 Incompressible (or nearly incompressible) flows
1.5 Numerical solutions: weak forms, weighted residual and finite element approximation
1.6 Concluding remarks
2 Convection dominated problems – finite element approximations to the convection–diffusion-reaction equation
2.2 The steady-state problem in one dimension
2.3 The steady-state problem in two (or three) dimensions
2.4 Steady state -- concluding remarks
2.5 Transients -- introductory remarks
2.6 Characteristic-based methods
2.7 Taylor--Galerkin procedures for scalar variables
2.8 Steady-state condition
2.9 Non-linear waves and shocks
2.10 Treatment of pure convection
2.11 Boundary conditions for convection--diffusion
2.12 Summary and concluding remarks
3 The characteristic-based split (CBS) algorithm. A general procedure for compressible and incompressible flow
3.2 Non-dimensional form of the governing equations
3.3 Characteristic-based split (CBS) algorithm
3.4 Explicit, semi-implicit and nearly implicit forms
3.5 Artificial compressibility and dual time stepping
3.6 ‘Circumvention’ of the Babu¡ska--Brezzi (BB) restrictions
3.7 A single-step version
- No. of pages:
- © 2005
24th November 2005
- Print ISBN:
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- Journal of the British Society for Strain Measurement