Summary on CFD in a nutshell
Important parts highlighted in blue
, Contents
1. Computational Fluid Dynamics in a Nutshell .............................................................................. 3
1.1 Mass conservation ............................................................................................................. 3
1.2 Momentum balance ........................................................................................................... 3
1.3 Energy balance ................................................................................................................... 4
1.4 Incompressible flow ........................................................................................................... 4
1.5 Navier-Stokes equations..................................................................................................... 4
1.6 Discretisation ..................................................................................................................... 4
1.7 The advection equation ...................................................................................................... 4
1.8 Comparison of finite difference and finite volume formulations ......................................... 4
1.9 Finite volume method for CFD ............................................................................................ 5
1.10 Analysis of discretisation .................................................................................................... 5
1.11 Stability and artificial viscosity ............................................................................................ 5
1.11.1 Artificial viscosity ........................................................................................................ 6
1.11.2 Artificial viscosity and first order finite volume method .............................................. 6
1.11.3 Artificial viscosity and second order finite volume method ......................................... 6
1.12 Boundary conditions and flow physics ................................................................................ 6
1.13 Wave-like solutions: hyperbolic equations ......................................................................... 7
1.14 Smoothing-type solutions: elliptic equations ...................................................................... 7
1.15 The borderline case- parabolic equations ........................................................................... 7
1.16 Characterisation of the Navier-Stokes Equations ................................................................ 7
1.17 Compressible and Incompressible flows ............................................................................. 7
1.18 Choice of boundary conditions ........................................................................................... 7
1.19 Boundary conditions “light” ............................................................................................... 8
1.20 Convergence ...................................................................................................................... 8
1.21 Cost of error reduction ....................................................................................................... 8
1.22 Increasing Mesh resolution and Frequency ........................................................................ 8
1.23 Multigrid ............................................................................................................................ 9
1.24 Grid Generation ................................................................................................................. 9
1.25 Analysis of the results ........................................................................................................ 9
1.26 Mesh convergence ............................................................................................................. 9
2. References............................................................................................................................... 10
Important parts highlighted in blue
, Contents
1. Computational Fluid Dynamics in a Nutshell .............................................................................. 3
1.1 Mass conservation ............................................................................................................. 3
1.2 Momentum balance ........................................................................................................... 3
1.3 Energy balance ................................................................................................................... 4
1.4 Incompressible flow ........................................................................................................... 4
1.5 Navier-Stokes equations..................................................................................................... 4
1.6 Discretisation ..................................................................................................................... 4
1.7 The advection equation ...................................................................................................... 4
1.8 Comparison of finite difference and finite volume formulations ......................................... 4
1.9 Finite volume method for CFD ............................................................................................ 5
1.10 Analysis of discretisation .................................................................................................... 5
1.11 Stability and artificial viscosity ............................................................................................ 5
1.11.1 Artificial viscosity ........................................................................................................ 6
1.11.2 Artificial viscosity and first order finite volume method .............................................. 6
1.11.3 Artificial viscosity and second order finite volume method ......................................... 6
1.12 Boundary conditions and flow physics ................................................................................ 6
1.13 Wave-like solutions: hyperbolic equations ......................................................................... 7
1.14 Smoothing-type solutions: elliptic equations ...................................................................... 7
1.15 The borderline case- parabolic equations ........................................................................... 7
1.16 Characterisation of the Navier-Stokes Equations ................................................................ 7
1.17 Compressible and Incompressible flows ............................................................................. 7
1.18 Choice of boundary conditions ........................................................................................... 7
1.19 Boundary conditions “light” ............................................................................................... 8
1.20 Convergence ...................................................................................................................... 8
1.21 Cost of error reduction ....................................................................................................... 8
1.22 Increasing Mesh resolution and Frequency ........................................................................ 8
1.23 Multigrid ............................................................................................................................ 9
1.24 Grid Generation ................................................................................................................. 9
1.25 Analysis of the results ........................................................................................................ 9
1.26 Mesh convergence ............................................................................................................. 9
2. References............................................................................................................................... 10
