FLOW AROUND A CYLINDER - istiarto

Chapter 4
– 4.i –
4 Numerical Model Development 4.1
Abstract ...................................................................................................................... 4.1
Résumé ....................................................................................................................... 4.1
4.1 Governing equations ....................................................................................... 4.2
4.2 Solution strategy: the iterative method .......................................................... 4.5
4.3 Numerical method: the finite-volume approximation ................................... 4.8
4.3.1 Grid arrangement ........................................................................................ 4.8
4.3.2 Computation of the surface area and of the cell volume .............................. 4.9
4.3.3 Cell-face interpolation and gradient computation ...................................... 4.10
4.3.4 Discretisation of the time derivative terms ................................................ 4.11
4.3.5 Discretisation of the convective terms ....................................................... 4.12
4.3.6 Discretisation of the diffusive terms .......................................................... 4.13
4.3.7 Convective-diffusive terms: hybrid and power-law schemes ..................... 4.15
4.3.8 Source terms ............................................................................................. 4.19
4.3.9 Assembly of the coefficients ..................................................................... 4.21
4.4 Pressure-velocity coupling ............................................................................ 4.24
4.4.1 SIMPLE algorithm.................................................................................... 4.24
4.4.2 Pressure correction procedure ................................................................... 4.28
4.4.3 Under-relaxation factor and time step ....................................................... 4.28
4.5 Boundary conditions ..................................................................................... 4.29
4.5.1 Boundary placement ................................................................................. 4.29
4.5.2 Inflow boundary ....................................................................................... 4.30
4.5.3 Outflow boundary ..................................................................................... 4.32
4.5.4 Wall boundary .......................................................................................... 4.33
4.5.5 Symmetry boundary .................................................................................. 4.41
4.5.6 Surface boundary ...................................................................................... 4.43
4.6 Solution procedures ...................................................................................... 4.47
4.6.1 Spatial discretisation ................................................................................. 4.47
4.6.2 Matrix solvers ........................................................................................... 4.49
4.7 Summary ....................................................................................................... 4.53
References................................................................................................................. 4.53
Notations ................................................................................................................... 4.54