Data structures

The physical parameters, information about the grid, precalculated discretizations and some other stuff is kept in the class Scene. The most important variables are listened below.

variable	description
gridp[3]	This defines the number of cells in every direction for the whole domain $\Omega_R$, the inner cells are numbered from 1 to gridp[$i$], $1\leq i\leq 3$. The cells which are computed by the actual process are defined in the class ParParams, which is described in ().
d[3][]	This variable contains the spaces between the grid lines in every direction (see figure ). For convenience: access is possible using the macros DX[$i$], DY[$j$] and DZ[$k$].
dm[3][]	This variable contains the spaces between the middles of the cells in every direction (marked by the circles in figure ). For convenience: access is possible using the macros DXM[$i$], DYM[$j$] and DZM[$k$].
kabs[3][]	This variable contains the absolute positions of the grid lines.
ddstar[3][3][], ddPstar[3][3][], ddSstar[3][3][]	These variables contain different discretizations for the second derivative, where the first index selects the direction and the second index selects the appropriate weight (left - 0, middle - 1, right - 2). The discretizations are described in ().
periodbound	This is a bit field indicating if periodic boundary conditions are set in the appropriate direction (bit 0 - $x$-direction, bit 1 - $y$-direction, bit 2 - $z$-direction).

The 3D matrices, for example velocity and pressure data, are kept in the class Navier. There are two derived classes, NavierSetup and NavierCalc. The dimensions of these matrices are defined in the following table.

matrix	dimension
flag, P, F, G, H, RHS, T, CH[$i$]	$\{{\tt biug-1,biog+1}\}\times\{{\tt bjug-1,bjog+1}\}\times\{{\tt bkug-1,bkog+1}\}$
U	$\{{\tt biug-1-}\mu_x{\tt ,biog+1}\}\times\{{\tt bjug-1,bjog+1}\}\times\{{\tt bkug-1,bkog+1}\}$
V	$\{{\tt biug-1,biog+1}\}\times\{{\tt bjug-1-}\mu_y{\tt ,bjog+1}\}\times\{{\tt bkug-1,bkog+1}\}$
W	$\{{\tt biug-1,biog+1}\}\times\{{\tt bjug-1,bjog+1}\}\times\{{\tt bkug-1-}\mu_z{\tt ,bkog+1}\}$

The variable $\mu_x$ is set to 1 if periodic boundary conditions are set in $x$-direction or if the current process has a neighbour in south-direction and 0 otherwise. The variables $\mu_y$ and $\mu_z$ are set in a similar way.

The cells where boundary values need to be set (for one specific parallel process) are stored in lists which are defined in NavierCalc.

list	contains
InflowList	cells where Inflow b.c. are set (parameters are stored in list)
SlipList	cells where Slip b.c. (Neumann) are set
NoslipList	cells where Noslip b.c. (Dirichlet) are set
PdpdnList[color][face]	cells where prescribed boundary conditions (b.c.) lead to homogeneous Neumann b.c. for the pressure and which have the color color. These cells have exactly one fluid cell neighbouring at face face.
PSpecdpdnList[color]	cells where prescribed boundary conditions (b.c.) lead to homogeneous Neumann b.c. for the pressure and which have the color color. These cells have more than one neighbouring fluid cell. This requires some more involved boundary treatment.
PInOut2List[color][face]	cells with the prescribed outflow condition 2, it is assumed that no cells with more than one neighbouring fluid cell exist. Some special boundary treatment is required.
PInOut1List[color][face]	same as PInOut2List for outflow condition 1.