Additional right_hand side source terms for turbulence models

Usage

The additional source term is decomposed into an explicit part $(crvexp)$ and an implic it part $(crvimp)$ that must be provided here. The resulting equations solved by the code are:

$\rho \norm{\vol{\celli}} \DP{\varia} + .... = crvimp \cdot \varia + crvexp$

where $\varia$ is the turbulence field of index $f_{id}$ .

Note

$crvexp \text{, } crvimp$ are defined after the Finite Volume integration over the cells, so they include the $\norm{\vol{\celli}}$ term. More precisely:

is expressed in $kg\cdot m^{-2} \cdot s^{-2}$
is expressed in $kg \cdot s^{-1}$

The $crvexp$ , $crvimp$ arrays are already initialized to 0 before entering the routine. It is not needed to do it in the routine (waste of CPU time).

For stability reasons, Code_Saturne will not add -crvimp directly to the diagonal of the matrix, but Max(-crvimp,0). This way, the crvimp term is treated implicitely only if it strengthens the diagonal of the matrix. However, when using the second-order in time scheme, this limitation cannot be done anymore and -crvimp is added directly. The user should therefore test the negativity of crvimp by himself.

When using the second-order in time scheme, one should supply:

at time n
at time n+1/2

The selection of cells where to apply the source terms is based on a getcel command. For more info on the syntax of the getcel command, refer to the user manual or to the comments on the similar command getfbr in the routine cs_user_boundary_conditions.

Local variables

! Local variables
integer          iel
double precision ff, tau
type(var_cal_opt) :: vcopt
character(len=80) :: fname
integer, allocatable, dimension(:) :: lstelt
double precision, dimension(:), pointer ::  cpro_rom
double precision, dimension(:), pointer ::  cvar_var

Initialization and finalization

The following initialization block needs to be added for the following examples:

! Allocate a temporary array for cells selection

allocate(lstelt(ncel))

At the end of the subroutine, it is recommended to deallocate the work array:

! Deallocate the temporary array

deallocate(lstelt)

In theory Fortran 95 deallocates locally-allocated arrays automatically, but deallocating arrays in a symetric manner to their alloacation is good pratice, and avoids using a different logic C and Fortran.

Remaining initialization

Get the density array in cpro_rom

call field_get_val_s(icrom, cpro_rom)

Get the array of the current turbulent variable and its name

call field_get_val_s(f_id, cvar_var)
call field_get_name(f_id, fname)
! --- Get variable calculation options
call field_get_key_struct_var_cal_opt(f_id, vcopt)
if (vcopt%iwarni.ge.1) then
  write(nfecra,1000)
endif

Example

Example of arbitrary additional source term for turbulence models (Source term on the TKE "k" here).

Source term for $\varia:$

$\rho \norm{\vol{\celli}} \frac{d(\varia)}{dt} = ... - \rho \norm{\vol{\celli}} \cdot ff - \rho \frac{ \varia}{\tau}$

with $ ff $ = 3.d0 an $\tau$ = 4.d0

Body

Note

The turbulence variable names are:

'k' and 'epsilon' for the k-epsilon models
'r11', 'r22', 'r33', 'r12', 'r13', 'r23' and 'epsilon' for the Rij-epsilon LRR and S SG
'r11', 'r22', 'r33', 'r12', 'r13', 'r23', 'epsilon' and 'alpha' for the EBRSM
'k', 'epsilon', 'phi' and 'f_bar' for the phi-model
'k', 'epsilon', 'phi' and 'alpha' for the Bl-v2-k model
'k' and 'omega' for the k-omega turbulence model
'nu_tilda' for the Spalart Allmaras model

Calculation of the explicit and implicit source terms

if (trim(fname).eq.'k') then
  ff  = 3.d0
  tau = 4.d0
  ! --- Explicit source terms
  do iel = 1, ncel
    crvexp(iel) = -cpro_rom(iel)*cell_f_vol(iel)*ff
  enddo
  ! --- Implicit source terms
  !        crvimp is already initialized to 0, no need to set it here
  do iel = 1, ncel
    crvimp(iel) = -cpro_rom(iel)*cell_f_vol(iel)/tau
  enddo
endif

Format

1000 format(' User source terms for turbulence model',/)