Introduction

User integration of the SDE for the user-defined variables.

The variables are constant by default. The SDE must be of the form:

$\frac{dT}{dt}=\frac{T - PIP}{Tca}$

T: particle attribute representing the variable

Tca: characteristic time for the sde to be prescribed in the array auxl1

PIP: coefficient of the SDE (pseudo RHS) to be prescribed in the array auxl2.

If the chosen scheme is first order (nordre=1) then, at the first and only call pip is expressed as a function of the quantities of the previous time step (contained in the particle data).

If the chosen scheme is second order (nordre=2) then, at the first call (nor=1) pip is expressed as a function of the quantities of the previous time step, and at the second passage (nor=2) pip is expressed as a function of the quantities of the current time step.

Example

Example of the integration of the SDE (Stochastic Differential Equation).

void
cs_user_lagr_sde
(
  [[maybe_unused]] const cs_real_t         dt,
  [[maybe_unused]] const cs_lnum_t         p_id,
  [[maybe_unused]] const cs_real_t        *taup,
  [[maybe_unused]] const cs_real_3_t      *tlag,
  [[maybe_unused]] const cs_real_2_t       tempct,
  [[maybe_unused]] const int               nor
)
{
  /* Note: taup and tlag are associated to the particle and its value
   * for all phase is provided */
 
  /* Initializations
     --------------- */
 
  cs_lagr_particle_set_t  *p_set = cs_lagr_get_particle_set();
  const cs_lagr_attribute_map_t *p_am = p_set->p_am;
  unsigned char *part = p_set->p_buffer + p_am->extents * p_id;
 
  cs_real_t tcarac;
  cs_real_t pip;
 
  /* Characteristic time of the current SDE
     -------------------------------------- */
 
  /* Loop on the additional variables */
 
  for (int i = 0;
       i < cs_glob_lagr_model->n_user_variables;
       i++) {
 
    cs_real_t *usr_var
      = cs_lagr_particle_attr_n_get_ptr<cs_real_t>(part, p_am, 0, CS_LAGR_USER);
    cs_real_t *prev_usr_var
      = cs_lagr_particle_attr_n_get_ptr<cs_real_t>(part, p_am, 1, CS_LAGR_USER);
 
    /* Characteristic time tca of the differential equation,
       This example must be adapted to the case */
    tcarac = 1.0;
 
    /* Prediction at the first substep;
       This example must be adapted to the case */
    if (nor == 1)
      pip = prev_usr_var[i];
 
    /* Correction at the second substep;
       This example must be adapted to the case */
    else
      pip = usr_var[i];
 
    /* Integration of the variable ipl
       ------------------------------- */
 
    cs_lagr_sde_attr(CS_LAGR_USER, p_id, nor, dt, tcarac, pip);
 
  }
}