Calculation of a local Nusselt number

This is an example of cs_user_extra_operations function which computes a local Nusselt number.

Local variables

Faces can be selected either using a selector (as is done here) or directly using boundary zone element ids if an appropriate zone has been defined.

    const cs_lnum_t n_cells     = domain->mesh->n_cells;
    const cs_lnum_t n_b_faces    = domain->mesh->n_b_faces;
    const cs_lnum_t *b_face_cells = domain->mesh->b_face_cells;
 
    const cs_real_3_t *cell_cen
      = (const cs_real_3_t *)domain->mesh_quantities->cell_cen;
    const cs_real_3_t *cdgfbo
      = (const cs_real_3_t *)domain->mesh_quantities->b_face_cog;
    const cs_real_t *volume  = domain->mesh_quantities->cell_vol;
 
    FILE *file = nullptr;
 
    cs_real_3_t *vel = (cs_real_3_t *)CS_F_(vel)->val;
    const cs_fluid_properties_t *phys_pro = cs_glob_fluid_properties;
 
    /* Parameters, case dependant */
    const cs_real_t prandtl = 0.71, height = 1., qwall = 1.;
 
    const cs_field_t *f = CS_F_(t);
    const cs_field_t *mu = CS_F_(mu);
 
    cs_lnum_t nlelt;
    cs_lnum_t *lstelt;
    BFT_MALLOC(lstelt, n_b_faces, cs_lnum_t);
 
    cs_selector_get_b_face_list
      ("normal[0, -1, 0, 0.1] and box[-1000, -1000, -1000, 1000, 0.01, 1000]",
       &nlelt, lstelt);

Reconstruct value at selected boundary faces

Allocate a local array for the selected boundary faces.

    cs_real_t *treloc;
    BFT_MALLOC(treloc, nlelt, cs_real_t);
 
    int iortho = 0;

General case (for non-orthogonal meshes)

    if (iortho == 0) {
      cs_post_field_cell_to_b_face_values(f, nlelt, lstelt, treloc);
    }

Case of orthogonal meshes

Compute boundary value without reconstruction

      const cs_real_t *coefap = CS_F_(t)->bc_coeffs->a;
      const cs_real_t *coefbp = CS_F_(t)->bc_coeffs->b;
 
      for (cs_lnum_t ielt = 0; ielt < nlelt; ielt++) {
        cs_lnum_t face_id = lstelt[ielt];
        cs_lnum_t c_id = b_face_cells[face_id];
        treloc[ielt] = coefap[face_id] + coefbp[face_id] * f->val[c_id];
      }

Note

Here, we assign the non-reconstructed value.

Open file to print values and broadcast values to all parallel ranks. Values are ordered by the xabs array values provided to the cs_parall_allgather_ordered_r, so this function is needed even when not running in parallel.

    if  (cs_glob_rank_id < 1) {
      file = fopen("Nusselt.dat", "w");
    }
 
    cs_gnum_t neltg = nlelt;
    cs_parall_counter(&neltg, 1);
 
    cs_real_t *xabs = nullptr, *xabsg = nullptr, *xnusselt = nullptr;
    cs_real_t *treglo = nullptr;
 
    BFT_MALLOC(xabs, nlelt, cs_real_t);
 
    BFT_MALLOC(xnusselt, neltg, cs_real_t);
    BFT_MALLOC(xabsg, neltg, cs_real_t);
    BFT_MALLOC(treglo, neltg, cs_real_t);
 
    for (cs_lnum_t ilelt = 0; ilelt < nlelt; ilelt ++) {
      cs_lnum_t face_id = lstelt[ilelt];
      xabs[ilelt] = cdgfbo[face_id][0];
    }
 
    cs_parall_allgather_ordered_r(nlelt, neltg, 1, xabs, xabs, xabsg);
    cs_parall_allgather_ordered_r(nlelt, neltg, 1, xabs, treloc, treglo);
 
    BFT_FREE(xabs);
    BFT_FREE(treloc);
    BFT_FREE(lstelt);

Compute the bulk temperature, finalize the Nusselt number, print it and free memory not already freed before:

    for (cs_gnum_t ilelt = 0; ilelt < neltg; ilelt ++) {
 
      cs_real_t xtbulk = 0;
      cs_real_t xubulk = 0;
      cs_real_t lambda = 0;
 
      int npoint = 200;
      cs_lnum_t c_id_prev = -1;
      int irang1 = -1;
      int irangv;
 
      for (int ii = 0; ii < npoint; ii++) {
 
        cs_lnum_t c_id;
 
        cs_real_t xyz[3] = {xabsg[ilelt],
                            (cs_real_t)ii/(cs_real_t)(npoint-1),
                            0.};
 
        cs_geom_closest_point(n_cells,
                              cell_cen,
                              xyz,
                              &c_id, &irangv);
 
        if (c_id != c_id_prev || irangv != irang1) {
          c_id_prev = c_id;
          irang1 = irangv;
          if (cs_glob_rank_id == irangv) {
            cs_real_t xtb = volume[c_id]*f->val[c_id]*vel[c_id][0];
            cs_real_t xub = volume[c_id]*vel[c_id][0];
            xtbulk += xtb;
            xubulk += xub;
            lambda = phys_pro->cp0*mu->val[c_id] / prandtl;
          }
        }
 
      }
 
      /* Note: only last location used for lambda.
         Would be more appropriate (but still not general at all)
         with visls0 in definition of lambda and from the derivation
         of Nusselt number; use of lambda at the wall (ii = 0)
         would seem better */
      cs_parall_bcast(irangv, 1, CS_REAL_TYPE, &lambda);
 
      cs_real_t xbulk[2] = {xtbulk, xubulk};
      cs_parall_sum(2, CS_REAL_TYPE, xbulk);
 
      xtbulk = xbulk[0] / xbulk[1];
      xubulk = xbulk[1];
 
      cs_real_t tfac = treglo[ilelt];
 
      xnusselt[ilelt] = qwall * 2. * height / lambda / (tfac - xtbulk);
    }
 
    for (cs_gnum_t ii = 0; ii < neltg; ii++)
      fprintf(file,
              "%17.9e %17.9e\n",
              xabsg[ii]*10.,
              xnusselt[ii]/(0.023*pow(30000., 0.8)*pow(0.71, 0.4)));
 
    if (file != nullptr)
      fclose(file);
 
    BFT_FREE(xnusselt);
    BFT_FREE(xabsg);
    BFT_FREE(treglo);