Global Balance of Squared Temperature

Sink (Dissipation)

There are 3 terms dissipating the squared temperature, which are computed separately.

\[\sumzc \sumyc \sumxf \dhdis{1}\]

src/logging/dissipated_squared_temperature.c

static int get_dtdx (
    const domain_t * domain,
    const fluid_t * fluid,
    double * quantity
) {
  const int isize = domain->mysizes[0];
  const int jsize = domain->mysizes[1];
#if NDIMS == 3
  const int ksize = domain->mysizes[2];
#endif
  const double * restrict hxxf = domain->hxxf;
  const double * restrict jdxf = domain->jdxf;
  const double * restrict t = fluid->t.data;
  const double diffusivity = fluid_compute_temperature_diffusivity(fluid);
#if NDIMS == 2
  for (int j = 1; j <= jsize; j++) {
    for (int i = 1; i <= isize + 1; i++) {
      const double hx = HXXF(i);
      const double jd = JDXF(i);
      const double dt =
        - T(i-1, j  )
        + T(i  , j  );
      *quantity += diffusivity * jd * pow(1. / hx * dt, 2.);
    }
  }
#else
  for (int k = 1; k <= ksize; k++) {
    for (int j = 1; j <= jsize; j++) {
      for (int i = 1; i <= isize + 1; i++) {
        const double hx = HXXF(i);
        const double jd = JDXF(i);
        const double dt =
          - T(i-1, j  , k  )
          + T(i  , j  , k  );
        *quantity += diffusivity * jd * pow(1. / hx * dt, 2.);
      }
    }
  }
#endif
  return 0;
}

\[\sumzc \sumyf \sumxc \dhdis{2}\]

src/logging/dissipated_squared_temperature.c

static int get_dtdy (
    const domain_t * domain,
    const fluid_t * fluid,
    double * quantity
) {
  const int isize = domain->mysizes[0];
  const int jsize = domain->mysizes[1];
#if NDIMS == 3
  const int ksize = domain->mysizes[2];
#endif
  const double hy = domain->hy;
  const double * restrict jdxc = domain->jdxc;
  const double * restrict t = fluid->t.data;
  const double diffusivity = fluid_compute_temperature_diffusivity(fluid);
#if NDIMS == 2
  for (int j = 1; j <= jsize; j++) {
    for (int i = 1; i <= isize; i++) {
      const double jd = JDXC(i);
      const double dt =
        - T(i  , j-1)
        + T(i  , j  );
      *quantity += diffusivity * jd * pow(1. / hy * dt, 2.);
    }
  }
#else
  for (int k = 1; k <= ksize; k++) {
    for (int j = 1; j <= jsize; j++) {
      for (int i = 1; i <= isize; i++) {
        const double jd = JDXC(i);
        const double dt =
          - T(i  , j-1, k  )
          + T(i  , j  , k  );
        *quantity += diffusivity * jd * pow(1. / hy * dt, 2.);
      }
    }
  }
#endif
  return 0;
}

\[\sumzf \sumyc \sumxc \dhdis{3}\]

src/logging/dissipated_squared_temperature.c

static int get_dtdz (
    const domain_t * domain,
    const fluid_t * fluid,
    double * quantity
) {
  const int isize = domain->mysizes[0];
  const int jsize = domain->mysizes[1];
  const int ksize = domain->mysizes[2];
  const double hz = domain->hz;
  const double * restrict jdxc = domain->jdxc;
  const double * restrict t = fluid->t.data;
  const double diffusivity = fluid_compute_temperature_diffusivity(fluid);
  for (int k = 1; k <= ksize; k++) {
    for (int j = 1; j <= jsize; j++) {
      for (int i = 1; i <= isize; i++) {
        const double jd = JDXC(i);
        const double dt =
          - T(i  , j  , k-1)
          + T(i  , j  , k  );
        *quantity += diffusivity * jd * pow(1. / hz * dt, 2.);
      }
    }
  }
  return 0;
}

Source (Injection)

\[\dhinjall\]

injects squared temperature, which will be elaborated later.