Global Balance of Squared Velocity

Sink (Dissipation)

There are 9 terms dissipating the squared velocity, which are computed separately.

\[\sumzc \sumyc \sumxc \dkdis{1}{1}\]

src/logging/dissipated_squared_velocity.c

static int get_duxdx (
    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 hxxc = domain->hxxc;
  const double * restrict jdxc = domain->jdxc;
  const double * restrict ux = fluid->ux.data;
  const double diffusivity = fluid_compute_momentum_diffusivity(fluid);
#if NDIMS == 2
  for (int j = 1; j <= jsize; j++) {
    for (int i = 1; i <= isize; i++) {
      const double hx = HXXC(i);
      const double jd = JDXC(i);
      const double dux =
        - UX(i  , j  )
        + UX(i+1, j  );
      *quantity += diffusivity * jd * pow(1. / hx * dux, 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 hx = HXXC(i);
        const double jd = JDXC(i);
        const double dux =
          - UX(i  , j  , k  )
          + UX(i+1, j  , k  );
        *quantity += diffusivity * jd * pow(1. / hx * dux, 2.);
      }
    }
  }
#endif
  return 0;
}

\[\sumzc \sumyf \sumxf \dkdis{2}{1}\]

src/logging/dissipated_squared_velocity.c

static int get_duxdy (
    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 jdxf = domain->jdxf;
  const double * restrict ux = fluid->ux.data;
  const double diffusivity = fluid_compute_momentum_diffusivity(fluid);
#if NDIMS == 2
  for (int j = 1; j <= jsize; j++) {
    for (int i = 1; i <= isize + 1; i++) {
      const double jd = JDXF(i);
      const double dux =
        - UX(i  , j-1)
        + UX(i  , j  );
      *quantity += diffusivity * jd * pow(1. / hy * dux, 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 jd = JDXF(i);
        const double dux =
          - UX(i  , j-1, k  )
          + UX(i  , j  , k  );
        *quantity += diffusivity * jd * pow(1. / hy * dux, 2.);
      }
    }
  }
#endif
  return 0;
}

\[\sumzf \sumyc \sumxf \dkdis{3}{1}\]

src/logging/dissipated_squared_velocity.c

static int get_duxdz (
    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 jdxf = domain->jdxf;
  const double * restrict ux = fluid->ux.data;
  const double diffusivity = fluid_compute_momentum_diffusivity(fluid);
  for (int k = 1; k <= ksize; k++) {
    for (int j = 1; j <= jsize; j++) {
      for (int i = 1; i <= isize + 1; i++) {
        const double jd = JDXF(i);
        const double dux =
          - UX(i  , j  , k-1)
          + UX(i  , j  , k  );
        *quantity += diffusivity * jd * pow(1. / hz * dux, 2.);
      }
    }
  }
  return 0;
}

\[\sumzc \sumyf \sumxf \dkdis{1}{2}\]

src/logging/dissipated_squared_velocity.c

static int get_duydx (
    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 uy = fluid->uy.data;
  const double diffusivity = fluid_compute_momentum_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 duy =
        - UY(i-1, j  )
        + UY(i  , j  );
      *quantity += diffusivity * jd * pow(1. / hx * duy, 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 duy =
          - UY(i-1, j  , k  )
          + UY(i  , j  , k  );
        *quantity += diffusivity * jd * pow(1. / hx * duy, 2.);
      }
    }
  }
#endif
  return 0;
}

\[\sumzc \sumyc \sumxc \dkdis{2}{2}\]

src/logging/dissipated_squared_velocity.c

static int get_duydy (
    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 uy = fluid->uy.data;
  const double diffusivity = fluid_compute_momentum_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 duy =
        - UY(i  , j  )
        + UY(i  , j+1);
      *quantity += diffusivity * jd * pow(1. / hy * duy, 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 duy =
          - UY(i  , j  , k  )
          + UY(i  , j+1, k  );
        *quantity += diffusivity * jd * pow(1. / hy * duy, 2.);
      }
    }
  }
#endif
  return 0;
}

\[\sumzf \sumyf \sumxc \dkdis{3}{2}\]

src/logging/dissipated_squared_velocity.c

static int get_duydz (
    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 uy = fluid->uy.data;
  const double diffusivity = fluid_compute_momentum_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 duy =
          - UY(i  , j  , k-1)
          + UY(i  , j  , k  );
        *quantity += diffusivity * jd * pow(1. / hz * duy, 2.);
      }
    }
  }
  return 0;
}

\[\sumzf \sumyc \sumxf \dkdis{1}{3}\]

src/logging/dissipated_squared_velocity.c

static int get_duzdx (
    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 * restrict hxxf = domain->hxxf;
  const double * restrict jdxf = domain->jdxf;
  const double * restrict uz = fluid->uz.data;
  const double diffusivity = fluid_compute_momentum_diffusivity(fluid);
  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 duz =
          - UZ(i-1, j  , k  )
          + UZ(i  , j  , k  );
        *quantity += diffusivity * jd * pow(1. / hx * duz, 2.);
      }
    }
  }
  return 0;
}

\[\sumzf \sumyf \sumxc \dkdis{2}{3}\]

src/logging/dissipated_squared_velocity.c

static int get_duzdy (
    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 hy = domain->hy;
  const double * restrict jdxc = domain->jdxc;
  const double * restrict uz = fluid->uz.data;
  const double diffusivity = fluid_compute_momentum_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 duz =
          - UZ(i  , j-1, k  )
          + UZ(i  , j  , k  );
        *quantity += diffusivity * jd * pow(1. / hy * duz, 2.);
      }
    }
  }
  return 0;
}

\[\sumzc \sumyc \sumxc \dkdis{3}{3}\]

src/logging/dissipated_squared_velocity.c

static int get_duzdz (
    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 uz = fluid->uz.data;
  const double diffusivity = fluid_compute_momentum_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 duz =
          - UZ(i  , j  , k  )
          + UZ(i  , j  , k+1);
        *quantity += diffusivity * jd * pow(1. / hz * duz, 2.);
      }
    }
  }
  return 0;
}

Source (Injection)

\[\sumzc \sumyc \sumxc J \vel{1} \ave{T}{\gcs{1}}\]

increases the total amount of the squared velocity. Physically this term accounts for the kinetic energy injection due to the buoyancy effects.

This quantity is implemented to monitor as follows:

src/logging/injected_squared_velocity.c

  double quantity = 0.;
  BEGIN
    const double jd_x0 = JDXF(i);
#if NDIMS == 2
    const double ux_x0 = UX(i, j);
    const double  t_x0 =
      + 0.5 * T(i-1, j  )
      + 0.5 * T(i  , j  );
#else
    const double ux_x0 = UX(i, j, k);
    const double  t_x0 =
      + 0.5 * T(i-1, j  , k  )
      + 0.5 * T(i  , j  , k  );
#endif
    quantity += jd_x0 * ux_x0 * t_x0;
  END
  const void * sendbuf = root == myrank ? MPI_IN_PLACE : &quantity;
  void * recvbuf = &quantity;
  MPI_Reduce(sendbuf, recvbuf, 1, MPI_DOUBLE, MPI_SUM, root, comm_cart);