**Syntax:**

compute ID grid group-ID mix-ID value1 value2 ...

- ID is documented in compute command
- grid = style name of this compute command
- group-ID = group ID for which grid cells to perform calculation on
- mix-ID = mixture ID to perform calculation on
- one or more values can be appended
- value =
*n*or*nrho*or*nfrac*or*mass*or*massrho*or*massfrac*or*u*or*v*or*w*or*usq*or*vsq*or*wsq*of*ke*or*temp*or*erot*or*trot*or*evib*or*tvib*or*pxrho*or*pyrho*or*pzrho*or*kerho**n*= particle count*nrho*= number density*nfrac*= number fraction*mass*= mass*massrho*= mass density*massfrac*= mass fraction*u*= x component of velocity*v*= y component of velocity*w*= z component of velocity*usq*= x component of velocity squared*vsq*= y component of velocity squared*wsq*= z component of velocity squared*ke*= kinetic energy*temp*= temperature*erot*= rotational energy*trot*= rotational temperature*evib*= vibrational energy*tvib*= vibrational temperature (classical definition)*pxrho*= x component of momentum density*pyrho*= y component of momentum density*pzrho*= z component of momentum density*kerho*= kinetic energy density

**Examples:**

compute 1 grid all species n u v w usq vsq wsq compute 1 grid subset air n u v w

These commands will dump time averages for each species and each grid cell to a dump file every 1000 steps:

compute 1 grid all species n u v w usq vsq wsq fix 1 ave/grid 10 100 1000 c_1[*] dump 1 grid all 1000 tmp.grid id f_1[*]

**Description:**

Define a computation that calculates one or more values for each grid
cell in a grid cell group, based on the particles in the cell. The
values are tallied separately for each group of species in the
specified mixture, as described in the Ouput section below. See the
mixture command for how a set of species can be
partitioned into groups. Only grid cells in the grid group specified
by *group-ID* are included in the calculations. See the group
grid command for info on how grid cells can be assigned to
grid groups.

The results of this compute can be used by different commands in different ways. The values for a single timestep can be output by the dump grid command.

The values over many sampling timesteps can be averaged by the fix ave/grid command. It does its averaging as if the particles in the cell at each sampling timestep were combined together into one large set of particles to compute the formulas below.

Note that for most of the values, this is a different form of averaging than taking the values produced by the formulas below for a single timestep, summing those values over the sampling timesteps, and then dividing by the number of sampling steps.

The *n* value counts the number of particles in each group. When
accumulated over multiple sampling steps, this value is normalized by
the number of sampling steps.

The *nrho* value computes the number density for the grid cell volume
due to particles in each group:

Nrho = fnum/volume * N

N is the number of particles (same as the *n* keyword), fnum is the
real/simulated particle ratio set by the global fnum
command, and volume is the flow volume of the grid cell. When
accumulated over multiple sampling steps, this value is normalized by
the number of sampling steps. Note that if particle weighting is
enabled via the global weight command, then the volume
used in the formula is divided by the weight assigned to the grid
cell.

The *nfrac* value computes the number fraction of particles in each
group:

Nfrac = Ngroup / Ntotal

Ngroup is the count of particles in the group and Ntotal is the total number of particles in all groups in the mixture. Note that this total is not (necessarily) all particles in the cell.

The *mass* value computes the average mass of particles in each group:

Mass = Sum_i (mass_i) / N

where Sum_i is a sum over particles in the group.

The *massrho* value computes the mass density for the grid cell volume
due to particles in each group:

Massrho = fnum/volume * Sum_i (mass_i)

where Sum_i is a sum over particles in the group, fnum is the real/simulated particle ratio set by the global fnum command, and volume is the flow volume of the grid cell. When accumulated over multiple sampling steps, this value is normalized by the number of sampling steps. Note that if particle weighting is enabled via the global weight command, then the volume used in the formula is divided by the weight assigned to the grid cell.

The *massfrac* value computes the mass fraction of particles in each
group:

Massfrac = Sum_i (mass_i) / Masstotal

where Sum_i is a sum over particles in the group and Masstotal is the total mass of particles in all groups in the mixture. Note that this total is not (necessarily) the mass of all particles in the cell.

The *u*, *v*, *w* values compute the components of the mass-weighted
average velocity of particles in each group:

U = Sum_i (mass_i Vx_i) / Sum_i (mass_i) V = Sum_i (mass_i Vy_i) / Sum_i (mass_i) W = Sum_i (mass_i Vz_i) / Sum_i (mass_i)

This is the same as the center-of-mass velocity of particles in each group.

The *usq*, *vsq*, *wsq* values compute the average mass-weighted
squared components of the velocity of particles in each group:

Usq = Sum_i (mass_i Vx_i Vx_i) / Sum_i (mass_i) Vsq = Sum_i (mass_i Vy_i Vy_i) / Sum_i (mass_i) Wsq = Sum_i (mass_i Vz_i Vz_i) / Sum_i (mass_i)

The *ke* value computes the average kinetic energy of particles in
each group:

Vsq = Vx*Vx + Vy*Vy + Vz*Vz KE = Sum_i (1/2 mass_i Vsq_i) / N

Note that this is different than the group's contribution to the
average kinetic energy of entire grid cells. That can be calculated
by multiplying the *ke* quantity by the *n* quantity.

The *temp* value first computes the average kinetic energy of
particles in each group, as for the *ke* value. This is then
converted to a temperature *T* by the following formula where *kB* is
the Boltzmann factor:

Vsq = Vx*Vx + Vy*Vy + Vz*Vz KE = Sum_i (1/2 mass_i Vsq_i) / N T = KE / (3/2 kB)

Note that this definition of temperature does not subtract out a net streaming velocity for particles in the grid cell, so it is not a thermal temperature when the particles have a non-zero streaming velocity. See the compute thermal/grid command to calculate thermal temperatures after subtracting out streaming components of velocity.

The *erot* value computes the average rotational energy of particles
in each group:

Erot = Sum_i (erot_i) / N

Note that this is different than the group's contribution to the
average rotational energy of entire grid cells. That can be
calculated by multiplying the *erot* quantity by the *n* quantity.

The *trot* value computes a rotational temperature by the following
formula where *kB* is the Boltzmann factor:

Trot = (2/kB) Sum_i (erot_i) / Sum_i (dof_i)

Dof_i is the number of rotational degrees of freedom for particle i.

The *evib* value computes the average vibrational energy of particles
in each group:

Evib = Sum_i (evib_i) / N

Note that this is different than the group's contribution to the
average vibrational energy of entire grid cells. That can be
calculated by multiplying the *evib* quantity by the *n* quantity.

The *tvib* value computes a classical definition of vibrational
temperature, valid for continous distributions of vibrational energy,
by the following formula where *kB* is the Boltzmann factor:

Tvib = (2/kB) Sum_i (evib_i) / Sum_i (dof_i)

Dof_i is the number of vibrational degrees of freedom for particle i.

The *pxrho*, *pyrho*, *pzrho* values compute components of momentum
density for the grid cell volume due to particles in each group:

Pxrho = fnum/volume * Sum_i (mass_i * Vx_i) Pyrho = fnum/volume * Sum_i (mass_i * Vy_i) Pzrho = fnum/volume * Sum_i (mass_i * Vz_i)

where Sum_i is a sum over particles in the group, fnum is the real/simulated particle ratio set by the global fnum command, and volume is the flow volume of the grid cell. When accumulated over multiple sampling steps, this value is normalized by the number of sampling steps. Note that if particle weighting is enabled via the global weight command, then the volume used in the formula is divided by the weight assigned to the grid cell.

The *kerho* value computes the kinetic energy density for the grid
cell volume due to particles in each group:

Vsq = Vx*Vx + Vy*Vy + Vz*Vz KErho = fnum/volume * Sum_i (mass_i * Vsq_i)

where Sum_i is a sum over particles in the group, fnum is the real/simulated particle ratio set by the global fnum command, and volume is the flow volume of the grid cell. When accumulated over multiple sampling steps, this value is normalized by the number of sampling steps. Note that if particle weighting is enabled via the global weight command, then the volume used in the formula is divided by the weight assigned to the grid cell.

**Output info:**

This compute calculates a per-grid array, with the number of columns
equal to the number of values times the number of groups. The
ordering of columns is first by values, then by groups. I.e. if the
*n* and *u* values were specified as keywords, then the first two
columns would be *n* and *u* for the first group, the 3rd and 4th
columns would be *n* and *u* for the second group, etc.

This compute performs calculations for all flavors of child grid cells in the simulation, which includes unsplit, cut, split, and sub cells. See Section 4.8 of the manual gives details of how SPARTA defines child, unsplit, split, and sub cells. Note that cells inside closed surfaces contain no particles. These could be unsplit or cut cells (if they have zero flow volume). Both of these kinds of cells will compute a zero result for all their values. Likewise, split cells store no particles and will produce a zero result. This is because their sub-cells actually contain the particles that are geometrically inside the split cell.

Grid cells not in the specified *group-ID* will output zeroes for all
their values.

The array can be accessed by any command that uses per-grid values from a compute as input. See Section 4.4 for an overview of SPARTA output options.

The per-grid array values will be in the units
appropriate to the individual values as described above. *N* is
unitless. *Nrho* is in 1/distance^3 units for 3d simulations and
1/distance^2 units for 2d simulations. *Mass* is in mass units.
*Massrho* is in is in mass/distance^3 units for 3d simulations and
mass/distance^2 units for 2d simulations. *U*, *v*, and *w* are in
velocity units. *Usq*, *vsq*, and *wsq* are in velocity squared
units. *Ke*, *erot*, and *evib* are in energy units. *Temp* and
*trot* and *tvib* are in temperature units. *Pxrho*, *pyrho*, *pzrho*
are in momentum/distance^3 units for 3d simulations and
momentum/distance^2 units for 2d simulations, where momentum is in
units of mass*velocity. *Kerho* is in units of energy/distance^3
units for 3d simulations and energy/distance^2 units for 2d
simulations.

**Restrictions:** none

**Related commands:**

fix ave/grid, dump grid, compute thermal/grid

**Default:** none