**Syntax:**

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

- ID is documented in compute command
- boundary = style name of this compute command
- group-ID = group ID for which surface elements to perform calculation on
- mix-ID = mixture ID for particles to perform calculation on
- one or more values can be appended
- value =
*n*or*nwt*or*mflux*or*fx*or*fy*or*fz*or*press*or*px*or*py*or*pz*or*shx*or*shy*or*shz*or*ke*n = count of particles hitting surface element nwt = weighted count of particles hitting surface element mflux = flux of mass on surface element fx,fy,fz = components of force on surface element press = magnitude of normal pressure on surface element px,py,pz = components of normal pressure on surface element shx,shy,shz = components of shear stress on surface element ke = flux of particle kinetic energy on surface element erot = flux of particle rotational energy on surface element evib = flux of particle vibrational energy on surface element etot = flux of particle total energy on surface element

**Examples:**

compute 1 surf all all n press eng compute mine surf sphere species press shx shy shz

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

compute 1 surf all species n press shx shy shz fix 1 ave/surf all 10 100 1000 c_1[*] dump 1 surf all 1000 tmp.surf id f_1[*]

These commands will time-average the force on each surface element then sum them across element to compute drag (fx) and lift (fy) on the body:

compute 1 surf all all fx fy fix 1 ave/surf all 10 100 1000 c_1[*] compute 2 reduce sum f_1[1] f_1[2] stats 1000 stats_style step cpu np c_2[1] c_2[2]

**Description:**

Define a computation that calculates one or more values for each
surface element in a surface element group, based on the particles
that collide with that element. The values are summed for each group
of species in the specified mixture. See the mixture
command for how a set of species can be partitioned into groups. Only
surface elements in the surface group specified by *group-ID* are
included in the calculations. See the group surf command
for info on how surface elements can be assigned to surface groups.

Surface elements are triangles for 3d simulations and line segments for 2d simulations. See the read_surf command for details.

Note that when a particle collides with a surface element, it can
bounce off (possibly as a different species), be captured by the
surface (vanish), or a 2nd particle can also be emitted. The formulas
below account for all the possible outcomes. For example, the kinetic
energy flux *ke* onto a suface element for a single collision includes
a positive contribution from the incoming particle and negative
contributions from 0, 1, or 2 outgoing particles. The exception is
the *n* and *nwt* values which simply tally counts of particles
colliding with the surface element.

Also note that all values for a collision are tallied based on the species group of the incident particle. Quantities associated with outgoing particles are part of the same tally, even if they are in different species 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 surf command.

The values over many sampling timesteps can be averaged by the fix ave/surf command. It does its averaging as if the particles striking the surface element at each sampling timestep were combined together into one large set to compute the formulas below. The answer is then divided by the number of sampling timesteps if it is not otherwise normalized by the number of particles. Note that in general this is a different normalization than taking the values produced by the formulas below for a single timestep, summing them over the sampling timesteps, and then dividing by the number of sampling steps. However for the current values listed below, the two normalization methods are the same.

NOTE: If particle weighting is enabled via the global
weight command, then all of the values below are scaled
by the weight assigned to the grid cell in which the particle
collision with the surface element occurs. The only exception is the
the *n* value, which is NOT scaled by the weight; it is a simple count
of particle collisions with the surface element.

The *n* value counts the number of particles in the group striking the
surface element.

The *nwt* value counts the number of particles in the group striking
the surface element and weights the count by the weight assigned to
the grid cell in which the particle collision with the surface element
occurs. The *nwt* quantity will only be different than *n* if
particle weighting is enabled via the global weight
command.

The *mflux* value calculates the mass flux imparted to the surface
element by particles in the group. This is computed as

Mflux = Sum_i (mass_i) / (A * dt / fnum)

where the sum is over all contributing particle masses, normalized by A = the area of the surface element, dt = the timestep, and fnum = the real/simulated particle ratio set by the global fnum command.

The *fx*, *fy*, *fz* values calculate the components of force extered
on the surface element by particles in the group, with respect to the
x, y, z coordinate axes. These are computed as

p_delta = mass * (V_post - V_pre) Px = - Sum_i (p_delta_x) / (dt / fnum) Py = - Sum_i (p_delta_y) / (dt / fnum) Pz = - Sum_i (p_delta_z) / (dt / fnum)

where p_delta is the change in momentum of a particle, whose velocity changes from V_pre to V_post when colliding with the surface element. The force exerted on the surface element is the sum over all contributing p_delta, normalized by dt and fnum as defined before.

The *press* value calculates the pressure *P* exerted on the surface
element in the normal direction by particles in the group, such that
outward pressure is positive. This is computed as

p_delta = mass * (V_post - V_pre) P = Sum_i (p_delta_i dot N) / (A * dt / fnum)

where p_delta, V_pre, V_post, dt, fnum are defined as before. The pressure exerted on the surface element is the sum over all contributing p_delta dotted into the outward normal N of the surface element, also normalized by A = the area of the surface element.

The *px*, *py*, *pz* values calculate the normal pressure Px, Py, Pz
extered on the surface element in the direction of its normal by
particles in the group, with respect to the x, y, z coordinate axes.
These are computed as

p_delta = mass * (V_post - V_pre) p_delta_n = (p_delta dot N) N Px = - Sum_i (p_delta_n_x) / (A * dt / fnum) Py = - Sum_i (p_delta_n_y) / (A * dt / fnum) Pz = - Sum_i (p_delta_n_z) / (A * dt / fnum)

where p_delta, V_pre, V_post, N, A, and dt are defined as before. P_delta_n is the normal component of the change in momentum vector p_delta of a particle. P_delta_n_x (and y,z) are its x, y, z components.

The *shx*, *shy*, *shz* values calculate the shear pressure Sx, Sy, Sz
extered on the surface element in the tangential direction to its
normal by particles in the group, with respect to the x, y, z
coordinate axes. These are computed as

p_delta = mass * (V_post - V_pre) p_delta_t = p_delta - (p_delta dot N) N Sx = - Sum_i (p_delta_t_x) / (A * dt / fnum) Sy = - Sum_i (p_delta_t_y) / (A * dt / fnum) Sz = - Sum_i (p_delta_t_z) / (A * dt / fnum)

where p_delta, V_pre, V_post, N, A, and dt are defined as before. P_delta_t is the tangential component of the change in momentum vector p_delta of a particle. P_delta_t_x (and y,z) are its x, y, z components.

The *ke* value calculates the kinetic energy flux *Eflux* imparted to
the surface element by particles in the group, such that energy lost
by a particle is a positive flux. This is computed as

e_delta = 1/2 mass (V_post^2 - V_pre^2) Eflux = - Sum_i (e_delta) / (A * dt / fnum)

where e_delta is the kinetic energy change in a particle, whose velocity changes from V_pre to V_post when colliding with the surface element. The energy flux imparted to the surface element is the sum over all contributing e_delta, normalized by A = the area of the surface element and dt = the timestep and fnum = the real/simulated particle ratio set by the global fnum command.

The *erot* value calculates the rotational energy flux *Eflux*
imparted to the surface element by particles in the group, such that
energy lost by a particle is a positive flux. This is computed as

e_delta = Erot_post - Erot_pre Eflux = - Sum_i (e_delta) / (A * dt / fnum)

where e_delta is the rotational energy change in a particle, whose
internal rotational energy changes from Erot_pre to Erot_post when
colliding with the surface element. The flux equation is the same as
for the *ke* value.

The *evib* value calculates the vibrational energy flux *Eflux*
imparted to the surface element by particles in the group, such that
energy lost by a particle is a positive flux. This is computed as

e_delta = Evib_post - Evib_pre Eflux = - Sum_i (e_delta) / (A * dt / fnum)

where e_delta is the vibrational energy change in a particle, whose
internal vibrational energy changes from Evib_pre to Evib_post when
colliding with the surface element. The flux equation is the same as
for the *ke* value.

The *etot* value calculates the total energy flux imparted to the
surface element by particles in the group, such that energy lost by a
particle is a positive flux. This is simply the sum of kinetic,
rotational, and vibrational energies. Thus the total energy flux is
the sum of what is computed by the *ke*, *erot*, and *evib* values.

**Output info:**

This compute calculates a per-surf 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.

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

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

The per-surf array values will be in the units
appropriate to the individual values as described above. *N* is
unitless. *Press*, *px*, *py*, *pz*, *shx*, *shy*, *shz* are in in
pressure units. *Ke*, *erot*, *evib*, and *etot* are in
energy/area-time units for 3d simulations and energy/length-time units
for 2d simulations.

**Restrictions:** none

**Related commands:**

**Default:** none