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compute sonine/grid command

Syntax:

compute ID sonine/grid group-ID mix-ID keyword values ... 

Examples:

compute 1 sonine/grid all air a x 5 b xy 5
compute 1 sonine/grid subset air a x 5 

These commands will dump 10 time averaged sonine moments for each species and each grid cell to a dump file every 1000 steps:

compute 1 sonine/grid all species a x 5 b xy 5
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 the sonine moments of the velocity distribution of the particles in each grid cell in a grid cell group. The values are tallied separately for each group of species in the specified mixture, as described in the Output 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 A,B formulas below.

Note however that the center-of-mass (COM) velocity that is subtracted from each particle to yield a squared thermal velocity Csq for each particle, as described below, is the COM velocity for only the particles in the current timestep. When time-averaging it is NOT the COM velocity for all particles across all timesteps.

Note that 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.


Calculation of both the A and B sonine moments is done by first calcuating the center-of-mass (COM) velocity of particles for each group within a grid cell. This is done as follows:

COMx = Sum_i (mass_i Vx_i) / Sum_i (mass_i)
COMy = Sum_i (mass_i Vy_i) / Sum_i (mass_i)
COMz = Sum_i (mass_i Vz_i) / Sum_i (mass_i)
Cx = Vx - COMx
Cy = Vy - COMy
Cz = Vz - COMz
Csq = Cx*Cx + Cy*Cy + Cz*Cz 

The COM velocity is (COMx,COMy,COMz). The thermal velocity of each particle is (Cx,Cy,Cz), i.e. its velocity minus the COM velocity of particles in its group and cell. This allows computation of Csq for each particle which is used in the formulas below to calculate the sonine moments.


The a keyword calculates the average of one or more sonine A moments for all particles in each group:

A1 = Sum_i (mass_i * Vdim * pow(Csq,1)) / Sum_i (mass_i)
A2 = Sum_i (mass_i * Vdim * pow(Csq,2)) / Sum_i (mass_i)
A3 = Sum_i (mass_i * Vdim * pow(Csq,3)) / Sum_i (mass_i)
A4 = Sum_i (mass_i * Vdim * pow(Csq,4)) / Sum_i (mass_i)
A5 = Sum_i (mass_i * Vdim * pow(Csq,5)) / Sum_i (mass_i) 

Vdim is Vx or Vy or Vz as specified by the dim value. Csq is the squared thermal velocity of the particle, as in the COM equations above. The number of moments computed is specified by the order value, e.g. for order = 3, the first 3 moments are computed, which leads to 3 columns of output as explained below.

The b keyword calculates the average of one or more sonine B moments for all particles in each group:

B1 = Sum_i (mass_i * Vdim1 * Vdim2 * pow(Csq,1)) / Sum_i (mass_i)
B2 = Sum_i (mass_i * Vdim1 * Vdim2 * pow(Csq,2)) / Sum_i (mass_i)
B3 = Sum_i (mass_i * Vdim1 * Vdim2 * pow(Csq,3)) / Sum_i (mass_i)
B4 = Sum_i (mass_i * Vdim1 * Vdim2 * pow(Csq,4)) / Sum_i (mass_i)
B5 = Sum_i (mass_i * Vdim1 * Vdim2 * pow(Csq,5)) / Sum_i (mass_i) 

Vdim is Vx or Vy or Vz as specified by the dim value. Csq is the squared thermal velocity of the particle, as in the COM equations above. The number of moments computed is specified by the order value, e.g. for order = 2, the first 2 moments are computed, which leads to 2 columns of output as explained below.


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 a z 3 and b xy 2 moments were specified as keywords, then the 1st thru 3rd columns would be the A1, A2, A3 moments of the first group, the 4th and 5th columns would be the B1 and B2 moments of the first group, the 6th thru 8th columns would be the A1, A2, A3 moments of the 2nd 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 have 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. These are units like velocity cubed or velocity to the 6th power.

Restrictions: none

Related commands:

fix ave/grid, dump grid

Default: none