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compute pflux/grid command

Syntax:

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

Examples:

compute 1 pflux/grid all species momxx momyy momzz
compute 1 pflux/grid subset species momxx momxy 

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

compute 1 pflux/grid all species momxx momyy momzz
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 components of the momemtum flux density tensor for each grid cell in a grid cell group. This is equivalent to the kinetic energy density tensor, and is based on the thermal velocity of the particles in each grid cell. 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 values listed above rely on first computing and subtracting the center-of-mass (COM) velocity for all particles in the group and grid cell from each particle to yield a thermal velocity. This thermal velocity is used to compute the components of the momentum flux density tensor, as described below. This is in contrast to some of the values tallied by the compute grid temp command which simply uses the full velocity of each particle to compute a momentum or kinetic energy density. For non-streaming simulations, the two results should be similar, but for streaming flows, they will be different.

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 the center-of-mass (COM) velocity that is subtracted from each particle to yield a thermal velocity for each particle, as described below, is also computed over one large set of particles (across all timesteps), in contrast to using a COM velocity computed only for particles in the current timestep, which is what the compute sonine/grid command does.

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 the momentum flux density 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 

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.

The momxx, momyy, momzz values compute the diagonal components of the momentum flux density tensor due to particles in the group as follows:

momxx = fnum/volume Sum_i (mass_i Cx^2)
momyy = fnum/volume Sum_i (mass_i Cy^2)
momzz = fnum/volume Sum_i (mass_i Cz^2) 

The momxy, momyz, momxz values compute the off-diagonal components of the momentum flux density tensor due to particles in the group as follows:

momxy = fnum/volume Sum_i (mass_i Cx Cy)
momyz = fnum/volume Sum_i (mass_i Cy Cz)
momxz = fnum/volume Sum_i (mass_i Cx Cz) 

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 momxx and momxy values were specified as keywords, then the first two columns would be momxx and momxy for the first group, the 3rd and 4th columns would be momxx and momxy 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 of momentum flux density = energy density = energy/volume units.

Restrictions: none

Related commands:

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

Default: none