Syntax:
compute ID lambda/grid nrho temp value1 value2 ...
lambda = calculate mean free path tau = calculate mean collision time knall = calculate Knudsen number based on cell size in all dimensions knx = calculate Knudsen number based on cell size in x dimension kny = calculate Knudsen number based on cell size in y dimension knz = calculate Knudsen number based on cell size in z dimension
Examples:
compute 1 lambda/grid c_GR[*] NULL lambda tau compute 1 lambda/grid f_ave[*] f_ave[3] lambda knall
These commands will dump time averages for the mean free path and mean collision time for each grid cell to a dump file every 1000 steps:
compute 1 grid species nrho temp fix 1 ave/grid 10 100 1000 c_1[*] compute 2 lambda/grid f_1[1] f_1[2] lambda tau dump 1 grid all 1000 tmp.grid id c_2
Description:
If the lambda keyword is specified, the mean free path will be computed. If the tau keyword is specified, the mean collision time between molecular collisions for each grid cell based on the particles in that cell will be computed. If one or more of the knall or knx or kny or knz keywords are specified, the dimensionless Knudsen number will be calculated, which is the ratio of the mean free path to the cell size. For knall, the cell size is taken to be the average of the three grid cell side lengths (or two cell lengths for a 2d simulation). For knx, kny, or knz, the cell size is the single cell side length in the corresponding x,y,z dimension. The Knudsen number can be useful for estimating the optimal grid cell size when adapting the grid, e.g. via the adapt_grid or fix adapt/grid commands, as well as the optimal time step size.
Unlike other computes that calculate per grid cell values, this compute does not take a "group-ID" for a grid cell group as an argument, nor a particle mixture ID as an argument. This is because it uses the number density and temperature calculated by other computes or fixes as input, and those computes or fixes use grid group IDs or mixture IDs as part of their computations.
The results of this compute can be used by different commands in different ways. For example, the values can be output by the dump grid command.
The formula used to calculate the mean free path (lambda) is given in (Bird94) as equation 4.77:
NOTE: In October 2024, the formula to compute the mean free path was updated to the equation above, from (Bird94), equation 4.65:
The new formula is more accurate as it uses the number densities, translational temperatures and VSS parameters of each gases in the mixture, as opposed to using the flow total number density and the VSS parameters of only one species. This will make a significant difference for gas mixtures, in particular for reacting flow problems where the composition of the mixture changes significantly in time.
The formula used to calculate the mean collision time (tau) is given in (Bird94) as equation 1.38 combined with 4.75:
These are the exact mean free path and mean collision time for a multi-species mixture, suitable for estimating optimal grid cell sizes and timestep as explained above.
dref and Tref and omega are collision properties for a pair of species species in the flow. Specifically, dref is the diameter of molecules of the species pair, Tref is the reference temperature, and omega is the viscosity temperature-dependence for the species pair.
In the formula above, n is the number density and T is the thermal temperature of particles in a grid cell. This compute does not calculate these quantities itself; instead it uses another compute or fix to perform the calculation. This is done by specifying the nrho and temp arguments like this:
c_ID = compute with ID that calculates temp as a vector output c_ID[m] = compute with ID that calculates temp as its Mth column of array output c_ID[*] = compute with ID that calculates nrho as an array output f_ID[m] = fix with ID that calculates a time-averaged temp as a vector output f_ID[m] = fix with ID that calculates a time-averaged temp as its Mth column of array output f_ID[*] = fix with ID that calculates a time-averaged nrho as an array output
The temp argument can also be specified as NULL, which drops the (Tref/T) ratio term from the formula above. That is also effectively the case if the reference species defines omega = 1/2. In that case, the temp argument is ignored, whether it is NULL or not.
IMPORTANT NOTE: A per species number density array calculated by either a compute or a fix has to be specified. The code will automatically detect the number of species in the mixture to perform the mean free path and mean collision time calculation. The compute_grid.html command with mixture "species" has to be invoked to ensure that the number density of all the species in the mixture is computed.
Note that if the value of n is 0.0 for a grid cell, its mean-free-path and mean-collision-time will be set to 1.0e20 (infinite length and time).
The compute_grid.html command can calculate a number density, using its nrho value. It can also calculate a temperature using its temp value. Note that this temperature is inferred from the translational kinetic energy of the particles, which is only appopriate for a mean free path calculation for systems with zero or small streaming velocities. For systems with streaming flow, an appropriate temperature can be calculated by the compute_thermal_grid.html thermal/grid command. The formulas on its doc page show that the the center-of-mass velocity from the particles in each grid cell is subtracted from each particle's velocity to yield a translational thermal velocity, from which a thermal temperature is calculated.
The fix_ave_grid.html ave/grid command can calculate the same values in a time-averaged sense, assuming it uses these same computes as input. Using this fix as input to this compute will thus yield less noisy values, due to the time averaging.
Note that the compute or fix (via the compute(s) it uses as input) has to perform its number density calculation for a subset of the particles based on the "mixture" it uses. See the mixture.html command for how a set of species can be partitioned into groups.
IMPORTANT NOTE: If the ID of a fix_ave_grid.html ave/grid command is used as the nrho or temp argument, it only produces output on timesteps that are multiples of its Nfreq argument. Thus this compute can only be invoked on those timesteps. For example, if a dump.html grid command invokes this compute to write values to a dump file, it must do so on timesteps that are multiples of Nfreq.
Output info:
If only one output value is specified, this compute outputs a per-grid vector. Otherwise outputs a per-grid array with two or more columns, in the order the output values were specified in the input.
This compute performs calculations for all flavors of child grid cells in the simulation, which includes unsplit, cut, split, and sub cells. See Section 6.8 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 the individual 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.
The vector or 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 values for the column of output corresponding to lambda will will be in distance units.html. The column corresponding to tau will be time distance divided by time units.html. Columns of corresponding to knall or knx or kny or knz will be dimensionless.
Styles with a kk suffix are functionally the same as the corresponding style without the suffix. They have been optimized to run faster, depending on your available hardware, as discussed in the Accelerating SPARTA section of the manual. The accelerated styles take the same arguments and should produce the same results, except for different random number, round-off and precision issues.
These accelerated styles are part of the KOKKOS package. They are only enabled if SPARTA was built with that package. See the Making SPARTA section for more info.
You can specify the accelerated styles explicitly in your input script by including their suffix, or you can use the -suffix command-line switch when you invoke SPARTA, or you can use the suffix command in your input script.
See the Accelerating SPARTA section of the manual for more instructions on how to use the accelerated styles effectively.
Restrictions:
To use this compute, a collision style must be defined via the collide.html command, which defines properties for the mixture species.
As explained above, to use this compute with nrho or temp defined as input from a fix_ave_grid.html ave/grid command, this compute must only be invoked on timesteps that are multiples of the Nfreq argument used by the fix, since those are the steps when it produces output.
One or more output values must be specified. The same output value cannot be repeated more than once. The knz value cannot but used in a two-dimensional simulation.
Related commands:
compute grid, compute thermal/grid, fix ave/grid, dump grid
Default: none
(Bird94) G. A. Bird, Molecular Gas Dynamics and the Direct Simulation of Gas Flows, Clarendon Press, Oxford (1994).