calculate mixing index command

Purpose

This command creates one output file for each defined material (examples).

Note

This command is supported by Aspherix GPU.

Syntax

calculate mixing_index keyword/value pairs

Keywords	Description
id	user-assigned name for the command call default: `mixing_index`
region	region in which the mixing index is evaluated default: `simulation_domain_region_`

Examples

calculate mixing_index
calculate mixing_index region container id mixingContainer

Description

This command calculates the GMMI (Generalized Mean Mixing Index) defined by Asmar et al. [1]. It produces an array that contains the x, y and z component of the GMMI for each material in the simulation, the single components are given as

GMMIx/y/z_i = x/y/z-center of volume of all particles of material i / x/y/z-center of volume of all particles

The center of volume $(c_x,c_y,c_z)$ is calculated by summing over all eligible particles:

$x_c = \frac{\sum_{k = 1}^{P} V_k(x_k - x_{ref})}{ \sum_{k = 1}^{P} V_k}, y_c = \frac{\sum_{k = 1}^{P} V_k(y_k - y_{ref})}{ \sum_{k = 1}^{P} V_k}, z_c = \frac{\sum_{k = 1}^{P} V_k(z_k - z_{ref})}{ \sum_{k = 1}^{P} V_k},$

where $P$ is the number of particles, $(x_k,y_k,z_k)$ is the position of the kth particle, $(x_{ref},y_{ref},z_{ref})$ is a reference position and $V_k$ is the volume of kth particle.

The value range of the GMMI can be interpreted as follows:

GMMI = 0	no data available
GMMI = 1	perfect mixing
0 < GMMI < 1	particles of material i have lower coordinate than average
1 < GMMI < …	particles of material i have higher coordinate than average

If the region keyword is used, mixing of particles in the specified geometric region is evaluated. The reference position is then equal to the minimum coordinates of the regions bounding box in each direction.

The time interval at which the mixing index is calculated is defined by the write_to_terminal_timestep command.

Output information

The calculate mixing_index command produces a global array with the x, y and z position of the center of volume of each material. The components of the generated array with ID MIXID can be accessed by id_MIXID[i][1], id_MIXID[i][2] and MIXID[i][3] where i is the index of the respective material. The material indicse start with 1 and are automatically assigned in the order of their definition in the materials command.

When using the output_settings command, the results are automatically written to the simulation_data_aspherix.csv / result_monitor.txt file.

Alternatively, also the write_to_file command can be used to output the data to a specified file.

materials {coarse_sand, fine_sand}
calculate mixing_index id mix
write_to_file file mixing_index_output.txt
    string "id_time id_mix[1][1] id_mix[1][1] id_mix[1][2] id_mix[1][3] id_mix[2][1] id_mix[2][2] id_mix[2][3]" &
    title "# time coarse_x coarse_y coarse_z fine_x fine_y fine_z"

Per default, this command also produces an output file for each defined material called ‘data_id_material_i.txt’, where id is the user specified command-ID (set to mixing_index if none specified), $i=0,..,N-1$ and $N$ is the number of materials. The structure of the output file for the material i is:

material_i_segregation_x material_i_segregation_y material_i_segregation_z
GMMIx_i1 GMMIy_i1 GMMIz_i1
...
GMMIx_ij GMMIy_ij GMMIz_ij
...
GMMIx_iM GMMIy_iM GMMIz_iM

where $M$ is the number of outputs in time GMMIx/y/z_ij is the respective GMMI component of material i at time j.