fix eos/table/rx command

Syntax

fix ID group-ID eos/table/rx style file1 N keyword file2
  • ID, group-ID are documented in fix command
  • eos/table/rx = style name of this fix command
  • style = linear = method of interpolation
  • file1 = filename containing the tabulated equation of state
  • N = use N values in linear tables
  • keyword = name of table keyword correponding to table file
  • file2 = filename containing the heats of formation of each species

Examples

fix 1 all eos/table/rx linear eos.table 10000 KEYWORD thermo.table

Description

Fix eos/table/rx applies a tabulated mesoparticle equation of state to relate the concentration-dependent particle internal energy (u_i) to the particle internal temperature (dpdTheta_i).

The concentration-dependent particle internal energy (u_i) is computed according to the following relation:

_images/fix_eos_table_rx.jpg

where m is the number of species, c_i,j is the concentration of species j in particle i, u_j is the internal energy of species j, DeltaH_f,j is the heat of formation of species j, N is the number of molecules represented by the coarse-grained particle, kb is the Boltzmann constant, and T is the temperature of the system.

Fix eos/table/rx creates interpolation tables of length N from m internal energy values of each species u_j listed in a file as a function of internal temperature. During a simulation, these tables are used to interpolate internal energy or temperature values as needed. The interpolation is done with the linear style. For the linear style, the internal temperature is used to find 2 surrounding table values from which an internal energy is computed by linear interpolation. A secant solver is used to determine the internal temperature from the internal energy.

The first filename specifies a file containing tabulated internal temperature and m internal energy values for each species u_j. The keyword specifies a section of the file. The format of this file is described below.

The second filename specifies a file containing heat of formation DeltaH_f,j for each species.

The format of a tabulated file is as follows (without the parenthesized comments):

# EOS TABLE                (one or more comment or blank lines)

KEYWORD                    (keyword is first text on line)
N 500 h2 no2 n2 ... no     (N  parameter species1 species2 ... speciesN)
                           (blank)
1   1.00 0.000 ... 0.0000  (index, internal temperature, internal energy of species 1, ..., internal energy of species m)
2   1.02 0.001 ... 0.0002
...
500 10.0 0.500 ... 1.0000

A section begins with a non-blank line whose 1st character is not a “#”; blank lines or lines starting with “#” can be used as comments between sections. The first line begins with a keyword which identifies the section. The line can contain additional text, but the initial text must match the argument specified in the fix command.

The next line lists the number of table entries and the species names that correspond with all the species listed in the reaction equations through the fix rx command. The parameter “N” is required and its value is the number of table entries that follow. Let Nfile = “N” in the tabulated file. What LAMMPS does is a preliminary interpolation by creating splines using the Nfile tabulated values as nodal points.

Following a blank line, the next N lines list the tabulated values. On each line, the 1st value is the index from 1 to N, the 2nd value is the internal temperature (in temperature units), the 3rd value until the m+3 value are the internal energies of the m species (in energy units).

Note that all internal temperature and internal energy values must increase from one line to the next.

Note that one file can contain many sections, each with a tabulated potential. LAMMPS reads the file section by section until it finds one that matches the specified keyword.

The format of a heat of formation file is as follows (without the parenthesized comments):

# HEAT OF FORMATION TABLE  (one or more comment or blank lines)

                           (blank)
h2      0.00               (species name, heat of formation)
no2     0.34
n2      0.00
...
no      0.93

Note that the species can be listed in any order. The tag that is used as the species name must correspond with the tags used to define the reactions with the fix rx command.

Restrictions

This command is part of the USER-DPD package. It is only enabled if LAMMPS was built with that package. See the Making LAMMPS section for more info.

This command also requires use of the atom_style dpd command.

The equation of state must be a monotonically increasing function.

An error will occur if the internal temperature or internal energies are not within the table cutoffs.