fix rx command — LAMMPS documentation

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# fix rx command

Accelerator Variants: rx/kk

## Syntax

    fix ID group-ID rx file localTemp matrix solver minSteps ...

- ID, group-ID are documented in fix command

- rx = style name of this fix command

- file = filename containing the reaction kinetic equations and Arrhenius parameters

- localTemp = none,lucy = no local temperature averaging or local temperature defined through Lucy weighting function

- matrix = sparse, dense format for the stoichiometric matrix

- solver = lammps_rk4,rkf45 = rk4 is an explicit fourth order Runge-Kutta method; rkf45 is an adaptive fourth-order Runge-Kutta-Fehlberg method

- minSteps = # of steps for rk4 solver or minimum # of steps for rkf45 (rk4 or rkf45)

- maxSteps = maximum number of steps for the rkf45 solver (rkf45 only)

- relTol = relative tolerance for the rkf45 solver (rkf45 only)

- absTol = absolute tolerance for the rkf45 solver (rkf45 only)

- diag = Diagnostics frequency for the rkf45 solver (optional, rkf45 only)

## Examples

    fix 1 all rx kinetics.rx none dense lammps_rk4
    fix 1 all rx kinetics.rx none sparse lammps_rk4 1
    fix 1 all rx kinetics.rx lucy sparse lammps_rk4 10
    fix 1 all rx kinetics.rx none dense rkf45 1 100 1e-6 1e-8
    fix 1 all rx kinetics.rx none dense rkf45 1 100 1e-6 1e-8 -1

## Description

Fix rx solves the reaction kinetic ODEs for a given reaction set that is defined within the file associated with this command.

For a general reaction such that

\[\nu_{A}A + \nu_{B}B \rightarrow \nu_{C}C\]

the reaction rate equation is defined to be of the form

\[r = k(T)[A]^{\nu_{A}}[B]^{\nu_{B}}\]

In the current implementation, the exponents are defined to be equal to the stoichiometric coefficients. A given reaction set consisting of n reaction equations will contain a total of m species. A set of m ordinary differential equations (ODEs) that describe the change in concentration of a given species as a function of time are then constructed based on the n reaction rate equations.

The ODE systems are solved over the full DPD timestep dt using either a fourth order Runge-Kutta rk4 method with a fixed step-size h, specified by the lammps_rk4 keyword, or a fourth order Runge-Kutta-Fehlberg (rkf45) method with an adaptive step-size for h. The number of ODE steps per DPD timestep for the rk4 method is optionally specified immediately after the rk4 keyword. The ODE step-size is set as dt/num_steps. Smaller step-sizes tend to yield more accurate results but there is not control on the error. For error control, use the rkf45 ODE solver.

The rkf45 method adjusts the step-size so that the local truncation error is held within the specified absolute and relative tolerances. The initial step-size h0 can be specified by the user or estimated internally. It is recommended that the user specify h0 since this will generally reduced the number of ODE integration steps required. h0 is defined as dt / min_steps if min_steps >= 1. If min_steps == 0, h0 is estimated such that an explicit Euler method would likely produce an acceptable solution. This is generally overly conservative for the fourth-order method and users are advised to specify h0 as some fraction of the DPD timestep. For small DPD timesteps, only one step may be necessary depending upon the tolerances. Note that more than min_steps ODE steps may be taken depending upon the ODE stiffness but no more than max_steps will be taken. If max_steps is reached, an error warning is printed and the simulation is stopped.

After each ODE step, the solution error e is tested and weighted using the absTol and relTol values. The error vector is weighted as e / (relTol * |u| + absTol) where u is the solution vector. If the norm of the error is <= 1, the solution is accepted, h is increased by a proportional amount, and the next ODE step is begun. Otherwise, h is shrunk and the ODE step is repeated.

Run-time diagnostics are available for the rkf45 ODE solver. The frequency (in timesteps) that diagnostics are reported is controlled by the last (optional) 12th argument. A negative frequency means that diagnostics are reported once at the end of each run. A positive value N means that the diagnostics are reported once per N timesteps.

The diagnostics report the average # of integrator steps and RHS function evaluations and run-time per ODE as well as the average/RMS/min/max per process. If the reporting frequency is 1, the RMS/min/max per ODE are also reported. The per ODE statistics can be used to adjust the tolerance and min/max step parameters. The statistics per MPI process can be useful to examine any load imbalance caused by the adaptive ODE solver. (Some DPD particles can take longer to solve than others. This can lead to an imbalance across the MPI processes.)

The filename specifies a file that contains the entire set of reaction kinetic equations and corresponding Arrhenius parameters. The format of this file is described below.

There is no restriction on the total number or reaction equations that are specified. The species names are arbitrary string names that are associated with the species concentrations. Each species in a given reaction must be preceded by it’s stoichiometric coefficient. The only delimiters that are recognized between the species are either a + or = character. The = character corresponds to an irreversible reaction. After specifying the reaction, the reaction rate constant is determined through the temperature dependent Arrhenius equation:

\[k = AT^{n}e^{\frac{-E_{a}}{k_{B}T}}\]

where A is the Arrhenius factor in time units or concentration/time units, n is the unitless exponent of the temperature dependence, and \(E_a\) is the activation energy in energy units. The temperature dependence can be removed by specifying the exponent as zero.

The internal temperature of the coarse-grained particles can be used in constructing the reaction rate constants at every DPD timestep by specifying the keyword none. Alternatively, the keyword lucy can be specified to compute a local-average particle internal temperature for use in the reaction rate constant expressions. The local-average particle internal temperature is defined as:

\[\theta_i^{-1} = \frac{\sum_{j=1}\omega_{Lucy}\left(r_{ij}\right)\theta_j^{-1}}{\sum_{j=1}\omega_{Lucy}\left(r_{ij}\right)}\]

where the Lucy function is expressed as:

\[\omega_{Lucy}\left(r_{ij}\right) = \left( 1 + \frac{3r_{ij}}{r_c} \right) \left( 1 - \frac{r_{ij}}{r_c} \right)^3\]

The self-particle interaction is included in the above equation.

The stoichiometric coefficients for the reaction mechanism are stored in either a sparse or dense matrix format. The dense matrix should only be used for small reaction mechanisms. The sparse matrix should be used when there are many reactions (e.g., more than 5). This allows the number of reactions and species to grow while keeping the computational cost tractable. The matrix format can be specified as using either the sparse or dense keywords. If all stoichiometric coefficients for a reaction are small integers (whole numbers <= 3), a fast exponential function is used. This can save significant computational time so users are encouraged to use integer coefficients where possible.

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

    # Rxn equations and parameters                                               (one or more comment or blank lines)

    1.0 hcn + 1.0 no2 = 1.0  no + 0.5 n2  + 0.5 h2 + 1.0 co   2.49E+01 0.0 1.34  (rxn equation, A, n, Ea)
    1.0 hcn + 1.0  no = 1.0  co + 1.0 n2  + 0.5 h2            2.16E+00 0.0 1.52
    ...
    1.0  no + 1.0  co = 0.5  n2 + 1.0 co2                     1.66E+06 0.0 0.69

A section begins with a non-blank line whose first character is not a “#”; blank lines or lines starting with “#” can be used as comments between sections.

Following a blank line, the next N lines list the N reaction equations. Each species within the reaction equation is specified through its stoichiometric coefficient and a species tag. Reactant species are specified on the left-hand side of the equation and product species are specified on the right-hand side of the equation. After specifying the reactant and product species, the final three arguments of each line represent the Arrhenius parameter A, the temperature exponent n, and the activation energy Ea.

Note that the species tags that are defined in the reaction equations are used by the fix eos/table/rx command to define the thermodynamic properties of each species. Furthermore, the number of species molecules (i.e., concentration) can be specified either with the set command using the “d_” prefix or by reading directly the concentrations from a data file. For the latter case, the read_data command with the fix keyword should be specified, where the fix-ID will be the “fix rx`ID with a <SPECIES”>`_ suffix, e.g.

fix foo all rx reaction.file … read_data data.dpd fix foo_SPECIES NULL Species

Styles with a gpu, intel, kk, omp, or opt 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 on the Accelerator packages page. The accelerated styles take the same arguments and should produce the same results, except for round-off and precision issues.

These accelerated styles are part of the GPU, INTEL, KOKKOS, OPENMP, and OPT packages, respectively. They are only enabled if LAMMPS was built with those packages. See the Build package page 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 LAMMPS, or you can use the suffix command in your input script.

See the Accelerator packages page for more instructions on how to use the accelerated styles effectively.

## Restrictions

This command is part of the DPD-REACT package. It is only enabled if LAMMPS was built with that package. See the Build package page for more info.

This command also requires use of the atom_style dpd command.

This command can only be used with a constant energy or constant enthalpy DPD simulation.

## Related commands

fix eos/table/rx, fix shardlow, pair dpd/fdt/energy

## Default

none