\(\renewcommand{\AA}{\text{Å}}\)

# fix wall/flow command

Accelerator Variants: wall/flow/kk

## Syntax

    fix ID group-ID wall/flow axis vflow T seed N coords ... keyword value

- ID, group-ID are documented in fix command

- wall/flow = style name of this fix command

- axis = flow axis (x, y, or z)

- vflow = generated flow velocity in axis direction (velocity units)

- T = flow temperature (temperature units)

- seed = random seed for stochasticity (positive integer)

- N = number of walls

- coords = list of N wall positions along the axis direction in ascending order (distance units)

- zero or more keyword/value pairs may be appended

- keyword = units

      units value = lattice or box
        lattice = wall positions are defined in lattice units
        box = the wall positions are defined in simulation box units

## Examples

    fix 1 all wall/flow x 0.4 1.5 593894 4 2.0 4.0 6.0 8.0

## Description

Added in version 17Apr2024.

This fix implements flow boundary conditions (FBC) introduced in (Pavlov1) and (Pavlov2). The goal is to generate a stationary flow with a shifted Maxwell velocity distribution:

\[f_a(v_a) \propto \exp{\left(-\frac{m (v_a-v_{\text{flow}})^2}{2 kB T}\right)}\]

where \(v_a\) is the component of velocity along the specified axis argument (a = x,y,z), \(v_{\text{flow}}\) is the flow velocity specified as the vflow argument, T is the specified flow temperature, m is the particle mass, and kB is the Boltzmann constant.

This is achieved by defining a series of N transparent walls along the flow axis direction. Each wall is at the specified position listed in the coords argument. Note that an additional transparent wall is defined by the code at the boundary of the (periodic) simulation domain in the axis direction. So there are effectively N+1 walls.

Each time a particle in the specified group passes through one of the transparent walls, its velocity is re-assigned. Particles not in the group do not interact with the wall. This can be used, for example, to add obstacles composed of atoms, or to simulate a solution of complex molecules in a one-atom liquid (note that the fix has been tested for one-atom systems only).

Conceptually, the velocity re-assignment represents creation of a new particle within the system with simultaneous removal of the particle which passed through the wall. The velocity components in directions parallel to the wall are re-assigned according to the standard Maxwell velocity distribution for the specified temperature T. The velocity component perpendicular to the wall is re-assigned according to the shifted Maxwell distribution defined above:

\[f_{\text{a generated}}(v_a) \propto v_a f_a(v_a)\]

It can be shown that for an ideal-gas scenario this procedure makes the velocity distribution of particles between walls exactly as desired.

Since in most cases simulated systems are not an ideal gas, multiple walls can be defined, since a single wall may not be sufficient for maintaining a stationary flow without “congestion” which can manifest itself as regions in the flow with increased particle density located upstream from static obstacles.

For the same reason, the actual temperature and velocity of the generated flow may differ from what is requested. The degree of discrepancy is determined by how different from an ideal gas the simulated system is. Therefore, a calibration procedure may be required for such a system as described in (Pavlov).

Note that the interactions between particles on different sides of a transparent wall are not disabled or neglected. Likewise particle positions are not altered by the velocity reassignment. This removes the need to modify the force field to work correctly in cases when a particle is close to a wall.

For example, if particle positions were uniformly redistributed across the surface of a wall, two particles could end up too close to each other, potentially causing the simulation to explode. However due to this compromise, some collective phenomena such as regions with increased/decreased density or collective movements are not fully removed when particles cross a wall. This unwanted consequence can also be potentially mitigated by using more multiple walls.

Note

When the specified flow has a high velocity, a lost atoms error can occur (see error messages). If this happens, you should ensure the checks for neighbor list rebuilds, set via the neigh_modify command, are as conservative as possible (every timestep if needed). Those are the default settings.

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.

## Restart, fix_modify, output, run start/stop, minimize info

No information about this fix is written to binary restart files.

None of the fix_modify options are relevant to this fix.

No global or per-atom quantities are stored by this fix for access by various output commands.

No parameter of this fix can be used with the start/stop keywords of the run command.

This fix is not invoked during energy minimization.

## Restrictions

Fix wall_flow is part of the EXTRA-FIX package. It is only enabled if LAMMPS was built with that package. See the Build package page for more info.

Flow boundary conditions should not be used with rigid bodies such as those defined by a “fix rigid” command.

This fix can only be used with periodic boundary conditions along the flow axis. The size of the box in this direction must not change. Also, the fix is designed to work only in an orthogonal simulation box.

## Related commands

fix wall/reflect command

## Default

The default for the units keyword is lattice.

(Pavlov1) Pavlov, Kolotinskii, Stegailov, “GPU-Based Molecular Dynamics of Turbulent Liquid Flows with OpenMM”, Proceedings of PPAM-2022, LNCS (Springer), vol. 13826, pp. 346-358 (2023)

(Pavlov2) Pavlov, Galigerov, Kolotinskii, Nikolskiy, Stegailov, “GPU-based Molecular Dynamics of Fluid Flows: Reaching for Turbulence”, Int. J. High Perf. Comp. Appl., (2024)