\(\renewcommand{\AA}{\text{Å}}\)

fix rheo command

Syntax

fix ID group-ID rheo cut kstyle zmin keyword values...

  • ID, group-ID are documented in fix command

  • rheo = style name of this fix command

  • cut = cutoff for the kernel (distance)

  • kstyle = quintic or RK0 or RK1 or RK2

  • zmin = minimal number of neighbors for reproducing kernels

  • zero or more keyword/value pairs may be appended to args

  • keyword = thermal or interface/reconstruct or surface/detection or

    shift or rho/sum or density or self/mass or speed/sound

    thermal values = none, turns on thermal evolution
interface/reconstruct values = none, reconstructs interfaces with solid particles
surface/detection values = sdstyle limit limit/splash
  sdstyle = coordination or divergence
  limit = threshold for surface particles
  limit/splash = threshold for splash particles
shift values = none, turns on velocity shifting
rho/sum values = none, uses the kernel to compute the density of particles
self/mass values = none, a particle uses its own mass in a rho summation
density values = rho01, ... rho0N (density)
speed/sound values = cs0, ... csN (velocity)

Examples

fix 1 all rheo 3.0 quintic 0 thermal density 0.1 0.1 speed/sound 10.0 1.0
fix 1 all rheo 3.0 RK1 10 shift surface/detection coordination 40

Description

Added in version 29Aug2024.

Perform time integration for RHEO particles, updating positions, velocities, and densities. For an overview of other features available in the RHEO package, see the RHEO howto.

The type of kernel is specified using kstyle and the cutoff is cut. Four kernels are currently available. The quintic kernel is a standard quintic spline function commonly used in SPH. The other options, RK0, RK1, and RK2, are zeroth, first, and second order reproducing. To generate a reproducing kernel, a particle must have sufficient neighbors inside the kernel cutoff distance (a coordination number) to accurately calculate moments. This threshold is set by zmin. If reproducing kernels are requested but a particle has fewer neighbors, then it will revert to a non-reproducing quintic kernel until it gains more neighbors.

To model temperature evolution, one must specify the thermal keyword, define a separate instance of fix rheo/thermal, and use atom style rheo/thermal.

By default, the density of solid RHEO particles does not evolve and forces with fluid particles are calculated using the current velocity of the solid particle. If the interface/reconstruct keyword is used, then the density and velocity of solid particles are alternatively reconstructed for every fluid-solid interaction to ensure no-slip and pressure-balanced boundaries. This is done by estimating the location of the fluid-solid interface and extrapolating fluid particle properties across the interface to calculate a temporary apparent density and velocity for a solid particle.

A modified form of Fickian particle shifting can be enabled with the shift keyword. This effectively shifts particle positions to generate a more uniform spatial distribution. Shifting currently does not consider the type of a particle and therefore may be inappropriate in systems consisting of multiple fluid phases.

In systems with free surfaces, the surface/detection keyword can be used to classify the location of particles as being within the bulk fluid, on a free surface, or isolated from other particles in a splash or droplet. Shifting is then disabled in the normal direction away from the free surface to prevent particles from diffusing away. Surface detection can also be used to control surface-nucleated effects like oxidation when used in combination with fix rheo/oxidation. Surface detection is not performed on solid bodies.

The surface/detection keyword takes three arguments: sdstyle, limit, and limit/splash. The first, sdstyle, specifies whether surface particles are identified using a coordination number (coordination) or the divergence of the local particle positions (divergence). The threshold value for a surface particle for either of these criteria is set by the numerical value of limit. Additionally, if a particle’s coordination number is too low, i.e. if it has separated off from the bulk in a droplet, it is not possible to define surfaces and the particle is classified as a splash. The coordination threshold for this classification is set by the numerical value of limit/splash.

By default, RHEO integrates particles’ densities using a mass diffusion equation. Alternatively, one can update densities every timestep by performing a kernel summation of the masses of neighboring particles by specifying the rho/sum keyword.

The self/mass keyword modifies the behavior of the density summation in rho/sum. Typically, the density \(\rho\) of a particle is calculated as the sum over neighbors

\[\rho_i = \sum_{j} W_{ij} M_j\]

where \(W_{ij}\) is the kernel, and \(M_j\) is the mass of particle \(j\). The self/mass keyword augments this expression by replacing \(M_j\) with \(M_i\). This may be useful in simulations of multiple fluid phases with large differences in density, (Hu).

The density keyword is used to specify the equilibrium density of each of the N particle types. It must be followed by N numerical values specifying each type’s equilibrium density rho0.

The speed/sound keyword is used to specify the speed of sound of each of the N particle types. It must be followed by N numerical values specifying each type’s speed of sound cs.

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

This fix must be used with atom style rheo or rheo/thermal. This fix must be used in conjunction with fix rheo/pressure. and fix rheo/viscosity. If the thermal setting is used, there must also be an instance of fix rheo/thermal. The fix group must be set to all. Only one instance of fix rheo may be defined and it must be defined prior to all other RHEO fixes in the input script.

This fix is part of the RHEO package. It is only enabled if LAMMPS was built with that package. See the Build package page for more info.

Default

rho0 and cs are set to 1.0 for all atom types.

(Hu) Hu, and Adams J. Comp. Physics, 213, 844-861 (2006).