Many minor tweaks, adding self/mass + oxide noshift
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@ -17,7 +17,7 @@ Syntax
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* zmin = minimal number of neighbors for reproducing kernels
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* zero or more keyword/value pairs may be appended to args
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* keyword = *thermal* or *interface/reconstruct* or *surface/detection* or
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*shift* or *rho/sum* or *density* or *speed/sound*
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*shift* or *rho/sum* or *density* or *self/mass* or *speed/sound*
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.. parsed-literal::
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@ -29,6 +29,7 @@ Syntax
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*limit/splash* = threshold for splash particles
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*shift* values = none, turns on velocity shifting
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*rho/sum* values = none, uses the kernel to compute the density of particles
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*self/mass* values = none, a particle uses its own mass in a rho summation
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*density* values = *rho01*, ... *rho0N* (density)
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*speed/sound* values = *cs0*, ... *csN* (velocity)
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@ -106,24 +107,38 @@ threshold for this classification is set by the numerical value of
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By default, RHEO integrates particles' densities using a mass diffusion
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equation. Alternatively, one can update densities every timestep by performing
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a kernel summation of the masses of neighboring particles by specifying the *rho/sum* keyword.
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a kernel summation of the masses of neighboring particles by specifying the *rho/sum*
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keyword.
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The *density* is used to specify the equilbrium density of each of the N
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The *self/mass* keyword modifies the behavior of the density summation in *rho/sum*.
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Typically, the density :math:`\rho` of a particle is calculated as the sum
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.. math::
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\rho_i = \Sum_{j} W_{ij} M_j
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where the summation is over neighbors, :math:`W_{ij}` is the kernel, and :math:`M_j`
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is the mass of particle :math:`j`. The *self/mass* keyword augments this expression
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by replacing :math:`M_j` with :math:`M_i`. This may be useful in simulations of
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multiple fluid phases with large differences in density, :ref:`(Hu) <fix_rheo_hu>`.
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The *density* keyword is used to specify the equilbrium density of each of the N
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particle types. It must be followed by N numerical values specifying each
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type's equilibrium density *rho0*.
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The *density* is used to specify the speed of sound of each of the N particle
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types. It must be followed by N numerical values specifying each type's speed
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of sound *cs*.
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The *speed/sound* keyword is used to specify the speed of sound of each of the
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N particle types. It must be followed by N numerical values specifying each
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type's speed of sound *cs*.
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Restart, fix_modify, output, run start/stop, minimize info
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"""""""""""""""""""""""""""""""""""""""""""""""""""""""""""
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No information about this fix is written to :doc:`binary restart files <restart>`. None of the :doc:`fix_modify <fix_modify>` options
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No information about this fix is written to :doc:`binary restart files <restart>`.
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None of the :doc:`fix_modify <fix_modify>` options
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are relevant to this fix. No global or per-atom quantities are stored
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by this fix for access by various :doc:`output commands <Howto_output>`.
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No parameter of this fix can be used with the *start/stop* keywords of
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the :doc:`run <run>` command. This fix is not invoked during :doc:`energy minimization <minimize>`.
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the :doc:`run <run>` command. This fix is not invoked during
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:doc:`energy minimization <minimize>`.
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Restrictions
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""""""""""""
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@ -138,7 +153,8 @@ set to all. Only one instance of fix rheo may be defined and it
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must be defined prior to all other RHEO fixes.
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This fix is part of the RHEO package. It is only enabled if
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LAMMPS was built with that package. See the :doc:`Build package <Build_package>` page for more info.
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LAMMPS was built with that package. See the
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:doc:`Build package <Build_package>` page for more info.
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Related commands
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""""""""""""""""
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@ -156,6 +172,10 @@ Default
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----------
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.. _howto-howto_rheo_palermo:
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.. _howto_rheo_palermo:
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**(Palermo)** Palermo, Clemmer, Wolf, O'Connor, in preparation.
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.. _fix_rheo_hu:
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**(Hu)** Hu, and Adams J. Comp. Physics, 213, 844-861 (2006).
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@ -14,20 +14,26 @@ Syntax
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* rheo/viscosity = style name of this fix command
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* one or more types and viscosity styles must be appended
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* types = lists of types (see below)
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* vstyle = *constant*
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* vstyle = *constant* or *power*
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.. parsed-literal::
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*constant* args = *eta*
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*eta* = viscosity
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*power* args = *eta*, *gd0*, *K*, *n*
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*eta* = viscosity
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*gd0* = critical strain rate
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*K* = consistency index
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*n* = power-law exponent
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Examples
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""""""""
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.. code-block:: LAMMPS
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fix 1 all rheo/viscosity * constant 1.0
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fix 1 all rheo/viscosity 1 constant 1.0 2 constant 2.0
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fix 1 all rheo/viscosity 1 constant 1.0 2 power 0.1 5e-4 0.001 0.5
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Description
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"""""""""""
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@ -47,18 +53,38 @@ means all types from 1 to n (inclusive). A trailing asterisk means all types
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from m to :math:`N` (inclusive). A middle asterisk means all types from m to n
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(inclusive).
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The *types* definition is followed by the viscosity style, *vstyle*. Currently,
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the only option is *constant*. Style *constant* simply applies a constant value
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of the viscosity *eta* to each particle of the assigned type.
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The *types* definition is followed by the viscosity style, *vstyle*. Two
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options are available, *constant* and *power*. Style *constant* simply
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applies a constant value of the viscosity *eta* to each particle of the
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assigned type. Style *power* is a Hershchel-Bulkley constitutive equation
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for the stress :math:`\tau`
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.. math::
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\tau = \left(\frac{\tau_0}{\dot{\gamma}} + K \dot{\gamma}^{n - 1}\right) \dot{\gamma}, \tau \ge \tau_0
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where :math:`\dot{\gamma}` is the strain rate and :math:`tau_0` is the critical
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yield stress, below which :math:`\dot{\gamma} = 0.0`. To avoid divergences, this
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expression is regularized by defining a critical strain rate *gd0*. If the local
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strain rate on a particle falls below this limit, a constant viscosity of *eta*
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is assigned. This implies a value of
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.. math::
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\tau_0 = \eta * \dot{\gamma}_0 - K \dot{\gamma}_0^N
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as further discussed in :ref:`(Palermo) <howto_rheo_palermo>`.
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Restart, fix_modify, output, run start/stop, minimize info
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"""""""""""""""""""""""""""""""""""""""""""""""""""""""""""
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No information about this fix is written to :doc:`binary restart files <restart>`. None of the :doc:`fix_modify <fix_modify>` options
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No information about this fix is written to :doc:`binary restart files <restart>`.
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None of the :doc:`fix_modify <fix_modify>` options
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are relevant to this fix. No global or per-atom quantities are stored
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by this fix for access by various :doc:`output commands <Howto_output>`.
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No parameter of this fix can be used with the *start/stop* keywords of
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the :doc:`run <run>` command. This fix is not invoked during :doc:`energy minimization <minimize>`.
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the :doc:`run <run>` command. This fix is not invoked during
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:doc:`energy minimization <minimize>`.
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Restrictions
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""""""""""""
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@ -69,7 +95,8 @@ conjuction with :doc:`fix rheo <fix_rheo>`. The fix group must be
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set to all. Only one instance of fix rheo/viscosity can be defined.
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This fix is part of the RHEO package. It is only enabled if
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LAMMPS was built with that package. See the :doc:`Build package <Build_package>` page for more info.
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LAMMPS was built with that package. See the
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:doc:`Build package <Build_package>` page for more info.
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Related commands
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""""""""""""""""
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@ -82,3 +109,9 @@ Default
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"""""""
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none
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----------
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.. _howto_rheo_palermo:
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**(Palermo)** Palermo, Clemmer, Wolf, O'Connor, in preparation.
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