From c80a5395242b235611e2ca42e98d8f7ff7f0433d Mon Sep 17 00:00:00 2001
From: markus holzer <markus.holzer@fau.de>
Date: Thu, 10 Jun 2021 12:27:48 +0200
Subject: [PATCH] Added doc to turbuence model
---
lbmpy/turbulence_models.py | 23 +++++++++++++++++++++++
lbmpy/updatekernels.py | 18 ++++++++++--------
2 files changed, 33 insertions(+), 8 deletions(-)
diff --git a/lbmpy/turbulence_models.py b/lbmpy/turbulence_models.py
index 1a9bf911..b7370881 100644
--- a/lbmpy/turbulence_models.py
+++ b/lbmpy/turbulence_models.py
@@ -18,6 +18,29 @@ def frobenius_norm(matrix, factor=1):
def add_smagorinsky_model(collision_rule, smagorinsky_constant, omega_output_field=None):
+ r""" Adds a smagorinsky model to a lattice Boltzmann collision rule. To add the Smagorinsky model to a LB scheme
+ one has to first compute the strain rate tensor $S_{ij}$ in each cell, and compute the turbulent
+ viscosity :math:`nu_t` from it. Then the local relaxation rate has to be adapted to match the total viscosity
+ :math `\nu_{total}` instead of the standard viscosity :math `\nu_0`.
+
+ A fortunate property of LB methods is, that the strain rate tensor can be computed locally from the
+ non-equilibrium part of the distribution function. This is somewhat surprising, since the strain rate tensor
+ contains first order derivatives. The strain rate tensor can be obtained by
+
+ .. math ::
+ S_{ij} = - \frac{3 \omega_s}{2 \rho_{(0)}} \Pi_{ij}^{(neq)}
+
+ where :math `\omega_s` is the relaxation rate that determines the viscosity, :math `\rho_{(0)}` is :math `\rho`
+ in compressible models and :math `1` for incompressible schemes.
+ :math `\Pi_{ij}^{(neq)}` is the second order moment tensor of the non-equilibrium part of
+ the distribution functions
+ :math `f^{(neq)} = f - f^{(eq)}` and can be computed as
+
+ .. math ::
+ \Pi_{ij}^{(neq)} = \sum_q c_{qi} c_{qj} \; f_q^{(neq)}
+
+
+ """
method = collision_rule.method
omega_s = get_shear_relaxation_rate(method)
if isinstance(omega_s, float) or isinstance(omega_s, int):
diff --git a/lbmpy/updatekernels.py b/lbmpy/updatekernels.py
index 0673f37e..5092617f 100644
--- a/lbmpy/updatekernels.py
+++ b/lbmpy/updatekernels.py
@@ -20,7 +20,7 @@ def create_lbm_kernel(collision_rule, src_field, dst_field=None, accessor=Stream
src_field: field used for reading pdf values
dst_field: field used for writing pdf values if accessor.is_inplace this parameter is ignored
accessor: instance of PdfFieldAccessor, defining where to read and write values
- to create e.g. a fused stream-collide kernel
+ to create e.g. a fused stream-collide kernel See 'fieldaccess.PdfFieldAccessor'
Returns:
LbmCollisionRule where pre- and post collision symbols have been replaced
@@ -61,10 +61,11 @@ def create_stream_only_kernel(stencil, src_field, dst_field=None, accessor=Strea
"""Creates a stream kernel, without collision.
Args:
- stencil: lattice Boltzmann stencil which is used
- src_field: Field the pre-streaming values are read from
- dst_field: Field the post-streaming values are written to
- accessor: Field accessor which is used to create the update rule. See 'fieldaccess.PdfFieldAccessor'
+ stencil: lattice Boltzmann stencil which is used in the form of a tuple of tuples
+ src_field: field used for reading pdf values
+ dst_field: field used for writing pdf values if accessor.is_inplace this parameter is ignored
+ accessor: instance of PdfFieldAccessor, defining where to read and write values
+ to create e.g. a fused stream-collide kernel See 'fieldaccess.PdfFieldAccessor'
Returns:
AssignmentCollection of the stream only update rule
@@ -117,11 +118,12 @@ def create_stream_pull_with_output_kernel(lb_method, src_field, dst_field=None,
Args:
lb_method: lattice Boltzmann method see 'creationfunctions.create_lb_method'
- src_field: Field the pre-streaming values are read from
+ src_field: field used for reading pdf values
dst_field: field used for writing pdf values if accessor.is_inplace this parameter is ignored
- output: Dictonary which containes macroscopic quantities as keys which should be calculated and fields as
+ output: dictonary which containes macroscopic quantities as keys which should be calculated and fields as
values which should be used to write the data e.g.: {'density': density_field}
- accessor: Field accessor which is used to create the update rule. See 'fieldaccess.PdfFieldAccessor'
+ accessor: instance of PdfFieldAccessor, defining where to read and write values
+ to create e.g. a fused stream-collide kernel See 'fieldaccess.PdfFieldAccessor'
Returns:
AssignmentCollection of the stream only update rule
--
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