From 6cf5eab3af58851ddafacfd4f04d1789762f0e1b Mon Sep 17 00:00:00 2001
From: Martin Bauer <martin.bauer@fau.de>
Date: Fri, 26 Jul 2019 09:01:07 +0200
Subject: [PATCH] Added documentation
---
lbmpy/continuous_distribution_measures.py | 14 ++++++++------
lbmpy/cumulants.py | 2 +-
lbmpy/maxwellian_equilibrium.py | 18 ++++++++++++++++++
3 files changed, 27 insertions(+), 7 deletions(-)
diff --git a/lbmpy/continuous_distribution_measures.py b/lbmpy/continuous_distribution_measures.py
index 3edee60..c89960f 100644
--- a/lbmpy/continuous_distribution_measures.py
+++ b/lbmpy/continuous_distribution_measures.py
@@ -69,9 +69,10 @@ def multi_differentiation(generating_function, index, symbols):
Computes moment from moment-generating function or cumulant from cumulant-generating function,
by differentiating the generating function, as specified by index and evaluating the derivative at symbols=0
- :param generating_function: function with is differentiated
- :param index: the i'th index specifies how often to differentiate w.r.t. to symbols[i]
- :param symbols: symbol to differentiate
+ Args:
+ generating_function: function with is differentiated
+ index: the i'th index specifies how often to differentiate w.r.t. to symbols[i]
+ symbols: symbol to differentiate
"""
assert len(index) == len(symbols), "Length of index and length of symbols has to match"
@@ -119,9 +120,10 @@ def __continuous_moment_or_cumulant(func, moment, symbols, generating_function):
def continuous_moment(func, moment, symbols=None):
"""Computes moment of given function.
- :param func: function to compute moments of
- :param moment: tuple or polynomial describing the moment
- :param symbols: if moment is given as polynomial, pass the moment symbols, i.e. the dof of the polynomial
+ Args:
+ func: function to compute moments of
+ moment: tuple or polynomial describing the moment
+ symbols: if moment is given as polynomial, pass the moment symbols, i.e. the dof of the polynomial
"""
return __continuous_moment_or_cumulant(func, moment, symbols, moment_generating_function)
diff --git a/lbmpy/cumulants.py b/lbmpy/cumulants.py
index c7629ad..9544636 100644
--- a/lbmpy/cumulants.py
+++ b/lbmpy/cumulants.py
@@ -43,7 +43,7 @@ def __partition(collection):
def __cumulant_raw_moment_transform(index, dependent_var_dict, outer_function, default_prefix, centralized):
- """Function to express cumulants as function of moments as vice versa.
+ """Function to express cumulants as function of moments and vice versa.
Uses multivariate version of Faa di Bruno's formula.
diff --git a/lbmpy/maxwellian_equilibrium.py b/lbmpy/maxwellian_equilibrium.py
index 25a5779..98b73d8 100644
--- a/lbmpy/maxwellian_equilibrium.py
+++ b/lbmpy/maxwellian_equilibrium.py
@@ -199,6 +199,24 @@ def get_moments_of_discrete_maxwellian_equilibrium(stencil, moments,
def compressible_to_incompressible_moment_value(term, rho, u):
+ """Compressible to incompressible equilibrium moments
+
+ Transforms so-called compressible equilibrium moments (as obtained from the continuous Maxwellian) by
+ removing the density factor in all monomials where velocity components are multiplied to the density.
+
+ Examples:
+ >>> rho, *u = sp.symbols("rho u_:2")
+ >>> compressible_to_incompressible_moment_value(rho + rho * u[0] + rho * u[0]*u[1], rho, u)
+ rho + u_0*u_1 + u_0
+
+ Args:
+ term: compressible equilibrium value
+ rho: symbol for density
+ u: symbol for velocity
+
+ Returns:
+ incompressible equilibrium value
+ """
term = sp.sympify(term)
term = term.expand()
if term.func != sp.Add:
--
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