From b92676d3cd0907d5bfe6e6ad25e3e77210d107a8 Mon Sep 17 00:00:00 2001
From: Jonas Plewinski <jonas.plewinski@fau.de>
Date: Thu, 26 Nov 2020 09:16:00 +0100
Subject: [PATCH] Added function get_central_moments to moments.py
---
lbmpy/moments.py | 30 ++++++++++++++++++++++++++++++
1 file changed, 30 insertions(+)
diff --git a/lbmpy/moments.py b/lbmpy/moments.py
index cfb868a7..f46fd0f5 100644
--- a/lbmpy/moments.py
+++ b/lbmpy/moments.py
@@ -417,6 +417,36 @@ def shift_matrix(moments, stencil):
return sp.Matrix(shift_matrix_list)
+def get_central_moments(stencil, u=tuple(sp.symbols("u_0 u_1 u_2"))):
+ """
+ Returns the central moments for D2Q9 or D3Q27
+ """
+ x, y, z = MOMENT_SYMBOLS
+ if len(stencil) == 9:
+ central_moments = (sp.sympify(1), x - u[0], y - u[1],
+ (x - u[0]) ** 2, (y - u[1]) ** 2, (x - u[0]) * (y - u[1]),
+ (x - u[0]) ** 2 * (y - u[1]), (x - u[0]) * (y - u[1]) ** 2,
+ (x - u[0]) ** 2 * (y - u[1]) ** 2)
+ return central_moments
+ elif len(stencil) == 27:
+ central_moments = (sp.sympify(1),
+ x - u[0], y - u[1], z - u[2],
+ (x - u[0]) ** 2, (y - u[1]) ** 2, (z - u[2]) ** 2, (x - u[0]) * (y - u[1]),
+ (x - u[0]) * (z - u[2]), (y - u[1]) * (z - u[2]),
+ (x - u[0]) ** 2 * (y - u[1]), (x - u[0]) ** 2 * (z - u[2]), (x - u[0]) * (y - u[1]) ** 2,
+ (x - u[0]) * (z - u[2]) ** 2, (y - u[1]) ** 2 * (z - u[2]), (y - u[1]) * (z - u[2]) ** 2,
+ (x - u[0]) * (y - u[1]) * (z - u[2]),
+ (x - u[0]) ** 2 * (y - u[1]) ** 2, (x - u[0]) ** 2 * (z - u[2]) ** 2,
+ (y - u[1]) ** 2 * (z - u[2]) ** 2, (x - u[0]) ** 2 * (y - u[1]) * (z - u[2]),
+ (x - u[0]) * (y - u[1]) ** 2 * (z - u[2]), (x - u[0]) * (y - u[1]) * (z - u[2]) ** 2,
+ (x - u[0]) ** 2 * (y - u[1]) ** 2 * (z - u[2]),
+ (x - u[0]) ** 2 * (y - u[1]) * (z - u[2]) ** 2,
+ (x - u[0]) * (y - u[1]) ** 2 * (z - u[2]) ** 2,
+ (x - u[0]) ** 2 * (y - u[1]) ** 2 * (z - u[2]) ** 2)
+ return central_moments
+
+
+
def gram_schmidt(moments, stencil, weights=None):
r"""
Computes orthogonal set of moments using the method by Gram-Schmidt
--
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