Commit fec19283 authored by Markus Holzer's avatar Markus Holzer
Browse files

Implemented CM in momentbased.py

parent 45d2d7e2
%% Cell type:code id: tags:
``` python
# imports
from lbmpy.session import *
from lbmpy.moments import *
from lbmpy.forcemodels import Guo
from lbmpy.methods.abstractlbmethod import LbmCollisionRule
from lbmpy.methods.creationfunctions import create_with_discrete_maxwellian_eq_moments
from collections import OrderedDict
```
%% Cell type:markdown id: tags:
# Tutorial: Central Moments
In this tutorial, we will learn what central moments are, what advantages they have and how we can use them with lbmpy.
%% Cell type:markdown id: tags:
## 1) Theoretical Background
%% Cell type:markdown id: tags:
### What are Central Moments and why use them?
The most common collision operators are the SRT and MRT operators. Both of these operators are based on a second-order approximation of the Maxwell-Boltzmann distribution, where the relaxation is done in either single or multiple steps. However, both approaches have the disadvantage that at relaxation rates that are close to the limit, both methods become unstable. For these kinds of problems, other operators can be used, e.g. the entropic LB operator, which enforces an H-theorem on the lattice and is therefore unconditionally stable. In order to get this feature of unconditional stability, the relaxation time is modulated in dependence of the local entropy, which removes high frequencies from the flux fields. Nevertheless, the method that is presented in this notebook is another one, the Cascaded LBM (= CLBM), which uses central moments. It does not remove any frequencies, but instead tries to deal with the high frequencies with sufficient accuracy, such that these do not threaten the overall stability.
%% Cell type:markdown id: tags:
So CLBM has the goal to remove instabilities which can be traced back to an insufficient level of Galilean invariance (GI). GI describes the independence of physical processes from the speed of the reference system.
%% Cell type:markdown id: tags:
From tutorial 3 we know, that _lbmpy_ is using the following equation for moment based relaxations
$$K(f) = f - C^{-1}S\left(Cf - c^{(eq)}\right)$$
A few things are happening here:
* $Cf$ is transforming the distribution function $f$ into the moment space. The solution of this linear transformation is the moment-vector $c = Cf$.
* $c^{(eq)}$ defines the equilibrium in the moment space (alternatively $Cf^{(eq)}$, but it is more natural to define it directly in the moment space)
* In the moment space, the relaxation is executed by multiplying $S$ from left, to get $\Delta m = S \cdot \left(m - m^{(eq)}\right)$
* then an inverse transformation of the relaxed moments is done by $\Delta f = C^{-1} \Delta m$
* and in the end, the streaming is happening by $K(f) = f - \Delta f$
%% Cell type:markdown id: tags:
Now, in order to restore the Galilean invariance, we will use central moments. For that, we have to perform an additional transformation; we have to transform the raw moments into the central moment space. First, we define the continuous central moments:
%% Cell type:markdown id: tags:
$$\kappa_{\alpha \beta \gamma} = \int_{\mathbb{R}^3} (\xi_x - u_x)^\alpha \cdot (\xi_y - u_y)^\beta \cdot (\xi_z - u_z)^\gamma \cdot f(t, x, \xi) \,\, d\xi$$
%% Cell type:markdown id: tags:
where $u = \left( u_x, u_y, u_z \right)$ describes the macroscopic velocities. The discrete central moments are defined as
%% Cell type:markdown id: tags:
$$\kappa_{\alpha \beta \gamma} = \sum_{i = 0}^{n_v} [(c_i)_x - u_x]^\alpha \cdot [(c_i)_y - u_y]^\beta \cdot [(c_i)_z - u_z]^\gamma \cdot f_i \\
\qquad\qquad\quad = \sum_{i, j, k = -1}^{1} [(c_{ijk})_x - u_x]^\alpha \cdot [(c_{ijk})_y - u_y]^\beta \cdot [(c_{ijk})_z - u_z]^\gamma \cdot f_{ijk} $$
%% Cell type:markdown id: tags:
The main difference between the transformation to raw moments and the one to central moments is that the first is a linear transformation, while the second is a polynomial transformation. As a consequence, we cannot easily formulate this transformation as a simple matrix-vector multiplication; nevertheless, we can use the fast central moment transformation:
%% Cell type:markdown id: tags:
$$ \kappa_{ij\,\mid\,\gamma} = \sum_{k = -1}^{1} [(c_{ijk})_z - u_z]^\gamma \cdot f_{ijk} $$
$$ \kappa_{i\,\mid\,\beta \gamma} = \sum_{j = -1}^{1} [(c_{ijk})_y - u_y]^\beta \cdot \kappa_{ij\,\mid\,\gamma} $$
$$ \kappa_{\alpha \beta \gamma} = \sum_{i = -1}^{1} [(c_{ijk})_x - u_x]^\alpha \cdot \kappa_{i\,\mid\, \beta \gamma} $$
%% Cell type:markdown id: tags:
Now we can replace the transformation from the distribution function into the raw moment space with the fast central moment transformation into the central moment space, but because it is not a linear transformation, we are not able to write this as one equation as before, at least not directly. Therefore we have to do computations step by step and put the results together, such that we get the following algorithm:
%% Cell type:markdown id: tags:
* Transform distribution function $f_{ijk}$ with the fast central moment transformation into the central moments $\kappa_{\alpha \beta \gamma}$ $\left(f_{ijk} \Rightarrow \kappa_{\alpha\beta\gamma}\right)$
* Calculate the central equilibrium moments $\kappa_{i}^{(eq)}$ $\left(f_{ijk}^{(eq)} \Rightarrow \kappa_{\alpha\beta\gamma}^{(eq)}\right)$
* Relax the central moments $\kappa_i$ each with the relaxation frequency $\omega_i$ (diagonal elements of $S$) $\left(\kappa^{*} = S \left( \kappa_{\alpha\beta\gamma} - \kappa_{\alpha\beta\gamma}^{(eq)} \right)\right)$
* Transform the relaxed central moments with the inverse central moments transformation into the relaxed distribution function $f_{ijk}^{*}$ $\left(\kappa^{*} \Rightarrow f^{*}\right)$
* Do the update $\left(f(t+\Delta t, x+c_x \Delta t) = f(t, x) - f^{*}(t, x)\right)$ and streaming step
%% Cell type:markdown id: tags:
### Possible Solutions to Fix the Problem
%% Cell type:markdown id: tags:
However, there are two possibilities on how to solve the dilemma and write this again in one equation. One is to modify the above-described approach, and the other one uses features of lbmpy for a workaround:
1. Extract with the help of the fast central moment transformation a shift matrix, which is lower triangular, to transform the moment space into the central moment space.
2. Set up a method directly with the central moments. However, the problem with this approach is, that the transformation matrix which brings the distribution function into the moment space changes, and is not sparse anymore but full. As a consequence, the subexpression elimination is not able to reduce the operation count as much as in the case of the shift matrix (D2Q9, in D3Q27 case the subexpression elimination is not working anymore), which we will later see in an example.
Let us first look at the first possibility. We introduce a little modification to the approach described above. With the help of the fast central moment transformation, we can extract a shift matrix $N$, which transforms the raw moments into the central moment space via matrix multiplication. The shift matrix consists of the coefficients of the moments from the polynomials, which we get from the fast central moment transformation. Furthermore, with this, we can again write the collision equation in a form with matrix-matrix/vector multiplications and do not have to execute multiple things step after step.
%% Cell type:markdown id: tags:
$$K(f) = f - C^{-1}N^{-1}SN\left(Cf - c^{(eq)}\right)$$
%% Cell type:markdown id: tags:
## 2) Using Central Moments with *lbmpy* by Using the Shift Matrix $N$
%% Cell type:markdown id: tags:
First let us define variables which we later need, like the velocity $u$, the distribution function $f$, the relaxation rates $\omega$ and the viscosity $\rho$.
%% Cell type:code id: tags:
``` python
u = sp.Matrix(sp.symbols("u_:2")) # velocity
f = sp.Matrix(sp.symbols("f_:9")) # distribution function
ω = sp.Matrix(sp.symbols("omega_:9")) # relaxation rates
ρ = sp.symbols("rho") # viscosity
```
%% Cell type:markdown id: tags:
We will show the usage of the central moments in an easy setup, the simulation of a force-driven channel flow. First, we define a method with raw moments.
%% Cell type:code id: tags:
``` python
stencil = get_stencil("D2Q9", ordering='walberla')
force = [5e-5, 0]
F = Guo(force)
method = create_lb_method(stencil=stencil, method='mrt_raw', compressible=True,
equilibrium_order=4, force_model="Guo", force=force)
method
```
%%%% Output: execute_result
<lbmpy.methods.momentbased.MomentBasedLbMethod at 0x7f3c14ff4400>
<lbmpy.methods.momentbased.MomentBasedLbMethod at 0x7f61e2aea370>
%% Cell type:markdown id: tags:
For the sake of simplicity, we use an SRT approach and set the single relaxation rate to 1.9.
%% Cell type:code id: tags:
``` python
def modification_func(moment, eq, rr):
rr = 1.99
rr = sp.Symbol('rr')
return moment, eq, rr
method = create_lb_method_from_existing(method, modification_func)
method
```
%%%% Output: execute_result
<lbmpy.methods.momentbased.MomentBasedLbMethod at 0x7f3c14fbfdc0>
<lbmpy.methods.momentbased.MomentBasedLbMethod at 0x7f62081143a0>
%% Cell type:markdown id: tags:
With the help of the method, we can extract specific vectors/matrices, which we will need to define our collision equation (transformation matrix to transform distribution function $f$ into the moment space, the discrete equilibrium values in the moment space). Further, we use the extracted moments and the defined stencil to get the second transformation matrix with `get_shift_matrix`, to get from the moment space to the central moment space.
%% Cell type:code id: tags:
``` python
raw_moments = method.moments
C = moment_matrix(raw_moments, stencil)
S = sp.diag(*method.relaxation_rates)
c_eq = sp.Matrix(method.moment_equilibrium_values)
N = shift_matrix(raw_moments, stencil)
N = set_up_shift_matrix(raw_moments, stencil)
N
```
%%%% Output: execute_result
![](data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAmMAAADhCAYAAACEL7KHAAAACXBIWXMAAA7EAAAOxAGVKw4bAAAgAElEQVR4Ae2dUbLUNre2NxTXKQJVGUCYAYQRADOA/CMgzCAprvjuqDADwgg4YQaQEfDBDJIBpIp9qEzg/O/jbXUst91tt2W3Lb2qcsuSbVnrWcvqZUm2r7148eLuxcXFJy1d4d1//vOfJ10bnGcCJmACJmACJmACJnCcgHypP7XX9117atu1G40Nr7TOzs3wVzPhdRMwARMwARMwARMwgdEEfu044pHyHpPfdMZeyzuz89VBy1kmYAImYAImYAImcCoB+Ve/tY9VHll7zlh7v7OkVTmGTX/Xck/rX89SiUxOKn7BE/8ike5o+VV5drgT69echwEthVMpch7Tujn0EzKbmE0uPKbIcT1Gcp6UBLip5Xctr1WDN1o6x1XPU7ttnlUsmQf4UfEvWhiC/kXLe62bbUKVmvMwmKVwKkXOY1o3h35CZhOzyYXHVDnW4ox9lSBPtDyTmt7GqnJqLAFx/EnH4OC+C8dqnV5G0ji8DgkImPMwiKVwKkXOY1o3h35CZhOzyYVHCjlW4YzF6nEqAQGegP3cUc5H5T2U4dzs2Oas8QTMeRizUjiVIucxrZtDPyGzidnkwmOyHHbGYsPIJfVQglx2CBPmi7HdYToBcx7GsBROpch5TOvm0E/IbGI2ufCYLIedsdgwNp8a2Ot1a/OCnlkAcx6mgFI4lSLnMa2bQz8hs4nZ5MIjlRx2xmL7yCEVHK1DT6J6mHK6ps15GMNSOJUi5zGtm0M/IbOJ2eTCI4kcdsZi4ygldbsUQc8spzkPU0ApnEqR85jWzaGfkNnEbHLhcVQOO2Ox4nNIdc0VC3IFD573jjlMI2DOw/iVwqkUOY9p3Rz6CZlNzCYXHknksDMWG8fmUxq/DsOTXUORIS9M5N+8vOcSwJyHkS+FUylyHtO6OfQTMpuYTS48UslhZyy2j1xSHyTI9x3ChJ4xtjtMJ2DOwxiWwqkUOY9p3Rz6CZlNzCYXHpPlsDMWG0YuKT4n9UOHMPeU97nhyXfs4qwRBMx5GKxSOJUi5zGtm0M/IbOJ2eTCY7Ica3TGwkS30IsTq86powTkbPFB0kvF1QdIOUDrDFH+qOUpaYfpBMx5GMNSOJUi5zGtm0M/IbOJ2eTCI4UcN2I050tJGDxLAi9PI/CtSuY28T3Fva+dV3v45xABesH4MPh9xUzYJ36g9GfFDukImPMwlqVwKkXOY1o3h35CZhOzyYXHJDmuvXjx4q648FHpO7XzE2NyygRMwARMwARMwARMICkB+Vx8R/q14mtrHKZMKqwLMwETMAETMAETMIE1E7AztmbtuG4mYAImYAImYALZE7Azlr2KLaAJmIAJmIAJmMCaCdgZW7N2XDcTMAETMAETMIHsCdgZy17FFtAETMAETMAETGDNBOyMrVk7rpsJmIAJmIAJmED2BOyMZa9iC2gCJmACJmACJrBmAnbG1qwd180ETMAETMAETCB7AnbGslexBTQBEzABEzABE1gzATtja9aO62YCJmACJmACJpA9gdV8mzJ70mcSUJ9Z4HNXfPfznta/nqkaWZ9WXH+tBeQboHe08E1Qvqvq0CBQCqdS5GyotnPVHDqxVJlmE7PJhccUOdwzFttEFikZxE0tfGj9tQR6o+X7LARboRBizHddPyr+Rcsrrf+ihY/bm3lDX6VwKkXOhmo7V82hE0uVaTYxm1x4TJXDzlhsF1mkZBRftTzR8kwCvc1CqBUKIb585BXH912ontbpfSSNI+wgAqVwKkXOY0ZtDv2EzCZmkwuPFHLYGYttwykTGEPgiXb+3HHAR+U91AV6s2NbiVmlcCpFzmM2bA79hMwmZpMLj8ly2BmLDcMpExhD4KF2vuw4IMwXY7uDHFNBKIFTKXIes2lz6CdkNjGbXHhMluNGzOW8qbongaEfJkF/Uvq3Zo2UZiL6U8WeiN4E4/XFCdS2euy8t47tkPv2UjiVIucxezWHfkJmE7PJhUcqOdbWM/ZcgjEJ+r2W8IRapUHl46Q9VmxHrCLinzMTCI7WIXv0MOXFRSmcSpHz2GVnDv2EzCZmkwuPJHKspmdMTtZd6Ym5NoRHWtrDGuTtzc/RccFp47UCt5XmaTYHE1gDgdtrqMQG6lAKp1LkPGZy5tBPyGxiNrnwOCoHztg3tewhjlGMSMkRoifgDy1jegR46g8n66865ow/annJSiMwJhvlaX96y74opjftQjGTpnmtAI6bgwnMSeDyQOHhTokbhNJDKZxKkfOYPZtDPyGzidnkwmOKHN8FJEl7xuQEMWRzLxQ+Jq6PvVCM04Uzt5svprzv67wPrTLpFXsQ8rTfBy3VO54Uh0nUYbNjE0hGQPbF60Mor+vGI+QVb4OlcCpFzmMXkDn0EzKbmE0uPFLJwZyxf2pEIY6JLZ/iEVF6yXDsQnjMivI+hwytBwet/YfHcQx5OpjA3AS4OcAO2yH0jLVvHtr7lZIuhVMpch6zW3PoJ2Q2MZtceJwqx98BB87Y2gJ/bjunq64cw44Ii0P2kxZ6HkLvA9nNQJdh+DNs5nvdBFIT4OneHzoKpXf4s+y0eUPRsVsxWaVwKkXOY4ZrDv2EzCZmkwuPyXKs0RmLerr0h0YvF394wUG7c+RPDkesz1GLzaCMVJg4aAc1sb5lhwylXyquem4pXuvYHnMen5J2qJgUwcn2cGXt5tB/1ZtNzCYXHinkSDpnLMZ8coqnId9IOOaDMQEa54yeBj6+/LPit1oIfb0O/BlGDl21d2E/YoWnTmAOHoFvVcKFOXW7+XjVFv9MIRBs874KwV6JH4hxuHmYUnZOx5bCqRQ5j9mmOfQTMpuYTS48Jslx7cWLF/Q8fdJCj9OmnBjV939V7+iPT3n/t0VZVGcHEzABEzABEzCBQgjIX+GNEK8VX1vjMOUYNfCqi9DzcyGBWH+neFNO5RiBva8JmIAJmIAJmEBeBNY4TDmYsJyuV1oYvgxDmnxGyXN1BhP0jiZgAiZgAiZgAucmsGlnDHhyxPzG/XNbkc9vAiZgAiZgAiZwMoGtD1OeLLgPNAETMAETMAETMIE1ELAztgYtuA4mYAImYAImYALFErAzVqzqLbgJmIAJmIAJmMAaCOCM8eThMy28ud7BBEzABEzABEzABExgfgJ8WQj/6wJn7Hstr7X4De2C4GACJmACJmACJmACCxDgdVz4X5UztsD5fAoTMAETMAETMAETMIEuAp4z1kXFeSZgAiZgAiZgAiawEIHNv2dsIU6bPE39MlzqzjcTeSEuL8j11wkgkjiIK58V43ug97Te993UxGfdVnGl2GMpch6zPnPoJ2Q2MZtceEyRwz1jsU1kk5JR8L3Rj4p/0fJK67wcl4+EM0fQIQEBsbyphQ+wM+b/RovZ9nAVoyLssRQ5e9S8yzaHHYq9FbOJkeTCY6ocdsZiu8giJaPg46M4Cu+CQFqnt4Z0NVkw5Ds+nQBMtTzRwtMwb08vKe8jxacIeyxFzmPWag79hMwmZpMLjxRy2BmLbSOX1BMJ8rlDmI/KeyjDudmxzVkmMBeBUuyxFDmP2Yk59BMym5hNLjwmy2FnLDaMXFI8Ltv13rgwX4ztDiawFIFS7LEUOY/ZjTn0EzKbmE0uPCbLcSPmct5U3WPDkAaTzT8p/VuzRkozQfqpYk+QboJprNcMGzmdq36nXCcWZ6YmUIo9liLnMfswh35CZhOzyYVHKjnW1jP2XIIx2fy9ll+bqlM+TtpjxXbEmmD214OjdYiThyn3uTlnHgKl2GMpch6zEnPoJ2Q2MZtceCSRYzU9Y3Ky7kpPzGkiPNLSHmYjb28elI7DsfhRyzOt31PscJzA7eO7eA8TWIxAKfZYipzHDMcc+gmZTcwmFx5H5cAZ+6aWPcQxihGp2jH6Q4eM6XnhaTScrL/qmDPiXL1kpREYk43ytD8OHPmEMee8OiLP38sDYgUPnveOOZjAEgRKscdS5DxmM+bQT8hsYja58Jgix3cBCc7YP3UixGHb6FjO0VcddG/0gTqgPpYY5wrHajdfTHnf13l8VHMXlP9Zic+KH+8yC18RC163AIUu5zTkhYn8hdOy+HMTKMUeS5HzmL2YQz8hs4nZ5MJjohx/ByprmzNGvXhElF4yHLsQKmdLeThfDscJ4LTiwLZD6BmLnNr2Tk6bQGICpdhjKXIeMw9z6CdkNjGbXHhMlmONzhhORNvpYr4Ywl7IIftJS+jhIcthnwBPnf6wn131WtKT2HR0O3ZzlgkkJVCKPZYi5zHjMId+QmYTs8mFx2Q51uiMRUNochzuSnc4FsFBu2NnIrbmdkp8GOK9VLwbvtU6Dixz8Z6293c6CYEwQTP0PiYpNIdCSrHHUuQ8ZpPm0E/IbGI2ufBIIQdzxtYW+IbiGwnHqy2YaI5zxjw0PnL9s2J/dkYQBoTA7L72hSPxAzEMTu2AIrzLMQLiyR0RgbmOBL5Vic3yHdDdvMdqS9k/pdhjKXIes2Zz6CdkNjGbXHhMkuPaixcv6HniI770OEW9UjGv9aZUb3qAcNZ4WayDCZiACZiACZiACayagHwW3p/6WvG1NQ5TrhqeK2cCJmACJmACJmACKQmscZhysHzyJpns/0wLQ0TfK10NbSrmLf4OJmACJmACJmACJrB6Alt3xhhWZY6ZgwmYgAmYgAmYgAlskoCHKTepNlfaBEzABEzABEwgFwJ2xnLRpOUwARMwARMwARPYJAE7Y5tUmyttAiZgAiZgAiaQCwGcMeZdMQn+MhehLIcJmIAJmIAJmIAJrJwAXxbC/7pgAv/3Wl5rIXN1n8nRk5G8Of65FgJ1JTxV/urqelU1/5qACZiACZiACZjAUQK8CQL/67ctPE3Jy1wrzxGxtE7Fq5fUknYwARMwARMwARMwgS0T2MKcMT4MjvcYAu8S451ifDnAwQRMwARMwARMwAQ2TWALPWP0iv1305QXrLycVIZyw7vX+MA6cwF/Ub6/STmTHsSWGwQC3wDlk1z05m7y02IIMWcQF26i+J7nPa1nOdXA9nBlQebQfyWZTcwmFx5T5NjctylrYR8r9ncoY3u+EJNq/p/iR2GT1nEU+MD6I60zL9AhIQExZcj8peJ3FKuYOY7kwdsO2b9M3miVGwNuEHDIvhWf7JwxyWR7kHLNQRB6gtnEYHLhcYocOmab36ZUxWnE+Sg4X0d32CeA47WbX8dmMaOXjD89eiMcEhKoL6SbiitHjKK1DmvSzG10EAGYaHmiBdt8mysUyUfDWrw9mEO/hZtNzCYXHink2MKcsUp7EpZeH5yNbIc3YjM9KcXcuj/Fit6ZZqBHjD8JGDqkI/BERXUN/35U/sMOPaQ7s0taIwHbw5VWzKHfOs0mZpMLj8lybMIZq50I5j0x9MNdNhP47VjERk0Kp+svGO1vqnLaTlrPbs4eSADnl6G3dgjDk80HT9r7OJ0fAdvDlU7Nod+2zSZmkwuPyXLciLnMn5KjgENAdz5zvj4p/VvzrEoznLZ7j5jSOF0M+eCMhScoGe4Ik9S16gAB8cE77woVN22venEUj9JBV4Gl59UMj2G4dWwHb8+DgO3hSo/m0G/PZhOzyYVHKjnO0TP2XJV/JbW818Kw4y4oHyeNyfnNnh0mxOJ1EoeF110099Emhy4C4oQjhkPbdF7H6qCr6NLzgqN1yA5xeh3KIGB7uNKzOfTbu9nEbHLhkUSORXvGaseA+TQEnvhrD/GQF83B0THfsrPDyQToaXwnjjjAF6fooD4uOM5flL6tcprOHbs47BO4vZ/lnIIJ2B6ulG8O/ReB2cRscuFxVA6csW9q2UMco0ibYj5TcLZ+VNEvW8XTA9bOa+2Sb1Js6En5Q8uYHhWeUgtMIzjKZ3gX5s3hy9E60PH0WH5RHBw6Jqe/17J7hUZ04jISlwfEDHdKOK4OZRCwPVzp2Rz67d1sYja58Jgix3cBCc7YP3UixGFb8lh/3tWQjmKcLhyO3Xwx5TGURt7eu7C0rYhemZrPPTGYHFQWDtQtxZHDVJ/jQvEYHcD/QaiUjv2gBWeMBynCZPWwuYhYcvMgCbJ2Oc4hr0g2RRhAS0jbwxUQc2gZRiNpNg0YWs2Fx0Q5/g5UzjFnjHPTU9N+6o/3h6Ggz8QhKB16ZZjAX801U8x8M4ceAuIDyzuKdz1iWm8/gTpIBxynsnAu2o7FV+Xd1VJy4MYBPu0Qesb2bizaOzqdFQHbw5U6zaHfrM0mZpMLj8lynMsZ4w8scrqUpgcHgS7kADBBP/Qu0CtT5dfbWGeYrOtPkF2KDuKCg3RfcXtOFw5aszt1qA6CHtpcKSs4He1tpaSZj/dDh7D0bn6WDnBYHcohYHu40rU59Nu82cRscuExWY7rMZfFUlEvS+1A8KcWHDR6dar3iSkPZyDaX2n+5ErvlRGCOIgZDhZGwQteXzcX5T2DaeOIiKm2wXNPB43926s4Yuim2CBmDLNfKsbRrYLWYcJ8yKdXOf5tEQgTWbNz5G0PV5o2h5bFN5Jm04Ch1Vx4pJCDOWPnCPTavJEA9HoxyRnHgN4EPrDMdxTfaiH0/dm7V+aKT/uX4VscMoZ22yE4uiF/qA6aDlw4lhjdRA5dc2NB68Fu70tmbJn4gey4zbsgJPuiigc3CQTmKhJ+Vx72w9zD3dzRasu2f2wPV/ozh347NpuYTS48Jsmx6g+Fq5Gmt+aTluijwsr/X+Xxcebq6b5Yr06lJlDzjhwM5f2fzkMPph2y1MBdngmYgAmYQPYE9P9JxwmjWNfONUw5FLJ7ZYaSmnc/XjcSejQuZDis8+4yO2LzcnfpJmACJmACBRBYtTNW/9njkDH01g4eBmoTmSktPdADyYtewzAyT2J6TtRMvF2sCZiACZhAWQTONWdsDOXQK1M5X3II3Cszhl6ifcW9/XRmopJdjAmYgAmYgAmUTWD1zhi9MnWPTJjszwfG3StTtt1aehMwARMwARPIhsDqnTFIu1cmG3uzICZgAiZgAiZgAi0Cq54z1qqrkyZgAiZgAiZgAiaQHQGcMZ6Ie6blMjvpLJAJmIAJmIAJmIAJrJMAXxTC/7pgmJInFV9rIbPvVRLadJ6gIUpeLvq8Pnt4qvKp8ldX1/MQ8llNwARMwARMwAQ2SIAHEvG/ftvCnDFep1B5joDWOhXnRbBM5HcwARMwARMwARMwgU0T2MKcsZ/kgOE9hsBTld8rj7fzO5iACZiACZiACZjApglsoWeMXrH/bprymSovhxXHlcA3E+lJpJfRb82HyIQghgyXh/eu8XF15lv+ony/iPgA15LsUbJys8j3OO9pvcgpFSXp+4DZd24ymxhLLjymyLHqb1PG6rpK1cI+Vuxhyi5AdZ74MJTL9zvfkaWYuXfkPdK6HTKgnBDErppjqfhROFzrOL184B62zL10aBEQl+ztUTJyjb3RgnOOk45DFn1XV+kiQgn6PlWRZhOTy4XHKXLomM18mzLSmipO4/ZYC19Hd+ghUCv4puLKEWM3rXN3Tpo5dw6nE8Dx2s1hpBixpZcMvvSEOLQIiA8NTvb2yDWm5YkW7ONtC0MxyVL0fYpCzSamlguPFHJsYc5YpT0JS48Ef4TFdvvHZnwwxbcju4bMPir/oVhyB+9wGgHmL/7ZwZAeMRwO7NQhJmB7jHnknrK++zVsNjGbXHhMlmMTzlj9B8ecHIaBuPtkAr//9GKjbqZwGBgqaYcwPNl8IKK9j9OHCeB0/YUd9uxmR3cfjO1xn0nOOdZ3v3bNJmaTC4/JctyIucyf0p8Yf1YMWzDn65PSvzXPqjRDPbv3iCmN08XQGs5YeIKSYYAwgVqrDoGAGA1xBm6F/R2PIyC+3AF1hco2tb3qkaz1MNjOuwrMIc/2mIMWh8tgffezMpuYTS48Uslxjp6x56r8K6nlvRaGHXdB+fx5MTm/2evAxF+8TuKw8LqL5j7a5FATCI7WIT5DHDYDHUhAtogjxk1D8wZhrJ0PPNvmdrM9bk5lkypsfffjM5uYTS48ksixaM9Y/afFvCUCT6O1h9LIi+Y66Zhv2dkhKYHbSUtzYfTmvpOtcpNxcYqd18fhJP+o5ZnKKOkhFdsjBlBOsL77dW02MZtceByVA2fsm1r2EMco0qaYaxOcLf50XraKpwesndfaxckjBC4PbA8e/JcD+2S9SfaHw/OHljG9gzwhF+w24qN8htCx6+bw5Wg71/F3VQ72TxhTt6sj1vtre1yvbuaomfXdT9VsYja58Jgix3cBCc7YP3UixGFb8lh/OF8pVDF/Ovzh7OaLKY9hHvL23tOkbeSX2GMgsccFseIBBw6CWTuEvDCRv709+zR8JOS9FIKqLIbVbynevXOMcutzEA+2c+37WYd+VsyrW7IJksf2mI02jwtiffczMpuYTS48Jsrxd6CCM3aOQC9C+4m06k9IgvGntAtK59pjsJNxhhUcWpzbdrhVZ+w5vO0dnT5MQHaJvd5RvOsR03rFXHFwdgfb+eGzbX6r7XHzKhwlgPXdj8tsYja58Jgsx/WYy2Ip/rQip0tpehcQ6EJ/ZkzQr3pxFNNbwFyc8AfHLg6HCTCH6YeOXegRgie9Qw4nEhA/bhDuK25O2Kc0HLRml/VgO+fgjIPtMWPldohmfXdAqbPMJmaTC4/JcpzLGYscq/rPDechOGj0ONhhiI12cErsGP69VIxzUAWt49wy1Pv0Kse/pxAQRxwsLjxe8Pq6uSiPifdNu7WdC4qYlGiPYcJu6I0WiTJCofoepFyziTHlwiOFHOcapqRH4Y0E4NUWTCbnT4teGz5k/bPiYj8lItlThcDzvgqEMfED8Q0Ob6rzlFYOr2TBIWO+WDu02drO/yVUhD3q+sJRJzBfkPC78mjf3ivezZGttuT9U4S+T1Sh2cTgcuExSY7NfChcDRm9PDhr/kB4bMhOZUTAdp6RMi2KCZiACRwgoPaem3pGWK6da5jyQPW8yQRMwARMwARMwATKIXCuYcpyCFtSExhAQHdGDH3ymS+Gt/j2ajWEr7h6keyAIryLCZiACZjARgnYGduo4lztvAjI6WJeUfvpzLyEtDQmYAImYAKdBFbvjLnHoFNvzjQBEzABEzABE8iEwBacMfcYZGJsFsMETMAETMAETGCfgCfw7zNxjgmYgAmYgAmYgAksRgBnjJ4nJg433xy+WAV8IhMwARMwARMwARMokABfHcL/usAZ4ymu11qKe1O0ZHYwARMwARMwARMwgXMQ4Ol5/K/KGTtHBXxOEzABEzABEzABEzABEfCcMZuBCZiACZiACZiACZyRwOqfpjwjG5/aBEwgIYH6RbaUyLdS+awZnzdjzmpWoRQ5hyhNLO5qP77XeU/rX4ccU8I+tpFYy7nwmCKHe8Zim3DKBExgBgJqpD6p2I+Kf9HCVwV4wS0fz2bOajahFDkPKUwMbmrhA+nMhXmjJSsdH5J9yDbbSEwpFx5T5bAzFtuFUyZgAokJqJHiY7j8Qb8LRWudXhLS1eTVkL/luBQ5j+kI3Wp5ooWnxN4e27+k7baRWNu58Eghh52x2DacMgETSE/giYr83FHsR+U9VEN2s2PbFrNKkXOLullLnW0jsSZy4TFZDjtjsWE4ZQImkJ4Aj293vccwzBdjew6hFDlz0NW5ZLCNxORz4TFZjhsxl9NS9Z0tQxFMyv2k9G/NkpRmAudTxYMncM5RZrNOpayb4zKaNuduzjWX7o3/5m7+HYelyPmvyrw2loBtJCaWC49UcqTqGXuuCjEp972WX5vIlY+T9ljxYEesPn6OMptVK2XdHJfRtDl3cw6O1qHrP4dhylLk7Nayc4cQsI3ElHLhkUSOyT1jcrLuii9zPwiPtLSHI8jbmy+i44LTxmPut5Xm6aoqTCiTRv1HLc9Uxr2r0sr9NcdldD+Bc+81sEzNV3OW26upybwVKUXOeSnmXbptJNZvLjyOyoEz9k0te4hjFMdTf+nPKDhbOEIvW4cwlhrlaX96y74opjftQjGTeHnMHceNcEqZOIWci5DDnXYliJggyx8jZeJJJnRijhXF4z9n4HzsGjhe6W3scXmgmuGOkhuyrYdS5Ny6ns5Zf9tITD8XHlPk+C4gwRn7p06EOGwbFOtP7Cs7KsYRwnHYzRdT3vd1Hh/DbAZ6BB6EDO33QUv1ziHFOBCjy9Qxn1XeZ8WPQ7k5xDWLe6fIYo7DqS3NWTU7eA0Mr/m694SrFipJ29AOIS9M5G9v30y6FDk3o5AVVtQ2EislFx4T5fg7UEk1Z4zyeLRz50jVJ6gcI1UWR6kKWg8OWrsBxgGjd6sZBpXZPMDrnQTMsRNL8sxBnEdeA8kreYYCuRnjum+H0DPWvllr77eVdClybkUfa6ynbSTWSi48JstBz1iqQGO7c7rqQhl2pJIX+gNiWOZ/tIS7YbKbga6+0DiH/EFlqmwcOYd+AubYzybllkGcdcIx10DK+p2rLJ6mDvPjmnWgx5fe7Fyu31LkbOrQ6+MI2EZiXrnwmCzH9ZjLpFTU06UGll6uH7QEB+3OkUYXR6z9JzW1zEkCZXSwOS6jzKmcu66BZWo+41l03TN14VLxbgqB1rnWmWP6dMZTL1p0KXKOhBomLrdvtEcWk8futpFYj7nwSCFHyp4xnoZ8o0pxB8yEXP6YuPPlY8A/K36rhdB3F0zjHP2ZKT20TMp16Cdgjv1sUm4ZynnMNZCyfucsK7QF91UJ2gfiB2obws3aOeuW8tylyHmQmfRKTwGBucQEvlVJ+87c4N284mpLeT+2kVjnufCYJEcyZ0wXGH8wzJlphyiPC7Let2tIJ2qYh5bZPqHTMQFzjHnMlRrKWfsNvgbmquvS5dZs+FZh1qEUOY8pURyidv/Y/iVtt43E2s6Fx1Q5Ug5TxoQPp3jVRbhjupAQrL9T3O4ZO1yKt5rAdgn4Gtiu7lxzEzABE0hK4NqLFy+Y2/VJC3O6FnOGdK4woZchCz6j9Ivy+oZvtPlw0LH0tHHnjWOHTLzDbPcuM607DCBgjro08u0AABoCSURBVAMgJdol9TWQqFouxgRMwARMYAEC+g/gwcbXiq+dzRlbQE6fwgRMwARMwARMwARWSaDpjJ1rmHKVYFwpEzABEzABEzABE1iagJ2xpYn7fCZgAiZgAiZgAibQIIAz9k2dDnFjs1dNwARMwARMwARMwARmIJDu25QzVO5C46i8c+x5XTYT8wlPlX/yBP+rIvxrAssQsA0vw9lnMQETMIENE9h9mzLZe8YSw+BFsbt3Emn9tcqvnvhMfB4XZwJzEbANz0XW5ZqACZhAZgTWOmfsJzlgu/eQiTmvwfheebyywsEEtkDANrwFLbmOJmACJrACAmt1xugV++8K+LgKJnAqAdvwqeR8nAmYgAkURmCVw5TqAWt/u4w/Nj4hE30uKRddSS7mxfFdQwIfV7/Uwktws5QXIXMPpdlw7vocI590336hNUPWi71Qe0xdU+4rGd2OjQAqXoz08A3Pe1ovej605M/impkixyqdsaY91wb7GINt5ueyLvlowHgD76MgU63QT+Rp+RDyHW+TgHRIo5utDW9TK/PUWrpmbutLxe84g2IeRgrXcrYOmeR0O4bCj4TaHt5oN264ufGGW9FBTLK4ZqbKcX3NVlBf4HjMOd85IN/uYQX0IbnpJeNOibsmhw0TKMSGN6yhdFWXrvm0yU3FlSNGyVrnOibNQ0g5B7djA7SLPWh5ooU2/+2AQ7LeRRyyuGZSyLFaZ0zCccfAUB29QxgwE/hzvIvgQYU/JRt30M1AjxgNe44yN+XMdr3WXQk2nK0ORwr2RPt3TS34qPyHHdf4yOJXvbvbsVWrZ7WVy+WamSzHKocp6z8x7iT5IwtPUHInEeZVrdayTqgYTtddyckddFdoO2ld+zhvZQQKs+GV0T9bdXBI2vNdqUwYnmT7rteMDRkFt2MZKXNBUXK5ZibLcWMJ6PpjwqGgO/KOFuZPRA2W0gzHNV/qyhgyxxDvgvbbDeedUOaunDWtSA486q5QOaHaXt1pzyXvXOV2CbTlvBM4HbXhLfM4pe4nMDzlNGc5ppbt2LlvHdthq9sl/1nbsa1yK7neuVwzqeS4vpAxPFeFX+lc77Uwt2AXlI+T9ljxrmdI699qudZedgddrYwqs3XsqpOSG0eM4clmT+Bc8s5V7qoZn1C5UZwG2vAJ1dj0IaMYbkzS4Gjt2rGO+nODWUxYuB0rhmtGguZyzSSRY/aesfqCZM4EgScGeYqkGcjrmmfR3CdaP7VMHUdj+KOWZ1pf89OZ9BS+Ux1xYC8U45yNZqjjguP7RcffVrrp3E0pdyscwTc5nMp/8okzKuBUhjouJ1u7nZFKh4iySDs2pCLeZ7MEcrlmjsqBM8Z8Bob/2k7STnt1g/iHMsbc2fHECE5W8/1gOEIvdwVfrTDW2s5r7bKXHF1m/WfAuQhj5Lg6YqFf1ZO5csjX7PY/RV56HL+onODQMYH4vZbdKzTq8wRHeJBudDyO4eo5qo4pw2j+KU++lrKke66bxdqBjdlab/spZuHOmZuiVYaJut2TSeUt2Y7tnd8ZmyCw6WumQXiKHMy1rKZf4YwxHMaFQ+ZXLXtBFxb5J/Uk1cdeKOYPnMZ8N19MeZybPM4dBW3r7dXRtqqeY8rUvjgdnxXzvqdVBtUNB+qW4qbDdKH0aHlVDvweBEFVxgctOGM8lVpNKFY8ulwds3qOQeZU8SmcOLeO67XhVHVbspyaw2LtgM63GVuDjRbUQXvWDiEvTORvbz97eopu25VXWYu2Y+3zO70NAlu/ZgLliXLgF+F//bbUnDHqTU8PPQyVA0CGQuUYKY9GdxeUDr06PE1ZzTVTzHyzdhhcZvvAtaUlHyzuKN71iGm9/TqPQfJynMriD6Dd+MOenq12GFRu+6AC04M5SQdDbbg0jIMZbhAMN5Vce+0Qesb2bjrbO249Lbs/Zzu2dXwl1j+Xa2ayHEs6YzRSkdOlND1AVQPFn5eWcAdJj8Ku4VI+6wyztRu6MWWqiHUGyYWDdF9xNKdLeTRsl41aD5U3cGwcWq1SVvhjaG4bWm7zmBLXx3AaasOlcRzDcGtsmCP1Q0el6U2kV56boWzDCtqxbNlmLFgu18xkOa4vqOSol6a+cGm4goNGr1D1clfl4UxE+ytNQ9bu1Yn26StTx602qM78OaFIXvD6urkojwcNmg34VHlxxGDbDlPLbZeXa3oQp1qnQ204V1Z9cg1i2HfwmvOld6ZgXCrmJqoKWscOmI/59Conz9/a5s/djm0NbpjU3XWDvDVZTqpvLtdMCjmYM7ZUoNfnjSpNjwETWWmUuWPkI7o/K36rhdDlLJDf1asztEyOX2tg+BWHjGGtdgiOasgfKu/XcEAr7nIQ2GVoua3iiksO5TTGhkuDOJThVrmENu2+BKCdI36gNq59LW9Vvr56r6Ed66vbqvJlCzitBOYLEX5XHv+HzOndzamutpTxk8s1M0mOxZwxGRkOAvNF2qErr70P6b1enQRldp1n0TzJwItwB4Wh8mq/MDeva0ho709haLmDKpnxTgk47dlwxrg6RUvAsLPctWTW8lVPR62lTkvUQ3KfvR1bQs4U5xCrof95KU63+jJyuWamyrHkMOVQoxjbqzO03NL243Uh4c7rQobCOu8ui4aJSoOykLy24YVA+zTZE3A7lr2KLSAEFusZG4obZ0ELf2aDenVGlEt53LHilPCUYjVcqrh6D9fQcrayH3IhY5BT9ebOdfK8FZVXFMdT9C1Gs9jwKXXZ8jG2tS1rL03dZQOztGNpaudSTCAdgdU5Y7Vo4W6oGlLTBTm5V4c/SJXNfJVigmROLm+JHE80mOQ2fGI9NnuYbW2zqkta8TnasaQVdGEmkIDAKp0xXXy+G0qgXBdxPgK24fOx95lNwARMYGsEVumMAdF3Q1szJde3TcA23CbitAmYgAmYQBcBJvB/U28Icdd+zjMBEzABEzABEzABE0hH4LtQFD1j/9SJEIdtWcXqpbgpgZ7XQjEJnfBU+X1Pvl3tkdmvOWSmUItjAiZgAiawVQJ/h4qvdpgyVDBhzJOFPE1ZBa3zcc5PWga/H+fqyM3/msPmVWgBTMAETMAEciLAMGUp4Sc5YA8bwvJqC15xcbeRV8KqOZSgZctoAiZgAiawGQIlOWP0iv13M5qZr6LmMB9bl2wCJmACJmACowkUM0ypHrD2N79wSng5597ngUZT3NABJXOQ7MwVDO9e4yP1l6RLs4Fzmas40xtN4JuNTA9gyNxfhIBIBsHX13Al+lrYZyUmjFLx3c57Wt/kXO4pei3GGWuqvlb6Y5TezC9tvSQOkhVH7LXiR0HPWsc5+ESelg8h33F6AuLL/MyXit9RumIeqAns7ZABZcNB+vT1NVB/YuVroWZVtwNvlOTGmBtk7GiTYaper29S6gmVrhsN/oQ3631PEH93aIEc0PnuAQ5AiAG9ZNyBcTfmMBMBcf5JRd9UXDlinEbrcCfNgzQO2yfg62uADn0txJBoB7Q80ULb/Dbeup1UCr0W5YwJGF43w1L0hGAETODfrCd+qqnWMpfGgYc3/pTs9Mg0Az1iOArF2UETwszrT1R+13SAj8p/2KGTmavj4mcg4OtrGFRfC8M4bW2vyXotZpiy/rPlLhwnJDxBiTce5hBtTfkn1bdgDjhddyU/PTJdoe2kde3jvNMI8EfdnrNJSWF4ku27XjM2OGyOgK+vYSrztTCM09b2mqzXG0tIrD9A/ugYqmDSLvNEooZZaYaJRr2A9YQyGaenHsS7oHKioavdho2smMMwRYkTdy5doXLMtb3quTmBZ1eZUd4cZUYnWHGilv1YDW8d22Fr20vTueQ92/W1Fdso9VrYin5OrWcqvV4/tQIjj3uuCr/SMe+1MLdgF5SPk/ZYcV+PxW7f1sqoMlX+t1qutZdWmVtMmsOJWpMt4IgxPNnsHR3Fc+Cp5yhz4KnPvltwtA5d39wk5RZK1nmlywWvr63YTqnXwlb0c2o9k+h19p6x+oJkbgiBJ9l4aqIZyNubT6LjgtP2RdtvK737wzy1zOZJc1g3h8lapEf2nThyo3BxKk8dl9xWVSYOyo9anmk996d+b8M/lzCHHW2UTarry9fCRg3A1d4RONrG3VDDgSN0bXdIx0r9x/CHNo25g+UJCcpuvsuLP5eXrVMw1hrl6Th6y74oDn+STPJ9ryW8lmB0ma1z5pI0hxM1KVti/iD8msMro3nq+OS2qjLpseO6IIy55q6OWNdv++arWbtwR8kN16qCdAD3NbV5s/KZKO9e3VRequvL18IeXWesjMDJbZyuE6ZsVdO2cMYwduZR3dF6mFAbyar8r8o46e68PvZCMX8uNHC7+WLKY4iIvPY7nuhpeKClCtrvgxacMZ5+5A+T+lwoHlMm+3OubHobJI85VBYy7kfccKBuKQ7OfVXAiTyT26rqwU3MZ8W8C2/TAaZakIFrrx1CXme70955yTT11vlW0+bNLfsUedt1U1nJri+V5WuhDdjpVRHg2tFCnUJ71qxfyOts4+pr5bXia0vNGaNy9EDsHKm6ttWfjSrCBVcFrQcHrV15Gkccx2YYVCYHqFyOpZEATgCk1SyCOQxUo+wAm+PGY9cjpvX2K04G8eQ4lYUtJbXVgaJsaTdutmDVDrfqjPbNWHu/rabnsKNVs0h5fa1a0NMrV+q1cDqxbRw5Wa83FpSTxnjndNXnpWeiaoh1EeMo/Y+WPkfpUttC463VKgwqU2XjuWZzhxWEb8Tm0IDRtyobwCG/r3g3/7DeFwdt12Or9UE8td8stlrXKaeIuUNhXl1TLnqe6AH82szMaH0OO1otntTXV6Z2Ueq1sFq7TVSxyXq9nqgiQ4qJeg/qC/cHHRgcNHorDjXKOGLtP7+pZQ6p9xb2MYcjWpJt8cfIBcMLXukW3i3KY5J80/am8rStNvQhtji6l4qrnnA2aZ1rmSkDT0lnGuawo1Wikj6XvL5WyWBIpcSp1GthCJ4wyb3d6TLk2LPuk0KvS/aM0RvxRpXmDpkJuzRU3BnzseCfFb/VQmj+KV7lXP3SeEeNm9JDy2yWk+O6ORzXKq9V4Q+DHth2CDcEIX8oT9tqIHY8Dtf6fe3K9U/8QNd+m/3xkrazxxx2tFbp57i+1irr1HqVeC30MlMbwE0y4eFVdPG78vivZ554c8Si3rzaaJJeF3PGBJU/LuZQtEOUhxLqffnjbDfUUXpome0T5pY2h+MaFSNeODwoDOWp/Wyrg4hWPWFc/5t+wfJAUXe7zWFHu8JXtjLH9bUyEZNVp7aLoq6FQ/DEI/IBDu275m1T9Xp9pcLxqovgJV9ISNZ5H1S7Z2yl1Xe1CiJgWy1I2TOKajuaEa6LNoG1E1isZ2wMCDldr7QwfBmGNOnVyHluyRg83ndFBOawVZVJrzB3ztyE8KRndR1wrhWJ7qokJDCHHSWs3tmK8rVwNvQ+8cIEVumMwUAXIfMtHExg9QRS26rKowfY9r96zaetYGo7Slu785Tma+E83H3W5Qms1hlLjUIXtXsbBNUcUluWyzMBEzABEzCBaQRKcsbc2yBbkTNmDtOuGR9tAiZgAiZgAkkJrHUCf1IhXZgJmIAJmIAJmIAJrJXAWXrG1DvDO8Oe11AYPiQ8VX7fe5uu9jjwO0eZB07nTT0ErIcYjHnEPNqpUviUImdbv06bgAkMI3AWZ0xV40lJnhargtZfa6X6WHmddUo0R5mn1KP0Y6yH2ALMI+bRTpXCpxQ52/p12gRMYACBcw1T/iQH7GGjfjy6zyP8fDvw1DBHmafWpeTjrIdY++YR82inSuFTipxt/TptAiYwgMC5nDF6xf47oH5jdpmjzDHn975XBKyH2BLMI+bRTpXCpxQ52/p12gRMYACBswxTqges/b0pGio+LRN97mhA/Xe7zFHmrvAzr0g25tWF907xcfVL0lN4zSXSlvUwB+ct85jLRprllsJnS3KqroxQPFNMu+yQgIBYbqYNTyDuoCJyZVJfP3xv857WB8+DP4sz1tRUXfHHVLyZP2V9jjKn1GfKsZKFi/i14kehHK0zrPuJPC0fQv7aYtWNRj2pbueSUXWdnfOWeMzF+VC5pfDZgJz8kZx8Y3xIxyVuW6Jt2RrX3JhIHh5KfKOFjhI6TPg/GRWuj9o78c61QnAsRnmQh6oxR5mHzrfANvhEd6iSkV4yPO7wtfsFqjHuFBvUw6ycN8hjnMIn7l0Kn7XLqfr9PFGVPnyfwKxty/7pNpGTFRNdN1+1PNHCf/XbUzRwNmdMlcZzZKiN3h0EYQL/aG+yKXR9fNIym+WfaZ0HHf6UbHjezUCP2M2pzJoFplrfqB5m47xRHqnM4Wg5pfBZu5yqHz3Z3OSxOKQjMFvbkq6Ki5dkJi3kN1rpRZJ1o8TrLHCcwhOUeJRhXtToesxR5uhKzHMATtddydfXQLadtHlqMbDUDethFs4b5jFQ49N2K4XPRuT8f6onbXLUEz9Nwz5aBGZpWzZO1kxaCkzijOnixSH4ScsdLcxliiboK81wWvOlrrxTjGOId6HZCMxR5u5EG1oRhyc91a2cWG2v5nacwKun2Dj7hHKP6jY+wzpSM3I+yuMExuuA1lGLE2Q5yqfjNGfPyk1OycPwJDfIneEEeTvLaWbOUWaz/LWsS86ztuFr4dCsh5k0aVytJ3HGVNRzweWOisnaTGLbOWPKw0l73ISv9W+VdyzMUeaxc25iu/jhiFXDvI0Kj+LVOO7Y6qhyB+r22DlXsT0F54E8RjFeBZz+SoySZSCf/rOdb0s2ckoHtCVMFeG7tX1hlLx9hbTy5yizdYp1JsV6yTZ8nRBatSqdyWRnrAb4sebKE388TdAM5I16MmeOMpsVymCdnsZ34vQKWU7lpeOYREn4ouW20tEw8anlViXm8ZOE8yEUpzLWcfQs/6iFVxAkexL5UF2PbTtVlmPlrm17hnJiQ9G132R+qrw6rrd9mVDm6uy+yWrEepK2RRxz4QG6VEx67W6EfhbfdbIzpho33w/Gn8PLlhQPO/Jau+wl5yhz7yRLZNQXyx86FxfN0MBTGZ0OrPIZSoBPs+t7NC8dT4/lF8XBoXuo9fdadq/QqM8T6pFKt0MZjNpP9Ybv6jgPEOIU3XFXzXVFGGNXV0fM9ztalvmqMmvJ2cip64Z2oHd4sqY4Wt663EPtyyllnsXu19q2qF5n4YFNrJjJkP+12qzXFU12xqSUr7Vy+HPgj6E5REn3N3lM1ouCjuv1XieUybnW1lsAnyQ9F+KCod1S3HSYLk7kBf8HWqqgMj5owRnjqdZquEIxdb9QPFa3i+uhrusaOcMvqa2rPBzkz4qZFrCaoPpsxl6mQJsgZ68dTKnPqcdKjqp9VnxoePLiRHkPti+nlKljzmL3dV1X17aciwf2tlYmqtpBuzv1WlniuMnOWKOS9NRwt1M1yHV+9WdRG81uV6WHeq9jyjzbXcJOsBlXxAyWdxTvesS0TmN6oTg0poN41cfhMIXjKIaA7uDYzh9ULgWo7E3rQfVPxrnmkdzWKXfloRR7GSPnUDtYUrW0H/dl8wwPNQPXMDdl5NOmhyHMQfJq/3AT3m5HutqXQWU2K7fVdXFJ2rZslUOz3imZjLS7ZjVWsX49YS24AMOQViiWHpyqV0yg+FAuDgAB73XXW6Z81h/WMNkewuAydSw9BQy5tRuAUNZmY8lF40ijGRrFIAsX92VIKB7KK+ihcWi1Slm32plKDy33QnXcrB5m4AzK5LbeoZ+1ZRVhL4I+WM4RdrCYLmXv9IYzJSJaVAGcprCt2eYMlXdM+zK0zMW4zHGimdqWOaq6WJkzMBljd4vJOfREKXvGcIJ2f+Q16B+UF4Yt6dWpXu6qPKC1nSYaAJyOZv6gMnVMtkHMaKy4Q6VxbM/twIGt5nzVAAbx0jH17nsR+usy6EHl7pW2oYyZOKO7Em09e3upTXuQnLVtDbWDNVw11PXkdmBk+zKI4RqgnFqHOdqWU+uyluPmYDLS7uZEcbsunP/Tr0NPlNIZ4w7qjYDQE8DTeVxkjLP/qryfFb/VQui6yMnv6pUZWibH5xreSzD+1BnmaId2T+RQXn0Ggm7QWzsMLbd93JbSc3Au1dZLsBdse6icY+zgbNeM2mlu9mhrCNzocRP4UXG44Rsq75j2ZWiZVaU2+jNH27JRFLtqz8FkjN3tKpJqpb5eKO5hXebvyuP/lLnYoVOq3rQfJXPGdDJAMP7fDl157X1I7/XKJCiz6zybyhMDXqQ7KAzlpf3C3D4a3rZD105fDC13UCVXupNkTM75gKhZ23oJ9oJuE8i5ZwcHbGb2TZLn4Jv3h8qr/Qa3L0PLnF34GU8gGZdsW2aUJF3RczAZY3fpJPm3JJ1/qK/z70GNteuN9aVWz+q9LiXkBs7DK0iCB38hQ2Kdd5d19YxtQJxVVtG2vkq1LF6pEu3A7cviZuYTisBm7S5Zz9hQM+DPXguN06BemaHler9xBKSDV1oYQg7Dyty9PR1Xivc+REBsZ7F1lcu1Qy8GDjRPvVU6VByGkw5Vy9sWJjCXHSwsxqjTYYvYJYsOZNrK5PZFZdnuG1owjwaMelVMktvd/lnmyVncGavFCN5rNSQmgO6VmUe/B0sVd+ZrOMxLILmtS2/0Xlp38+otdenJ7SB1BVOXl7p9sd3HGjKPmEdIpba7UO7c8bUXL17c1Un4WC9POy42RKVzccdECHdNfNuyrzv/as8Dvzq2edeETPQS7N4AfeBQb0pIwHrYh5na1vfPsN2ckuzFdrBdO3XNTWAOAmoTeDDvteJrZ3PG5hDMZZqACZiACZiACZjAFgg0nbHmMOWf2tCuPxO6Jz0h0C7QaRMwARMwARMwARMoiYB8qT8lLyN4nQFnjKFJJgN3hcWGLbtO7jwTMAETMAETMAETyIBAmJrVKcr/B/cwelIWOd2xAAAAAElFTkSuQmCC)
$\displaystyle \left[\begin{matrix}1 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0\\- u_{0} & 1 & 0 & 0 & 0 & 0 & 0 & 0 & 0\\- u_{1} & 0 & 1 & 0 & 0 & 0 & 0 & 0 & 0\\u_{0}^{2} & - 2 u_{0} & 0 & 1 & 0 & 0 & 0 & 0 & 0\\u_{1}^{2} & 0 & - 2 u_{1} & 0 & 1 & 0 & 0 & 0 & 0\\u_{0} u_{1} & - u_{1} & - u_{0} & 0 & 0 & 1 & 0 & 0 & 0\\- u_{0}^{2} u_{1} & 2 u_{0} u_{1} & u_{0}^{2} & - u_{1} & 0 & - 2 u_{0} & 1 & 0 & 0\\- u_{0} u_{1}^{2} & u_{1}^{2} & 2 u_{0} u_{1} & 0 & - u_{0} & - 2 u_{1} & 0 & 1 & 0\\u_{0}^{2} u_{1}^{2} & - 2 u_{0} u_{1}^{2} & - 2 u_{0}^{2} u_{1} & u_{1}^{2} & u_{0}^{2} & 4 u_{0} u_{1} & - 2 u_{1} & - 2 u_{0} & 1\end{matrix}\right]$
⎡ 1 0 0 0 0 0 0 0 0⎤
⎢ ⎥
⎢ -u₀ 1 0 0 0 0 0 0 0⎥
⎢ ⎥
⎢ -u₁ 0 1 0 0 0 0 0 0⎥
⎢ ⎥
⎢ 2 ⎥
⎢ u₀ -2⋅u₀ 0 1 0 0 0 0 0⎥
⎢ ⎥
⎢ 2 ⎥
⎢ u₁ 0 -2⋅u₁ 0 1 0 0 0 0⎥
⎢ ⎥
⎢ u₀⋅u₁ -u₁ -u₀ 0 0 1 0 0 0⎥
⎢ ⎥
⎢ 2 2 ⎥
⎢-u₀ ⋅u₁ 2⋅u₀⋅u₁ u₀ -u₁ 0 -2⋅u₀ 1 0 0⎥
⎢ ⎥
⎢ 2 2 ⎥
⎢-u₀⋅u₁ u₁ 2⋅u₀⋅u₁ 0 -u₀ -2⋅u₁ 0 1 0⎥
⎢ ⎥
⎢ 2 2 2 2 2 2 ⎥
⎣u₀ ⋅u₁ -2⋅u₀⋅u₁ -2⋅u₀ ⋅u₁ u₁ u₀ 4⋅u₀⋅u₁ -2⋅u₁ -2⋅u₀ 1⎦
%% Cell type:markdown id: tags:
With the definition of all relevant variables, vectors and matrices, we can define the collision equation as described above.
%% Cell type:code id: tags:
``` python
collision_equation = f + C.inv() * N.inv() * S * N * (c_eq - C * f) + sp.Matrix(F(method))
collision_equation = f + C.inv() * N.inv() * S * N * (c_eq - C * f)# + sp.Matrix(F(method))
```
%% Cell type:markdown id: tags:
In order to use this collision equation later on in a predefined scenario, we have to convert it into a collision rule, which we will do below, while introducing three subexpressions for the calculation of $\rho$, $u_0$ and $u_1$.
%% Cell type:code id: tags:
``` python
collision_rule = [Assignment(lhs, rhs) for lhs, rhs in zip(method.post_collision_pdf_symbols, collision_equation)]
@ps.kernel
def subexpressions():
ρ @= sum(f)
u[0] @= sum(f.T * sp.Matrix(np.array(stencil)[:, 0]))/ρ + force[0]/(2*ρ)
u[1] @= sum(f.T * sp.Matrix(np.array(stencil)[:, 1]))/ρ + force[1]/(2*ρ)
u[0] @= sum(f.T * sp.Matrix(np.array(stencil)[:, 0])) /ρ # + force[0]/(2*ρ)
u[1] @= sum(f.T * sp.Matrix(np.array(stencil)[:, 1])) /ρ # + force[1]/(2*ρ)
collision_rule = LbmCollisionRule(method, main_assignments=collision_rule, subexpressions=[subexpressions[0],
subexpressions[1],
subexpressions[2]])
```
%% Cell type:code id: tags:
``` python
collision_rule
```
%%%% Output: execute_result
AssignmentCollection: d_0, d_5, d_6, d_3, d_4, d_8, d_2, d_7, d_1 <- f(f_0, f_3, f_4, f_5, f_2, f_8, f_7, rr, f_1, f_6)
%% Cell type:code id: tags:
``` python
collision_rule.simplification_hints['density'] = ρ
collision_rule.simplification_hints['velocity'] = (u[0], u[1])
collision_rule.simplification_hints['relaxation_rates'] = [sp.Symbol('rr')]*9
```
%% Cell type:code id: tags:
``` python
simplification = create_simplification_strategy(method, split_inner_loop=False)
```
%% Cell type:code id: tags:
``` python
simplification(collision_rule)
```
%%%% Output: execute_result
AssignmentCollection: d_0, d_5, d_6, d_3, d_4, d_8, d_2, d_7, d_1 <- f(f_0, f_3, f_4, f_5, f_2, f_8, f_7, rr, f_1, f_6)
%% Cell type:markdown id: tags:
After that, we can use the subexpression elimination from pystencils to reduce the number of operations needed to perform the collision.
%% Cell type:code id: tags:
``` python
generic_strategy = ps.simp.SimplificationStrategy()
generic_strategy.add(ps.simp.sympy_cse)
generic_strategy.create_simplification_report(collision_rule)
```
%%%% Output: execute_result
<pystencils.simp.simplificationstrategy.SimplificationStrategy.create_simplification_report.<locals>.Report at 0x7f3c14eaca60>
%% Cell type:code id: tags:
``` python
collision_rule = ps.simp.sympy_cse(collision_rule)
```
%% Cell type:code id: tags:
``` python
collision_rule.operation_count
```
%%%% Output: execute_result
{'adds': 393,
'muls': 246,
'divs': 1,
'sqrts': 0,
'fast_sqrts': 0,
'fast_inv_sqrts': 0,
'fast_div': 0}
%% Cell type:markdown id: tags:
Now we can pass our method and customized collision rule to the predefined scenario `create_channel` to simulate an easy channel flow.
%% Cell type:code id: tags:
``` python
ch_with_cm = create_channel((300,100), method=method, force=force[0], force_model="Guo", initial_velocity=(0.5, 0), collision_rule=collision_rule,
optimization={"target": "cpu", "openmp": 4})
ch_with_cm.run(10000)
plt.vector_field_magnitude(ch_with_cm.velocity[:, :])
```
%%%% Output: execute_result
<matplotlib.image.AxesImage at 0x7f3c149e1850>
%%%% Output: display_data
![](data:image/png;base64,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)
%% Cell type:markdown id: tags:
Just for verification, we simulate the same setup, but with a standard SRT approach, without central moments.
%% Cell type:code id: tags:
``` python
ch_normal_srt = create_channel(domain_size=(300,100), force=force[0], initial_velocity=(0.5,0),
relaxation_rate=1.99, optimization={'target': 'cpu'})
ch_normal_srt.run(10000)
plt.vector_field_magnitude(ch_normal_srt.velocity[:, :])
```
%%%% Output: execute_result
<matplotlib.image.AxesImage at 0x7f3c148f06d0>
%%%% Output: display_data
![](data:image/png;base64,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)
%% Cell type:code id: tags:
``` python
fig = plt.figure(figsize=(13, 10))
ax = plt.gca()
fontsize = 22
vel_profile_ch_with_cm = ch_with_cm.velocity[0.5, :, 0]
vel_profile_ch_normal_srt = ch_normal_srt.velocity[0.5, :, 0]
plt.xlabel('y-Direction', fontsize=fontsize)
plt.ylabel('Velocity Magnitude', fontsize=fontsize)
plt.grid(color='black', linestyle='-', linewidth=0.1)
plt.rc('font', size=fontsize)
plt.plot(vel_profile_ch_normal_srt, linestyle='-.', color='r')
plt.plot(vel_profile_ch_with_cm, color='b', linewidth=0.7)
plt.legend(['Velocity Profile Standard SRT', 'Velocity Profile Central Moments'], fontsize=fontsize)
```
%%%% Output: execute_result
<matplotlib.legend.Legend at 0x7f3c148392e0>
%%%% Output: display_data
![](data:image/png;base64,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)
%% Cell type:code id: tags:
``` python
fig = plt.figure(figsize=(13, 10))
ax = plt.gca()
fontsize = 22
plt.xlabel('y-Direction', fontsize=fontsize)
plt.ylabel('Difference in Velocity Magnitude', fontsize=fontsize)
plt.grid(color='black', linestyle='-', linewidth=0.1)
plt.rc('font', size=fontsize)
plt.plot(vel_profile_ch_with_cm - vel_profile_ch_normal_srt, color='b')
```
%%%% Output: execute_result
[<matplotlib.lines.Line2D at 0x7f3c067df5b0>]
%%%% Output: display_data
![](data:image/png;base64,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)
%% Cell type:markdown id: tags:
### Compare Operation Counts of Both Described Methods
%% Cell type:markdown id: tags:
First we set up a method directly with the central moments.
%% Cell type:code id: tags:
``` python
cm = get_central_moments(stencil, u = u)
mtrr = OrderedDict(zip(cm, ω))
```
%% Cell type:code id: tags:
``` python
method_dir = create_with_discrete_maxwellian_eq_moments(stencil, mtrr, compressible=True, equilibrium_order=4)
def modification_func(moment, eq, rr):
rr = 1.99
return moment, eq.subs(u[0], 0).subs(u[1], 0), rr
method_dir = create_lb_method_from_existing(method_dir, modification_func)
method_dir
```
%%%% Output: execute_result
<lbmpy.methods.momentbased.MomentBasedLbMethod at 0x7f3c0678c760>
%% Cell type:markdown id: tags:
Now let us first look at the moment matrix, to show, that it is indeed not sparse anymore.
%% Cell type:code id: tags:
``` python
method_dir.moment_matrix
```
%%%% Output: execute_result
![](data:image/png;base64,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)
$\displaystyle \left[\begin{matrix}1 & 1 & 1 & 1 & 1 & 1 & 1 & 1 & 1\\- u_{0} & - u_{0} & - u_{0} & - u_{0} - 1 & 1 - u_{0} & - u_{0} - 1 & 1 - u_{0} & - u_{0} - 1 & 1 - u_{0}\\- u_{1} & 1 - u_{1} & - u_{1} - 1 & - u_{1} & - u_{1} & 1 - u_{1} & 1 - u_{1} & - u_{1} - 1 & - u_{1} - 1\\u_{0}^{2} & u_{0}^{2} & u_{0}^{2} & \left(- u_{0} - 1\right)^{2} & \left(1 - u_{0}\right)^{2} & \left(- u_{0} - 1\right)^{2} & \left(1 - u_{0}\right)^{2} & \left(- u_{0} - 1\right)^{2} & \left(1 - u_{0}\right)^{2}\\u_{1}^{2} & \left(1 - u_{1}\right)^{2} & \left(- u_{1} - 1\right)^{2} & u_{1}^{2} & u_{1}^{2} & \left(1 - u_{1}\right)^{2} & \left(1 - u_{1}\right)^{2} & \left(- u_{1} - 1\right)^{2} & \left(- u_{1} - 1\right)^{2}\\u_{0} u_{1} & - u_{0} \left(1 - u_{1}\right) & - u_{0} \left(- u_{1} - 1\right) & - u_{1} \left(- u_{0} - 1\right) & - u_{1} \left(1 - u_{0}\right) & \left(1 - u_{1}\right) \left(- u_{0} - 1\right) & \left(1 - u_{0}\right) \left(1 - u_{1}\right) & \left(- u_{0} - 1\right) \left(- u_{1} - 1\right) & \left(1 - u_{0}\right) \left(- u_{1} - 1\right)\\- u_{0}^{2} u_{1} & u_{0}^{2} \left(1 - u_{1}\right) & u_{0}^{2} \left(- u_{1} - 1\right) & - u_{1} \left(- u_{0} - 1\right)^{2} & - u_{1} \left(1 - u_{0}\right)^{2} & \left(1 - u_{1}\right) \left(- u_{0} - 1\right)^{2} & \left(1 - u_{0}\right)^{2} \left(1 - u_{1}\right) & \left(- u_{0} - 1\right)^{2} \left(- u_{1} - 1\right) & \left(1 - u_{0}\right)^{2} \left(- u_{1} - 1\right)\\- u_{0} u_{1}^{2} & - u_{0} \left(1 - u_{1}\right)^{2} & - u_{0} \left(- u_{1} - 1\right)^{2} & u_{1}^{2} \left(- u_{0} - 1\right) & u_{1}^{2} \left(1 - u_{0}\right) & \left(1 - u_{1}\right)^{2} \left(- u_{0} - 1\right) & \left(1 - u_{0}\right) \left(1 - u_{1}\right)^{2} & \left(- u_{0} - 1\right) \left(- u_{1} - 1\right)^{2} & \left(1 - u_{0}\right) \left(- u_{1} - 1\right)^{2}\\u_{0}^{2} u_{1}^{2} & u_{0}^{2} \left(1 - u_{1}\right)^{2} & u_{0}^{2} \left(- u_{1} - 1\right)^{2} & u_{1}^{2} \left(- u_{0} - 1\right)^{2} & u_{1}^{2} \left(1 - u_{0}\right)^{2} & \left(1 - u_{1}\right)^{2} \left(- u_{0} - 1\right)^{2} & \left(1 - u_{0}\right)^{2} \left(1 - u_{1}\right)^{2} & \left(- u_{0} - 1\right)^{2} \left(- u_{1} - 1\right)^{2} & \left(1 - u_{0}\right)^{2} \left(- u_{1} - 1\right)^{2}\end{matrix}\right]$
⎡ 1 1 1 1 1
⎢ -u₀ -u₀ -u₀ -u₀ - 1 1 - u₀
⎢ -u₁ 1 - u₁ -u₁ - 1 -u₁ -u₁
⎢ 2 2 2 2 2
⎢ u₀ u₀ u₀ (-u₀ - 1) (1 - u₀) (
⎢ 2 2 2 2 2
⎢ u₁ (1 - u₁) (-u₁ - 1) u₁ u₁ (
⎢ u₀⋅u₁ -u₀⋅(1 - u₁) -u₀⋅(-u₁ - 1) -u₁⋅(-u₀ - 1) -u₁⋅(1 - u₀) (1 -
⎢ 2 2 2 2 2
⎢-u₀ ⋅u₁ u₀ ⋅(1 - u₁) u₀ ⋅(-u₁ - 1) -u₁⋅(-u₀ - 1) -u₁⋅(1 - u₀) (1 - u
⎢ 2 2 2 2 2
⎢-u₀⋅u₁ -u₀⋅(1 - u₁) -u₀⋅(-u₁ - 1) u₁ ⋅(-u₀ - 1) u₁ ⋅(1 - u₀) (1 - u
⎢ 2 2 2 2 2 2 2 2 2 2
⎣u₀ ⋅u₁ u₀ ⋅(1 - u₁) u₀ ⋅(-u₁ - 1) u₁ ⋅(-u₀ - 1) u₁ ⋅(1 - u₀) (1 - u
1 1 1 1
-u₀ - 1 1 - u₀ -u₀ - 1 1 - u₀
1 - u₁ 1 - u₁ -u₁ - 1 -u₁ - 1
2 2 2 2
-u₀ - 1) (1 - u₀) (-u₀ - 1) (1 - u₀)
2 2 2 2
1 - u₁) (1 - u₁) (-u₁ - 1) (-u₁ - 1)
u₁)⋅(-u₀ - 1) (1 - u₀)⋅(1 - u₁) (-u₀ - 1)⋅(-u₁ - 1) (1 - u₀)⋅(-u₁ - 1
2 2 2 2
₁)⋅(-u₀ - 1) (1 - u₀) ⋅(1 - u₁) (-u₀ - 1) ⋅(-u₁ - 1) (1 - u₀) ⋅(-u₁ - 1
2 2 2
₁) ⋅(-u₀ - 1) (1 - u₀)⋅(1 - u₁) (-u₀ - 1)⋅(-u₁ - 1) (1 - u₀)⋅(-u₁ - 1)
2 2 2 2 2 2 2
₁) ⋅(-u₀ - 1) (1 - u₀) ⋅(1 - u₁) (-u₀ - 1) ⋅(-u₁ - 1) (1 - u₀) ⋅(-u₁ - 1