Commit 0023726c authored by Markus Holzer's avatar Markus Holzer
Browse files

Merge branch 'extrapolation_outflow' into 'master'

Extrapolation Outflow Boundary

See merge request pycodegen/lbmpy!45
parents 93093c12 0289430a
......@@ -9,6 +9,7 @@ __pycache__
.cache
_build
/.idea
.cache
_local_tmp
**/.vscode
\ No newline at end of file
**/.vscode
doc/bibtex.json
/html_doc
\ No newline at end of file
......@@ -18,6 +18,8 @@ tests-and-coverage:
- echo "backend:template" > ~/.config/matplotlib/matplotlibrc
- mkdir public
- pip install git+https://gitlab-ci-token:${CI_JOB_TOKEN}@i10git.cs.fau.de/pycodegen/pystencils.git@master#egg=pystencils
- env
- pip list
- py.test -v -n $NUM_CORES --cov-report html --cov-report term --cov=. -m "not longrun"
tags:
- docker
......@@ -76,6 +78,8 @@ ubuntu:
- mkdir -p ~/.config/matplotlib
- echo "backend:template" > ~/.config/matplotlib/matplotlibrc
- pip3 install git+https://gitlab-ci-token:${CI_JOB_TOKEN}@i10git.cs.fau.de/pycodegen/pystencils.git@master#egg=pystencils
- env
- pip3 list
- pytest-3 -v -m "not longrun"
tags:
- docker
......
......@@ -62,11 +62,11 @@
plt.boundary_handling(sc1.boundary_handling, make_slice[0.5, :, :])
```
%%%% Output: display_data
![](data:image/png;base64,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)
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95z+JVq1Z9/61vfesDSXLttdc+cddtfvVXf/WHSX440ODT5Io+AAAAB7RRRv509zd37tz2tre9bXLNmjVH7/rYrbfeOv/UU089/vjjjz/h1FNPPf62226bnySbN29+wrHHHvvjR7dbsWLFll2f+wd/8AdPe9vb3rY4Sc4888wlb3nLWxafcsopy5YsWXLS5Zdffvhwf7IdhD4AAADsxm/91m9tvuKKK46877775u68/td//dcXv+Utb7nv1ltv/e6b3/zm+84777xFSfKe97zn+6effvrxL3vZy5574YUXPv3ee++du/s9/4u77rprwbXXXnvLn//5n992/vnnH/vwww/XsHMLfQAAANiNI488cvtZZ51130c/+tGn77z++uuvf9LKlSvvT5Lzzjvv/uuuu+7JSfLe9773vhtvvHH9m970pvuvueaaw174whc+b8uWLY8Z7meeeeb9c+fOzQte8IKtixYt2nrDDTccMuzcQh8AAAD24EMf+tD3P/e5zx310EMPTauflyxZ8pPzzz//vq997Wv/b968eZmYmPiZ9+nvrKoec3kQQh8AAAD24Oijj37kl3/5l3/wuc997qhH15188skPXXTRRUckyac+9akjx8fHH0ySL3zhC0/ZunVrJcmdd94574EHHpi783v2d+eKK6444pFHHsn69esX3HXXXQuWL1/+z8PO7K77AAAA8Bg+/OEPb7r00kvHHl3+5Cc/eee555675BOf+MQxT3va07Z99rOfvSNJvvrVrz7l/e9//+IFCxZsT5ILL7xw4+LFi7d95zvf2eO+jzvuuK0rVqxYdt999z3h4x//+D8ceuihbdh5hT4AAAAHtAULFmwb9cfr7W2bhx9++PpHv1+0aNG2LVu2/HR52bJlP/7mN795667PueiiizYm2bjr+jPOOONHZ5xxxo+SZNWqVfclue/Rx1760pc+ePHFF9818z/Fngl9AAAADmh7+8x7/jWhDwAAALPgi1/84h37Yr9uxgcAAAAdEfoAAAAcaLZv3759+M+Z69TU3832PT0u9AEAADjQ3DQ5OXm42P9Z27dvr8nJycOT3LSnbbxHHwAAgAPKtm3b3rVp06aLNm3adFJcoN7V9iQ3bdu27V172kDoAwAAcEA55ZRTNid5/WzPcbDyLyMAAADQEaEPAAAAHRH6AAAA0BGhDwAAAB0R+gAAANARoQ8AAAAdEfoAAADQkaFCv6qeWlVfqKrvVdXNVXXqqAYDAAAAZm7ekM//RJKvttb+XVXNT3LoCGYCAAAABjRw6FfVU5K8LMnbk6S19uMkPx7NWAAAAMAghnnp/tIkk0k+XVXXV9VFVfWkXTeqqpVVNVFVE5OTk0McDgAAANibYUJ/XpJ/k+STrbWTkzyU5IO7btRaW9taG2+tjY+NjQ1xOAAAAGBvhgn9jUk2tta+NbX8hewIfwAAAGCWDBz6rbVNSe6qqmVTq16V5LsjmQoAAAAYyLB33f+NJJdN3XF/Q5J3DD8SAAAAMKihQr+1dkOS8RHNAgAAAAxpmPfoAwAAAAcYoQ8AAAAdEfoAAADQkWFvxgfQrdVL7x7JftZsWDiS/QAHl1H9DgGAmXJFHwAAADoi9AEAAKAjQh8AAAA6IvQBAACgI0IfAAAAOiL0AQAAoCNCHwAAADoi9AEAAKAjQh8AAAA6IvQBAACgI0IfAAAAOiL0AQAAoCNCHwAAADoi9AEAAKAjQh8AAAA6IvQBAACgI0IfAAAAOiL0AQAAoCNCHwAAADoi9AEAAKAjQh8AAAA6IvQBAACgI0IfAAAAOjJ06FfV3Kq6vqquHMVAAAAAwOBGcUX/vUluHsF+AAAAgCENFfpV9awkr0ty0WjGAQAAAIYx7BX9jyf57STb97RBVa2sqomqmpicnBzycAAAAMBjGTj0q+qMJJtba9c91nattbWttfHW2vjY2NighwMAAACmYZgr+i9J8vqquiPJ55O8sqr+50imAgAAAAYycOi31j7UWntWa21JkrOT/J/W2ltHNhkAAAAwY6O46z4AAABwgJg3ip201v46yV+PYl8AAADA4FzRBwAAgI4IfQAAAOiI0AcAAICOjOQ9+gDs2eqld49kP2s2LBzJfoA9G9XPKwDMJlf0AQAAoCNCHwAAADoi9AEAAKAjQh8AAAA6IvQBAACgI0IfAAAAOiL0AQAAoCNCHwAAADoi9AEAAKAjQh8AAAA6IvQBAACgI0IfAAAAOiL0AQAAoCNCHwAAADoi9AEAAKAjQh8AAAA6IvQBAACgI0IfAAAAOjJvtgcAYHpWL717ZPtas2HhyPYFB4JR/nwAwMHOFX0AAADoiNAHAACAjgh9AAAA6IjQBwAAgI4MHPpVtaiqvl5VN1fV+qp67ygHAwAAAGZumLvub0vym621b1fVYUmuq6qrWmvfHdFsAAAAwAwNfEW/tXZPa+3bU9//KMnNSXxeEwAAAMyikbxHv6qWJDk5ybdGsT8AAABgMEOHflU9OckXk5zfWvun3Ty+sqomqmpicnJy2MMBAAAAj2Go0K+qJ2RH5F/WWrtid9u01ta21sZba+NjY2PDHA4AAADYi2Huul9JLk5yc2vt90c3EgAAADCoYa7ovyTJv0/yyqq6Yeq/00c0FwAAADCAgT9er7X2f5PUCGcBAAAAhjSSu+4DAAAABwahDwAAAB0R+gAAANARoQ8AAAAdGfhmfAAcvFYvvXu2R/hX1mxYONsjMEMH2jkEAPwLV/QBAACgI0IfAAAAOiL0AQAAoCNCHwAAADoi9AEAAKAjQh8AAAA6IvQBAACgI0IfAAAAOiL0AQAAoCNCHwAAADoi9AEAAKAjQh8AAAA6IvQBAACgI0IfAAAAOiL0AQAAoCNCHwAAADoi9AEAAKAj82Z7AABYvfTu2R4BAKAbrugDAABAR4Q+AAAAdEToAwAAQEeEPgAAAHRkqNCvqtOq6paqur2qPjiqoQAAAIDBDBz6VTU3yR8m+aUkJyQ5p6pOGNVgAAAAwMwNc0V/RZLbW2sbWms/TvL5JG8YzVgAAADAIIYJ/YVJ7tppeePUOgAAAGCWDBP6tZt17Wc2qlpZVRNVNTE5OTnE4QAAAIC9GSb0NyZZtNPys5L8464btdbWttbGW2vjY2NjQxwOAAAA2JthQv/vkjy3qp5dVfOTnJ3ky6MZCwAAABjEvEGf2FrbVlX/Icn/SjI3ySWttfUjmwwAAACYsYFDP0laa19J8pURzQIAAAAMaZiX7gMAAAAHGKEPAAAAHRH6AAAA0BGhDwAAAB2p1tr+O1jVZJJ/2G8HZJSOSnLvbA8BI+ScpkfOa3rjnKY3j4dz+tjW2thsD/F4t19Dn4NXVU201sZnew4YFec0PXJe0xvnNL1xTrO/eOk+AAAAdEToAwAAQEeEPtO1drYHgBFzTtMj5zW9cU7TG+c0+4X36AMAAEBHXNEHAACAjgh9HlNVnVVV66tqe1WN7/LYh6rq9qq6pap+cbZmhJmqqtOmztvbq+qDsz0PzFRVXVJVm6vqpp3WHVlVV1XVbVNfj5jNGWEmqmpRVX29qm6e+v+O906td15zUKqqQ6rq2qpaN3VOXzi13jnNfiH02ZubkrwpyTU7r6yqE5KcneTEJKcl+e9VNXf/jwczM3We/mGSX0pyQpJzps5nOJh8Jjt+9+7sg0m+1lp7bpKvTS3DwWJbkt9srT0/yYuSvGfqd7PzmoPV1iSvbK0tT/LzSU6rqhfFOc1+IvR5TK21m1trt+zmoTck+XxrbWtr7e+T3J5kxf6dDgayIsntrbUNrbUfJ/l8dpzPcNBorV2T5P5dVr8hyaVT31+a5Ff261AwhNbaPa21b099/6MkNydZGOc1B6m2w4NTi0+Y+q/FOc1+IvQZ1MIkd+20vHFqHRzonLv06ujW2j3JjmhK8vRZngcGUlVLkpyc5FtxXnMQq6q5VXVDks1JrmqtOafZb+bN9gDMvqr630mO2c1DH26t/dmenrabdT7CgYOBcxfgAFVVT07yxSTnt9b+qWp3v7Lh4NBaeyTJz1fVU5N8qapOmu2ZePwQ+qS19uoBnrYxyaKdlp+V5B9HMxHsU85devX9qnpGa+2eqnpGdlxBgoNGVT0hOyL/stbaFVOrndcc9FprD1TVX2fHvVWc0+wXXrrPoL6c5OyqWlBVz07y3CTXzvJMMB1/l+S5VfXsqpqfHTeV/PIszwSj8OUk5059f26SPb0iCw44tePS/cVJbm6t/f5ODzmvOShV1djUlfxU1ROTvDrJ9+KcZj+p1rxilT2rqjcm+a9JxpI8kOSG1tovTj324SS/lh13yj2/tfaXszYozEBVnZ7k40nmJrmktfafZnkkmJGqujzJLyQ5Ksn3k3wkyZ8m+ZMki5PcmeSs1tquN+yDA1JVvTTJN5LcmGT71OrV2fE+fec1B52q+rnsuNne3Oy4uPonrbXfqaqnxTnNfiD0AQAAoCNeug8AAAAdEfoAAADQEaEPAAAAHRH6AAAA0BGhDwAAAB0R+gAAANARoQ8AAAAdEfoAAADQkf8PB4v6pTw+KfoAAAAASUVORK5CYII=)
%% Cell type:markdown id: tags:
Now the setup is complete. We can run it and look at the velocity profile in the pipe.
......@@ -77,19 +77,21 @@
plt.scalar_field(sc1.velocity[domain_size[0] // 2, :, :, 0]);
```
%%%% Output: display_data
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)
![](data:image/png;base64,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)
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## Boundary Setup
Now instead of creating a periodic, force driven channel, we want to drive the flow with a velocity bounce back boundary condition (UBB) at the inlet and a pressure boundary at the outlet. We want the inflow velocity boundary set up to already prescribe the correct, parabolic flow profile. That means we need a different velocity value at each cell.
Now instead of creating a periodic, force driven channel, we want to drive the flow with a velocity bounce back boundary condition (UBB) at the inlet and a outflow boundary at the outlet. We want the inflow velocity boundary set up to already prescribe the correct, parabolic flow profile. That means we need a different velocity value at each cell. The outflow boundary condition takes the following form:
$$ f_{\overline{1}jkxyzt} = f_{\overline{1}jk(x - \Delta x)yz(t - \Delta t)} \left(c \theta^{\frac{1}{2}} -u \right) \frac{\Delta t}{\Delta x} + \left(1 - \left(c \theta^{\frac{1}{2}} -u \right) \frac{\Delta t}{\Delta x} \right) f_{\overline{1}jk(x - \Delta x)yzt}$$
More information on the outflow condition can be found in appendix F in https://doi.org/10.1016/j.camwa.2015.05.001
Again, we set up a scenario, but this time without external force and without periodicity.
Again, we set up a scenario, but this time without external force and without periodicity.
%% Cell type:code id: tags:
``` python
sc2 = LatticeBoltzmannStep(domain_size=domain_size, method='srt', relaxation_rate=1.9,
......@@ -125,19 +127,21 @@
else:
boundary_data['vel_0'] = 0
inflow = UBB(velocity_info_callback, dim=sc2.method.dim)
outflow = FixedDensity(1.0)
stencil = get_stencil('D3Q27')
outflow = ExtrapolationOutflow(stencil[4], sc2.method)
sc2.boundary_handling.set_boundary(inflow, make_slice[0, :, :])
sc2.boundary_handling.set_boundary(outflow, make_slice[-1, :, :])
```
%%%% Output: execute_result
512
4
%% Cell type:markdown id: tags:
Lastly we can use the callback function from above to set the pipe geometry. This is intentionally done at the end of the setup to overwrite the in- and outflow boundaries in the outermost slices.
......@@ -147,11 +151,11 @@
sc2.boundary_handling.set_boundary(wall, mask_callback=pipe_geometry_callback)
```
%%%% Output: execute_result
32
8
%% Cell type:markdown id: tags:
To see the full setup, a few slices through the domain are plotted
......@@ -159,29 +163,29 @@
``` python
plt.rc('figure', figsize=(14, 8))
plt.subplot(231)
plt.boundary_handling(sc2.boundary_handling, make_slice[-1, :, :], show_legend=False)
plt.boundary_handling(sc2.boundary_handling, make_slice[0, :, :], show_legend=False)
plt.title('Inflow')
plt.subplot(232)
plt.boundary_handling(sc2.boundary_handling, make_slice[0.5, :, :], show_legend=False)
plt.title('Middle')
plt.subplot(233)
plt.boundary_handling(sc2.boundary_handling, make_slice[0, :, :], show_legend=False)
plt.boundary_handling(sc2.boundary_handling, make_slice[-1, :, :], show_legend=False)
plt.title('Outflow')
plt.subplot(212)
plt.boundary_handling(sc2.boundary_handling, make_slice[:, 0.5, :], show_legend=True)
plt.title('Cross section');
```
%%%% Output: display_data
![](data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAA6QAAAHiCAYAAAD/IQGFAAAABHNCSVQICAgIfAhkiAAAAAlwSFlzAAALEgAACxIB0t1+/AAAADl0RVh0U29mdHdhcmUAbWF0cGxvdGxpYiB2ZXJzaW9uIDIuMS4xLCBodHRwOi8vbWF0cGxvdGxpYi5vcmcvAOZPmwAAIABJREFUeJzs3Xt4VfWd9v/7JuEggnggIiIQAQMCFh0iTy1Uq1alHtv6a0VrEccRtFrbqq2Hdmydx3G01aeHsY8FFdGpxfbnYWppp5XaFqr1MEFBOShYinKUAAIiFAn5PH9kx4kxIcnea7Oyd96v6+LK3mt991qflZ3rQ+5811rbESEAAAAAAPa2TmkXAAAAAADomAikAAAAAIBUEEgBAAAAAKkgkAIAAAAAUkEgBQAAAACkgkAKAAAAAEgFgRTNst3H9lzb79i+0/Z3bP807boAFAbbP7H9z3tYH7aHNLNuku2nWzMWACTJ9mdsr7S9zfYxtlfY/mTadQHYMwJpB9SGBj1Z0gZJ+0XENXkuC0AByfSR92z3brR8fiY8lkfEZRHxv9OqEUD7lvnD0yu2t9teZ/tu2/u38rVN/S5zh6QrI6JHRLyUfMUA8oFAij0ZKGlxRETahQBol/4m6fz6J7aPkrRPeuUAKBS2r5F0u6SvS+ol6aOq+71jtu0uWW52oKRFyVQIYG8hkHZg9afE2b7D9tu2/2b7U5l1MyRdJOkbmVNfPjSjavts24tsb7b9J9tHZpZfbPtXDca9bvsXDZ6vtH103g8QQL79h6SJDZ5fJOnB+ie2Z9i+pcHzr9tea3uN7X9suCHbB9l+wvZW2y9IGtzcTm13zfStN22/lTk1mCAMFAjb+0m6WdKXI+K3EbErIlZI+rzqQuWFTfSPT9helXn8H5IGSPpV5neU62xvk1QiaYHtvzaxz662f5DpP2syj7tm1s2xfW7m8bjMWR6nZ55/0vb8fH4/gI6OQIr/Jek1Sb0lfVfSfbYdEZMkPSTpu5lTX37f8EW2KyTNlPRVSWWSfqO6/xi6SJoj6eO2O9nuK6mzpLGZ1w2S1EPSy3vj4ADk1XOS9rN9pO0SSedJavI6c9vjJV0r6RRJR0hq/EeuH0v6u6S+kv4x8685t0uqkHS0pCGS+km6KfvDALCXfUxSN0mPNVwYEdsk/Zfq+kSzIuKLkt6UdFbmd5TbI6JHZvWoiGjqD1rfVN0s7NGSRkkaI+lbmXVzJH0i8/h4ScslndDg+ZxWHxmANiOQ4o2IuCcidkt6QHW/DPZpxevOk/TriJgdEbtUd93GPpI+FhHLJb2juqZ/gqTfSVpte1jm+Z8jojYPxwJg76ufJT1F0quSVjcz7vOS7o+IhRHxrqTv1K/IhNlzJd0UEe9GxELV9aMPsW1Jl0r6WkRsioh3JN0qaUJCxwMg/3pL2hARNU2sW5tZn7QvSPqXiFgfEdWqm6H9YmbdHH0wgP5bg+cniEAK5FVp2gUgdevqH0TE9rrf9dSj+eHvO1TSGw1eW2t7pepmKqT/+WvjkMzjzapr6seJxg4Uk/+QNFfS4Wpwum4TDpU0r8HzNxo8LlPd/0crm1mvRmO7S5qX6VeSZNWdqgegMGyQ1Nt2aROhtG9mfdI+8HtL5vGhmcfPSqqw3Ud1f0w/W9LNmZu2jVFdjwOQJ8yQIltrVHedh6T3Zy36639mR+oD6cczj+v/+shfGoEiEhFvqO7mRqer0el3jaxVXY+oN6DB42pJNXtY39AGSTskjYiI/TP/ejU4XQ9A+/espJ2SPttwoe19JX1K0lOS3lXdH5/qHdJoG2294eIHfm9RXY9ZI9X9QV51fzD7iqSFEfGepL9IulrSXyMiHwEZQAaBFNn6haQzbJ9su7Oka1T3n8tfMuvnSDpR0j4RsUrSnyWNl3SQJG7FDhSXSySdlDkVtzm/kDTJ9nDb3SV9u35F5pKBxyR9x3Z328NVd4OkD8mc7n+PpO/bPliSbPezfVpCxwIgzyJii+pOmf132+Ntd7ZdLun/l7RKdWdezJd0uu0DbR+iuntWNPSWpEFt2O1MSd+yXZaZ+bxJH7zmfY6kK/U/fzT/U6PnAPKEQIqsRMRrki6U9O+qm7E4S3U3F3gvs36ppG2qC6KKiK2qu0nAM5lfPgEUiYj4a0RUtTDmvyT9QNIfJL2e+drQlaq7XGCdpBmS7t/D5q7LbOM521sl/V7S0KyKB5CKiPiupBtVdw+KrZKeV91p+ydHxE7VhdIFklZIelLSzxtt4t9UFzA32762Fbu8RVKV6m6q+IqkFzPL6s2R1FP/c3pu4+cA8sR8xCQAAAAAIA3MkAIAAAAAUkEgBQAAAACkgkAKAAAAAEgFgRQAAAAAkAoCKQAAAAAgFaV7c2e9e/eO8vLyrF9fXV2dXDFAkSgrK8vp9fPmzdsQEbltJAX0EyB5ufQTegmAeh31dxNkZ68G0vLyclVV7fGj6vZo2rRpCVYDFIfJkyfn9HrbbyRUyl5FPwGSl0s/oZcAqNdRfzdBdjhlFwAAAACQCgIpAAAAACAVBFIAAAAAQCoIpAAAAACAVBBIAQAAAACpIJACAAAAAFJBIAUAAAAApIJACgAAAABIBYEUAAAAAJCK0rQLQNtN6bw07RLaham7KtIuASh4ty7vl3YJ7cKNg1anXQJQ0MY9MyXtEtqFp8dOTbsEoOAwQwoAAAAASEWLgdT2dNvrbS9stPzLtl+zvcj2d/NXIoBiQT8BkBT6CQAUh9bMkM6QNL7hAtsnSjpH0kciYoSkO5IvDUARmiH6CYBkzBD9BAAKXouBNCLmStrUaPHlkm6LiJ2ZMevzUBuAIkM/AZAU+gkAFIdsryGtkPRx28/bnmP72OYG2p5su8p2VXV1dZa7A1DE6CcAktKqfkIvAYD2I9tAWirpAEkflfR1Sb+w7aYGRsS0iKiMiMqysrIsdwegiNFPACSlVf2EXgIA7Ue2gXSVpMeizguSaiX1Tq4sAB0I/QRAUugnAFBgsg2k/ynpJEmyXSGpi6QNSRUFoEOhnwBICv0EAApMaUsDbM+U9AlJvW2vkvRtSdMlTc/cav09SRdFROSzUACFj34CICn0EwAoDi0G0og4v5lVFyZcC4AiRz8BkBT6CQAUhxYDKbI3pfPStEsoavn6/k7dVZGX7QK5uHV5v7RLKGr5+v7eOGh1XrYLZGvcM1PSLqGo5ev7+/TYqXnZLtAeZHsNKQAAAAAAOSGQAgAAAABSQSAFAAAAAKSCQAoAAAAASAWBFAAAAACQCgIpAAAAACAVBFIAAAAAQCoIpAAAAACAVBBIAQAAAACpIJACAAAAAFJRmnYBhWZK56Vpl4A8a8t7PHVXRR4rQbG7dXm/tEtAnrXlPb5x0Oo8VoJiNu6ZKWmXgDxry3v89NipeawESB4zpAAAAACAVLQYSG1Pt73e9sIm1l1rO2z3zk95AIoJ/QRAUugnAFAcWjNDOkPS+MYLbfeXdIqkNxOuCUDxmiH6CYBkzBD9BAAKXouBNCLmStrUxKrvS/qGpEi6KADFiX4CICn0EwAoDlldQ2r7bEmrI2JBK8ZOtl1lu6q6ujqb3QEoYvQTAElpbT+hlwBA+9HmQGq7u6RvSrqpNeMjYlpEVEZEZVlZWVt3B6CI0U8AJKUt/YReAgDtRzYzpIMlHS5pge0Vkg6T9KLtQ5IsDECHQD8BkBT6CQAUoDZ/DmlEvCLp4PrnmaZfGREbEqwLQAdAPwGQFPoJABSm1nzsy0xJz0oaanuV7UvyXxaAYkQ/AZAU+gkAFIcWZ0gj4vwW1pcnVg2AokY/AZAU+gkAFIc2n7JbjKZ0Xpp2CShQbfnZmbqrIo+VoL24dXm/tEtAgWrLz86Ng1bnsRK0B+OemZJ2CShQbfnZeXrs1DxWArROVh/7AgAAAABArgikAAAAAIBUEEgBAAAAAKkgkAIAAAAAUkEgBQAAAACkgkAKAAAAAEgFgRQAAAAAkAoCKQAAAAAgFQRSAAAAAEAqCKQAAAAAgFQQSAEAAAAAqSCQAgAAAABS0WIgtT3d9nrbCxss+57tV22/bPtx2/vnt0wAxYB+AiAp9BMAKA6tmSGdIWl8o2WzJY2MiI9IWirphoTrAlCcZoh+AiAZM0Q/AYCC12IgjYi5kjY1WvZkRNRknj4n6bA81AagyNBPACSFfgIAxSGJa0j/UdJ/NbfS9mTbVbarqqurE9gdgCJGPwGQlGb7Cb0EANqPnAKp7W9KqpH0UHNjImJaRFRGRGVZWVkuuwNQxOgnAJLSUj+hlwBA+1Ga7QttXyTpTEknR0QkVxKAjoZ+AiAp9BMAKCxZBVLb4yVdJ+mEiNiebEkAOhL6CYCk0E8AoPC05mNfZkp6VtJQ26tsXyLpLkk9Jc22Pd/2T/JcJ4AiQD8BkBT6CQAUhxZnSCPi/CYW35eHWgAUOfoJgKTQTwCgOGR9DWl7N6Xz0rRLAD6gLT+TU3dV5LEStNWty/ulXQLwAW35mbxx0Oo8VoK2GPfMlLRLAD6gLT+TT4+dmsdK0JEl8bEvAAAAAAC0GYEUAAAAAJAKAikAAAAAIBUEUgAAAABAKgikAAAAAIBUEEgBAAAAAKkgkAIAAAAAUkEgBQAAAACkgkAKAAAAAEgFgRQAAAAAkAoCKQAAAAAgFQRSAAAAAEAqWgyktqfbXm97YYNlB9qebXtZ5usB+S0TQDGgnwBICv0EAIpDa2ZIZ0ga32jZ9ZKeiogjJD2VeQ4ALZkh+gmAZMwQ/QQACl6LgTQi5kra1GjxOZIeyDx+QNKnE64LQBGinwBICv0EAIpDtteQ9omItZKU+XpwcwNtT7ZdZbuquro6y90BKGL0EwBJaVU/oZcAQPuR95saRcS0iKiMiMqysrJ87w5AEaOfAEgCvQQA2o9sA+lbtvtKUubr+uRKAtDB0E8AJIV+AgAFJttA+oSkizKPL5L0y2TKAdAB0U8AJIV+AgAFpjUf+zJT0rOShtpeZfsSSbdJOsX2MkmnZJ4DwB7RTwAkhX4CAMWhtKUBEXF+M6tOTrgWAEWOfgIgKfQTACgOeb+pEQAAAAAATSGQAgAAAABSQSAFAAAAAKSCQAoAAAAASAWBFAAAAACQCgIpAAAAACAVBFIAAAAAQCoIpAAAAACAVBBIAQAAAACpIJACAAAAAFJBIAUAAAAApIJACgAAAABIBYEUAAAAAJCKnAKp7a/ZXmR7oe2ZtrslVRiAjoV+AiAp9BMAKBxZB1Lb/SRdJakyIkZKKpE0IanCAHQc9BMASaGfAEBhyfWU3VJJ+9guldRd0prcSwLQQdFPACSFfgIABSLrQBoRqyXdIelNSWslbYmIJxuPsz3ZdpXtqurq6uwrBVC06CcAktKafkIvAYD2I5dTdg+QdI6kwyUdKmlf2xc2HhcR0yKiMiIqy8rKsq8UQNGinwBISmv6Cb0EANqPXE7Z/aSkv0VEdUTskvSYpI8lUxaADoZ+AiAp9BMAKCC5BNI3JX3UdnfblnSypCXJlAWgg6GfAEgK/QQACkgu15A+L+kRSS9KeiWzrWkJ1QWgA6GfAEgK/QQACktpLi+OiG9L+nZCtQDowOgnAJJCPwGAwpHrx74AAAAAAJAVAikAAAAAIBUEUgAAAABAKgikAAAAAIBUEEgBAAAAAKkgkAIAAAAAUkEgBQAAAACkgkAKAAAAAEgFgRQAAAAAkAoCKQAAAAAgFQRSAAAAAEAqCKQAAAAAgFTkFEht72/7Eduv2l5i+7ikCgPQsdBPACSFfgIAhaM0x9f/UNJvI+L/s91FUvcEagLQMdFPACSFfgIABSLrQGp7P0nHS5okSRHxnqT3kikLQEdCPwGQFPoJABSWXE7ZHSSpWtL9tl+yfa/tfROqC0DHQj8BkBT6CQAUkFwCaamkf5B0d0QcI+ldSdc3HmR7su0q21XV1dU57A5AEaOfAEhKi/2EXgIA7UcugXSVpFUR8Xzm+SOq+w/gAyJiWkRURkRlWVlZDrsDUMToJwCS0mI/oZcAQPuRdSCNiHWSVtoemll0sqTFiVQFoEOhnwBICv0EAApLrnfZ/bKkhzJ3sFsu6eLcSwLQQdFPACSFfgIABSKnQBoR8yVVJlQLgA6MfgIgKfQTACgcuVxDCgAAAABA1nI9ZbfdmrqrotVjp3RemsdKgDpt+ZlE+3LjoNWtHnvr8n55rASo05afSbQfT4+d2uqx456ZksdKgDpt+ZkE8oUZUgAAAABAKgikAAAAAIBUEEgBAAAAAKkgkAIAAAAAUkEgBQAAAACkgkAKAAAAAEgFgRQAAAAAkAoCKQAAAAAgFQRSAAAAAEAqCKQAAAAAgFQQSAEAAAAAqcg5kNousf2S7VlJFASg46KfAEgK/QQACkMSM6RfkbQkge0AAP0EQFLoJwBQAHIKpLYPk3SGpHuTKQdAR0U/AZAU+gkAFI5cZ0h/IOkbkmoTqAVAx0Y/AZAU+gkAFIisA6ntMyWtj4h5LYybbLvKdlV1dXW2uwNQxOgnAJLSmn5CLwGA9iOXGdKxks62vULSw5JOsv3TxoMiYlpEVEZEZVlZWQ67A1DE6CcAktJiP6GXAED7kXUgjYgbIuKwiCiXNEHSHyLiwsQqA9Bh0E8AJIV+AgCFhc8hBQAAAACkojSJjUTEnyT9KYltAejY6CcAkkI/AYD2jxlSAAAAAEAqEpkhLXRTd1W0euyUzkvzWAkKTVt+dtAx3DhodavH3rq8Xx4rQaFpy88Oit/TY6e2euy4Z6bksRIUmrb87ADtATOkAAAAAIBUEEgBAAAAAKkgkAIAAAAAUkEgBQAAAACkgkAKAAAAAEgFgRQAAAAAkAoCKQAAAAAgFQRSAAAAAEAqCKQAAAAAgFQQSAEAAAAAqShNu4BCM3VXRavHTum8NI+VIF/a8h4Dubhx0OpWj711eb88VoJ8act7DGTr6bFTWz123DNT8lgJ8qUt7zFQaLKeIbXd3/YfbS+xvcj2V5IsDEDHQT8BkBT6CQAUllxmSGskXRMRL9ruKWme7dkRsTih2gB0HPQTAEmhnwBAAcl6hjQi1kbEi5nH70haIolzygC0Gf0EQFLoJwBQWBK5qZHtcknHSHo+ie0B6LjoJwCSQj8BgPYv50Bqu4ekRyV9NSK2NrF+su0q21XV1dW57g5AEaOfAEjKnvoJvQQA2o+cAqntzqpr9g9FxGNNjYmIaRFRGRGVZWVluewOQBGjnwBISkv9hF4CAO1HLnfZtaT7JC2JiP+TXEkAOhr6CYCk0E8AoLDkMkM6VtIXJZ1ke37m3+kJ1QWgY6GfAEgK/QQACkjWH/sSEU9LcoK1AOig6CcAkkI/AYDCkshddgEAAAAAaKusZ0jRsqm7KvKy3Smdl+Zlu4UmX99foD26cdDqvGz31uV8PKOUv+8v0N48PXZqXrY77pkpedluocnX9xcoZsyQAgAAAABSQSAFAAAAAKSCQAoAAAAASAWBFAAAAACQCgIpAAAAACAVBFIAAAAAQCoIpAAAAACAVBBIAQAAAACpIJACAAAAAFJBIAUAAAAApKI07QLQdlN3VaRdAoAiceOg1WmXAKAIPD12atolAChQOc2Q2h5v+zXbr9u+PqmiAHQ89BMASaGfAEDhyDqQ2i6R9GNJn5I0XNL5tocnVRiAjoN+AiAp9BMAKCy5zJCOkfR6RCyPiPckPSzpnGTKAtDB0E8AJIV+AgAFJJdA2k/SygbPV2WWAUBb0U8AJIV+AgAFJJdA6iaWxYcG2ZNtV9muqq6uzmF3AIoY/QRAUlrsJ/QSAGg/cgmkqyT1b/D8MElrGg+KiGkRURkRlWVlZTnsDkARo58ASEqL/YReAgDtRy6B9L8lHWH7cNtdJE2Q9EQyZQHoYOgnAJJCPwGAApL155BGRI3tKyX9TlKJpOkRsSixygB0GPQTAEmhnwBAYck6kEpSRPxG0m8SqgVAB0Y/AZAU+gkAFI5cTtkFAAAAACBrjvjQjSzztzO7WtIbCW+2t6QNCW+zveDYClOhHdvAiCi4u3rQT9qMYytMhXRs9JIPKqT3rq04tsJUSMdWkP0E2dmrgTQfbFdFRGXadeQDx1aYivnYil0xv3ccW2Eq5mMrdsX83nFshamYjw2FjVN2AQAAAACpIJACAAAAAFJRDIF0WtoF5BHHVpiK+diKXTG/dxxbYSrmYyt2xfzecWyFqZiPDQWs4K8hBQAAAAAUpmKYIQUAAAAAFKCCDqS2x9t+zfbrtq9Pu54k2V5h+xXb821XpV1PLmxPt73e9sIGyw60Pdv2sszXA9KsMVvNHNt3bK/OvHfzbZ+eZo1oHfpJYaCf0E/aO3pJ4SjWfkIvQaEp2EBqu0TSjyV9StJwSefbHp5uVYk7MSKOLoJbdM+QNL7RsuslPRURR0h6KvO8EM3Qh49Nkr6fee+Ojojf7OWa0Eb0k4IyQ/QTtFP0koIzQ8XZT2aIXoICUrCBVNIYSa9HxPKIeE/Sw5LOSbkmNCEi5kra1GjxOZIeyDx+QNKn92pRCWnm2FB46CcFgn6Cdo5eUkCKtZ/QS1BoCjmQ9pO0ssHzVZllxSIkPWl7nu3JaReTB30iYq0kZb4enHI9SbvS9suZ02YK7nSfDoh+UtjoJ2gv6CWFr5j7Cb0E7VIhB1I3sayYbhk8NiL+QXWn/Vxh+/i0C0Kr3S1psKSjJa2VdGe65aAV6Cdor+gnhYVegvaKXoJ2q5AD6SpJ/Rs8P0zSmpRqSVxErMl8XS/pcdWdBlRM3rLdV5IyX9enXE9iIuKtiNgdEbWS7lHxvXfFiH5S2OgnaC/oJYWvKPsJvQTtWSEH0v+WdITtw213kTRB0hMp15QI2/va7ln/WNKpkhbu+VUF5wlJF2UeXyTplynWkqj6/8gyPqPie++KEf2ksNFP0F7QSwpfUfYTegnas9K0C8hWRNTYvlLS7ySVSJoeEYtSLispfSQ9bluqe49+FhG/Tbek7NmeKekTknrbXiXp25Juk/QL25dIelPS59KrMHvNHNsnbB+tutO0VkiaklqBaBX6SeGgn9BP2jN6SWEp1n5CL0GhcUQxXdoAAAAAACgUhXzKLgAAAACggBFIAQAAAACpIJACAAAAAFJBIAUAAAAApIJACgAAAABIBYEUAAAAAJAKAikAAAAAIBUEUgBAUbL9E9v/nHYdAACgeQRSAOgAbF9gu8r2Nttrbf+X7XFp15UU25NsP91wWURcFhH/O62aAABAywikAFDkbF8t6QeSbpXUR9IASf9X0jnNjC/de9UBAICOjEAKAEXMdi9J/yLpioh4LCLejYhdEfGriPh6Zsx3bD9i+6e2t0qaZLur7R/YXpP59wPbXTPje9ueZXuz7U22/2y7U2bddbZX237H9mu2T26mrtNtL86MW2372gbrzrQ9P7P9v9j+SIN1/W0/Zrva9kbbd9k+UtJPJB2XmQHenBk7w/YtDV57qe3XMzU/YfvQBuvC9mW2l9l+2/aPbTvBtwIAADSBQAoAxe04Sd0kPd7CuHMkPSJpf0kPSfqmpI9KOlrSKEljJH0rM/YaSasklaluxvVGSWF7qKQrJR0bET0lnSZpRTP7u0/SlMy4kZL+IEm2/0HSdElTJB0kaaqkJzIBuUTSLElvSCqX1E/SwxGxRNJlkp6NiB4RsX/jndk+SdK/Sfq8pL6ZbTzcaNiZko7NHO/nM/UDAIA8IpACQHE7SNKGiKhpYdyzEfGfEVEbETskfUHSv0TE+oiolnSzpC9mxu5SXagbmJlt/XNEhKTdkrpKGm67c0SsiIi/NrO/XZlx+0XE2xHxYmb5pZKmRsTzEbE7Ih6QtFN14XiMpEMlfT0z0/v3iHi66c1/yBckTY+IFyNip6QbVDejWt5gzG0RsTki3pT0R9WFcQAAkEcEUgAobhsl9W7FdaErGz0/VHWziPXeyCyTpO9Jel3Sk7aX275ekiLidUlflfQdSettP9zwtNhGzpV0uqQ3bM+xfVxm+UBJ12RO192cOf22f2bf/SW90Ypw3ZQPHE9EbFPd96ZfgzHrGjzeLqlHFvsBAABtQCAFgOL2rKS/S/p0C+Oi0fM1qguH9QZkliki3omIayJikKSzJF1df61oRPwsIsZlXhuSbm9yZxH/HRHnSDpY0n9K+kVm1UpJ/xoR+zf41z0iZmbWDWgmXDeuv7EPHI/tfVU3e7y6hdcBAIA8IpACQBGLiC2SbpL0Y9uftt3ddmfbn7L93T28dKakb9kus907s42fSu/fdGhI5qY/W1V3qu5u20Ntn5S5+dHfJe3IrPsA211sf8F2r4jY1WAbknSPpMts/y/X2df2GbZ7SnpB0lpJt2WWd7M9NvO6tyQdZrtLM8fzM0kX2z46U9+tkp6PiBWt+T4CAID8IJACQJGLiP8j6WrV3ZSoWnUzjVeqbmayObdIqpL0sqRXJL2YWSZJR0j6vaRtqpuB/b8R8SfVXT96m6QNqjv99WDV3fCoKV+UtCJzV9/LJF2YqbVKddeR3iXpbdWdGjwps2636mZkh0h6U3U3Vjovs70/SFokaZ3tDU18D56S9M+SHlVdqB0sacIejh8AAOwFrrsPBQAAAAAAexczpAAAAACAVBBIAQAAAACpIJACAAAAAFJBIAUAAAAApIJACgAAAABIRVMfLp43vXv3jvLy8r22v+rq6r22LwAAAKAYlZWV7dX9zZs3b0NE7N2dIjV7NZCWl5erqqpqr+1v2rRpe21fAAAAQDGaPHnyXt2f7Tf26g6RKk7ZBQAAAACkgkAKAAAAAEgFgRQAAAAAkAoCKQAAAAAgFQRSAAAAAEAqCKQAAAAAgFQQSAEAAAAAqSCQAgAAAABSQSAFAAAAAKSiNO0C8mncM1NaPfb0vrPyWAkAAADQfrwx9I+tHjs5j3UAzJACAAAAAFLRYiC1Pd32etsLGy3/su3XbC+y/d38lQgAAAAAKEatmSGdIWl8wwW2T5R0jqSPRMQISXckXxoAAAAAoJi1GEgjYq6kTY0WXy7ptojYmRmzPg+1AQAAAACKWLbXkFZI+rjt523PsX1skkUBAAAAAIpftnfZLZV0gKSPSjpW0i9sD4qIaDzQ9mRlbs41YMCAbOsEAAAAABSZbGdIV0l6LOq8IKlWUu+mBkbEtIj0EWmOAAAei0lEQVSojIjKsrKybOsEAAAAABSZbAPpf0o6SZJsV0jqImlDUkUBAAAAAIpfi6fs2p4p6ROSetteJenbkqZLmp75KJj3JF3U1Om6AAAAAAA0p8VAGhHnN7PqwoRrAQAAAAB0INmesgsAAAAAQE4IpAAAAACAVBBIAQAAAACpIJACAAAAAFJBIAUAAAAApIJACgAAAABIBYEUAAAAAJAKAikAAAAAIBUEUgAAAABAKgikAAAAAIBUEEgBAAAAAKkgkAIAAAAAUkEgBQAAAACkosVAanu67fW2Fzax7lrbYbt3fsoDAAAAABSr1syQzpA0vvFC2/0lnSLpzYRrAgAAAAB0AC0G0oiYK2lTE6u+L+kbkiLpogAAAAAAxS+ra0htny1pdUQsSLgeAAAAAEAHUdrWF9juLumbkk5t5fjJkiZL0oABA9q6OwAAAABAkcpmhnSwpMMlLbC9QtJhkl60fUhTgyNiWkRURkRlWVlZ9pUCAAAAAIpKm2dII+IVSQfXP8+E0sqI2JBgXQAAAACAIteaj32ZKelZSUNtr7J9Sf7LAgAAAAAUuxZnSCPi/BbWlydWDQAAAACgw8jqLrsAAAAAAOSKQAoAAAAASAWBFAAAAACQCgIpAAAAACAVBFIAAAAAQCoIpAAAAACAVBBIAQAAAACpIJACAAAAAFJBIAUAAAAApIJACgAAAABIBYEUAAAAAJAKAikAAAAAIBUEUgAAAABAKloMpLan215ve2GDZd+z/artl20/bnv//JYJAAAAACg2rZkhnSFpfKNlsyWNjIiPSFoq6YaE6wIAAAAAFLkWA2lEzJW0qdGyJyOiJvP0OUmH5aE2AAAAAEARS+Ia0n+U9F8JbAcAAAAA0IHkFEhtf1NSjaSH9jBmsu0q21XV1dW57A4AAAAAUESyDqS2L5J0pqQvREQ0Ny4ipkVEZURUlpWVZbs7AAAAAECRKc3mRbbHS7pO0gkRsT3ZkgAAAAAAHUFrPvZlpqRnJQ21vcr2JZLuktRT0mzb823/JM91AgAAAACKTIszpBFxfhOL78tDLQAAAACADiSJu+wCAAAAANBmBFIAAAAAQCoIpAAAAACAVBBIAQAAAACpIJACAAAAAFJBIAUAAAAApIJACgAAAABIBYEUAAAAAJAKAikAAAAAIBUEUgAAAABAKgikAAAAAIBUEEgBAAAAAKkgkAIAAAAAUtFiILU93fZ62wsbLDvQ9mzbyzJfD8hvmQAAAACAYtOaGdIZksY3Wna9pKci4ghJT2WeAwAAAADQai0G0oiYK2lTo8XnSHog8/gBSZ9OuC4AAAAAQJHL9hrSPhGxVpIyXw9ubqDtybarbFdVV1dnuTsAAAAAQLHJ+02NImJaRFRGRGVZWVm+dwcAAAAAKBDZBtK3bPeVpMzX9cmVBAAAAADoCLINpE9Iuijz+CJJv0ymHAAAAABAR9Gaj32ZKelZSUNtr7J9iaTbJJ1ie5mkUzLPAQAAAABotdKWBkTE+c2sOjnhWgAAAAAAHUjeb2oEAAAAAEBTCKQAAAAAgFQQSAEAAAAAqSCQAgAAAABSQSAFAAAAAKSCQAoAAAAASAWBFAAAAACQCgIpAAAAACAVBFIAAAAAQCoIpAAAAACAVBBIAQAAAACpKE27AAAAAABIyrx58w4uLS29V9JIMQGXtlpJC2tqav5p9OjR65saQCAFAAAAUDRKS0vvPeSQQ44sKyt7u1OnTpF2PR1ZbW2tq6urh69bt+5eSWc3NSanvxjY/prtRbYX2p5pu1su2wMAAACAHI0sKyvbShhNX6dOnaKsrGyL6marmx6T7cZt95N0laTKiBgpqUTShGy3BwAAAAAJ6EQYbT8y70WzuTPXc6pLJe1ju1RSd0lrctweAAAAABSNq6+++tCbbrqpT762f8IJJwzZsGFDSb62n29ZX0MaEatt3yHpTUk7JD0ZEU82Hmd7sqTJkjRgwIBsdwcAAAAAbXb0vzw5avP2XYndO2f/7p1r5t906oKktperOXPmvJ52DbnI5ZTdAySdI+lwSYdK2tf2hY3HRcS0iKiMiMqysrLsKwUAAACANkoyjLZ2e9ddd90h5eXlIz/2sY9VLFu2rKsk/eUvf9ln1KhRwyoqKoafcsopg6urq0skacyYMUMvueSS/pWVlUMHDRo0Ys6cOd1PPfXUwQMHDhx51VVXHVq/zU9+8pODR4wYceSQIUNG3HHHHb3rl/fr1++otWvXlr722mtdBg0aNGLChAkDhwwZMmLs2LFHbNu2zUkeez7kcsruJyX9LSKqI2KXpMckfSyZsgAAAACg8Pz5z3/u/vjjjx/4yiuvLJ41a9brCxYs2FeSJk2adPitt966aunSpYtHjBix47rrrns/bHbp0qW2qqrqtYsvvrj6c5/73JB77rnnzVdffXXRz3/+897r1q0rkaSHHnpoxaJFi5bMnz9/8dSpU/vUL2/ozTff7HbVVVetf/311xf16tVr94MPPnjA3jvy7OQSSN+U9FHb3W1b0smSliRTFgAAAAAUnj/+8Y89Tj/99M09e/asPfDAA2tPPfXUze+++26nd955p+SMM87YJkmXXnrpxueee65H/Ws+85nPbJakUaNG7RgyZMiOgQMH7tpnn32if//+O5cvX95Fkm6//fY+Q4cOHT569Ogj161b13nRokUf+oSTfv367fzYxz62Q5KOOeaY7StWrOi6d446e7lcQ/q87UckvSipRtJLkqYlVRgAAAAAFKK6+brW69atW0hSp06d1LVr1/fvENypUyfV1NR41qxZPefMmdOzqqrq1Z49e9aOGTNm6I4dOz40udilS5f3X1tSUhJNjWlvciowIr4dEcMiYmREfDEidiZVGAAAAAAUmpNOOmnbr3/96/23bdvmt99+u9Ps2bP333fffWv322+/3b/97W97SNJ999130HHHHbettdvcvHlzSa9evXb37Nmz9qWXXupWfxpwMUj0Al8AAAAA6MjGjRu3/TOf+cymkSNHjujXr9/OMWPGbJOk+++//2+XX375wKuuuqrTgAEDds6cOXNFa7d57rnnbpk2bVpZRUXF8MGDB/991KhR7+ar/r3NEXvvM2MrKyujqqpqr+1v8UWtnyo/ve+sPFYCAAAAtB9vDP1jq8fGxXfksZIPsz0vIiqzff2CBQtWjBo1akP982L/2JdCsGDBgt6jRo0qb2odM6QAAAAAihbhsX1r9xe5AgAAAACKE4EUAAAAAJAKAikAAAAAIBUEUgAAAABAKgikAAAAAIBUEEgBAAAAIEG2R1966aWH1T+/6aab+lx99dWH7uk1CxYs6DpmzJihw4YNGz5o0KAR559//kBJmjVrVs8TTzxxiCQ99NBDvW688cZD8lv93sXHvgAAAAAoWg888MConTt3JpZ7unbtWnPRRRft8aNkunTpEr/5zW8OWLt27bq+ffvWtGa7V1xxxYCrrrrqrQsvvHCzJL3wwgv7NB7zhS98YYukLVkV3k4xQwoAAACgaCUZRlu7vZKSkpg4cWL1rbfe2qfxuqVLl3Y57rjjKioqKoYfd9xxFcuWLesiSevXr+88cODA9+rHjRkzZkfj1/7oRz86aOLEiQMk6dxzzy2/4IILBowePXpoeXn5yJkzZ/bK7cjSQSAFAAAAgIR9/etfX//YY48duHHjxpKGyy+77LIBF1xwwcalS5cuPu+88zZefvnl/SXpiiuueOv000+vOP7444+4+eabD96wYUNJ01v+HytXruz6wgsvvParX/1q2Ve/+tWB27dvd76OJ18IpAAAAACQsAMPPLD2c5/73Mbbbrvt4IbLX3rppX0nT568SZIuv/zyTfPmzeshSV/5ylc2vvLKK4s++9nPbpo7d27PY489dtiOHTv2GDDPPffcTSUlJTrqqKN29u/ff+f8+fO75e+I8iOnQGp7f9uP2H7V9hLbxyVVGAAAAAAUshtuuOGtn/3sZ73ffffdVuWu8vLyXV/96lc3PvXUU38tLS1VVVXVh64jbcj2Hp8XglxnSH8o6bcRMUzSKElLci8JAAAAAApfnz59dp911llv/+xnP+tdv+yYY45599577z1AkqZOnXpgZWXlNkl65JFH9tu5c6cl6c033yzdvHlzScNrSpvy2GOPHbB7924tWrSo68qVK7uOGjXq7/k8nnzI+gJf2/tJOl7SJEmKiPck7fEbBgAAAAAdyTe/+c11DzzwQFn987vvvvvNiy66qPyHP/zhIQcddFDNgw8+uEKSfvvb3+537bXXDujatWutJN18882rBgwYUPPyyy83u+0hQ4bsHDNmzNCNGzd2/sEPfvBG9+7dI9/Hk7Rc7jg1SFK1pPttj5I0T9JXIuLdhoNsT5Y0WZIGDBiQw+4AAAAAoG26du1ak/THvrQ0Zvv27S/VP+7fv3/Njh073n8+dOjQ95577rmljV9z7733rpK0qvHyM888850zzzzzHUm66qqrNkraWL9u3Lhx2+67776VbT+K9iOXN6ZU0j9I+nJEPG/7h5Kul/TPDQdFxDRJ0ySpsrKy4BI7AAAAgMLV0meGIl25BNJVklZFxPOZ54+oLpACAAAAAPLo0UcfXZF2DUnI+qZGEbFO0krbQzOLTpa0OJGqAAAAAABFL9dzqb8s6SHbXSQtl3Rx7iUBAAAAADqCnAJpRMyXVJlQLQAAAACADiTXzyEFAAAAACArid3+GAAAAAAgvfbaa13OPPPMI5YtW7aoftnVV199aI8ePXYvWrRon+eee65nz549d+/cudOf/exnN915551rJWnMmDFD169f37lbt2617733nr/0pS+9de21125I70jyj0AKAAAAoGi9dkXvUbu3bUws95T0OKhm6I835PRRMrfccsuqiy+++O3t27e7oqJi5KWXXrpx2LBh70nSgw8+uPz444/f/tZbb5UcccQRR1155ZUbu3XrVrQfn8kpuwAAAACKVpJhNOntbd++vZMk9ezZs7bxuq1bt5bss88+taWlpUUbRiUCKQAAAADsVd/61rcOGzZs2PABAwZ85NOf/vSmfv361dSvmzhx4qCKiorhRx111Mhrr712TWlpcZ/USiAFAAAAgATZ3uPyW265ZdWrr766eO3atQvmzp3bc/bs2fvWj3nwwQeXL126dPHy5ctfvuuuuw5ZunRpl71TdToIpAAAAACQoD59+tRs2bKlpOGyTZs2lfTu3bum4bJevXrVjh079p05c+b0aLyNQw89tGbkyJHb586du2/jdcWEQAoAAAAACerVq1ftwQcfvOuXv/xlT0l66623Sv70pz/1Oumkk7Y1HLdr1y7Nmzevx5AhQ3Y23sY777zTadGiRd2HDh36oXXFpLhPSAYAAACAFDzwwAN/+9KXvjTguuuu6y9J11133ZoRI0bslOquIb399tv77tq1y+PGjds6ceLEzfWvmzhx4qD6j32ZMGHCho9//OPb0zqGvYFACgAAAKBolfQ4qCbpj31pzbjRo0f//fnnn1/aePmjjz66ornXvPDCC6/lUFpBIpACAAAAKFq5fmYo8otrSAEAAAAAqSCQAgAAAABSkXMgtV1i+yXbs5IoCAAAAADQMSQxQ/oVSUsS2A4AAAAAoAPJKZDaPkzSGZLuTaYcAAAAAEBHkesM6Q8kfUNSbXMDbE+2XWW7qrq6OsfdAQAAAED7VlJSMnrYsGHD6/+99tprXebOndt90qRJ/ZPYfr9+/Y5au3ZtacN9DRkyZMTQoUOHf+c73+mze/fuJHbzvu9+97tld91110GS9KMf/eigFStWdE5q21l/7IvtMyWtj4h5tj/R3LiImCZpmiRVVlZGtvsDAAAAgLbq/bObRm3cuT2xj7s8qGv3mg0X/MseP0qma9euta+++urihsuGDh363vHHH789qTqa2tfq1atLP/e5zw3asmVLyfe///01Se3jG9/4xvsziz/96U97H3300TvKy8t3JbHtXGZIx0o62/YKSQ9LOsn2T5MoCgAAAACSkGQYzWV7s2bN6nniiScOkaRJkyb1v/baa/tK0qOPPrpfZWXl0N27d2vNmjWlp5122uCRI0ceOXLkyCOffPLJfSVp3bp1JWPHjj3iyCOPHH7BBRcMjGh6nq9fv341995774r777//4NraWtXU1GjKlCmHjRw58siKiorh3/ve93rX1zJmzJih48ePH3T44YePOPvssw+vra076fVLX/pSv8GDB4+oqKgYPnny5MMk6eqrrz70pptu6nP//fcfsHDhwu4TJ04cNGzYsOEPP/xwr1NOOWVw/f4ff/zx/U499dTBTRbXjKzfnIi4QdINkpSZIb02Ii7MdnsAAAAAUAx27tzZadiwYcMlqX///jtnz57914br//3f/331Mcccc+QJJ5yw7Zprrhnw61//ellJSYmmTJnS/+qrr37rtNNO27Zs2bIup5122hHLly9fdP311x963HHHbbvjjjvWPvzww71mzpzZu7l9Dx8+/L3a2lqtXr269Oc///n+vXr12r1w4cIlO3bs8LHHHjvsrLPO2ipJS5Ys2Wf+/PnLy8vLd40ePXrY7Nmzexx99NE7fvOb3xywfPnyhZ06ddKGDRtKGm774osvfvvuu+8++I477lh5/PHHb6+trdUNN9xw2Jo1a0oPPfTQmunTpx80adKkDW35XiX61wIAAAAA6OiaOmW3oZ49e9befffdKz71qU8Nu/nmm1eOGDFipyQ988wz+y1btmyf+nHbtm0refvttzs999xzPR977LHXJWnChAlbpkyZsseLROtnUH//+9/v9+qrr3Z/4oknDpCkd955p2Tx4sXdunTpEkcdddS7gwcP3iVJI0aM2P7Xv/61y0knnbSta9eutRMmTBh4xhlnbDnvvPO27Gk/nTp10uc///mN99xzz4FXXHHFxhdffLHHY4899rdWfpskJRRII+JPkv6UxLYAAAAAoNjNnz9/n169etWsWbPm/RsERYSqqqqW9OjR40Pn5Hbq1LqrLRcvXtylpKRE/fr1q4kI33nnnW+ee+65WxuOmTVrVs+uXbu+v4+SkhLV1NS4c+fOmj9//pInnnhiv4cffviAu+++++Dnnntu6Z72d/nll28844wzhnTr1i3OOuustzt3btv9jpL4HFIAAAAAQCstXbq0y49//OND5s2bt/ipp57q9Yc//GFfSRo3btzW22+//eD6cX/5y1/2kaSPfvSj70yfPv0gSfrFL36x39atW0ua2u6aNWtKL7300oEXX3zx+k6dOumUU07Zcvfdd5ft3LnTkvTyyy933bp1a7MZcMuWLZ02bdpUct555235yU9+snLJkiXdG4/p0aPH7i1btry///Ly8l19+vTZdeedd/a99NJL23S6rkQgBQAAAIC9pra2VpMmTSr/13/915Xl5eW77rnnnhWXXXbZwO3bt3vatGkrX3zxxX0rKiqGDx48eMRdd91VJkm33XbbmmeeeabH8OHDj/zd737Xq2/fvu/Vb6/+etUhQ4aMOPHEEytOPvnkrXfccccaSfra1762YdiwYX8/6qijjjziiCNGXHrppQN37drl5mrbvHlzyfjx44+oqKgY/vGPf3zoLbfcsrLxmIkTJ2748pe/PHDYsGHDt23bZkmaMGHCxr59+743evTov7f1++Hm7tCUD5WVlVFVVbXX9rf4oma/1x9yet9ZeawEAAAAaD/eGPrHVo+Ni+/IYyUfZnteRFRm+/oFCxasGDVq1PszdWl87EtHM3HixAHHHHPM9q997WtNzpAuWLCg96hRo8qbWsdNjQAAAAAULcJjfo0YMeLIffbZp3bq1Kkfmk1tDQIpAAAAACArixYtWpLL67mGFAAAAACQCgIpAAAAgGJSW1tb2/qbySCvMu9FbXPrCaQAAAAAisnC6urqXoTS9NXW1rq6urqXpIXNjeEaUgAAAABFo6am5p/WrVt377p160aKCbi01UpaWFNT80/NDSCQAgAAACgao0ePXi/p7LTrQOvwFwMAAAAAQCoIpAAAAACAVBBIAQAAAACpyDqQ2u5v+4+2l9heZPsrSRYGAAAAAChuudzUqEbSNRHxou2ekubZnh0RixOqDQAAAABQxLKeIY2ItRHxYubxO5KWSOqXVGEAAAAAgOKWyDWktsslHSPp+SbWTbZdZbuquro6id0BAAAAAIpAzoHUdg9Jj0r6akRsbbw+Iv5fe/cX+lddx3H8+eK3jcKKpf6K2FYqWLmLnDLEWIitiGnSuihQKiQCbwwMiljeRIEX3VhdSDTcygvLZGmNkErMKG+mMxdqS1rD2q+ZW5T058K1endxTvRz+679+X63z/n+vs8HfPmez+d3fpw3vPidL+/vOefz21pV66tq/fz8/LiHkyRJkiQtEWM1pEmW0zWj91bVA5MpSZIkSZI0C8ZZZTfANmBvVd05uZIkSZIkSbNgnCukG4CPARuT7Olf10+oLkmSJEnSEnfG//alqh4DMsFaJEmSJEkzZCKr7EqSJEmSdLpsSCVJkiRJTdiQSpIkSZKasCGVJEmSJDVhQypJkiRJasKGVJIkSZLUhA2pJEmSJKkJG1JJkiRJUhM2pJIkSZKkJmxIJUmSJElN2JBKkiRJkppY1rqAs+mxDV8/5X1v5w9nsRJJkiRpQP751tYVSIBXSCVJkiRJjYzVkCbZlOS5JPuSbJlUUZIkSZKkpe+MG9Ikc8BdwHXAWuCmJGsnVZgkSZIkaWkb5wrpVcC+qtpfVUeA+4DNkylLkiRJkrTUjdOQrgIOLBov9HOvkOSWJLuT7D58+PAYh5MkSZIkLSXjNKQZMVfHTVRtrar1VbV+fn5+jMNJkiRJkpaScRrSBWDNovFq4OB45UiSJEmSZsU4DekTwKVJLk6yArgR2DmZsiRJkiRJS92yM/3Fqjqa5JPAj4A5YHtVPTuxyiRJkiRJS9oZN6QAVfUQ8NCEapEkSZIkzZBUHbcO0dk7WHIY+N05O+CJXQj8qXUROi1mNp3MbTqZ23Qyt+lkbtPJ3M6ut1SVq6HOiHPakA5Fkt1Vtb51HTp1ZjadzG06mdt0MrfpZG7TydykyRlnUSNJkiRJks6YDakkSZIkqYlZbUi3ti5Ap83MppO5TSdzm07mNp3MbTqZmzQhM/kMqSRJkiSpvVm9QipJkiRJamymGtIkm5I8l2Rfki2t69FoSbYnOZTkmUVz5yd5OMlv+vfXt6xRx0uyJsmjSfYmeTbJbf282Q1YklcleTzJL/vcvtDPX5xkV5/bd5KsaF2rXinJXJKnkvygH5vZwCV5PsnTSfYk2d3PeY4cuCQrk+xI8uv+M+6d5iZNzsw0pEnmgLuA64C1wE1J1ratSifwTWDTMXNbgEeq6lLgkX6sYTkKfLqqLgOuBm7t/8bMbtheBjZW1eXAOmBTkquBLwFf7nP7C/CJhjVqtNuAvYvGZjYd3l1V6xb9yxDPkcP3VeCHVfV24HK6vztzkyZkZhpS4CpgX1Xtr6ojwH3A5sY1aYSq+hnw52OmNwP39Nv3AB88p0XppKrqhar6Rb/9N7oP7FWY3aBV5+/9cHn/KmAjsKOfN7eBSbIaeD9wdz8OZjatPEcOWJLXAdcA2wCq6khVvYS5SRMzSw3pKuDAovFCP6fp8MaqegG6xgd4Q+N69H8kuQi4AtiF2Q1ef+vnHuAQ8DDwW+Clqjra7+L5cni+AnwW+Hc/vgAzmwYF/DjJk0lu6ec8Rw7bJcBh4Bv9LfJ3JzkPc5MmZpYa0oyYc4lhacKSvAb4LvCpqvpr63p0clX1r6paB6ymu5vkslG7nduqdCJJbgAOVdWTi6dH7Gpmw7Ohqq6ke3zo1iTXtC5IJ7UMuBL4WlVdAfwDb8+VJmqWGtIFYM2i8WrgYKNadPpeTPImgP79UON6NEKS5XTN6L1V9UA/bXZTor8N7ad0zwCvTLKs/5Hny2HZAHwgyfN0j59spLtiamYDV1UH+/dDwIN0XwB5jhy2BWChqnb14x10Daq5SRMySw3pE8Cl/SqEK4AbgZ2Na9Kp2wnc3G/fDHy/YS0aoX+GbRuwt6ruXPQjsxuwJPNJVvbbrwbeS/f876PAh/rdzG1AqupzVbW6qi6i+yz7SVV9BDMbtCTnJXntf7eB9wHP4Dly0Krqj8CBJG/rp94D/ApzkyYmVbNzR0+S6+m+RZ4DtlfVHY1L0ghJvg1cC1wIvAh8HvgecD/wZuD3wIer6tiFj9RQkncBPwee5n/Ptd1O9xyp2Q1UknfQLcgxR/cl5f1V9cUkl9BdfTsfeAr4aFW93K5SjZLkWuAzVXWDmQ1bn8+D/XAZ8K2quiPJBXiOHLQk6+gWEFsB7Ac+Tn++xNyksc1UQypJkiRJGo5ZumVXkiRJkjQgNqSSJEmSpCZsSCVJkiRJTdiQSpIkSZKasCGVJEmSJDVhQypJkiRJasKGVJIkSZLUhA2pJEmSJKmJ/wA53EZae4acPAAAAABJRU5ErkJggg==)
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)
%% Cell type:markdown id: tags:
We run the channel for a few steps...
......@@ -193,11 +197,11 @@
plt.colorbar();
```
%%%% Output: display_data
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)
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)
%% Cell type:markdown id: tags:
And then switch off the inflow...
......@@ -215,6 +219,6 @@
plt.colorbar();
```
%%%% Output: display_data
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)
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)
......
......@@ -13,5 +13,6 @@ API Reference
continuous_distribution_measures.rst
moments.rst
cumulants.rst
boundary_conditions.rst
forcemodels.rst
zbibliography.rst
*******************
Boundary Conditions
*******************
.. automodule:: lbmpy.boundaries.boundaryconditions
:members:
......@@ -75,4 +75,12 @@ pages = {1--11},
title = {{Ternary free-energy lattice Boltzmann model with tunable surface tensions and contact angles}},
volume = {033305},
year = {2016}
}
@article{geier2015,
author = {Geier, Martin and Sch{\"{o}}nherr, Martin and Pasquali, Andrea and Krafczyk, Manfred},
title = {{The cumulant lattice Boltzmann equation in three dimensions: Theory and validation}},
journal = {Computers \& Mathematics with Applications},
year = {2015},
doi = {10.1016/j.camwa.2015.05.001}
}
\ No newline at end of file
......@@ -80,12 +80,14 @@ class AccessPdfValues:
"""Allows to access values from a PDF array correctly depending on
the streaming pattern."""
def __init__(self, pdf_field, stencil,
def __init__(self, stencil,
streaming_pattern='pull', timestep=Timestep.BOTH, streaming_dir='out',
accessor=None):
if streaming_dir not in ['in', 'out']:
raise ValueError('Invalid streaming direction.', streaming_dir)
pdf_field = ps.Field.create_generic('pdfs', len(stencil[0]), index_shape=(len(stencil),))
if accessor is None:
accessor = get_accessor(streaming_pattern, timestep)
self.accs = accessor.read(pdf_field, stencil) \
......
from lbmpy.boundaries.boundaryconditions import (
UBB, FixedDensity, NeumannByCopy, NoSlip, StreamInConstant)
UBB, FixedDensity, SimpleExtrapolationOutflow, ExtrapolationOutflow, NeumannByCopy, NoSlip, StreamInConstant)
from lbmpy.boundaries.boundaryhandling import LatticeBoltzmannBoundaryHandling
__all__ = ['NoSlip', 'UBB', 'FixedDensity', 'NeumannByCopy', 'LatticeBoltzmannBoundaryHandling', 'StreamInConstant']
__all__ = ['NoSlip', 'UBB', 'SimpleExtrapolationOutflow', 'ExtrapolationOutflow', 'FixedDensity', 'NeumannByCopy',
'LatticeBoltzmannBoundaryHandling', 'StreamInConstant']
from lbmpy.advanced_streaming.utility import AccessPdfValues, Timestep
from pystencils.simp.assignment_collection import AssignmentCollection
import sympy as sp
from pystencils import Assignment, Field
from lbmpy.boundaries.boundaryhandling import LbmWeightInfo
......@@ -5,10 +7,15 @@ from pystencils.data_types import create_type
from pystencils.sympyextensions import get_symmetric_part
from lbmpy.simplificationfactory import create_simplification_strategy
from lbmpy.advanced_streaming.indexing import NeighbourOffsetArrays
from pystencils.stencil import offset_to_direction_string, direction_string_to_offset
class LbBoundary:
"""Base class that all boundaries should derive from"""
"""Base class that all boundaries should derive from.
Args:
name: optional name of the boundary.
"""
inner_or_boundary = True
single_link = False
......@@ -52,7 +59,11 @@ class LbBoundary:
return None
def get_additional_code_nodes(self, lb_method):
"""Return a list of code nodes that will be added in the generated code before the index field loop."""
"""Return a list of code nodes that will be added in the generated code before the index field loop.
Args:
lb_method: lattice Boltzmann method. See :func:`lbmpy.creationfunctions.create_lb_method`
"""
return []
@property
......@@ -70,16 +81,18 @@ class LbBoundary:
class NoSlip(LbBoundary):
def __init__(self, name=None):
"""Set an optional name here, to mark boundaries, for example for force evaluations"""
super(NoSlip, self).__init__(name)
"""
No-Slip, (half-way) simple bounce back boundary condition, enforcing zero velocity at obstacle.
Extended for use with any streaming pattern.
Args:
name: optional name of the boundary.
"""
def __init__(self, name=None):
"""Set an optional name here, to mark boundaries, for example for force evaluations"""
super(NoSlip, self).__init__(name)
def __call__(self, f_out, f_in, dir_symbol, inv_dir, lb_method, index_field):
return Assignment(f_in(inv_dir[dir_symbol]), f_out(dir_symbol))
......@@ -95,16 +108,20 @@ class NoSlip(LbBoundary):
class UBB(LbBoundary):
"""Velocity bounce back boundary condition, enforcing specified velocity at obstacle"""
"""Velocity bounce back boundary condition, enforcing specified velocity at obstacle
Args:
velocity: can either be a constant, an access into a field, or a callback function.
The callback functions gets a numpy record array with members, 'x','y','z', 'dir' (direction)
and 'velocity' which has to be set to the desired velocity of the corresponding link
adapt_velocity_to_force: adapts the velocity to the correct equilibrium when the lattice Boltzmann method holds
a forcing term. If no forcing term is set and adapt_velocity_to_force is set to True
it has no effect.
dim: number of spatial dimensions
name: optional name of the boundary.
"""
def __init__(self, velocity, adapt_velocity_to_force=False, dim=None, name=None):
"""
Args:
velocity: can either be a constant, an access into a field, or a callback function.
The callback functions gets a numpy record array with members, 'x','y','z', 'dir' (direction)
and 'velocity' which has to be set to the desired velocity of the corresponding link
adapt_velocity_to_force:
"""
super(UBB, self).__init__(name)
self._velocity = velocity
self._adaptVelocityToForce = adapt_velocity_to_force
......@@ -116,6 +133,8 @@ class UBB(LbBoundary):
@property
def additional_data(self):
""" In case of the UBB boundary additional data is a velocity vector. This vector is added to each cell to
realize velocity profiles for the inlet."""
if callable(self._velocity):
return [('vel_%d' % (i,), create_type("double")) for i in range(self.dim)]
else:
......@@ -123,10 +142,22 @@ class UBB(LbBoundary):
@property
def additional_data_init_callback(self):
"""Initialise additional data of the boundary. For an example see
`tutorial 02 <https://pycodegen.pages.i10git.cs.fau.de/lbmpy/notebooks/02_tutorial_boundary_setup.html>`_
or lbmpy.geometry.add_pipe_inflow_boundary"""
if callable(self._velocity):
return self._velocity
def get_additional_code_nodes(self, lb_method):
"""Return a list of code nodes that will be added in the generated code before the index field loop.
Args:
lb_method: Lattice Boltzmann method. See :func:`lbmpy.creationfunctions.create_lb_method`
Returns:
list containing LbmWeightInfo and NeighbourOffsetArrays
"""
return [LbmWeightInfo(lb_method), NeighbourOffsetArrays(lb_method.stencil)]
def __call__(self, f_out, f_in, dir_symbol, inv_dir, lb_method, index_field):
......@@ -174,7 +205,197 @@ class UBB(LbBoundary):
# end class UBB
class SimpleExtrapolationOutflow(LbBoundary):
r"""
Simple Outflow boundary condition :cite:`geier2015`, equation F.1 (listed below).
This boundary condition extrapolates missing populations from the last layer of
fluid cells onto the boundary by copying them in the normal direction.
.. math ::
f_{\overline{1}jkxyzt} = f_{\overline{1}jk(x - \Delta x)yzt}
Args:
normal_direction: direction vector normal to the outflow
stencil: stencil used for the lattice Boltzmann method
name: optional name of the boundary.
"""
# We need each fluid cell only once, the direction of the outflow is given
# in the constructor.
single_link = True
def __init__(self, normal_direction, stencil, name=None):
if isinstance(normal_direction, str):
normal_direction = direction_string_to_offset(normal_direction, dim=len(stencil[0]))
if name is None:
name = f"Simple Outflow: {offset_to_direction_string(normal_direction)}"
self.normal_direction = normal_direction
super(SimpleExtrapolationOutflow, self).__init__(name)
def __call__(self, f_out, f_in, dir_symbol, inv_dir, lb_method, index_field):
stencil = lb_method.stencil
boundary_assignments = []
for i, stencil_dir in enumerate(stencil):
if all(n == 0 or n == -s for s, n in zip(stencil_dir, self.normal_direction)):
asm = Assignment(f_out[self.normal_direction](i), f_out.center(i))
boundary_assignments.append(asm)
print(boundary_assignments)
return boundary_assignments
# end class SimpleExtrapolationOutflow
class ExtrapolationOutflow(LbBoundary):
r"""
Outflow boundary condition :cite:`geier2015`, equation F.2, with u neglected (listed below).
This boundary condition interpolates missing on the boundary in normal direction. For this interpolation, the
PDF values of the last time step are used. They are interpolated between fluid cell and boundary cell.
To get the PDF values from the last time step an index array is used which stores them.
.. math ::
f_{\overline{1}jkxyzt} = f_{\overline{1}jk(x - \Delta x)yz(t - \Delta t)} c \theta^{\frac{1}{2}}
\frac{\Delta t}{\Delta x} + \left(1 - c \theta^{\frac{1}{2}} \frac{\Delta t}{\Delta x} \right)
f_{\overline{1}jk(x - \Delta x)yzt}
Args:
normal_direction: direction vector normal to the outflow
lb_method: the lattice boltzman method to be used in the simulation
dt: lattice time step size
dx: lattice spacing distance
name: optional name of the boundary.
streaming_pattern: Streaming pattern to be used in the simulation
zeroth_timestep: for in-place patterns, whether the initial setup corresponds to an even or odd time step
initial_density: floating point constant or callback taking spatial coordinates (x, y [,z]) as
positional arguments, specifying the initial density on boundary nodes
initial_velocity: tuple of floating point constants or callback taking spatial coordinates (x, y [,z]) as
positional arguments, specifying the initial velocity on boundary nodes
"""
# We need each fluid cell only once, the direction of the outflow is given
# in the constructor.
single_link = True
def __init__(self, normal_direction, lb_method, dt=1, dx=1, name=None,
streaming_pattern='pull', zeroth_timestep=Timestep.BOTH,
initial_density=None, initial_velocity=None):
self.lb_method = lb_method
self.stencil = lb_method.stencil
self.dim = len(self.stencil[0])
if isinstance(normal_direction, str):
normal_direction = direction_string_to_offset(normal_direction, dim=self.dim)
if name is None:
name = f"Outflow: {offset_to_direction_string(normal_direction)}"
self.normal_direction = normal_direction
self.streaming_pattern = streaming_pattern
self.zeroth_timestep = zeroth_timestep
self.dx = sp.Number(dx)
self.dt = sp.Number(dt)
self.c = sp.sqrt(sp.Rational(1, 3)) * (self.dx / self.dt)
self.initial_density = initial_density
self.initial_velocity = initial_velocity
self.equilibrium_calculation = None
if initial_density and initial_velocity:
equilibrium = lb_method.get_equilibrium(conserved_quantity_equations=AssignmentCollection([]))
rho = lb_method.zeroth_order_equilibrium_moment_symbol
u_vec = lb_method.first_order_equilibrium_moment_symbols
eq_lambda = equilibrium.lambdify((rho,) + u_vec)
post_pdf_symbols = lb_method.post_collision_pdf_symbols
def calc_eq_pdfs(density, velocity, j):
return eq_lambda(density, *velocity)[post_pdf_symbols[j]]
self.equilibrium_calculation = calc_eq_pdfs
super(ExtrapolationOutflow, self).__init__(name)
def init_callback(self, boundary_data, **_):
dim = boundary_data.dim
coord_names = ['x', 'y', 'z'][:dim]
pdf_acc = AccessPdfValues(self.stencil, streaming_pattern=self.streaming_pattern,
timestep=self.zeroth_timestep, streaming_dir='out')
def get_boundary_cell_pdfs(fluid_cell, boundary_cell, j):
if self.equilibrium_calculation is not None:
density = self.initial_density(
*boundary_cell) if callable(self.initial_density) else self.initial_density
velocity = self.initial_velocity(
*boundary_cell) if callable(self.initial_velocity) else self.initial_velocity
return self.equilibrium_calculation(density, velocity, j)
else:
return pdf_acc.read_pdf(boundary_data.pdf_array, fluid_cell, j)
for entry in boundary_data.index_array:
fluid_cell = tuple(entry[c] for c in coord_names)
boundary_cell = tuple(f + o for f, o in zip(fluid_cell, self.normal_direction))
# Initial fluid cell PDF values
for j, stencil_dir in enumerate(self.stencil):
if all(n == 0 or n == -s for s, n in zip(stencil_dir, self.normal_direction)):
entry[f'pdf_{j}'] = pdf_acc.read_pdf(boundary_data.pdf_array, fluid_cell, j)
entry[f'pdf_nd_{j}'] = get_boundary_cell_pdfs(fluid_cell, boundary_cell, j)
@property
def additional_data(self):
"""Used internally only. For the ExtrapolationOutflow information of the precious PDF values is needed. This
information is added to the boundary"""
data = []
for i, stencil_dir in enumerate(self.stencil):
if all(n == 0 or n == -s for s, n in zip(stencil_dir, self.normal_direction)):
data.append((f'pdf_{i}', create_type("double")))
data.append((f'pdf_nd_{i}', create_type("double")))
return data
@property
def additional_data_init_callback(self):
"""The initialisation of the additional data is implemented internally for this class.
Thus no callback can be provided"""
if callable(self.init_callback):
return self.init_callback
def __call__(self, f_out, f_in, dir_symbol, inv_dir, lb_method, index_field):
subexpressions = []
boundary_assignments = []
dtdx = sp.Rational(self.dt, self.dx)
for i, stencil_dir in enumerate(self.stencil):
if all(n == 0 or n == -s for s, n in zip(stencil_dir, self.normal_direction)):
interpolated_pdf_sym = sp.Symbol(f'pdf_inter_{i}')
interpolated_pdf_asm = Assignment(interpolated_pdf_sym, (index_field[0](f'pdf_{i}') * (self.c * dtdx))
+ ((sp.Number(1) - self.c * dtdx) * index_field[0](f'pdf_nd_{i}')))
subexpressions.append(interpolated_pdf_asm)
asm = Assignment(f_out[self.normal_direction](i), interpolated_pdf_sym)
boundary_assignments.append(asm)
asm = Assignment(index_field[0](f'pdf_{i}'), f_out.center(i))
boundary_assignments.append(asm)
asm = Assignment(index_field[0](f'pdf_nd_{i}'), interpolated_pdf_sym)
boundary_assignments.append(asm)
return AssignmentCollection(boundary_assignments, subexpressions=subexpressions)
# end class ExtrapolationOutflow
class FixedDensity(LbBoundary):
"""Boundary condition that fixes the density/pressure at the obstacle.
Args: