ee39b39805
* modify examples/problems * modify tutorials --------- Co-authored-by: Dario Coscia <dariocoscia@dhcp-235.eduroam.sissa.it> Co-authored-by: Dario Coscia <dariocoscia@dhcp-015.eduroam.sissa.it>
60 lines
2.5 KiB
Python
60 lines
2.5 KiB
Python
""" Navier Stokes Problem """
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import torch
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from pina.problem import SpatialProblem
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from pina.operators import laplacian, grad, div
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from pina import Condition, LabelTensor
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from pina.geometry import CartesianDomain
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from pina.equation import SystemEquation, Equation
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# ===================================================== #
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# #
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# This script implements the two dimensional #
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# Stokes problem. The Stokes class is defined #
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# inheriting from SpatialProblem. We denote: #
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# ux --> field variable velocity along x #
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# uy --> field variable velocity along y #
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# p --> field variable pressure #
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# x,y --> spatial variables #
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# #
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# ===================================================== #
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class Stokes(SpatialProblem):
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# assign output/ spatial variables
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output_variables = ['ux', 'uy', 'p']
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spatial_domain = CartesianDomain({'x': [-2, 2], 'y': [-1, 1]})
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# define the momentum equation
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def momentum(input_, output_):
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delta_ = torch.hstack((LabelTensor(laplacian(output_.extract(['ux']), input_), ['x']),
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LabelTensor(laplacian(output_.extract(['uy']), input_), ['y'])))
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return - delta_ + grad(output_.extract(['p']), input_)
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def continuity(input_, output_):
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return div(output_.extract(['ux', 'uy']), input_)
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# define the inlet velocity
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def inlet(input_, output_):
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value = 2 * (1 - input_.extract(['y'])**2)
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return output_.extract(['ux']) - value
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# define the outlet pressure
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def outlet(input_, output_):
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value = 0.0
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return output_.extract(['p']) - value
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# define the wall condition
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def wall(input_, output_):
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value = 0.0
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return output_.extract(['ux', 'uy']) - value
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# problem condition statement
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conditions = {
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'gamma_top': Condition(location=CartesianDomain({'x': [-2, 2], 'y': 1}), equation=Equation(wall)),
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'gamma_bot': Condition(location=CartesianDomain({'x': [-2, 2], 'y': -1}), equation=Equation(wall)),
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'gamma_out': Condition(location=CartesianDomain({'x': 2, 'y': [-1, 1]}), equation=Equation(outlet)),
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'gamma_in': Condition(location=CartesianDomain({'x': -2, 'y': [-1, 1]}), equation=Equation(inlet)),
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'D': Condition(location=CartesianDomain({'x': [-2, 2], 'y': [-1, 1]}), equation=SystemEquation([momentum, continuity]))
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}
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