53 lines
2.1 KiB
Python
53 lines
2.1 KiB
Python
""" Burgers' problem. """
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# ===================================================== #
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# #
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# This script implements the one dimensional Burger #
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# problem. The Burgers1D class is defined inheriting #
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# from TimeDependentProblem, SpatialProblem and we #
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# denote: #
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# u --> field variable #
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# x --> spatial variable #
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# t --> temporal variable #
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# #
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# ===================================================== #
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import torch
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from pina.domain import CartesianDomain
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from pina import Condition
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from pina.problem import TimeDependentProblem, SpatialProblem
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from pina.operators import grad
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from pina.equation import FixedValue, Equation
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class Burgers1D(TimeDependentProblem, SpatialProblem):
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# define the burger equation
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def burger_equation(input_, output_):
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du = grad(output_, input_)
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ddu = grad(du, input_, components=['dudx'])
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return (
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du.extract(['dudt']) +
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output_.extract(['u'])*du.extract(['dudx']) -
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(0.01/torch.pi)*ddu.extract(['ddudxdx'])
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)
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# define initial condition
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def initial_condition(input_, output_):
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u_expected = -torch.sin(torch.pi*input_.extract(['x']))
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return output_.extract(['u']) - u_expected
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# assign output/ spatial and temporal variables
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output_variables = ['u']
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spatial_domain = CartesianDomain({'x': [-1, 1]})
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temporal_domain = CartesianDomain({'t': [0, 1]})
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# problem condition statement
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conditions = {
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'gamma1': Condition(location=CartesianDomain({'x': -1, 't': [0, 1]}), equation=FixedValue(0.)),
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'gamma2': Condition(location=CartesianDomain({'x': 1, 't': [0, 1]}), equation=FixedValue(0.)),
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't0': Condition(location=CartesianDomain({'x': [-1, 1], 't': 0}), equation=Equation(initial_condition)),
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'D': Condition(location=CartesianDomain({'x': [-1, 1], 't': [0, 1]}), equation=Equation(burger_equation)),
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} |