54 lines
2.1 KiB
Python
54 lines
2.1 KiB
Python
import torch
|
|
|
|
from pina.problem import TimeDependentProblem, SpatialProblem
|
|
from pina.operators import grad
|
|
from pina import Condition
|
|
from pina.span import Span
|
|
|
|
# ===================================================== #
|
|
# #
|
|
# This script implements the one dimensional Burger #
|
|
# problem. The Burgers1D class is defined inheriting #
|
|
# from TimeDependentProblem, SpatialProblem and we #
|
|
# denote: #
|
|
# u --> field variable #
|
|
# x --> spatial variable #
|
|
# t --> temporal variable #
|
|
# #
|
|
# ===================================================== #
|
|
|
|
class Burgers1D(TimeDependentProblem, SpatialProblem):
|
|
|
|
# assign output/ spatial and temporal variables
|
|
output_variables = ['u']
|
|
spatial_domain = Span({'x': [-1, 1]})
|
|
temporal_domain = Span({'t': [0, 1]})
|
|
|
|
# define the burger equation
|
|
def burger_equation(input_, output_):
|
|
du = grad(output_, input_)
|
|
ddu = grad(du, input_, components=['dudx'])
|
|
return (
|
|
du.extract(['dudt']) +
|
|
output_.extract(['u'])*du.extract(['dudx']) -
|
|
(0.01/torch.pi)*ddu.extract(['ddudxdx'])
|
|
)
|
|
|
|
# define nill dirichlet boundary conditions
|
|
def nil_dirichlet(input_, output_):
|
|
u_expected = 0.0
|
|
return output_.extract(['u']) - u_expected
|
|
|
|
# define initial condition
|
|
def initial_condition(input_, output_):
|
|
u_expected = -torch.sin(torch.pi*input_.extract(['x']))
|
|
return output_.extract(['u']) - u_expected
|
|
|
|
# problem condition statement
|
|
conditions = {
|
|
'gamma1': Condition(location=Span({'x': -1, 't': [0, 1]}), function=nil_dirichlet),
|
|
'gamma2': Condition(location=Span({'x': 1, 't': [0, 1]}), function=nil_dirichlet),
|
|
't0': Condition(location=Span({'x': [-1, 1], 't': 0}), function=initial_condition),
|
|
'D': Condition(location=Span({'x': [-1, 1], 't': [0, 1]}), function=burger_equation),
|
|
}
|