68 lines
2.6 KiB
Python
68 lines
2.6 KiB
Python
""" Steady Stokes Problem """
|
|
|
|
import torch
|
|
from pina.problem import SpatialProblem
|
|
from pina.operators import laplacian, grad, div
|
|
from pina import Condition, LabelTensor
|
|
from pina.domain import CartesianDomain
|
|
from pina.equation import SystemEquation, Equation
|
|
|
|
# ===================================================== #
|
|
# #
|
|
# This script implements the two dimensional #
|
|
# Stokes problem. The Stokes class is defined #
|
|
# inheriting from SpatialProblem. We denote: #
|
|
# ux --> field variable velocity along x #
|
|
# uy --> field variable velocity along y #
|
|
# p --> field variable pressure #
|
|
# x,y --> spatial variables #
|
|
# #
|
|
# ===================================================== #
|
|
|
|
class Stokes(SpatialProblem):
|
|
|
|
# assign output/ spatial variables
|
|
output_variables = ['ux', 'uy', 'p']
|
|
spatial_domain = CartesianDomain({'x': [-2, 2], 'y': [-1, 1]})
|
|
|
|
# define the momentum equation
|
|
def momentum(input_, output_):
|
|
delta_ = torch.hstack((LabelTensor(laplacian(output_.extract(['ux']), input_), ['x']),
|
|
LabelTensor(laplacian(output_.extract(['uy']), input_), ['y'])))
|
|
return - delta_ + grad(output_.extract(['p']), input_)
|
|
|
|
def continuity(input_, output_):
|
|
return div(output_.extract(['ux', 'uy']), input_)
|
|
|
|
# define the inlet velocity
|
|
def inlet(input_, output_):
|
|
value = 2 * (1 - input_.extract(['y'])**2)
|
|
return output_.extract(['ux']) - value
|
|
|
|
# define the outlet pressure
|
|
def outlet(input_, output_):
|
|
value = 0.0
|
|
return output_.extract(['p']) - value
|
|
|
|
# define the wall condition
|
|
def wall(input_, output_):
|
|
value = 0.0
|
|
return output_.extract(['ux', 'uy']) - value
|
|
|
|
domains = {
|
|
'gamma_top': CartesianDomain({'x': [-2, 2], 'y': 1}),
|
|
'gamma_bot': CartesianDomain({'x': [-2, 2], 'y': -1}),
|
|
'gamma_out': CartesianDomain({'x': 2, 'y': [-1, 1]}),
|
|
'gamma_in': CartesianDomain({'x': -2, 'y': [-1, 1]}),
|
|
'D': CartesianDomain({'x': [-2, 2], 'y': [-1, 1]})
|
|
}
|
|
|
|
# problem condition statement
|
|
conditions = {
|
|
'gamma_top': Condition(domain='gamma_top', equation=Equation(wall)),
|
|
'gamma_bot': Condition(domain='gamma_bot', equation=Equation(wall)),
|
|
'gamma_out': Condition(domain='gamma_out', equation=Equation(outlet)),
|
|
'gamma_in': Condition(domain='gamma_in', equation=Equation(inlet)),
|
|
'D': Condition(domain='D', equation=SystemEquation([momentum, continuity]))
|
|
}
|