diffusion/laplace_time_ebcs.py

Description

Example explaining how to change Dirichlet boundary conditions depending on time. It is shown on the stationary Laplace equation for temperature, so there is no dynamics, only the conditions change with time.

Five time steps are solved on a cube domain, with the temperature fixed to zero on the bottom face, and set to other values on the left, right and top faces in different time steps.

Find

System Message: WARNING/2 (t)

latex exited with error [stdout] This is pdfTeX, Version 3.1415926-2.5-1.40.14 (TeX Live 2013/TeX Live for SUSE Linux) restricted \write18 enabled. entering extended mode (./math.tex LaTeX2e <2011/06/27> Babel <3.9f> and hyphenation patterns for 78 languages loaded. (/usr/share/texmf/tex/latex/base/article.cls Document Class: article 2007/10/19 v1.4h Standard LaTeX document class (/usr/share/texmf/tex/latex/base/size12.clo)) (/usr/share/texmf/tex/latex/base/inputenc.sty ! LaTeX Error: File `utf8x.def’ not found. Type X to quit or <RETURN> to proceed, or enter new name. (Default extension: def) Enter file name: ! Emergency stop. <read *> l.131 \endinput ^^M No pages of output. Transcript written on math.log.

such that:

System Message: WARNING/2 (\int_{\Omega} c \nabla s \cdot \nabla t = 0 \;, \quad \forall s \;. )

latex exited with error [stdout] This is pdfTeX, Version 3.1415926-2.5-1.40.14 (TeX Live 2013/TeX Live for SUSE Linux) restricted \write18 enabled. entering extended mode (./math.tex LaTeX2e <2011/06/27> Babel <3.9f> and hyphenation patterns for 78 languages loaded. (/usr/share/texmf/tex/latex/base/article.cls Document Class: article 2007/10/19 v1.4h Standard LaTeX document class (/usr/share/texmf/tex/latex/base/size12.clo)) (/usr/share/texmf/tex/latex/base/inputenc.sty ! LaTeX Error: File `utf8x.def’ not found. Type X to quit or <RETURN> to proceed, or enter new name. (Default extension: def) Enter file name: ! Emergency stop. <read *> l.131 \endinput ^^M No pages of output. Transcript written on math.log.

source code

r"""
Example explaining how to change Dirichlet boundary conditions depending
on time. It is shown on the stationary Laplace equation for temperature,
so there is no dynamics, only the conditions change with time.

Five time steps are solved on a cube domain, with the temperature fixed
to zero on the bottom face, and set to other values on the left, right
and top faces in different time steps.

Find :math:`t` such that:

.. math::
    \int_{\Omega} c \nabla s \cdot \nabla t
    = 0
    \;, \quad \forall s \;.
"""
from sfepy import data_dir

filename_mesh = data_dir + '/meshes/3d/cube_medium_tetra.mesh'

options = {
    'nls' : 'newton',
    'ls' : 'ls',
    'ts' : 'ts',
}

regions = {
    'Omega' : ('all', {}),
    'Left' : ('nodes in (x < -0.499)', {}),
    'Right' : ('nodes in (x > 0.499)', {}),
    'Bottom' : ('nodes in (z < -0.499)', {}),
    'Top' : ('nodes in (z > 0.499)', {}),
}

materials = {
    'one' : ({'val' : 1.0},),
}

fields = {
    'temperature' : ('real', 1, 'Omega', 1),
}

variables = {
    't'   : ('unknown field', 'temperature', 0),
    's'   : ('test field',    'temperature', 't'),
}

ebcs = {
    'fixed' : ('Bottom', {'t.all' : 0}),
    't_t02' : ('Left', [(-0.5, 0.5), (2.5, 3.5)], {'t.all' : 1.0}),
    't_t1' : ('Right', [(0.5, 1.5)], {'t.all' : 2.0}),
    't_t4' : ('Top', 'is_ebc', {'t.all' : 3.0}),
}

def is_ebc(ts):
    if ts.step in (2, 4):
        return True

    else:
        return False

functions = {
    'is_ebc' : (is_ebc,),
}

integrals = {
    'ivol' : ('v', 2),
    'isurf' : ('s', 2),
}

equations = {
    'eq' : """dw_laplace.2.Omega( one.val, s, t ) = 0""",
}

solvers = {
    'ls' : ('ls.scipy_direct', {}),
    'newton' : ('nls.newton', {
        'i_max'      : 1,
        'eps_a'      : 1e-10,
        'problem'   : 'nonlinear',
    }),
    'ts' : ('ts.simple', {
        't0'     : 0.0,
        't1'     : 4.0,
        'dt'     : None,
        'n_step' : 5, # has precedence over dt!

        'quasistatic' : True,
    }),
}