Source code for pymordemos.burgers

#!/usr/bin/env python
# This file is part of the pyMOR project (http://www.pymor.org).
# Copyright 2013-2019 pyMOR developers and contributors. All rights reserved.
# License: BSD 2-Clause License (http://opensource.org/licenses/BSD-2-Clause)

"""Burgers demo.

Solves a two-dimensional Burgers-type equation. See pymor.analyticalproblems.burgers for more details.

Usage:
  burgers.py [-h] [--grid=NI] [--grid-type=TYPE] [--initial-data=TYPE] [--lxf-lambda=VALUE] [--nt=COUNT]
             [--not-periodic] [--num-flux=FLUX] [--vx=XSPEED] [--vy=YSPEED] EXP

Arguments:
  EXP                    Exponent

Options:
  --grid=NI              Use grid with (2*NI)*NI elements [default: 60].
  --grid-type=TYPE       Type of grid to use (rect, tria) [default: rect].
  --initial-data=TYPE    Select the initial data (sin, bump) [default: sin]
  --lxf-lambda=VALUE     Parameter lambda in Lax-Friedrichs flux [default: 1].
  --nt=COUNT             Number of time steps [default: 100].
  --not-periodic         Solve with dirichlet boundary conditions on left
                         and bottom boundary.
  --num-flux=FLUX        Numerical flux to use (lax_friedrichs, engquist_osher)
                         [default: engquist_osher].
  -h, --help             Show this message.
  --vx=XSPEED            Speed in x-direction [default: 1].
  --vy=YSPEED            Speed in y-direction [default: 1].
"""

import sys
import math
import time

from docopt import docopt

from pymor.analyticalproblems.burgers import burgers_problem_2d
from pymor.discretizers.fv import discretize_instationary_fv
from pymor.grids.rect import RectGrid
from pymor.grids.tria import TriaGrid


[docs]def burgers_demo(args): args['--grid'] = int(args['--grid']) args['--grid-type'] = args['--grid-type'].lower() assert args['--grid-type'] in ('rect', 'tria') args['--initial-data'] = args['--initial-data'].lower() assert args['--initial-data'] in ('sin', 'bump') args['--lxf-lambda'] = float(args['--lxf-lambda']) args['--nt'] = int(args['--nt']) args['--not-periodic'] = bool(args['--not-periodic']) args['--num-flux'] = args['--num-flux'].lower() assert args['--num-flux'] in ('lax_friedrichs', 'engquist_osher', 'simplified_engquist_osher') args['--vx'] = float(args['--vx']) args['--vy'] = float(args['--vy']) args['EXP'] = float(args['EXP']) print('Setup Problem ...') problem = burgers_problem_2d(vx=args['--vx'], vy=args['--vy'], initial_data_type=args['--initial-data'], parameter_range=(0, 1e42), torus=not args['--not-periodic']) print('Discretize ...') if args['--grid-type'] == 'rect': args['--grid'] *= 1. / math.sqrt(2) m, data = discretize_instationary_fv( problem, diameter=1. / args['--grid'], grid_type=RectGrid if args['--grid-type'] == 'rect' else TriaGrid, num_flux=args['--num-flux'], lxf_lambda=args['--lxf-lambda'], nt=args['--nt'] ) print(m.operator.grid) print(f'The parameter type is {m.parameter_type}') mu = args['EXP'] print(f'Solving for exponent = {mu} ... ') sys.stdout.flush() tic = time.time() U = m.solve(mu) print(f'Solving took {time.time()-tic}s') m.visualize(U)
if __name__ == '__main__': # parse arguments args = docopt(__doc__) # run demo burgers_demo(args)