Coverage for src/pymor/analyticalproblems/advection : 100%

# -*- coding: utf-8 -*- 

# This file is part of the pyMOR project (http://www.pymor.org). 

# Copyright Holders: Rene Milk, Stephan Rave, Felix Schindler 

# License: BSD 2-Clause License (http://opensource.org/licenses/BSD-2-Clause) 

from __future__ import absolute_import, division, print_function 

import numpy as np 

from pymor.core import ImmutableInterface 

from pymor.domaindescriptions import RectDomain 

from pymor.functions import ConstantFunction 

from pymor.tools import Named 

class InstationaryAdvectionProblem(ImmutableInterface, Named): 

    '''Instationary advection problem. 

    The problem is to solve :: 

        ∂_t u(x, t, μ)  +  ∇ ⋅ f(u(x, t, μ), t, μ) = s(x, t, μ) 

                                        u(x, 0, μ) = u_0(x, μ) 

    for u with t in [0, T], x in Ω. 

    Parameters 

    ---------- 

    domain 

        A |DomainDescription| of the domain Ω the problem is posed on. 

    flux_function 

        The |Function| f. The current time is provided by adding the key `'_t'` 

        to the |Parameter| `mu`. 

    flux_function_derivative 

        The derivative of f with respect to u. 

    rhs 

        The |Function| s. The current time is provided by adding the key `'_t'` 

        to the |Parameter| `mu`. 

    dirichlet_data 

        |Function| providing the Dirichlet boundary values in global coordinates. 

    initial_data 

        |Function| providing the initial values in global coordinates. 

    T 

        The end time T. 

    name 

        Name of the problem. 

    Attributes 

    ---------- 

    domain 

    rhs 

    flux_function 

    flux_function_derivative 

    initial_data 

    dirichlet_data 

    T 

    ''' 

    def __init__(self, domain=RectDomain(), rhs=ConstantFunction(dim_domain=2), 

                 flux_function=ConstantFunction(value=np.array([0, 0]), dim_domain=2), 

                 flux_function_derivative=ConstantFunction(value=np.array([0, 0]), dim_domain=2), 

                 dirichlet_data=ConstantFunction(value=0, dim_domain=2), 

                 initial_data=ConstantFunction(value=1, dim_domain=2), T=1, name=None): 

        self.domain = domain 

        self.rhs = rhs 

        self.flux_function = flux_function 

        self.flux_function_derivative = flux_function_derivative 

        self.dirichlet_data = dirichlet_data 

        self.initial_data = initial_data 

        self.T = T 

        self.name = name