swe_resting_lake.py

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# This file is part of the ExaHyPE2 project. For conditions of distribution and
# use, please see the copyright notice at www.peano-framework.org
from .scenario import Scenario
 
import os, sys
import jinja2
 
sys.path.insert(0, os.path.abspath("../equations"))
from equations import SWE_W_Bathymetry
 
class SWERestingLake(Scenario):
    """
    Resting lake scenario for the shallow water equations.
    The real water height H as defined by the sum of the water column h and
    the bathymetry b is constant over the entire domain, meaning that there
    should be no changes on the entire domain, but because we use the sum of
    the derivatives of h and b (h' + b') instead of the derivative of the sum
    (h + b)' some rounding errors will creep in, which causes unphysical
    waves to appear.
    As such this scenario is nice for testing how large these unphysical waves
    are for a given algorithm, and how stable the algorithm is, i.e. does it
    dampen out these waves or do they oscillate out of control.
    """
 
    _plot_dt = 0.0
    _offset = -0.5
    _domain_size = 1.0
    _periodic_bc = True
    _dimensions = 2
    _equation = SWE_W_Bathymetry()
    _end_time = 1.0
 
    def __init__(
        self,
        initial_conditions="sinusoidal",
    ):
        self._scenario = initial_conditions
 
    def _initial_conditions(self, Q):
        d = {"VARIABLE": Q}
        return {
        "bilinear": jinja2.Template("""
    {{VARIABLE}}[1] = 0.0;
    {{VARIABLE}}[2] = 0.0;
    {{VARIABLE}}[3] = 1.0 - std::abs(x[0]) - std::abs(x[1]);
    {{VARIABLE}}[0] = 2.0 - {{VARIABLE}}[3];
""").render(**d),
    "sinusoidal": jinja2.Template("""
    {{VARIABLE}}[1] = 0.0;
    {{VARIABLE}}[2] = 0.0;
    {{VARIABLE}}[3] = sin( 2*M_PI * (x[0]+x[1]) );
    {{VARIABLE}}[0] = 2.0 - {{VARIABLE}}[3];
""").render(**d),
    "constant": jinja2.Template("""
    {{VARIABLE}}[1] = 0.0;
    {{VARIABLE}}[2] = 0.0;
    {{VARIABLE}}[3] = 1.0;
    {{VARIABLE}}[0] = 2.0 - {{VARIABLE}}[3];
""").render(**d)
    }
 
    def initial_conditions(self):
        return self._initial_conditions("Q")[self._scenario]
 
    def analytical_solution(self):
        return self._initial_conditions("solution")[self._scenario]