euler_isotropic_vortex.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
import sys
 
sys.path.insert(0, os.path.abspath("../equations"))
from equations import Euler
 
 
class EulerIsotropicVortex(Scenario):
    """
    Scenario reproduced from Ioratti, Dumbser & Loubère, https://doi.org/10.1007/s10915-020-01209-w (p. 43)
    """
 
    _plot_dt = 0.0
    _offset = -5.0
    _domain_size = 10.0
    _end_time = 10.0
    _periodic_bc = True
 
    def __init__(self, velocity=1.0):
        self._dimensions_dimensions = 2
        self._equation_equation = Euler(dimensions=2, gamma=1.4)
        self._velocity = velocity
 
    def initial_conditions(self):
        return (
            """
  static constexpr double epsilon = 5.0;
  static constexpr double pi = std::numbers::pi;
  static constexpr double i_pi = 1./pi;
  static constexpr double eos_gamma = 1.4;
 
  const double r = tarch::la::norm2(x);
  const double du = 0.5 * epsilon / pi * exp(0.5 * (1. - r * r)) * (- x[1]);
  const double dv = 0.5 * epsilon / pi * exp(0.5 * (1. - r * r)) * (x[0]);
  const double dTemp = -(eos_gamma - 1.) * epsilon*epsilon / 8. / eos_gamma / pi / pi *
                 exp(1. - r * r);
  const double drho = pow(1. + dTemp, 1. / (eos_gamma - 1.)) - 1.;
  const double dp = pow(1. + dTemp, eos_gamma / (eos_gamma - 1.)) - 1.;
 
  constexpr double rho_inf = 1.;
  constexpr double p_inf = 1.;
  constexpr double u_inf = """
            + str(self._velocity)
            + """;
  constexpr double v_inf = """
            + str(self._velocity)
            + """;
 
    Q[0] = rho_inf + drho; // fluid density
    Q[1] = Q[0] * (u_inf + du); // momentum
    Q[2] = Q[0] * (v_inf + dv);
    // total energy = internal energy + kinetic energy
    Q[3] = (p_inf + dp) / (eos_gamma-1) + 0.5*Q[0] * ((u_inf+du)*(u_inf+du)+(v_inf+dv)*(v_inf+dv));
"""
        )
 
    def analytical_solution(self):
        return (
            """
  /*
    The initial condition is transported without deformation in a periodic
    domain [-5., +5.], i.e. the value at a given point is the value at the
    position x - v*t but accounting for periodicity.
    Therefore we find the point x - v*t, and then shift this by instances
    of 10.0 until we find the point within the domain.
  */
  constexpr double rho_inf = 1.;
  constexpr double p_inf = 1.;
  constexpr double u_inf = """
            + str(self._velocity)
            + """;
  constexpr double v_inf = """
            + str(self._velocity)
            + """;
 
  const double t_capped = t  - (int) t / 10;
  tarch::la::Vector<Dimensions,double> pos = { (x[0] - u_inf*t_capped) < -5.0 ? (x[0] - u_inf*t_capped) + 10. : (x[0] - u_inf*t_capped),
                                               (x[1] - v_inf*t_capped) < -5.0 ? (x[1] - v_inf*t_capped) + 10. : (x[1] - v_inf*t_capped) };
 
  static constexpr double epsilon = 5.0;
  static constexpr double pi = std::numbers::pi;
  static constexpr double i_pi = 1./pi;
  static constexpr double eos_gamma = 1.4;
 
  const double r = tarch::la::norm2(pos);
  const double du = 0.5 * epsilon / pi * exp(0.5 * (1. - r * r)) * (- pos[1]);
  const double dv = 0.5 * epsilon / pi * exp(0.5 * (1. - r * r)) * (pos[0]);
  const double dTemp = -(eos_gamma - 1.) * epsilon*epsilon / 8. / eos_gamma / pi / pi *
                 exp(1. - r * r);
  const double drho = pow(1. + dTemp, 1. / (eos_gamma - 1.)) - 1.;
  const double dp = pow(1. + dTemp, eos_gamma / (eos_gamma - 1.)) - 1.;
 
    solution[0] = rho_inf + drho; // fluid density
    solution[1] = solution[0] * (u_inf + du); // momentum
    solution[2] = solution[0] * (v_inf + dv);
    // total energy = internal energy + kinetic energy
    solution[3] = (p_inf + dp) / (eos_gamma-1) + 0.5*solution[0] * ((u_inf+du)*(u_inf+du)+(v_inf+dv)*(v_inf+dv));
"""
        )