euler.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 .equation import Equation
 
 
class Euler(Equation):
    def __init__(self, dimensions, gamma=1.4):
        self.dimensions = dimensions
        self.num_unknowns = 4 if dimensions == 2 else 5
        self.num_auxiliary_variables = 0
        self.gamma = gamma
 
    def eigenvalues(self):
        return (
            """
  const double irho = 1.0 / Q[0];
  constexpr double Gamma = """
            + str(self.gamma)
            + """;
  const double p = (Gamma - 1.0) * (Q[4] - 0.5 * irho * (Q[1]*Q[1]+Q[2]*Q[2]+Q[3]*Q[3]));
 
  const double c = std::sqrt(Gamma * p * irho);
  const double u = Q[normal + 1] * irho;
 
  return std::fmax(std::abs(u-c), std::abs(u+c));
"""
            if self.dimensions == 3
            else """
  const double irho = 1.0 / Q[0];
  constexpr double Gamma = """
            + str(self.gamma)
            + """;
  const double p = (Gamma - 1.0) * (Q[3] - 0.5 * irho * (Q[1]*Q[1]+Q[2]*Q[2]));
 
  const double c = std::sqrt(Gamma * p * irho);
  const double u = Q[normal + 1] * irho;
 
  return std::fmax(std::abs(u-c), std::abs(u+c));
"""
        )
 
    def flux(self):
        return (
            """
  const double irho = 1.0 / Q[0];
  constexpr double Gamma = """
            + str(self.gamma)
            + """;
  const double p = (Gamma - 1.0) * (Q[4] - 0.5 * irho * (Q[1]*Q[1]+Q[2]*Q[2]+Q[3]*Q[3]));
 
  F[0] = Q[normal + 1];
  F[1] = Q[normal + 1] * Q[1] * irho;
  F[2] = Q[normal + 1] * Q[2] * irho;
  F[3] = Q[normal + 1] * Q[3] * irho;
  F[4] = Q[normal + 1] * irho * (Q[4] + p);
 
  F[normal + 1] += p;
"""
            if self.dimensions == 3
            else """
  const double irho = 1.0 / Q[0];
  constexpr double Gamma = """
            + str(self.gamma)
            + """;
  const double p = (Gamma - 1.0) * (Q[3] - 0.5 * irho * (Q[1]*Q[1]+Q[2]*Q[2]));
 
  F[0] = Q[normal + 1];
  F[1] = Q[normal + 1] * Q[1] * irho;
  F[2] = Q[normal + 1] * Q[2] * irho;
  F[3] = Q[normal + 1] * irho * (Q[3] + p);
 
  F[normal + 1] += p;
"""
        )