FrictionLaws Namespace Reference

Variables
str	friction_coefficients
str	max_eigenvalue
str	flux
str	nonconservative_product
str	coulomb_friction
str	material_dependent_basal_friction

Variable Documentation

coulomb_friction

str FrictionLaws.coulomb_friction

Initial value:

=  friction_coefficients + r"""
  S[Shortcuts::h] = 0.0;
  S[Shortcuts::hu] = 0.0;
  S[Shortcuts::hv] = 0.0;
 
  if (tarch::la::greater(Q[Shortcuts::h], 0.0)) {
    const double u{Q[Shortcuts::hu + 0] / Q[Shortcuts::h]};
    const double v{Q[Shortcuts::hu + 1] / Q[Shortcuts::h]};
    const double velMagnitudeSqr{u * u + v * v};
    if (tarch::la::greater(velMagnitudeSqr, 0.0)) {
      const double zx{Q[Shortcuts::bx] / h(0)};
      const double zy{Q[Shortcuts::by] / h(1)};
      const double c{1.0 / std::sqrt(1.0 + zx * zx + zy * zy)};
      const double friction{-GRAV * (Mu1 * Q[Shortcuts::h] * c)};
      const double velMagnitude{std::sqrt(velMagnitudeSqr)};
      S[Shortcuts::hu] += u / velMagnitude * friction;
      S[Shortcuts::hv] += v / velMagnitude * friction;
    }
  }
"""

Definition at line 98 of file FrictionLaws.py.

flux

str FrictionLaws.flux

Initial value:

=  friction_coefficients + r"""
  if (tarch::la::greater(Q[Shortcuts::h], 0.0)) {
    const double ih = 1.0 / Q[Shortcuts::h];
    F[Shortcuts::h] = Q[Shortcuts::hu + normal];
    switch (normal) {
    case 0:
      F[Shortcuts::hu] = ih * Q[Shortcuts::hu] * Q[Shortcuts::hu] + 0.5 * GRAV * std::cos(Zeta) * Q[Shortcuts::h] * Q[Shortcuts::h];
      F[Shortcuts::hv] = ih * Q[Shortcuts::hu] * Q[Shortcuts::hv];
      break;
    case 1:
      F[Shortcuts::hu] = ih * Q[Shortcuts::hv] * Q[Shortcuts::hu];
      F[Shortcuts::hv] = ih * Q[Shortcuts::hv] * Q[Shortcuts::hv] + 0.5 * GRAV * std::cos(Zeta) * Q[Shortcuts::h] * Q[Shortcuts::h];
      break;
    }
  } else {
    F[Shortcuts::h]  = 0.0;
    F[Shortcuts::hu] = 0.0;
    F[Shortcuts::hv] = 0.0;
  }
"""

Definition at line 42 of file FrictionLaws.py.

friction_coefficients

str FrictionLaws.friction_coefficients

Initial value:

=  r"""
  const double Zeta = 35.0 * tarch::la::PI / 180.0; // Conversion of degrees to radians
  const double Zeta1 = 28.95 * tarch::la::PI / 180.0;
  const double Zeta2 = 44.09 * tarch::la::PI / 180.0;
  const double Zeta3 = 31.81 * tarch::la::PI / 180.0;
 
  const double Mu1 = std::tan(Zeta1);
  const double Mu2 = std::tan(Zeta2);
  const double Mu3 = std::tan(Zeta3);
 
  constexpr double Beta = 1.07;
  constexpr double Gamma = 2.01;
  constexpr double BetaStar = 0.06;
  // Kappa in the friction law is assumed to be 1 and is just initialised as a
  // const double here using Kappa. The user can apply std::pow((Fr/BetaStar),
  // Kappa) for evaluating T here in case the value of Kappa is different
  // from 1.
 
  constexpr double Kappa = 1.0;
  constexpr double FrictionLengthScale = 0.00035;
 
  const double Nu = (2.0 / 9.0) * (FrictionLengthScale / Beta) * (GRAV * std::sin(Zeta) / std::sqrt(GRAV * std::cos(Zeta))) * (((Mu2 - Mu1) / (std::tan(Zeta) - Mu1)) - 1.0);
  const double Hstart = FrictionLengthScale * (((Mu2 - Mu1) / (std::tan(Zeta) - Mu3)) - 1.0);
  const double Hstop = FrictionLengthScale * (((Mu2 - Mu1) / (std::tan(Zeta) - Mu1)) - 1.0);
"""

Definition at line 4 of file FrictionLaws.py.

material_dependent_basal_friction

str FrictionLaws.material_dependent_basal_friction

Definition at line 119 of file FrictionLaws.py.

max_eigenvalue

str FrictionLaws.max_eigenvalue

Initial value:

=  friction_coefficients + r"""
  double result{0.0};
 
  if (tarch::la::greater(Q[Shortcuts::h], 0.0)) {
    const double u = Q[Shortcuts::hu + normal] / Q[Shortcuts::h];
    const double c = std::sqrt(GRAV * std::cos(Zeta) * Q[Shortcuts::h]);
    result = std::fmax(std::fabs(u - c), std::fabs(u + c));
  }
 
  return result;
"""

Definition at line 30 of file FrictionLaws.py.

nonconservative_product

str FrictionLaws.nonconservative_product

Definition at line 63 of file FrictionLaws.py.