PDE Namespace Reference

Variables
str	compute_primitive_variables
str	max_eigenvalue
str	flux
str	source_term
str	eigenvalue
str	stiff_eigenvalue
str	nonconservative_product
str	stiff_nonconservative_product
str	stiff_source_term_aderdg
str	stiff_source_term_fv

Variable Documentation

compute_primitive_variables

str PDE.compute_primitive_variables

Initial value:

=  r"""
  const auto irho = 1.0 / Q[Shortcuts::rho];
  const auto u0 = Q[Shortcuts::rhoU + 0] * irho;
  const auto u1 = Q[Shortcuts::rhoU + 1] * irho;
#if DIMENSIONS == 3
  const auto u2 = Q[Shortcuts::rhoU + 2] * irho;
#endif
 
#if DIMENSIONS == 3
  const auto uSq = u0 * u0 + u1 * u1 + u2 * u2;
  const auto u_n = (normal == 0) ? u0 : (normal == 1) ? u1 : u2;
#else
  const auto uSq = u0 * u0 + u1 * u1;
  const auto u_n = (normal == 0) ? u0 : u1;
#endif
 
  const auto internalE = Q[Shortcuts::rhoE] - 0.5 * Q[Shortcuts::rho] * uSq;
  const auto p = (GAMMA - 1.0) * internalE;
"""

Definition at line 4 of file PDE.py.

eigenvalue

str PDE.eigenvalue

Initial value:

=  r"""
  if (Q[Shortcuts::h] <= hThreshold) {
    return 0.0;
  }
 
  // Wave speed estimation based on the flux Jacobian
  const auto Vn{Q[Shortcuts::hu + normal] / Q[Shortcuts::h]};
  const auto c{std::sqrt(g * Q[Shortcuts::h])};
  const auto sFlux{std::fmax(std::fabs(Vn + c), std::fabs(Vn - c))};
"""

Definition at line 4 of file PDE.py.

flux

str PDE.flux

Initial value:

=  r"""
  {compute_primitive_variables}
 
  F[Shortcuts::rho] = Q[Shortcuts::rhoU + normal];
 
  F[Shortcuts::rhoU + 0] = Q[Shortcuts::rhoU + 0] * u_n;
  F[Shortcuts::rhoU + 1] = Q[Shortcuts::rhoU + 1] * u_n;
#if DIMENSIONS == 3
  F[Shortcuts::rhoU + 2] = Q[Shortcuts::rhoU + 2] * u_n;
#endif
 
  F[Shortcuts::rhoU + normal] += p;
 
  F[Shortcuts::rhoE] = (Q[Shortcuts::rhoE] + p) * u_n;
""".format(
    compute_primitive_variables=compute_primitive_variables
)

Definition at line 34 of file PDE.py.

max_eigenvalue

str PDE.max_eigenvalue

Initial value:

=  r"""
  {compute_primitive_variables}
  const auto speedOfSound = std::sqrt(GAMMA * p * irho);
  auto result = std::fmax(0.0, std::fabs(u_n - speedOfSound));
  result = std::fmax(result, std::fabs(u_n + speedOfSound));
  return result;
""".format(
    compute_primitive_variables=compute_primitive_variables
)

Definition at line 24 of file PDE.py.

nonconservative_product

str PDE.nonconservative_product

Initial value:

=  r"""
  for (int n = 0; n < NumberOfUnknowns; n++) {
    BTimesDeltaQ[n] = 0.0;
  }
 
  if (Q[Shortcuts::h] <= hThreshold) {
    return;
  }
 
  // Bathymetry/topography-related effects
  BTimesDeltaQ[Shortcuts::hu + normal] = g * Q[Shortcuts::h] * (deltaQ[Shortcuts::h] + deltaQ[Shortcuts::z]);
"""

Definition at line 37 of file PDE.py.

source_term

str PDE.source_term

Initial value:

=  r"""
  S[Shortcuts::rho]       = 0.0;
  S[Shortcuts::rhoU + 0]  = 0.0;
  S[Shortcuts::rhoU + 1]  = -Q[Shortcuts::rho] * GRAVITY;
#if DIMENSIONS == 3
  S[Shortcuts::rhoU + 2]  = 0.0;
#endif
  S[Shortcuts::rhoE]      = -Q[Shortcuts::rhoU + 1] * GRAVITY;
"""

Definition at line 52 of file PDE.py.

stiff_eigenvalue

str PDE.stiff_eigenvalue

Initial value:

=  r"""
  // Wave speed estimation based on the stiff source
  const auto momentum{std::sqrt(Q[Shortcuts::hu] * Q[Shortcuts::hu] + Q[Shortcuts::hv] * Q[Shortcuts::hv])};
  const auto sSource{2.0 * g * momentum * invXi / (Q[Shortcuts::h] * Q[Shortcuts::h])};
"""

Definition at line 15 of file PDE.py.

stiff_nonconservative_product

str PDE.stiff_nonconservative_product

Initial value:

=  r"""
  // Compute stiff turbulent drag on the interface
  const auto momentumSQR{Q[Shortcuts::hu] * Q[Shortcuts::hu] + Q[Shortcuts::hv] * Q[Shortcuts::hv]};
  const auto momentum{std::sqrt(momentumSQR)};
  if (tarch::la::greater(momentum / Q[Shortcuts::h], 0.0)) {
    const auto turbulentDrag{g * momentumSQR * invXi / (Q[Shortcuts::h] * Q[Shortcuts::h])};
    const auto directionVect{Q[Shortcuts::hu + normal] / momentum};
    BTimesDeltaQ[Shortcuts::hu + normal] += h[normal] * turbulentDrag * directionVect;
  }
"""

Definition at line 50 of file PDE.py.

stiff_source_term_aderdg

str PDE.stiff_source_term_aderdg

Initial value:

=  r"""
  for (int n = 0; n < NumberOfUnknowns; n++) {
    S[n] = 0.0;
  }
 
  if (Q[Shortcuts::h] <= hThreshold) {
    return;
  }
 
  // Compute local slope cF
  const auto dzx{deltaQ[Shortcuts::z]};
  const auto dzy{deltaQ[Shortcuts::z + NumberOfUnknowns + NumberOfAuxiliaryVariables]};
  const auto cF{1.0 / std::sqrt(1.0 + dzx * dzx + dzy * dzy)};
 
  // Apply friction only if there is some movement
  const auto momentumSQR{Q[Shortcuts::hu] * Q[Shortcuts::hu] + Q[Shortcuts::hv] * Q[Shortcuts::hv]};
  const auto momentum{std::sqrt(momentumSQR)};
  if (tarch::la::greater(momentum / Q[Shortcuts::h], 0.0)) {
    const auto coulombFriction{mu * cF * Q[Shortcuts::h]};
    const auto turbulentDrag{momentumSQR * invXi / (Q[Shortcuts::h] * Q[Shortcuts::h])};
    const auto frictionTerm{-g * (coulombFriction + turbulentDrag) / momentum};
    S[Shortcuts::hu] = Q[Shortcuts::hu] * frictionTerm;
    S[Shortcuts::hv] = Q[Shortcuts::hv] * frictionTerm;
  }
"""

Definition at line 61 of file PDE.py.

stiff_source_term_fv

str PDE.stiff_source_term_fv

Initial value:

=  r"""
  for (int n = 0; n < NumberOfUnknowns; n++) {
    S[n] = 0.0;
  }
 
  if (Q[Shortcuts::h] <= hThreshold) {
    return;
  }
 
  // Compute local slope cF
  const auto dzx{deltaQ[Shortcuts::z]};
  const auto dzy{deltaQ[Shortcuts::z + NumberOfUnknowns + NumberOfAuxiliaryVariables]};
  const auto cF{1.0 / std::sqrt(1.0 + dzx * dzx + dzy * dzy)};
 
  // Apply friction only if there is some movement
  const auto momentumSQR{Q[Shortcuts::hu] * Q[Shortcuts::hu] + Q[Shortcuts::hv] * Q[Shortcuts::hv]};
  const auto momentum{std::sqrt(momentumSQR)};
  if (tarch::la::greater(momentum / Q[Shortcuts::h], 0.0)) {
    const auto coulombFriction{mu * cF * Q[Shortcuts::h]};
    const auto frictionTerm{-g * coulombFriction / momentum};
    S[Shortcuts::hu] = Q[Shortcuts::hu] * frictionTerm;
    S[Shortcuts::hv] = Q[Shortcuts::hv] * frictionTerm;
  }
"""

Definition at line 87 of file PDE.py.