Source Terms Reference

Source terms add volumetric forcing, reactions, body forces, and coupling contributions to the PDE residual.

Volume Source

Text2Code:

function Source(x, uq, v, w, eta, mu, t)
  output_size(s) = ncu;
  ...
end

C++ model:

KOKKOS_INLINE_FUNCTION static
void source(dstype s[], const dstype x[], const dstype uq[],
            const dstype v[], const dstype w[], const dstype mu[],
            const dstype uinf[], dstype t);

Arguments

Argument	Meaning
x	Coordinates.
uq	Solution and, for ModelD/ModelW, auxiliary entries.
v	External/other-DG field.
w	Auxiliary state.
mu	Physics parameters.
eta / uinf	Reference/free-stream data.
t	Time.

Source Categories

Category	Examples
Body forces	Gravity, Lorentz force, rotating-frame force.
Reactions	Chemical kinetics, source/sink terms.
Coupling	Energy exchange, multiphysics transfer, forcing from external fields.
Manufactured forcing	Source chosen to reproduce an analytical solution.
Stabilization support	Model-specific artificial source terms.

Auxiliary Source Sourcew

Sourcew controls the auxiliary w equation:

function Sourcew(x, uq, v, w, eta, mu, t)
  output_size(sw) = ncw;
  ...
end

See Auxiliary equations.

Jacobians

For HDG and implicit solves, generated code can provide derivatives with respect to vectors listed in the jacobian declaration. Direct C++ models can override:

• source_jac_uq
• source_jac_w

Incorrect source Jacobians can degrade or break Newton convergence.

Example

function Source(x, uq, v, w, eta, mu, t)
  output_size(s) = 1;
  s[0] = sin(pi*x[0])*sin(pi*x[1]);
end