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Auxiliary Equations Reference

Auxiliary variables w are stored in wdg and configured by ncw. They can represent algebraic closures, ODE states, relaxation variables, turbulence variables, chemistry states, or other model-specific fields.

Configuration

Field Meaning
ncw Number of auxiliary w components.
Initw / initwdg Initial value for w.
Sourcew / sourcew Auxiliary equation source/evolution term.
EoS Optional closure depending on w.

Text2Code Interface

function Initw(x, eta, mu)
  output_size(w0) = ncw;
  ...
end

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

C++ Interface

KOKKOS_INLINE_FUNCTION static
void initwdg(dstype w[], const dstype x[],
             const dstype uinf[], const dstype mu[]);

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

Common Auxiliary Forms

Form Interpretation
Algebraic w = G(u, q, v, x, t; mu) through EOS/closure style logic.
ODE dw/dt = G(u, q, w, v, x, t; mu).
Relaxation tau_w dw/dt + w = G(...).
ADE Memory or dispersive auxiliary differential equations.

The exact time integration semantics are controlled by the backend model and problem settings; this Reference documents the callback interface.

Coupling to Other Functions

w can appear in:

  • Flux
  • Source
  • Tdfunc
  • EoS
  • Ubou
  • Fbou
  • FbouHdg
  • VisScalars, VisVectors, VisTensors
  • QoIvolume, QoIboundary

Sweep and Restart Notes

If sol.bin or saved solution files contain wdg, Exasim trusts the file contents. If wdg is absent and ncw > 0, Exasim computes it from Initw using the active physicsparam.