Auxiliary Equations Through w¶
The w variables are auxiliary state variables independent of ModelC,
ModelD, and ModelW. They can be used with any primary model class.
A useful abstraction is
\[
\alpha \frac{\partial w}{\partial t}
+ \beta w
= \mathcal{G}(u,q,w,v,x,t;\mu).
\]
The exact interpretation is supplied by the model callbacks. Exasim provides the storage and generated kernels; the model author defines the physics.
Supported Callback Mapping¶
| Purpose | Frontend callback | Text2Code function | Generated/contract name |
|---|---|---|---|
Initialize w |
initw(x,mu,eta) |
Initw / Initwdg |
initwdg |
Source/update for w |
sourcew(u,q,w,v,x,t,mu,eta) |
Sourcew |
sourcew |
EOS dependence on w |
eos(...) |
EoS |
eos, eos_dw |
Common Forms¶
| Form | Equation | Typical use |
|---|---|---|
| Algebraic auxiliary equation | \(\beta w = \mathcal{G}\) | Equilibrium closures or material state. |
| Auxiliary ODE | \(\partial w/\partial t = \mathcal{G}\) | Chemistry, turbulence, internal variables. |
| Relaxation model | \(\tau \partial w/\partial t + w = \mathcal{G}\) | Nonequilibrium or memory models. |
| ADE model | Same callback structure | Dispersive or constitutive auxiliary differential equations. |
Examples¶
- Chemical kinetics in
examples/Euler/reacting_flowandexamples/ReactingFlows/reactingcylinder. - High-temperature gas modeling under
frontends/Matlab/Modeling/CNS5air. - Turbulence-like or internal material variables supplied through
w. - Vibrational nonequilibrium and multi-temperature state variables.
- Constitutive relaxation and memory effects.
w may enter fluxes, sources, EOS, boundary conditions, initial conditions,
QoI, and visualization callbacks.