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Equations Of State

Equation-of-state callbacks provide closures and derived quantities. They are not a separate primary PDE formulation.

Generic form:

\[ y = \mathcal{E}(u,q,w,v,x,t;\mu). \]

In frontend models the callback is eos(...); in Text2Code the function is EoS; in the generated model contract the method is eos. The generated backend also supports derivatives with respect to u and w through EoSdu/EoSdw or eos_du/eos_dw when generated.

Typical Outputs

  • Pressure.
  • Temperature.
  • Enthalpy.
  • Sound speed.
  • Transport coefficients.
  • Reaction rates.
  • Material constitutive quantities.

Typical EOS Families

  • Ideal gas EOS.
  • Thermally perfect gas EOS.
  • Real-gas EOS.
  • Plasma EOS.
  • Material constitutive laws.

Interaction With Other Model Terms

EOS outputs may be used by:

  • Flux functions.
  • Source functions.
  • Auxiliary w equations.
  • Boundary conditions.
  • Artificial-viscosity sensors or coefficients.
  • Visualization and QoI functions.

Repository examples include reacting-flow and high-temperature-gas models such as examples/Euler/reacting_flow, examples/ReactingFlows/reactingcylinder, and frontends/Matlab/Modeling/CNS5air.