Equations of State Reference¶

Equation-of-state callbacks provide closure or derived quantities used by fluxes, sources, auxiliary equations, and postprocessing.

Text2Code Function¶

function EoS(x, uq, v, w, eta, mu, t)
  output_size(e) = N;
  ...
end

EoS is optional. If omitted, generated code supplies an empty/default implementation where supported.

C++ Model Functions¶

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

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

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

Arguments¶

Argument	Meaning
`x`	Spatial coordinates.
`uq`	Packed solution state.
`v`	External/other-DG field.
`w`	Auxiliary state.
`mu`	Physics parameters.
`uinf` / `eta`	Reference/free-stream values.
`t`	Current time.

Typical Outputs¶

EOS callbacks can compute:

Pressure.
Temperature.
Enthalpy.
Sound speed.
Transport coefficients.
Reaction-rate inputs.
Material properties.

The exact output size and ordering are model-defined and must match the generated or hand-written model code that consumes it.

Derivatives¶

eos_du and eos_dw provide derivatives with respect to uq and w. They are needed when EOS values affect HDG Jacobian assembly or coupled auxiliary equations.

Interactions¶

Consumer	EOS role
Fluxes	Provide pressure, transport coefficients, or closure variables.
Sources	Provide reaction rates, thermodynamic state, or material response.
Auxiliary equations	Couple `w` evolution to thermodynamic closure.
Boundary conditions	Compute characteristic or thermodynamic boundary states.
Visualization	Expose derived variables as scalar/vector/tensor fields.

Example Pattern¶

function EoS(x, uq, v, w, eta, mu, t)
  output_size(e) = 2;
  gamma = mu[0];
  rho = uq[0];
  energy = uq[3];
  pressure = (gamma - 1.0)*energy;
  e[0] = pressure;
  e[1] = gamma*pressure/rho;
end

Use the actual state ordering for the selected PDE model.