12 #include "libmesh/utility.h" 32 Real lower_density = 1.0e-2;
33 Real upper_density = 100.0;
59 (2.0 * da_dd +
delta * d2a_dd2);
90 de_dp = tau * d2a_ddt / (
density * (2.0 * da_dd +
delta * d2a_dd2));
92 (
delta * tau * d2a_ddt * (da_dd - tau * d2a_ddt) / (2.0 * da_dd +
delta * d2a_dd2) +
178 ds_dT = -
_R * tau * (da_dt -
alpha(
delta, tau) + tau * (d2a_dt2 - da_dt)) /
211 dh_dp = (da_dd +
delta * d2a_dd2 + tau * d2a_ddt) / (
density * (2.0 * da_dd +
delta * d2a_dd2));
213 (
delta * da_dd * (1.0 - tau * d2a_ddt / da_dd) * (1.0 - tau * d2a_ddt / da_dd) /
214 (2.0 +
delta * d2a_dd2 / da_dd) -
virtual Real d2alpha_ddeltatau(Real delta, Real tau) const =0
Second derivative of Helmholtz free energy wrt delta and tau.
virtual Real d2alpha_dtau2(Real delta, Real tau) const =0
Second derivative of Helmholtz free energy wrt tau.
static InputParameters validParams()
virtual virtual std Real molarMass() const
Fluid name.
static const std::string density
int delta(unsigned int i, unsigned int j)
Delta function, which returns zero if $i j$ and unity if $i=j$.
static const Real _R
Universal gas constant (J/mol/K)
virtual Real c_from_p_T(Real pressure, Real temperature) const override
static const std::string temperature
virtual Real d2alpha_ddelta2(Real delta, Real tau) const =0
Second derivative of Helmholtz free energy wrt delta.
ADRealEigenVector< T, D, asd > sqrt(const ADRealEigenVector< T, D, asd > &)
virtual Real cp_from_p_T(Real pressure, Real temperature) const override
static const std::string cp
HelmholtzFluidProperties(const InputParameters ¶meters)
virtual Real cv_from_p_T(Real pressure, Real temperature) const override
virtual Real criticalTemperature() const
Critical temperature.
virtual Real dalpha_ddelta(Real delta, Real tau) const =0
Derivative of Helmholtz free energy wrt delta.
const std::vector< double > x
Real root(std::function< Real(Real)> const &f, Real x1, Real x2, Real tol=1.0e-12)
Finds the root of a function using Brent's method.
virtual Real h_from_p_T(Real pressure, Real temperature) const override
Common class for single phase fluid properties.
virtual Real rho_from_p_T(Real pressure, Real temperature) const override
e e e e s T T T T T rho v v T h
static InputParameters validParams()
virtual Real dalpha_dtau(Real delta, Real tau) const =0
Derivative of Helmholtz free energy wrt tau.
virtual Real p_from_rho_T(Real rho, Real T) const
Pressure as a function of density and temperature.
virtual Real alpha(Real delta, Real tau) const =0
Helmholtz free energy.
virtual Real criticalDensity() const
Critical density.
DIE A HORRIBLE DEATH HERE typedef LIBMESH_DEFAULT_SCALAR_TYPE Real
virtual Real s_from_p_T(Real pressure, Real temperature) const override
static const std::string pressure
void bracket(std::function< Real(Real)> const &f, Real &x1, Real &x2)
Function to bracket a root of a given function.
virtual Real e_from_p_T(Real pressure, Real temperature) const override