Grand Potential Density

The GrandPotentialDensity class manages the grand potential density

$$\begin{array}{}\text{(1)}& \omega =\sum _{\alpha }{\varphi }_{\alpha }{\omega }_{\alpha }({\mu }_i,T)\end{array}$$

which is the sum of the grand potential densities ${\omega }_{\alpha }({\mu }_i,T)$ of each thermodynamic phase $\alpha$ weighted by the phase-field ${\varphi }_{\alpha }$.

Dependencies

• GrandPotentialPhaseDensity
• GrandPotentialPhaseDensity_Parabolic
• PhaseField
• Settings
• VTK

Usage

The grand potential class is required as input for the solve functions of the GrandPotentialSolver class. Below a minimalistic usage example is given

// ....
Settings              OPSettings (InputFileName);
GrandPotentialDensity omega      (OPSettings, InputFileName);
// ....
omega.Set(Temp.Tx,GPS.ChemicalPotential);
// ....

for(RTC.tStep = RTC.tStart; RTC.tStep <= RTC.nSteps; RTC.IncrementTimeStep())
{
    // ....
    GPS.Solve(Phase,omega,BC,IP,Tx,RTC.dt);
    // ....
}

Input Parameters

The GrandPotentialDensity class has only one required input parameter for each thermodynamic phase. Currently, only the Parabolic is supported. Below an example is given for two thermodynamic phases is given

@GrandPotentialDensity

$OMEGA_0    Vapor phase model    : Parabolic
$OMEGA_1    Solid phase model    : Parabolic

Each grand potential density model

Interface

GrandPotentialDensity (Settings& locSettings, std::string InputFileName);   ///< Allocates and initializes memory

Read requested grand potential density model for each thermodynamic phase form class form .opi file. Each grand potential density model is a class hat inherits from GrandPotentialPhaseDensity. An object of each requested class is created. For each object GrandPotentialPhaseDensity::Initialize and GrandPotentialPhaseDensity::ReadInput are called.

void Set(const Storage3D<double,0>& Temperature, const Storage3D<double,1>& ChemicalPotential)

Sets and stores reference to Temperature and chemical potential class. The Set method needs to be called explicitly only once but will it be implicitly invoked by the compiler on each function call when the external external memory is accessed during that function call! This allow to abstract the definition ${\omega }_{\alpha }({\mu }_i,T)$ independent of (i,j,k).

GrandPotentialPhaseDensity& operator() (size_t PhaseIdx) const

Returns grand potential density ${\omega }_{\alpha }({\mu }_i)$ of phase $\alpha$

double operator() (int i, int j, int k, const PhaseField& Phase) const

Returns grand potential density $\omega$ at (i,j,k).