## Description🔗

The totalPressure is a boundary condition that sets the static pressure at the patch $$p_p$$ based on a specification of the total pressure, $$p_0$$. The mode of operation is determined via the input entries and the dimensions of the convective flux, phi ($$\phi$$).

Four variants are possible:

### Incompressible subsonic🔗

Patch pressure described by subtracting the dynamic pressure from the total pressure, where the flux has dimensions of $$m^3/s$$.

$p_p = p_0 - \frac{1}{2}\mag{\u}^2$

where:

Property Description
$$p_p$$ Incompressible pressure at patch [m^2/s^2]
$$p_0$$ Incompressible total pressure [m^2/s^2]
$$\u$$ Velocity

### Compressible subsonic🔗

Patch pressure described by subtracting the dynamic pressure from the total pressure, where the flux has dimensions of $$kg/s$$.

$p_p = p_0 - \frac{1}{2}\rho\mag{\u}^2$

where:

Property Description
$$p_p$$ Pressure at patch [Pa]
$$p_0$$ Total pressure [Pa]
$$\rho$$ Density [kg/m^3]
$$\u$$ Velocity

### Compressible transonic ($$\gamma = 1$$)🔗

Ratio of specific heats, $$\gamma = C_p/C_v$$ equal to 1.

$p_p = \frac{p_0}{1 + \frac{1}{2} \psi \mag{\u}^2}$

where:

Property Description
$$p_p$$ Pressure at patch [Pa]
$$p_0$$ Total pressure [Pa]
$$\psi$$ Compressibility [m^2/s^2]
$$\u$$ Velocity

### Compressible supersonic ($$\gamma > 1$$)🔗

Ratio of specific heats, $$\gamma = C_p/C_v$$ greater than 1.

$p_p = \frac{p_0}{\left(1 + \frac{\gamma - 1}{2} \psi \mag{\u}^2\right)^{\frac{\gamma}{\gamma - 1}}}$
Property Description
$$p_p$$ Pressure at patch [Pa]
$$p_0$$ Total pressure [Pa]
$$\psi$$ Compressibility [m^2/s^2]
$$G$$ Coefficient given by $$\frac{\gamma}{1-\gamma}$$
$$\u$$ Velocity

The modes of operation are set by the dimensions of the pressure field to which this boundary condition is applied, the psi entry and the value of gamma:

Mode Dimensions psi gamma
Incompressible subsonic p/rho - -
Compressible subsonic p none -
Compressible transonic p psi 1
Compressible supersonic p psi > 1

## Usage🔗

The condition requires entries in both the boundary and field files.

### Boundary file🔗

<patchName>
{
type            patch;
...
}


### Field file🔗

<patchName>
{
// Mandatory entries
type            totalPressure;

// Conditional entries

// Incompressible subsonic
rho             none;
p0              uniform 0;

// Compressible subsonic
p0              uniform 100000;

// Compressible transonic
psi             psi;
p0              uniform 100000;

// Compressible supersonic
psi             psi;
gamma           1.4;
p0              uniform 100000;

// Optional entries
U               <word>;
phi             <word>;
rho             <word>;
psi             <word>;

// Inherited entries
...
}


where:

Property Description Type Required Default
type Type name: totalPressure word yes -
p0 Total pressure field scalarField yes -
U Name of velocity field word no U
phi Name of flux field word no phi
rho Name of density field word no rho
psi Name of compressibility field word no none
gamma Heat capacity ratio scalar conditional -

## Further information🔗

Tutorial:

Source code:

API:

History:

• Introduced in version 1.5