josie.ns package¶

Subpackages¶

josie.ns.schemes package

Submodules¶

josie.ns.eos module¶

josie.ns.fields module¶

Navier-Stokes Equations take much of the implementations from euler

josie.ns.problem module¶

class josie.ns.problem.NSProblem(eos, transport)¶

Bases: josie.euler.problem.EulerProblem, josie.fluid.problem.DiffusiveProblem

K(cells)¶

This method returns the diffusive tensor $\pdeDiffusiveMultiplier$ for the Navier-Stokes system.

In 2D it’s

$\ipdeDiffusiveMultiplier = \nsDiffusiveMultiplierXX (xx) \nsDiffusiveMultiplierXY (xy) \nsDiffusiveMultiplierYX (yx) \nsDiffusiveMultiplierYY (yy)$

Return type: np.ndarray

josie.ns.state module¶

We create one big state that contains the actual conservative variables that are used in the flux together with the “auxiliary” variables that are instead needed, for example, to compute the speed of sound.

$\nsState$

rho: density $\rho$
rhoU: component along $x$ of the velocity $\vb{u}$ ,

multiplied by the density
rhoV: component along $y$ of the velocity $\vb{u}$ ,

multiplied by the density
rhoE: total energy multiplied by the density $\rho E$
rhoe: internal energy multiplied by the density $\rho e$
U: component along $x$ of the velocity $u$
V: component along $y$ of the velocity $v$
p: pressure $p$
c: sound velocity $c$

class josie.ns.state.NSGradientState(*args, **kwargs)¶

Bases: josie.state.SubsetState

A State class representing the diffusive state variables of the Navier-Stokes system, i.e. the variables whose gradient is required in the diffusive term

fields¶: alias of josie.fields.NSGradientFields

full_state_fields¶: alias of josie.fields.EulerFields

class josie.ns.state.NSState(*args, **kwargs)¶

Bases: josie.euler.state.EulerState, josie.fluid.state.DiffState

diff_state¶: alias of josie.ns.state.NSGradientState

josie.ns.transport module¶

class josie.ns.transport.NSConstantTransport(viscosity, bulk_viscosity, thermal_diffusivity)¶

Bases: josie.ns.transport.NSTransport

A NSTransport providing constant coefficients

Parameters

viscosity (float) – the constant value of the viscosity
bulk_viscosity (float) – the constant value of the bulk viscosity
thermal_diffusivity (float) – The constant value of the thermal diffusivity

bulk_viscosity(cells)¶

The second viscosity coefficient also called second viscosity or bulk viscosity $\bulkViscosity$ . Units: $\qty[\si{\pascal \second}]$

It returns a value per each cell centroid

Return type: np.ndarray

thermal_diffusivity(cells)¶

Thermal diffusivity $\thermalDiffusivity$ . Units: $\qty[\si{\square \meter \per \second}]$

$\thermalDiffusivity = \frac{\thermalConductivity}% {\specificHeat_\volume \density}$

It returns a value per each cell centroid

Return type: np.ndarray

viscosity(cells)¶

Momentum diffusivity also called dynamic viscosity $\viscosity$ . Units: $\qty[\si{\pascal \second}]$

It returns a value per each cell centroid

Return type: np.ndarray

class josie.ns.transport.NSTransport¶

Bases: josie.transport.Transport

abstract bulk_viscosity(cells)¶

The second viscosity coefficient also called second viscosity or bulk viscosity $\bulkViscosity$ . Units: $\qty[\si{\pascal \second}]$

It returns a value per each cell centroid

Return type: np.ndarray

abstract thermal_diffusivity(cells)¶

Thermal diffusivity $\thermalDiffusivity$ . Units: $\qty[\si{\square \meter \per \second}]$

$\thermalDiffusivity = \frac{\thermalConductivity}% {\specificHeat_\volume \density}$

It returns a value per each cell centroid

Return type: np.ndarray

abstract viscosity(cells)¶

Momentum diffusivity also called dynamic viscosity $\viscosity$ . Units: $\qty[\si{\pascal \second}]$

It returns a value per each cell centroid

Return type: np.ndarray

josie.ns package¶

Subpackages¶

Submodules¶

josie.ns.eos module¶

josie.ns.fields module¶

josie.ns.problem module¶

josie.ns.state module¶

josie.ns.transport module¶

Module contents¶