The third example of this tutorial allows the development of a module for very simplified Lagrangian hydrodynamics:

the only supported cell type is the hexahedron,
no pseudo viscosity supported,
the only supported characteristic length calculation type is the one using medians,
the only supported boundary condition type is imposing a velocity component on a surface,
the nodal mass is assumed constant and is not recalculated at each iteration,
no value consistency test (positive pressure, positive volume, ...) is performed.

The list of operations performed by the module is as follows:

calculation of pressure forces,
calculation of momentum,
taking into account boundary conditions,
node displacement,
calculation of new geometric values: cell volume, characteristic cell length, results at the vertices of each cell,
calculation of density,
calculation of pressure and energy using the equation of state. This calculation is performed by a service ARCANE. Two implementations are available for the service: perfect gas, and "stiffened" gas.
calculation of the new time step.

The list of values manipulated by the module is as follows:

Name	Element	Type	Description
Density	Cell	Real	Density per cell
Pressure	Cell	Real	Pressure per cell
CellMass	Cell	Real	Mass per cell
InternalEnergy	Cell	Real	Internal energy per cell
CellVolume	Cell	Real	Volume of the cell
OldCellVolume	Cell	Real	Volume of the cell at the previous iteration
Force	Node	Coordinate	Force at the nodes
Velocity	Node	Coordinate	Velocity at the nodes
NodeMass	Node	Real	Nodal mass
AdiabaticCst	Cell	Real	Adiabatic constant per cell
CaracteristicLength	Cell	Real	Characteristic length per cell
SoundSpeed	Cell	Real	Speed of sound in the cell
NodeCoord	Node	Coordinate	Coordinates of the nodes
CellCQs	Cell	Array of coordinates	Resultant at the vertices

Application Design

Prerequisites

Having completed the first two examples of this tutorial: "Hello World !" Application and The "Poisson" Application.

Actions to perform

Based on the exercise statement and the documentation of the methods of the MicroHydroModule class:

Write the module descriptor:
- Provide the list of entry points. Each previously mentioned operation becomes an entry point and an initialization entry point is added,
- Provide the list of variables,
- Complete the configuration options for boundary conditions according to the MicroHydro.arc dataset
Then describe the sequence of entry points in the configuration file of the MicroHydro.config application.

Equation of State Service

Prerequisites

Actions to perform

Create a service capable of calculating the equation of state for a given group of cells:

Look at the service interface in the IEquationOfState file and the perfect gas and stiffened gas implementations,
Register the 2 implementations in ARCANE using the macro,
In the module descriptor (MicroHydro.axl), enter the configuration options for the equation of state service according to the MicroHydro.arc dataset,
Write the code for the perfect gas equation of state service in the PerfectGasEOSService.cc file. The formulas are:
\[P = (\gamma - 1) \rho e\]

\[s = \sqrt{\gamma P / \rho} \]
with \(P\) = pressure, \(e\) = internal energy, \(s\) = speed of sound, \(\gamma\) = adiabatic constant, and \(\rho\) = density
Write the code for the "stiffened gas" equation of state service in the StiffenedGasEOSService.cc file. The formulas are:
\[P = ((\gamma - 1) \rho e) - (\gamma P_0)\]

\[s = \sqrt{(\gamma / \rho)(P+P_0)} \]
with \(P\) = pressure, \(P_0\) = limiting tension, \(e\) = internal energy, \(s\) = speed of sound, \(\gamma\) = adiabatic constant, and \(\rho\) = density
Complete the calls to the equation of state service in the MicroHydroModule.cc file
Compile
Choose the desired equation of state service in the MicroHydro.arc dataset. Don't forget to specify the limiting tension in the case of the "stiffened gas" service.
Run sequentially and in parallel and observe the results.

Prerequisites: This module, not using any internal data structure other than variables, has nothing to do to account for the saved checkpoints.

Actions to perform

Edit the MicroHydro.config file and add the ArcaneCheckpoint module allowing checkpoints to be written.
Run the code for 100 iterations: option -arcane_opt max_iteration 100.
Resume execution: option -arcane_opt continue.
No longer save the cell volume and add a new initialization entry point for resumption allowing the calculation of the cell volume from the node positions.