1D Lagrangian Hydrocode

Input

All ASCII, read from stdin. Where an index is required, this uses the C numbering conventions i.e. the first index is 0.

Verbosity

verbose	(1: diagnostic output)

Geometry

Space

scale_function

Standard settings:

Plane geometry

constant 1.0

Cylindrical symmetry (centre at x = 0)

monomial 1.0 1.0

Spherical symmetry (centre at x = 0)

x²:

monomial 2.0 1.0

Duct of varying profile

table1d
n # number of points in table
x₁ A₁
x₂ A₂
...
x_n A_n

where (x,A) are (position,area) pairs.

Materials

number
For each:
   definition

Materials are of type mat_type in Ariadne.

Nodes

number
For each:
   position velocity
   number_of_cells_using_node
   For each:
      index

Cells

number
For each:
   density specific_internal_energy fraction_reacted
   index_of_material
   number_of_nodes_defining_cell
   For each:
      index

Boundary conditions

Left then right:

For each:
   type (applied_velocity or applied_pressure) function_of_time

State sources

number
For each:
   cell_location velocity material_name material_state amplitude

The amplitude is a function of time, used to scale the velocity and state. The material name is needed to determine the tye of state to read in; this cannot be determined from the cell index because of the structure of the program so this degree of redundancy is needed. (See note below on defining locations.)

Heat sources

number
For each:
   cell_location_1 cell_location_2 heating_rate

The heating rate is a function of time. It defines the heat energy per time applied to each cell in the range. (See note below on defining locations.)

Detonics control points

number
For each:
   cell_location time

At a control point, the time is for the detonation wave to pass the cell centre. (See note below on defining locations.)

Detonics inert boundary nodes

number
For each:
   node_location location_of_nearest_node_inside_explosive

(See note below on defining locations.)

Timestep safety factors

sound_speed divergence artificial_viscosity evolution_rate detonation

The timestep safety factors are used to ensure that the numerical scheme is stable, accurate and convergent. Each physical process has an associated timescale. The time increments taken during a simulation must be small enough that each process can be represented properly. On the other hand, unnecessarily small time steps require more computer time, and can make the result less accurate because of numerical rounding and diffusion processes.

If all the safety factors are set to 1 then the numerical scheme would take its best guess at a timestep. This assumes linear physics, which is not really the case. For non-linear processes it is common to adopt a safety factor ~0.7 say. For stiffer problems, 0.4 seems more reliable.

The timescales are:

Causality: hydrodynamic signals can't travel faster than the local sound speed.
Velocity divergence: nodes can't really pass one another.
Viscous stress: the artificial viscosity introduces an additional relaxation timescale. (This depends on the material properties and can often be ignored, i.e. set to some huge value such as 10¹⁰.)
Evolution rate: for accuracy, the evolution should take several timesteps, e.g. a safety factor of 0.1 say.
In many cases evolution rates are so fast in comparison with macroscopic hydrodynamics that it is better to subcycle the evolution and not permit it to influence the hydrodynamic timestep. If subcycling is used, the safety factor can be set to a large number such as 10¹⁰.

The sound speed and divergence safety factors

Artificial viscosity parameters

quadratic linear
qmode
q_evolve_cut		maximum q/p for evolution to proceed

Notes:

Allowed values of qmode are 1 (calculate q once per time step, copy full-timestep value for half-timestep) or 2 (calculate q twice per time step).
The reaction cutoff acts to suppress reaction during the passage of a shock wave. `Physical' processes should not take place within the smeared-out shock.

Evolution integration

order

Permissible values:

1: evolution updated once per time step (after corrector).
2: evolution updated twice per time step (after predictor and corrector).

Detonics controls

flag (0: off, 1: on)
psi_store_u (value of psi field at which to store local particle velocity)
trigger_delay (delay between triggering of WBL/DSD initiation point
   and actual value used for the new control point)
psi_trigger_disable (value of psi at which to disable WBL/DSD triggering)
psi_wake (value of psi at which to start full detonics)
psi_dead (value of psi at which to ignore detonics)

Timestep controls

initial_timestep growth_factor
minimum_timestep action
maximum_timestep action

"action" can be "set" or "abort". The action is taken if the calculated timestep falls outwith the corresponding limit.

Numerical bandwidths

approximate_zero approximate_infinity

Control of imaginary sound speeds

cc_option

Permitted values:

raw	no action (will probably fail if imaginary speeds are calculated)
ignore	don't use imaginary values in calculating time step
abs	take (sq. root of) absolute value of square of sound speed

Time integration

start_time final_time maximum_timesteps

Automatic stop controls

number_of_conditions
For each:
   position_in_initial_mesh (as a cell location)
   parameter (pressure / temperature)
   relation  (above / below)
   test_value

(See note below on defining locations.)

Output control

Complete state dumps and plotting data are written to two series of numbered output files, of the form STEMXXX, where XXX is a three digit number.

number_of_steps_between_outputs  output_file_stem  first_output_index
time_interval_between_node_plot_dumps  node_plot_file_stem  first_output_index
time_interval_between_cell_plot_dumps  cell_plot_file_stem  first_output_index
name_of_shock_location_file artificial_viscosity_cutoff
number_of_Lagrangian_sensors
For each:
   initial_position filename type
number_of_extremum_sensors
For each:
   cell_location_end1 cell_location_end2 sense (maximum / minimum) parameter (pressure/temperature/velocity) filename

"type" is "node" or "cell". Position is specified as a location (see note below on defining locations).

The artificial viscosity cutoff is used to select the level at which a compression wave is taken to be a shock. The cell centre closest to each Lagrangian sensor is found, and the state in this cell written to the specified file at each time step.

Defining locations

Lagrangian locations in the mesh may be defined in several ways, according to preference. In each case, a keyword is given, followed by a numerical value if necessary.

Index of cell or node (as appropriate for the quantity being defined)

   index index_value

Indices are base zero, following the C array convention.

Position in real space

   position ordinate

Logical end of mesh

   sense end

where end may be left or right.

Output

All ASCII. Apart from timestep information, restart and graphics dumps are written.

Restart dumps

# dump at time = ...
(geometry information)

The geometry information consists of node and cell states, followed by the boundary conditions. It can be used to restart the calculation by inserting the rest of the control data round about.

Graphics dumps

Node plot:

# node plot at time = ....
# parameters: pos, vel, stress, T, csq, q, psi, u0, d
For each node:
   position velocity stress (6 components) T c² q psi u0 D

Cell plot:

# cell plot at time = ....
# parameters: pos, vel, stress, T, csq, q, psi, u0, d, material, state
For each node:
   position velocity stress (6 components) T c² q psi u₀ D material state

For node plots, apart from position and velocity, quantities are averaged from the cells containing the node. For cell plots, position and velocity are averaged from nodes defining the cell.

The graphics dumps are suitable for display using Gnuplot.

Shock location

A single file is produced containing the position of shocks (maxima in q/rho) after each time step. This method can also identify any small variations in q/rho as a shock, so a cutoff value of q is supplied in the input below which would-be shocks are ignored. The cutoff varies with mesh resolution, smaller cells requiring a smaller cutoff to pick up the same shocks, all else being equal.

Lagrangian sensor points

A set of files is produced, each containing the position, particle velocity and state at the cell centre chosen.

Files

Ariadne V7.0 material model library
WXC++ class library