Manual for LAGC V1.3

Purpose

LAGC is a multidimensional continuum mechanics code for time-dependent problems, solving the Lagrangian version of the dynamical equations.

Methods

The spatial domain is represented by a staggered mesh of arbitrary connectivity. Material state is defined at cell centres, velocity at the nodes. Spatial gradients are calculated by fitting (hyper)planes to sets of values (velocities around a cell, or stresses around a node). Calculations are implemented for 1D, 2D, and 3D. Tensor stresses are always 3D, with the spare components ignored for simulations in lower numbers of dimensions. Time-integration uses the second-order Runge-Kutta scheme (also known as predictor-corrector) with artificial viscosity to treat shock compression. As an alternative and complement to explicit reactive flow, detonations can be treated using the advanced programmed burn method of detonics.

Initial conditions are specified in terms of spatial regions, which may have a constant state and velocity within, or a set of constant states within "grains" defined by their centres, or by a spatially-varying state and velocity. For spatially-varying conditions, a function of position is defined, and a tabulation of function values against material state and velocity; in this way the material state and/or velocity can be made a continuously-varying function of position, using linear interpolation over a single degree of freedom. The function may be a general function of position, or radial distance from a chosen position, or linear distance from a point in a given direction.

The code is written in C++, and uses the WSTS maths and Ariadne material properties libraries to allow very general function forms and material types to be defined in the input.

Input

All input is ASCII and read from the standard input stream.

verbosity (0:low)

number_of_materials
For each:
   name
   material_data (mat_type)

number_of_graphics_specifications
For each:
   x_pixels y_pixels
   auto_flag (0: inline / 1: graphics_data_files)
   wx1 wx2 wy1 wy2 (fractional range of window to use)
   sx1 sx2 sy1 sy2 (corresponding range of "real" parameter)
   bred bgreen bblue (background colour)
   output_file_stem first_dump_index
   number_of_plot_objects (drawn in the order they are specified)
   For each:
      type parameters (see below)
   pause_after_flag (0/1: yes/no)
   clear_before_flag (0/1: yes/no)

Repeated until command is "end":
command parameters (see below)

Notes:

Realfunctionnd is the maths class library type.
mat_type is the ARIADNE class library type.

Plot specifications

Generic functions are used to map graphical objects to the display, allowing offsets, rotations, reflections etc to be introduced. Options for the mapping are:

direct: direct mapping from problem to graphics coordinates.
reflect_x: reflect x-ordinates in y-axis.
reflect_y: reflect y-ordinates in x-axis.
translate followed by translation 2-vector dx dy.
rotate followed by angle anticlockwise in degrees
scale followed by x and y scalings
polar: r,theta (degrees)
Nested series of mappings (from the other options):
```
   nested number_of_mappings
   For each:
      mapping_name parameters
   
```
where the mappings are applied in reverse sequence.

general Two functions must be defined: each takes coordinates in the xy space of the graph and maps it to the x and y ordinates, respectively, of the display. Each function is a Realfunction2d object. All the other maps can be reproduced, but the simple ones are not obvious to look at. For a 1:1 map, the definition would be

   1dproduct monomial 1.0 1.0 constant 1.0 # x-map
   1dproduct constant 1.0 monomial 1.0 1.0 # y-map

For a reflection about the x-axis, the definition could be

   1dproduct monomial 1.0 1.0 constant 1.0 # x-map
   1dproduct constant 1.0 monomial 1.0 -1.0 # y-map

Colours are specified by red, green and blue intensities, each a floating point number in the range 0 to 1.

Mesh lines: type `mesh`

colour
xmap ymap

Region boundaries: type `boundary`

colour
xmap ymap

Scalar field, colormap: type `scalar_field_colored`

Parameters:

parameter_name (pressure / stress_11 / stress_22 / stress_33 / stress_23 / stress_31 / stress_12 / mass_density / temperature / divu / csqv / velocity_x / velocity_y / velocity_z / artificial_viscosity / material / region / grain)
colormap_type (thermal / greyscale / spectral)
cyclic_setting (fixed / cyclic)
vmin vmax (colormap range)
number_of_colors
xmap ymap

If the cyclic setting is "cyclic", the colormap cycles through the same series of colours for field values outside the colormap range. If set to "fixed", field values outside the range are set to the range endpoints.

Scalar field, contours: type `scalar_field_contoured`

Parameters:

parameter_name (pressure / stress_11 / stress_22 / stress_33 / stress_23 / stress_31 / stress_12 / mass_density / temperature / divu / csqv / velocity_x / velocity_y / velocity_z / artificial_viscosity)
definition_type (specified or uniform)
If specified:
   number_of_contours
   For each:
      value colour thickness
If uniform:
   value1 value2 interval colour thickness
xmap ymap

Vector field, arrows: type `vector_field`

Parameters:

parameter_name (velocity)
scale_vector
colour
head_length head_angle
xmap ymap

Draw a line: type `line`

Parameters:

colour
thickness (pixels)
start_point end_point

Draw an arrow: type `arrow`

Parameters:

colour
thickness (pixels)
start_point end_point
head_length (fraction of arrow length)
head_angle (degrees)

Draw text: type `text`

Parameters:

colour
thickness (pixels)
italic_shift (fraction, 0 for non-italic)
writing_angle (degrees anticlockwise from horizontal)
xscale yscale
scale_type (pixel / subject / screen)
start_position
text (no whitespace)

Write time stamp: type `time`

Parameters:

colour
thickness (pixels)
italic_shift (fraction, 0 for non-italic)
writing_angle (degrees anticlockwise from horizontal)
xscale yscale
scale_type (pixel / subject / screen)
format (C I/O string, e.g. %6.2f for float 6 characters wide with 2 decimal places)
start_position

Commands

Generate new mesh: `generate`

Subsequent input:

dump_file

number_of_dimensions_D (1/2/3)
spatial_metric (type name followed by parameters as required):
   plane
   axisymmetric_x reps (x is rotation axis, y radius; reps cuts off small radii)
   axisymmetric_y reps (y is rotation axis, x radius)
   spherical reps (x is radius)
   general fn (Realfunctionnd)
gravity (type name followed by parameters as required):
   none
   constant d (D-vector)`
   radial fr (Realfunction1d)
   radial_extrapolated fr rmax power (fr is Realfunction1d; uses (r/rmax)^(-power) at larger radii)
   time_scale ft gg (ft is Realfunction1d of time; gg is a gravity object as above)

time

generation_mode: independent or specified
If "independent":
   origin_vector_wrt_lab origin_vector_wrt_axes
   If >1D: For each dimension:
      vxi (D-vector giving direction for that axis, should be a unit vector)
   For each direction:
      number_of_tiling_regions
      For each:
         type parameters (see below)
   If >1D: mesh_type (rectilinear / triangulated / tetrahedral)
If "specified":
   number_of_nodes
   For each: position
   number_of_cells
   For each:
      number_of_nodes_defining_cell
      For each: index (base 0)

number_of_foreground_regions
For each:
   name type parameters boundary (WSTS Surface* object)
Possible types, with parameters
   constant material_name state velocity
   table1d_radial reference_position_vector material_name number_of_table_entries
      For each table entry: function_value material_state velocity_vector
   table1d_linear reference_position_vector direction_vector
      material_name number_of_table_entries
      For each table entry: function_value material_state velocity_vector
   table1d_function map_function (WSTS Realfunctionnd * with dimensionality of the problem)
      material_name number_of_table_entries
      For each table entry: function_value material_state velocity_vector
   polygrain number_of_seeds
      For each seed: material_name state velocity centre weight 
      number_of_images_of_seed_array
      For each image: displacement_vector

number_of_detonics_regions
For each:
   name (from list of region names)

boundary_accuracy
number_of_velocity_constraints
For each:
   type parameters:
      applied
         enclosing_surface (Surface)
         amplitude (Realfunction1d of time)
      spatially_varying
         enclosing_surface (Surface)
         amplitude (Realfunction1d of time)
         orientation_vector
         spatial_scaling_functions (Realfunction1d of each ordinate in turn; values are multiplied)
      applied_normal
         enclosing_surface (Surface)
         amplitude (Realfunction1d of time)
      translation
         enclosing_surface (Surface)
         translation_vector
number_of_stress_constraints
For each:
   type parameters:
      applied
         enclosing_surface (Surface)
         pressure (Realfunction1d of time)
         deviatoric stress components (each Realfunction1d of time)
            s11 s22 s33 s23 s31 s12
      spatially_varying
         enclosing_surface (Surface)
         pressure (Realfunction1d of time)
         deviatoric stress components (each Realfunction1d of time)
            s11 s22 s33 s23 s31 s12
         spatial_scaling_functions (Realfunction1d of each ordinate in turn; values are multiplied)
number_of_passes_for_fitting_mesh_to_regions
mesh_margin_fitting_option (0: don't move nodes on margin, 1: only move margin nodes along margin, 2: move margin nodes freely)
number_of_passes_for_fitting_mesh_to_grains
number_of_propellors
For each:
   enclosing_surface (Surface)
   orientation_vector
   pressure (Realfunction1d of magnitude of velocity)
number_of_material_sources
For each:
   location velocity material_name material_state amplitude (Realfunction1d of time)
number_of_heat_sources
For each:
   location heating_rate (power / volume)
number_of_detonics_sources
For each:
   location time
number_of_detonics_inert_boundary_nodes
For each:
   node_index inner_node_index

Types of tiling definition:

uniform
uniform region_width cell_width
geometric
geometric region_width initial_cell_width expansion_factor
modified_geometric
modified_geometric region_width initial_cell_width final_cell_width
weighted: cell size is a general function of position
weighted region_width cell_width_function (type Realfunction1d)
relative weighted: cell size is a general function of fractional position across the width
relative_weighted region_width cell_width_function (type Realfunction1d)
absolute position: specify final ordinate instead of width, modifies any other tiling type
absolute tiling_type parameters
randomised, modifies any other tiling type
randomised random_amplitude tiling_type parameters

How to define a location: location_type_name parameters

Either:
   index cell_or_node_index
Or:
   nearest_position position_vector
Or:
   region surface (Surface type)

Read mesh from file: `read`

Subsequent input:

dump_file

Integrate continuum equations in time: `integrate`

Subsequent input:

dump_file

Courant_factor divergence_factor artificial_viscosity_factor evolution_factor detonation_factor (timestep safety factors)

qquad qlin (artificial viscosity parameters)

q_evolution_cutoff (max q/p for evolution to be allowed)
evolution_update_mode (1/2 for once/twice per time step)

initial_timestep growth_factor
min_timestep min_timestep_action (set / abort)
max_timestep max_timestep_action (set / abort)

eps_min eps_max (general small and large numerical cutoffs)

imaginary_sound_treatment (raw / ignore / abs)

detonics_flag (0/1 for off/on)
psi_store_u trigger_delay psi_trigger_disable
psi_wake psi_dead

autorezone_frequency (timesteps) autorezone_tolerance (0 to < 1, e.g. 0.1)

Integration period, either:
   until end_time
Or:
   for time_duration
max_timesteps

number_of_stop_sensors
For each:
   location parameter comparison value

dump_frequency dump_filename_stem first_dump_index
node_plot_interval node_plot_filename_stem first_node_plot_index
cell_plot_interval cell_plot_filename_stem first_cell_plot_index
shock_location_file artificial_viscosity_sensitivity
graphics_time_interval
number_of_history_files
For each:
   position (D-vector) filename type (node / cell)

Rezone mesh: `rezone`

Subsequent input:

dump_file

Contents of dump file:

background_node_array
background_cell_array

position_offset_vector
velocity_offset_vector
enclosing_surface (Surface)

number_of_foreground_regions
For each:
   node_array
   cell_array
   enclosing_surface
   position_offset_vector
   velocity_offset_vector

Auto-rezone mesh: `autorezone`

Subsequent input:

dump_file
tolerance (0 to < 1, e.g. 0.1)

Supporting software

Libraries:

WSTS mathematical class library
WSTS material properties library "ARIADNE"
WSTS graphical class library

Limitations

There are no slide lines, but large shears can be accommodated by automatic mesh reconnection. There is no detection of collision between different parts of the mesh, which also limits resistance to some forms of mesh-tangling. The way that triangular meshes interact with the boundary is not perfectly symmetric, and can lead to a departure from perfect planarity in a wave running along a rigid boundary. No anti-hourglassing stress is included, so the deformation of strength-free material in rectangular and cuboidal meshes may lead to distortion problems. Because the program uses very general internal structures, the number of dimensions must be repeated when defining position and direction vectors in the problem generator, which is redundant data. The built-in problem generator produces a limited set of mesh configurations, though configurations of any connectivity can be read in if prepared in the correct format by a separate program.

Bugs

In the graphics, the algorithm used to draw region boundaries breaks down at corners, and additional lines are drawn in some places.

A code error in which, after many remeshings, cell indexing could lead to pairs of cells with the same nodes, is believed to be fixed when compiled with version 2.3 of the maths library.

Manual for LAGC V1.3

Purpose

Methods

Input

Plot specifications

Mesh lines: type mesh

Region boundaries: type boundary

Scalar field, colormap: type scalar_field_colored

Scalar field, contours: type scalar_field_contoured

Vector field, arrows: type vector_field

Draw a line: type line

Draw an arrow: type arrow

Draw text: type text

Write time stamp: type time

Commands

Generate new mesh: generate

Read mesh from file: read

Integrate continuum equations in time: integrate

Rezone mesh: rezone

Auto-rezone mesh: autorezone

Supporting software

Limitations

Bugs

Mesh lines: type `mesh`

Region boundaries: type `boundary`

Scalar field, colormap: type `scalar_field_colored`

Scalar field, contours: type `scalar_field_contoured`

Vector field, arrows: type `vector_field`

Draw a line: type `line`

Draw an arrow: type `arrow`

Draw text: type `text`

Write time stamp: type `time`

Generate new mesh: `generate`

Read mesh from file: `read`

Integrate continuum equations in time: `integrate`

Rezone mesh: `rezone`

Auto-rezone mesh: `autorezone`