Regions

Most users interact with RIOT by specifying initial conditions, and in RIOT initial conditions are built from regions. A region is a geometric subdomain assigned to one or more materials together with an initial thermodynamic and kinematic state. The problem generator paints the mesh by evaluating each region over every cell; where regions overlap, higher-numbered regions take precedence. This chapter describes the region model and its text input-deck parameters; the Python interface in Chapter The Python Interface offers a more powerful way to define the same regions.

Concept

Regions are declared in numbered input blocks <region0>, <region1>, …; the numeric suffix is the region id. Each region selects a geometric mask (a shape), a list of materials (matid), and an initial state. The problem generator processes regions in order of increasing id so that a later (higher-id) region overrides earlier ones where they overlap. By convention <region0> uses the background mask (which covers the whole domain) to provide a default state that subsequent regions carve into.

Where two regions meet within a single cell, RIOT can adaptively subdivide the cell to compute accurate volume fractions; the depth of this subdivision is controlled by nlev_min and nlev_max in the global <regions> block. Defaults placed in the <regions> block apply to every region unless overridden locally.

Region Shapes

The geometric mask is chosen with the mask_type parameter. The available shapes and their defining parameters are listed in the table below. All center/coordinate parameters default to 0; radii default to 1.

mask_type	Shape and defining parameters
background	Entire domain (default state); no parameters.
inside_sphere	Sphere: center x0,y0,z0, radius.
inside_spherical_shell	Spherical shell: center x0,y0,z0, inner_radius, outer_radius.
inside_cylinder	Finite cylinder: axis endpoints x0,y0,z0 to x1,y1,z1, radius.
inside_cylindrical_shell	Cylindrical shell: axis x0,y0,z0 to x1,y1,z1, inner_radius, outer_radius.
inside_ellipsoid	Ellipsoid: center x0,y0,z0, semi-axes ax,ay,az.
inside_ellipsoidal_shell	Ellipsoidal shell: center x0,y0,z0, inner_ax..az, outer_ax..az.
inside_rectangle	Axis-aligned box: bounds x0,y0,z0 to x1,y1,z1 (defaults \(\pm\infty\), i.e. a half-space or slab if only some bounds are set).
python	Mask supplied by a user Python function (Chapter The Python Interface).
cad	Solid imported from a STEP CAD file: cadfile, name (Section CAD Geometry).

Initial State

A region’s thermodynamic state is set by providing two independent thermodynamic quantities per material; RIOT infers the initialization mode from which pair is given. The settable material-averaged quantities are density (c_m_rho), pressure (c_m_pressure), temperature (c_m_temperature), and specific internal energy (c_m_sie). The supported combinations are summarized in the table below. The equation of state (Chapter Materials and Equations of State) closes the remaining variables and produces the conserved state.

Provide	Sets state from
c_m_rho + c_m_temperature	density and temperature (most common).
c_m_rho + c_m_pressure	density and pressure.
c_m_rho + c_m_sie	density and specific internal energy.
c_m_pressure + c_m_temperature	pressure and temperature.

When ionization is active, the electron temperature may be set independently (c_c_bulk_electron_temperature) or placed in equilibrium with the ions. The bulk velocity is set with c_c_bulk_velocity (a three-vector). Passive scalars are tagged in a region with passive_scalars. In multi-material regions, per-material state is given by suffixing the material label (e.g. c_m_rho_Tungsten), and volume fractions default such that each material fills its region.

Input Parameters

Per-region parameters in each <region\(N\)> block.

Parameter	Type	Default	Description
mask_type	string	—	Region shape (the table below).
matid	int/list	—	Material id(s) present in the region.
name	string	—	Optional label (also the Python class name).
c_m_rho	Real	—	Initial density (with a second state variable).
c_m_pressure	Real	—	Initial pressure.
c_m_temperature	Real	—	Initial temperature.
c_m_sie	Real	—	Initial specific internal energy.
c_c_bulk_velocity	list	0,0,0	Initial velocity vector.
passive_scalars	list	—	Passive scalars tagged in this region.

Shape-specific geometry parameters (x0, radius, etc.) are listed in the table below. The global <regions> block holds defaults and the overlap-refinement controls:

Parameters in the global <regions> block.

Parameter	Type	Default	Description
nlev_min	int	0	Minimum subdivision level in cells spanning multiple regions.
nlev_max	int	0	Maximum subdivision level for computing overlap volume fractions.

Example

A Sedov-like setup: a uniform background of material 0 with a small high-pressure cylinder at the origin. The regions are shown here in the text input-deck form to illustrate the block syntax; the equivalent Python calls (riot.input("region0", …), etc.) are the recommended way to write them (Chapter The Python Interface).

<regions>
nlev_max = 5

<region0>
mask_type = background
matid     = 0
c_m_rho      = 1.0
c_m_pressure = 0.1

<region1>
mask_type = inside_cylinder
matid     = 0
x0 = 0.0
y0 = 0.0
z0 = -0.75
x1 = 0.0
y1 = 0.0
z1 = 0.75
radius = 0.1
c_m_rho      = 1.0
c_m_pressure = 10.0