2D grids: about

Definition

A 2D grid is a face support, on which the user can evaluate a spatial quantity.

Use

A 2D grid is used for:

  • plotting of scalar spatial quantities as color-shading isovalues
  • plotting of scalar spatial quantities as arrows
  • exportation of values

Shapes of 2D grids

2D grids can be of rectangular, annular, cylindrical or spherical shape.

2D grid and infinite box

The spatial support of the 2D grid type can be extended beyond the bounded study domain.

Mesh

The mesh of a 2D grid is based on a user-defined discretization: computation points are regularly spaced on the surface of the support.

Rectangular 2D grid

A 2D grid of rectangular type is built in one of the planes XY, YZ or XZ and characterized by a position, dimensions and discretizations.

An example of the definition of a rectangular 2D grid is presented below.

Definition of the "Rectangular" 2D grid

The position is defined by:

  • a coordinate system
  • an origin (in the coordinate system)

The dimensions are defined by:

  • characteristics along the two main axes of the plane:
  • a value in a positive direction of the axis
  • a value in a negative direction of the axis

The discretization are defined by a number of elements along the two main axes of the plane

Annular 2D grid

A 2D grid of annular type is built in the XY plane of the coordinate system for definition and is characterized by a position, dimensions and discretizations.

An example of the definition of an annular 2D grid is presented below.

Definition of the "Annular" 2D grid

The position is defined by:

  • a coordinate system
  • an origin (in the coordinate system)

The dimensions are defined by:

  • two values of radius:
    • an internal radius
    • an external radius

  • an opening angle θ about the Z-axis with θ = θmin - θmax:

    • a minimal value of θ

    • a maximal value of θ

The discretization are defined by:
  • a number of elements along the radius
  • a number of elements along the angle θ
Angle unit of coordinate system Angle θ
degree 0<| θ | ≤ 360
radian 0<| θ | ≤ 2 π

Cylindrical 2D grid

A 2D grid of cylindrical type is characterized by a position, dimensions and discretizations.

An example of the definition of a cylindrical 2D grid (a part of a hollow cylinder) is presented below.

Definition of the "Cylindrical" 2D grid

The position is defined by:

  • a coordinate system
  • an origin (in the coordinate system)

The dimensions are defined by:

  • a radius R
  • a height:
    • a value in a positive direction of the Z-axis
    • a value in a negative direction of the Z-axis

  • an opening angle θ about the Z-axis with θ = θmin - θmax:

    • a minimal value of θ

    • a maximal value of θ

The discretization are defined by:
  • a number of elements along the angle θ (angle about the Z-axis)
  • a number of elements along the Z-axis
Angle unit of coordinate system Angle θ
degree 0<| θ | ≤ 360
radian 0<| θ | ≤ 2 π

Spherical 2D grid

A 2D grid of spherical type is characterized by a position, dimensions and discretizations.

An example of the definition of a spherical 2D grid (a part of a hollow sphere) is presented below.

Definition of the "Cylindrical" 2D grid

The position is defined by:

  • a coordinate system
  • an origin (in the coordinate system)

The dimensions are defined by:

  • a radius
  • an opening angle θ about the Z-axis with θ = θmin - θmax:
    • a minimal value of θ
    • a maximal value of θ
  • an angle φ about the origin in the plane passing through the Z-axis with φ = φmin - φmax :
  • a minimal value of φ
  • a maximal value of φ

The discretizations are defined by:
  • a number of elements along the angle θ (angle about the Z-axis)
  • a number of elements along the angle φ (angle about the origin in the plane passing through the Z-axis)
Angle unit of coordinate system Angle θ Angle φ
degree 0<| θ | ≤ 360 0<| φ | ≤ 180
radian 0<| θ | ≤ 2 π 0<| φ | ≤π