3D grid: about

Definition

A 3D grid is a volume support, on which the user can evaluate a spatial quantity.

Use

A 3D 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 3D grids

3D grids can be of the following shapes: cube, rectangular parallelepiped, sphere, cylinder or a part of cylinder.

3D grid and infinite box

The spatial support of the 3D grid type can be extended beyond the bounded study domain.

Mesh

The mesh of a 3D grid is based on a user-defined discretization: computation points are regularly spaced in the volume of the support.

Cube

A 3D grid of the cube type is characterized by a position, a dimension and a discretization.

An example of the definition of a cube-shaped 3D grid is presented below.

Definition of the "Cube" 3D grid

The position is defined by:

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

The dimension is defined by an edge length L of the cube

The discretization are defined by a number of elements along the cube edge

Parallelepiped

A 3D grid of the parallelepiped type is characterized by a position, dimensions and discretizations.

An example of the definition of a parallelepiped-shaped 3D grid is presented below.

Definition of the "Parallelepiped" 3D grid

The position is defined by:

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

The dimensions are defined by:

  • characteristics along the three main axes (X, Y, Z)
  • 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 three main axes (X, Y, Z)

Cylinder

A 3D grid of the cylinder type is characterized by a position, dimensions and discretizations.

An example of the definition of a cylinder-shaped 3D grid is presented below.

Definition of the "Cylinder" 3D grid

The position is defined by:

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

The dimensions are defined by:

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

The discretization are defined by:
  • a number of elements along the radius
  • a number of elements along the angle θ (angle about the Z-axis)
  • a number of elements along the Z-axis

Part of cylinder

A 3D grid of the type of a part of cylinder is characterized by a position, dimensions and discretizations.

An example of the definition of a 3D grid of a part of cylinder (a part of a full cylinder) is presented below.

Definition of the "Part of Cylinder" 3D 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
  • 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 radius
  • 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

Sphere

A 3D grid of the sphere type is characterized by a position, dimensions and discretizations.

An example of the definition of a sphere-shaped 3D grid is presented below.

Definition of the "Part of Cylinder" 3D grid

The position is defined by:

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

The dimensions are defined by a radius

The discretization are defined by:
  • a number of elements along the radius

  • 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)