Grid generation

Compute grid coordinates and spatial steps. More...

Functions
subroutine, public	mod_grid_generator::initialize_grid_generator (coordg_fx, coordg_fy, coordg_fz)
	Allocate 3 directional grids.
subroutine, public	mod_grid_generator::grid_generate_regular (cell_range, coordinate_range, coordg)
	Generate a regular grid.
subroutine, public	mod_grid_generator::grid_generate_chebyshev (cell_range, coordinate_range, coordg)
	Generate a Chebyshev grid.
subroutine, public	mod_grid_generator::grid_generate_exponential (cell_range, coordinate_range, expansion_ratio, coordg)
	Generate an exponential grid from the expansion ratio.
subroutine, public	mod_grid_generator::grid_generate_exponential2 (cell_range, coordinate_range, first_step, reverse, coordg)
	Generate an exponential grid from the first step.
subroutine, public	mod_grid_generator::read_grid_dimensions_from_file (filename)
	Create a grid from a file.
subroutine, public	mod_grid_generator::create_grid_from_file (coordg_fx, coordg_fy, coordg_fz, filename)
	Create a grid from a file.
subroutine, public	mod_grid_generator::complete_grid_structure (coordg_fx, coordg_fy, coordg_fz)
	Compute coordinates and spatial steps using global face coordinates.
subroutine	mod_grid_generator_refined_grid::complete_grid_structure_refined_grid ()
	Compute coordinates and spatial steps of the refined grid using the main grid.

Detailed Description

Function Documentation

complete_grid_structure()

subroutine, public mod_grid_generator::complete_grid_structure	(	double precision, dimension(nxg+1), intent(in)	coordg_fx,
		double precision, dimension(nyg+1), intent(in)	coordg_fy,
		double precision, dimension(nzg+1), intent(in)	coordg_fz )

Parameters

[in]	coordg_fx	Global face coordinates along x-axis
[in]	coordg_fy	Global face coordinates along y-axis
[in]	coordg_fz	Global face coordinates along z-axis

create_grid_from_file()

subroutine, public mod_grid_generator::create_grid_from_file	(	double precision, dimension(:), intent(inout)	coordg_fx,
		double precision, dimension(:), intent(inout)	coordg_fy,
		double precision, dimension(:), intent(inout)	coordg_fz,
		character(len=*), intent(in)	filename )

Parameters

[in,out]	coordg_fx	Global face coordinates along x-axis
[in,out]	coordg_fy	Global face coordinates along y-axis
[in,out]	coordg_fz	Global face coordinates along z-axis
[in]	filename	Mesh file name

grid_generate_chebyshev()

subroutine, public mod_grid_generator::grid_generate_chebyshev	(	integer, dimension(2), intent(in)	cell_range,
		double precision, dimension(2), intent(in)	coordinate_range,
		double precision, dimension(:), intent(inout)	coordg )

The spacial steps are determined by

\begin{align} x_i = x_1 + \frac{L}{2} \Big( 1 - \cos\big( \frac{\pi}{L} (i - 1) \big) \Big) \end{align}

where \(L\) is the coordinate range and \(i\) ranges from 1 to the number of cells.

Parameters

[in]	cell_range	cell range of the sub-grid (e.g. [3,6] means from cell 3 to cell 6)
[in]	coordinate_range	coordinate range of the sub_grid (e.g. [1.0,2.0] means from 1.0 to 2.0)
[in,out]	coordg	face coordinates along a given axis

grid_generate_exponential()

subroutine, public mod_grid_generator::grid_generate_exponential	(	integer, dimension(2), intent(in)	cell_range,
		double precision, dimension(2), intent(in)	coordinate_range,
		double precision, intent(in)	expansion_ratio,
		double precision, dimension(:), intent(inout)	coordg )

The expansion ratio is defined as the ratio of the last step over the first step

   !!         length = l
   !!  ┌──┬────┬─ ─ ─ ─┬───────┐
   !!   Δ1  Δ2             Δn
   !! 

The spacial steps are determined by

\[ \Delta_i = l \dfrac{1-q}{1-q^n}q^{i-1} \]

where \( q = \frac{\Delta_n}{\Delta_1}^{\frac{1}{n-1}} \)

Parameters

[in]	cell_range	cell range of the sub-grid (e.g. [3,6] means from cell 3 to cell 6)
[in]	coordinate_range	coordinate range of the sub_grid (e.g. [1.0,2.0] means from 1.0 to 2.0)
[in]	expansion_ratio	ratio of the last step over the first step
[in,out]	coordg	face coordinates along a given axis

grid_generate_exponential2()

subroutine, public mod_grid_generator::grid_generate_exponential2	(	integer, dimension(2), intent(in)	cell_range,
		double precision, dimension(2), intent(in)	coordinate_range,
		double precision, intent(in)	first_step,
		logical, intent(in)	reverse,
		double precision, dimension(:), intent(inout)	coordg )

   !!         length = l
   !!  ┌──┬────┬─ ─ ─ ─┬───────┐
   !!   Δ1  Δ2             Δn
   !! 

The spatial steps are determined by

\[ \Delta_i = \Delta_1 k^{i-1} \]

The common ratio k is determinated by solving the following equation using a Newton-Raphson algorithm.

\[ \Delta_1 \dfrac{1-k^n}{1-k} = l \]

Reordering the equation and taking the logarithm on both sides prevents the term \( k^n \) to explode.

\[ n \log(k) - \log\bigl(1 + d\frac{l}{\Delta_1(k - 1)}\bigr) = 0 \]

Parameters

[in]	cell_range	cell range of the sub-grid (e.g. [3,6] means from cell 3 to cell 6)
[in]	coordinate_range	coordinate range of the sub_grid (e.g. [1.0,2.0] means from 1.0 to 2.0)
[in]	first_step	first step of the exponential mesh (also last_step if reverse is set to .true.)
[in]	reverse	the first step becomes the last step if this flag is set to .true.
[in,out]	coordg	face coordinates along a given axis

grid_generate_regular()

subroutine, public mod_grid_generator::grid_generate_regular	(	integer, dimension(2), intent(in)	cell_range,
		double precision, dimension(2), intent(in)	coordinate_range,
		double precision, dimension(:), intent(inout)	coordg )

Parameters

[in]	cell_range	cell range of the sub-grid (e.g. [3,6] means from cell 3 to cell 6)
[in]	coordinate_range	coordinate range of the sub_grid (e.g. [1.0,2.0] means from 1.0 to 2.0)
[in,out]	coordg	face coordinates along a given axis

read_grid_dimensions_from_file()

subroutine, public mod_grid_generator::read_grid_dimensions_from_file

(

character(len=*), intent(in)

filename

)

Parameters

[in]

filename

Mesh file name