type_rec_point_lagrange_1d Module Reference

The type for generic 1D point reconstruction that has to be derived. More...

Functions/Subroutines
subroutine	rec_point_lagrange_1d_construct (self, index_start, index_end)
	Initialize a 1D point reconstructant.
subroutine	rec_point_1d_place (self, x, coordinates, control_volumes)
	Place (position) the interpolant to the corresponding 'index' given the coordinate 'X' of the point and the discrete nodes. The resulting index corresponds to the node that is just before (less than or equal) the point.
double precision function	rec_point_1d_interpolate (self, x, coordinates, values, derivative, control_volumes)
	Directly compute the reconstruction at the given position.
subroutine	rec_point_lagrange_1d_compute_stencil (self, coordinates, derivative, control_volumes)
pure integer function	rec_compute_point_index_sorted_array_dichotomic (x, coordinates, control_volumes)
	Returns the index of the node that is just before (<=) 'X'.

Detailed Description

This type is based on the same principle as the t_int_point_lagrange_1D and uses an underlying t_rec_scheme for computing the 1D reconstruction. However, we have to deal with the particular of the reconstruction control volumes. Hence, the functions place and interpolate are redefined. The generic compute_stencil has also been redefined.

Function/Subroutine Documentation

rec_compute_point_index_sorted_array_dichotomic()

pure integer function type_rec_point_lagrange_1d::rec_compute_point_index_sorted_array_dichotomic	(	double precision, intent(in)	x,
		double precision, dimension(:), intent(in)	coordinates,
		double precision, dimension(:), intent(in)	control_volumes )

Parameters

[in]	X	the point position
[in]	coordinates	the control_volumes centroids array
[in]	control_volumes	the control_volumes (width) array

rec_point_1d_interpolate()

double precision function type_rec_point_lagrange_1d::rec_point_1d_interpolate	(	class(t_rec_point_lagrange_1d), intent(inout)	self,
		double precision, intent(in)	x,
		double precision, dimension(:), intent(in)	coordinates,
		double precision, dimension(:), intent(in)	values,
		integer, intent(in), optional	derivative,
		double precision, dimension(:), intent(in), optional	control_volumes )

Parameters

[in,out]	self	the element
[in]	X	the position where to reconstruct
[in]	coordinates	the coordinates of the cell centers (in the interval '1:nx')
[in]	values	the mean values of the field (in the interval '1:nx')
[in]	derivative	*(optional)* the derivative number: 0 (default) for value interpolation, 1 for first derivative, etc.
[in]	control_volumes	the control volumes

Returns

the reconstructed value at X

rec_point_1d_place()

subroutine type_rec_point_lagrange_1d::rec_point_1d_place	(	class(t_rec_point_lagrange_1d), intent(inout)	self,
		double precision, intent(in)	x,
		double precision, dimension(:), intent(in)	coordinates,
		double precision, dimension(:), intent(in), optional	control_volumes )

Warning

if 'X' is less than 'coordinates(1)', then 'index' is set to '1'.

if 'X' is greater than 'coordinates(nx)', then 'index' is set to 'nx'.

Note

the index search algorithm is dichotomic

Precondition

coordinates is ordered and is at least of size 2