Weighted essentially non-oscillatory (WENO) reconstruction scheme that is supplemented with monotonicity preserving bounds (MPWENO) and a mapping function that boosts the accuracy of the non-linear weights (WENOM). MPWENO, see Balsara and Shu (2000), prevents the reconstructed values to lay outside the range set by the stencil, while WENOM, see Henrick et al. (2005), recovers the formal order of accuracy of the reconstruction at critical points. Please note that the basic WENO approach is implemented according to the work of Jiang and Shu (1996). WENO-Z, which is less dissipative than WENO-JS and WENO-M, is implemented according to the work of Borges, et al. (2008). TENO, which is even less dissipative than WENO-Z but is less robust, is implemented according to the work of Fu et al. (2016). More...

Functions/Subroutines
impure subroutine, public	s_initialize_weno_module
	The computation of parameters, the allocation of memory, the association of pointers and/or the execution of any other procedures that are necessary to setup the module.

subroutine	s_compute_weno_coefficients (weno_dir, is)
	The purpose of this subroutine is to compute the grid dependent coefficients of the WENO polynomials, ideal weights and smoothness indicators, provided the order, the coordinate direction and the location of the WENO reconstruction.

subroutine, public	s_weno (v_vf, vl_rs_vf_x, vl_rs_vf_y, vl_rs_vf_z, vr_rs_vf_x, vr_rs_vf_y, vr_rs_vf_z, weno_dir, is1_weno_d, is2_weno_d, is3_weno_d)

subroutine, public	s_initialize_weno (v_vf, weno_dir)
	The computation of parameters, the allocation of memory, the association of pointers and/or the execution of any other procedures that are required for the setup of the WENO reconstruction.

subroutine	s_preserve_monotonicity (v_rs_ws, vl_rs_vf, vr_rs_vf)
	The goal of this subroutine is to ensure that the WENO reconstruction is monotonic. The latter is achieved by enforcing monotonicity preserving bounds of Suresh and Huynh (1997). The resulting MPWENO reconstruction, see Balsara and Shu (2000), ensures that the reconstructed values do not reside outside the range spanned by WENO stencil.

impure subroutine, public	s_finalize_weno_module ()
	Module deallocation and/or disassociation procedures.

Variables
integer	v_size
	Number of WENO-reconstructed cell-average variables.

The cell-average variables that will be WENO-reconstructed. Formerly, they
are stored in v_vf. However, they are transferred to v_rs_wsL and v_rs_wsR as to be reshaped (RS) and/or characteristically decomposed. The reshaping allows the WENO procedure to be independent of the coordinate direction of the reconstruction. Lastly, notice that the left (L) and right (R) results of the characteristic decomposition are stored in custom-constructed WENO- stencils (WS) that are annexed to each position of a given scalar field.
real(wp), dimension(:, :, :, :), allocatable	v_rs_ws_x

real(wp), dimension(:, :, :, :), allocatable	v_rs_ws_y

real(wp), dimension(:, :, :, :), allocatable	v_rs_ws_z

Polynomial coefficients at the left and right cell-boundaries (CB) and at
the left and right quadrature points (QP), in the x-, y- and z-directions. Note that the first dimension of the array identifies the polynomial, the second dimension identifies the position of its coefficients and the last dimension denotes the cell-location in the relevant coordinate direction.
real(wp), dimension(:, :, :), allocatable, target	poly_coef_cbl_x

real(wp), dimension(:, :, :), allocatable, target	poly_coef_cbl_y

real(wp), dimension(:, :, :), allocatable, target	poly_coef_cbl_z

real(wp), dimension(:, :, :), allocatable, target	poly_coef_cbr_x

real(wp), dimension(:, :, :), allocatable, target	poly_coef_cbr_y

real(wp), dimension(:, :, :), allocatable, target	poly_coef_cbr_z

The ideal weights at the left and the right cell-boundaries and at the
left and the right quadrature points, in x-, y- and z-directions. Note that the first dimension of the array identifies the weight, while the last denotes the cell-location in the relevant coordinate direction.
real(wp), dimension(:, :), allocatable, target	d_cbl_x

real(wp), dimension(:, :), allocatable, target	d_cbl_y

real(wp), dimension(:, :), allocatable, target	d_cbl_z

real(wp), dimension(:, :), allocatable, target	d_cbr_x

real(wp), dimension(:, :), allocatable, target	d_cbr_y

real(wp), dimension(:, :), allocatable, target	d_cbr_z

Smoothness indicator coefficients in the x-, y-, and z-directions. Note
that the first array dimension identifies the smoothness indicator, the second identifies the position of its coefficients and the last denotes the cell-location in the relevant coordinate direction.
real(wp), dimension(:, :, :), allocatable, target	beta_coef_x

real(wp), dimension(:, :, :), allocatable, target	beta_coef_y

real(wp), dimension(:, :, :), allocatable, target	beta_coef_z

Indical bounds in the s1-, s2- and s3-directions
type(int_bounds_info)	is1_weno

type(int_bounds_info)	is2_weno

type(int_bounds_info)	is3_weno

Detailed Description

Weighted essentially non-oscillatory (WENO) reconstruction scheme that is supplemented with monotonicity preserving bounds (MPWENO) and a mapping function that boosts the accuracy of the non-linear weights (WENOM). MPWENO, see Balsara and Shu (2000), prevents the reconstructed values to lay outside the range set by the stencil, while WENOM, see Henrick et al. (2005), recovers the formal order of accuracy of the reconstruction at critical points. Please note that the basic WENO approach is implemented according to the work of Jiang and Shu (1996). WENO-Z, which is less dissipative than WENO-JS and WENO-M, is implemented according to the work of Borges, et al. (2008). TENO, which is even less dissipative than WENO-Z but is less robust, is implemented according to the work of Fu et al. (2016).

Function/Subroutine Documentation

◆ s_compute_weno_coefficients()

subroutine m_weno::s_compute_weno_coefficients	(	integer, intent(in)	weno_dir,
		type(int_bounds_info), intent(in)	is )

The purpose of this subroutine is to compute the grid dependent coefficients of the WENO polynomials, ideal weights and smoothness indicators, provided the order, the coordinate direction and the location of the WENO reconstruction.

Parameters

weno_dir	Coordinate direction of the WENO reconstruction
is	Index bounds in the s-direction