plm_functions module reference¶

Piecewise linear reconstruction functions.

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Functions/Subroutines¶

 plm_slope_wa() Returns a limited PLM slope following White and Adcroft, 2008. plm_slope_cw() Returns a limited PLM slope following Colella and Woodward 1984. plm_monotonized_slope() Returns a limited PLM slope following Colella and Woodward 1984. plm_extrapolate_slope() Returns a PLM slope using h2 extrapolation from a cell to the left. plm_reconstruction() Reconstruction by linear polynomials within each cell. plm_boundary_extrapolation() Reconstruction by linear polynomials within boundary cells.

Detailed Description¶

This module contains routines that handle one-dimensionnal finite volume reconstruction using the piecewise linear method (PLM).

Function/Subroutine Documentation¶

function plm_functions/plm_slope_wa(h_l, h_c, h_r, h_neglect, u_l, u_c, u_r) [pure]

Returns a limited PLM slope following White and Adcroft, 2008. [units of u] Note that this is not the same as the Colella and Woodward method.

Parameters
• h_l :: [in] Thickness of left cell [units of grid thickness]

• h_c :: [in] Thickness of center cell [units of grid thickness]

• h_r :: [in] Thickness of right cell [units of grid thickness]

• h_neglect :: [in] A negligible thickness [units of grid thickness]

• u_l :: [in] Value of left cell [units of u]

• u_c :: [in] Value of center cell [units of u]

• u_r :: [in] Value of right cell [units of u]

Called from
function plm_functions/plm_slope_cw(h_l, h_c, h_r, h_neglect, u_l, u_c, u_r) [pure]

Returns a limited PLM slope following Colella and Woodward 1984.

Parameters
• h_l :: [in] Thickness of left cell [units of grid thickness]

• h_c :: [in] Thickness of center cell [units of grid thickness]

• h_r :: [in] Thickness of right cell [units of grid thickness]

• h_neglect :: [in] A negligible thickness [units of grid thickness]

• u_l :: [in] Value of left cell [units of u]

• u_c :: [in] Value of center cell [units of u]

• u_r :: [in] Value of right cell [units of u]

function plm_functions/plm_monotonized_slope(u_l, u_c, u_r, s_l, s_c, s_r) [pure]

Returns a limited PLM slope following Colella and Woodward 1984.

Parameters
• u_l :: [in] Value of left cell [units of u]

• u_c :: [in] Value of center cell [units of u]

• u_r :: [in] Value of right cell [units of u]

• s_l :: [in] PLM slope of left cell [units of u]

• s_c :: [in] PLM slope of center cell [units of u]

• s_r :: [in] PLM slope of right cell [units of u]

Called from
function plm_functions/plm_extrapolate_slope(h_l, h_c, h_neglect, u_l, u_c) [pure]

Returns a PLM slope using h2 extrapolation from a cell to the left. Use the negative to extrapolate from the a cell to the right.

Parameters
• h_l :: [in] Thickness of left cell [units of grid thickness]

• h_c :: [in] Thickness of center cell [units of grid thickness]

• h_neglect :: [in] A negligible thickness [units of grid thickness]

• u_l :: [in] Value of left cell [units of u]

• u_c :: [in] Value of center cell [units of u]

Called from
subroutine plm_functions/plm_reconstruction(N, h, u, edge_values, ppoly_coef, h_neglect)

Reconstruction by linear polynomials within each cell.

It is assumed that the size of the array ‘u’ is equal to the number of cells defining ‘grid’ and ‘ppoly’. No consistency check is performed here.

Parameters
• n :: [in] Number of cells

• h :: [in] cell widths (size N)

• u :: [in] cell averages (size N)

• edge_values :: [inout] edge values of piecewise polynomials, with the same units as u.

• ppoly_coef :: [inout] coefficients of piecewise polynomials, mainly with the same units as u.

• h_neglect :: [in] A negligibly small width for the purpose of cell reconstructions in the same units as h

Call to

hneglect_dflt plm_monotonized_slope plm_slope_wa

Called from
subroutine plm_functions/plm_boundary_extrapolation(N, h, u, edge_values, ppoly_coef, h_neglect)

Reconstruction by linear polynomials within boundary cells.

The left and right edge values in the left and right boundary cells, respectively, are estimated using a linear extrapolation within the cells.

This extrapolation is EXACT when the underlying profile is linear.

It is assumed that the size of the array ‘u’ is equal to the number of cells defining ‘grid’ and ‘ppoly’. No consistency check is performed here.

Parameters
• n :: [in] Number of cells

• h :: [in] cell widths (size N)

• u :: [in] cell averages (size N)

• edge_values :: [inout] edge values of piecewise polynomials, with the same units as u.

• ppoly_coef :: [inout] coefficients of piecewise polynomials, mainly with the same units as u.

• h_neglect :: [in] A negligibly small width for the purpose of cell reconstructions in the same units as h

Call to

hneglect_dflt plm_extrapolate_slope

Called from