recon1d_ppm_cwk module reference¶

Piecewise Parabolic Method 1D reconstruction in model index space.

Data Types¶

ppm_cwk

PPM reconstruction in index space (no grid dependence).

Functions/Subroutines¶

`init()`	Initialize a 1D PPM_CWK reconstruction for n cells.
`reconstruct()`	Calculate a 1D PPM_CWK reconstructions based on h(:) and u(:)
`f()`	Value of PPM_CWK reconstruction at a point in cell k [A].
`dfdx()`	Derivative of PPM_CWK reconstruction at a point in cell k [A].
`average()`	Average between xa and xb for cell k of a 1D PPM reconstruction [A].
`destroy()`	Deallocate the PPM_CWK reconstruction.
`check_reconstruction()`	Checks the PPM_CWK reconstruction for consistency.
`unit_tests()`	Runs PPM_CWK reconstruction unit tests and returns True for any fails, False otherwise.

Detailed Description¶

This implementation of PPM follows Colella and Woodward, 1984, using uniform thickness and with cells resorting to PCM for local extrema including the first and last cells.

“Fourth order” estimates of edge values use PLM also calculated in index space (i.e. with no grid dependence). First and last PLM slopes are extrapolated. Limiting follows Colella and Woodward thereafter. The high accuracy of this scheme is realized only when the grid-spacing is exactly uniform. This scheme deviates from CW84 when the grid spacing is variable.

Type Documentation¶

type recon1d_ppm_cwk/ppm_cwk¶

PPM reconstruction in index space (no grid dependence).

Type fields:

% ul [real(:),allocatable, private] :: Left edge value [A].
% ur [real(:),allocatable, private] :: Right edge value [A].
% plm [type( plm_cwk ),private] :: The PLM reconstruction used to estimate edge values.
% init [procedure,private] :: Implementation of the PPM_CWK initialization.
% reconstruct [procedure,private] :: Implementation of the PPM_CWK reconstruction.
% average [procedure,private] :: Implementation of the PPM_CWK average over an interval [A].
% f [procedure,private] :: Implementation of evaluating the PPM_CWK reconstruction at a point [A].
% dfdx [procedure,private] :: Implementation of the derivative of the PPM_CWK reconstruction at a point [A].
% destroy [procedure,private] :: Implementation of deallocation for PPM_CWK.
% check_reconstruction [procedure,private] :: Implementation of check reconstruction for the PPM_CWK reconstruction.
% unit_tests [procedure,private] :: Implementation of unit tests for the PPM_CWK reconstruction.
% init_parent [procedure,private] :: Duplicate interface to
% reconstruct_parent [procedure,private] :: Duplicate interface to

Function/Subroutine Documentation¶

subroutine recon1d_ppm_cwk/init(this, n, h_neglect, check)¶

Initialize a 1D PPM_CWK reconstruction for n cells.

Parameters:

this :: [out] This reconstruction
n :: [in] Number of cells in this column
h_neglect :: [in] A negligibly small width used in cell reconstructions [H]
check :: [in] If true, enable some consistency checking

subroutine recon1d_ppm_cwk/reconstruct(this, h, u)¶

Calculate a 1D PPM_CWK reconstructions based on h(:) and u(:)

Parameters:

this :: [inout] This reconstruction
h :: [in] Grid spacing (thickness) [typically H]
u :: [in] Cell mean values [A]

function recon1d_ppm_cwk/f(this, k, x) [real]¶

Value of PPM_CWK reconstruction at a point in cell k [A].

Parameters:

this :: [in] This reconstruction
k :: [in] Cell number
x :: [in] Non-dimensional position within element [nondim]

function recon1d_ppm_cwk/dfdx(this, k, x) [real]¶

Derivative of PPM_CWK reconstruction at a point in cell k [A].

Parameters:

this :: [in] This reconstruction
k :: [in] Cell number
x :: [in] Non-dimensional position within element [nondim]

function recon1d_ppm_cwk/average(this, k, xa, xb) [real]¶

Average between xa and xb for cell k of a 1D PPM reconstruction [A].

Parameters:

this :: [in] This reconstruction
k :: [in] Cell number
xa :: [in] Start of averaging interval on element (0 to 1)
xb :: [in] End of averaging interval on element (0 to 1)

subroutine recon1d_ppm_cwk/destroy(this)¶

Deallocate the PPM_CWK reconstruction.

Parameters:: this :: [inout] This reconstruction

function recon1d_ppm_cwk/check_reconstruction(this, h, u) [logical]¶

Checks the PPM_CWK reconstruction for consistency.

Parameters:

this :: [in] This reconstruction
h :: [in] Grid spacing (thickness) [typically H]
u :: [in] Cell mean values [A]

function recon1d_ppm_cwk/unit_tests(this, verbose, stdout, stderr) [logical]¶

Runs PPM_CWK reconstruction unit tests and returns True for any fails, False otherwise.

Parameters:

this :: [inout] This reconstruction
verbose :: [in] True, if verbose
stdout :: [in] I/O channel for stdout
stderr :: [in] I/O channel for stderr