recon1d_ppm_h4_2019 module reference¶

Piecewise Parabolic Method 1D reconstruction with h4 interpolation for edges.

Data Types¶

ppm_h4_2019

PPM reconstruction following White and Adcroft, 2008.

Functions/Subroutines¶

`init()`	Initialize a 1D PPM_H4_2019 reconstruction for n cells.
`reconstruct()`	Calculate a 1D PPM_H4_2019 reconstructions based on h(:) and u(:)
`end_value_h4()`	Determine a one-sided 4th order polynomial fit of u to the data points for the purposes of specifying edge values, as described in the appendix of White and Adcroft JCP 2008.
`f()`	Value of PPM_H4_2019 reconstruction at a point in cell k [A].
`dfdx()`	Derivative of PPM_H4_2019 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_H4_2019 reconstruction.
`check_reconstruction()`	Checks the PPM_H4_2019 reconstruction for consistency.
`unit_tests()`	Runs PPM_H4_2019 reconstruction unit tests and returns True for any fails, False otherwise.

Detailed Description¶

This implementation of PPM follows White and Adcroft 2008 [87], with cells resorting to PCM for extrema including first and last cells in column. This scheme differs from Colella and Woodward, 1984 [17], in the method of first estimating the fourth-order accurate edge values. This uses numerical expressions refactored at the beginning of 2019. The first and last cells are always limited to PCM.

Type Documentation¶

type recon1d_ppm_h4_2019/ppm_h4_2019¶

PPM reconstruction following White and Adcroft, 2008.

Type fields:

% ul [real(:),allocatable, private] :: Left edge value [A].
% ur [real(:),allocatable, private] :: Right edge value [A].
% init [procedure,private] :: Implementation of the PPM_H4_2019 initialization.
% reconstruct [procedure,private] :: Implementation of the PPM_H4_2019 reconstruction.
% average [procedure,private] :: Implementation of the PPM_H4_2019 average over an interval [A].
% f [procedure,private] :: Implementation of evaluating the PPM_H4_2019 reconstruction at a point [A].
% dfdx [procedure,private] :: Implementation of the derivative of the PPM_H4_2019 reconstruction at a point [A].
% destroy [procedure,private] :: Implementation of deallocation for PPM_H4_2019.
% check_reconstruction [procedure,private] :: Implementation of check reconstruction for the PPM_H4_2019 reconstruction.
% unit_tests [procedure,private] :: Implementation of unit tests for the PPM_H4_2019 reconstruction.
% init_parent [procedure,private] :: Duplicate interface to
% reconstruct_parent [procedure,private] :: Duplicate interface to

Function/Subroutine Documentation¶

subroutine recon1d_ppm_h4_2019/init(this, n, h_neglect, check)¶

Initialize a 1D PPM_H4_2019 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_h4_2019/reconstruct(this, h, u)¶

Calculate a 1D PPM_H4_2019 reconstructions based on h(:) and u(:)

Parameters:

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

Call to:

end_value_h4

subroutine recon1d_ppm_h4_2019/end_value_h4(dz, u, Csys)¶

Determine a one-sided 4th order polynomial fit of u to the data points for the purposes of specifying edge values, as described in the appendix of White and Adcroft JCP 2008.

Parameters:

dz :: [in] The thicknesses of 4 layers, starting at the edge [H]. The values of dz must be positive.
u :: [in] The average properties of 4 layers, starting at the edge [A]
csys :: [out] The four coefficients of a 4th order polynomial fit of u as a function of z [A H-(n-1)]

Called from:

reconstruct

function recon1d_ppm_h4_2019/f(this, k, x) [real]¶

Value of PPM_H4_2019 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_h4_2019/dfdx(this, k, x) [real]¶

Derivative of PPM_H4_2019 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_h4_2019/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_h4_2019/destroy(this)¶

Deallocate the PPM_H4_2019 reconstruction.

Parameters:: this :: [inout] This reconstruction

function recon1d_ppm_h4_2019/check_reconstruction(this, h, u) [logical]¶

Checks the PPM_H4_2019 reconstruction for consistency.

Parameters:

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

function recon1d_ppm_h4_2019/unit_tests(this, verbose, stdout, stderr) [logical]¶

Runs PPM_H4_2019 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