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 white2008, with cells resorting to PCM for extrema including first and last cells in column. This scheme differs from Colella and Woodward, 1984 colella1984, 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