namespace regrid_interp

Overview

Vertical interpolation for regridding. More…

namespace regrid_interp {

// global variables

integer, parameter, public degree_max = 5;
real, parameter, public nr_offset = 1e-6;
integer, parameter, public nr_iterations = 8;
real, parameter, public nr_tolerance = 1e-12;
integer, parameter interpolation_p1m_h2 = 0;

// global functions

subroutine, public regridding_set_ppolys(
    CS CS,
    densities densities,
    n0 n0,
    h0 h0,
    ppoly0_E ppoly0_E,
    ppoly0_S ppoly0_S,
    ppoly0_coefs ppoly0_coefs,
    degree degree,
    h_neglect h_neglect,
    h_neglect_edge h_neglect_edge
    );

subroutine, public interpolate_grid(
    n0 n0,
    h0 h0,
    x0 x0,
    ppoly0_E ppoly0_E,
    ppoly0_coefs ppoly0_coefs,
    target_values target_values,
    degree degree,
    n1 n1,
    h1 h1,
    x1 x1
    );

subroutine, public build_and_interpolate_grid(
    CS CS,
    densities densities,
    n0 n0,
    h0 h0,
    x0 x0,
    target_values target_values,
    n1 n1,
    h1 h1,
    x1 x1,
    h_neglect h_neglect,
    h_neglect_edge h_neglect_edge
    );

subroutine, public set_interp_scheme(CS CS, interp_scheme interp_scheme);
subroutine, public set_interp_extrap(CS CS, extrap extrap);

} // namespace regrid_interp

Detailed Documentation

Vertical interpolation for regridding.

Global Variables

integer, parameter, public degree_max = 5

Interpolant degrees.

real, parameter, public nr_offset = 1e-6

When the N-R algorithm produces an estimate that lies outside [0,1], the estimate is set to be equal to the boundary location, 0 or 1, plus or minus an offset, respectively, when the derivative is zero at the boundary.

integer, parameter, public nr_iterations = 8

Maximum number of Newton-Raphson iterations. Newton-Raphson iterations are used to build the new grid by finding the coordinates associated with target densities and interpolations of degree larger than 1.

real, parameter, public nr_tolerance = 1e-12

Tolerance for Newton-Raphson iterations (stop when increment falls below this)

integer, parameter interpolation_p1m_h2 = 0

O(h^2)

Global Functions

subroutine, public regridding_set_ppolys(
    CS CS,
    densities densities,
    n0 n0,
    h0 h0,
    ppoly0_E ppoly0_E,
    ppoly0_S ppoly0_S,
    ppoly0_coefs ppoly0_coefs,
    degree degree,
    h_neglect h_neglect,
    h_neglect_edge h_neglect_edge
    )

Builds an interpolated profile for the densities within each grid cell.

It may happen that, given a high-order interpolator, the number of available layers is insufficient (e.g., there are two available layers for a third-order PPM ih4 scheme). In these cases, we resort to the simplest continuous linear scheme (P1M h2).

Parameters:

cs	Interpolation control structure
densities	Actual cell densities
n0	Number of cells on source grid
h0	cell widths on source grid
ppoly0_e	Edge value of polynomial
ppoly0_s	Edge slope of polynomial
ppoly0_coefs	Coefficients of polynomial
degree	The degree of the polynomials
h_neglect	A negligibly small width for the purpose of cell reconstructions in the same units as h0.
h_neglect_edge	A negligibly small width for the purpose of edge value calculations in the same units as h0.

subroutine, public interpolate_grid(
    n0 n0,
    h0 h0,
    x0 x0,
    ppoly0_E ppoly0_E,
    ppoly0_coefs ppoly0_coefs,
    target_values target_values,
    degree degree,
    n1 n1,
    h1 h1,
    x1 x1
    )

Given target values (e.g., density), build new grid based on polynomial.

Given the grid ‘grid0’ and the piecewise polynomial interpolant ‘ppoly0’ (possibly discontinuous), the coordinates of the new grid ‘grid1’ are determined by finding the corresponding target interface densities.

Parameters:

n0	Number of points on source grid
h0	Thicknesses of source grid cells
x0	Source interface positions
ppoly0_e	Edge values of interpolating polynomials
ppoly0_coefs	Coefficients of interpolating polynomials
target_values	Target values of interfaces
degree	Degree of interpolating polynomials
n1	Number of points on target grid
h1	Thicknesses of target grid cells
x1	Target interface positions

subroutine, public build_and_interpolate_grid(
    CS CS,
    densities densities,
    n0 n0,
    h0 h0,
    x0 x0,
    target_values target_values,
    n1 n1,
    h1 h1,
    x1 x1,
    h_neglect h_neglect,
    h_neglect_edge h_neglect_edge
    )

Build a grid by interpolating for target values.

Parameters:

cs	A control structure for regrid_interp
densities	Input cell densities [kg m-3]
target_values	Target values of interfaces
n0	The number of points on the input grid
h0	Initial cell widths
x0	Source interface positions
n1	The number of points on the output grid
h1	Output cell widths
x1	Target interface positions
h_neglect	A negligibly small width for the purpose of cell reconstructions in the same units as h0.
h_neglect_edge	A negligibly small width for the purpose of edge value calculations in the same units as h0.

subroutine, public set_interp_scheme(CS CS, interp_scheme interp_scheme)

Store the interpolation_scheme value in the interp_CS based on the input string.

Parameters:

cs	A control structure for regrid_interp
interp_scheme	Name of the interpolation scheme Valid values include “P1M_H2”, “P1M_H4”, “P1M_IH2”, “PLM”, “PPM_H4”, “PPM_IH4”, “P3M_IH4IH3”, “P3M_IH6IH5”, “PQM_IH4IH3”, and “PQM_IH6IH5”

subroutine, public set_interp_extrap(CS CS, extrap extrap)

Store the boundary_extrapolation value in the interp_CS.

Parameters:

cs	A control structure for regrid_interp
extrap	Indicate whether high-order boundary extrapolation should be used in boundary cells