pqm_functions real, parameter real, parameter pqm_functions::hneglect_dflt hneglect_dflt = 1.E-30 Default negligible cell thickness. pqm_boundary_extrapolation_v1 pqm_limiter subroutine, public subroutine, public pqm_functions::pqm_reconstruction (N, h, u, edge_values, edge_slopes, ppoly_coef, h_neglect, answers_2018) pqm_reconstruction N N h h u u edge_values edge_values edge_slopes edge_slopes ppoly_coef ppoly_coef h_neglect h_neglect answers_2018 answers_2018 Reconstruction by quartic polynomials within each cell. It is assumed that the dimension of 'u' is equal to the number of cells defining 'grid' and 'ppoly'. No consistency check is performed. n Number of cells h cell widths (size N) [H] u cell averages (size N) [A] edge_values Edge value of polynomial [A] edge_slopes Edge slope of polynomial [A H-1] ppoly_coef Coefficients of polynomial, mainly [A] h_neglect A negligibly small width for the purpose of cell reconstructions [H] answers_2018 If true use older, less acccurate expressions. pqm_limiter mom_remapping::build_reconstructions_1d regrid_interp::regridding_set_ppolys subroutine subroutine pqm_functions::pqm_limiter (N, h, u, edge_values, edge_slopes, h_neglect, answers_2018) pqm_limiter N N h h u u edge_values edge_values edge_slopes edge_slopes h_neglect h_neglect answers_2018 answers_2018 Limit the piecewise quartic method reconstruction. Standard PQM limiter (White & Adcroft, JCP 2008). It is assumed that the dimension of 'u' is equal to the number of cells defining 'grid' and 'ppoly'. No consistency check is performed. n Number of cells h cell widths (size N) [H] u cell average properties (size N) [A] edge_values Potentially modified edge values [A] edge_slopes Potentially modified edge slopes [A H-1] h_neglect A negligibly small width for the purpose of cell reconstructions [H] answers_2018 If true use older, less acccurate expressions. regrid_edge_values::bound_edge_values regrid_edge_values::check_discontinuous_edge_values hneglect_dflt pqm_reconstruction subroutine, public subroutine, public pqm_functions::pqm_boundary_extrapolation (N, h, u, edge_values, ppoly_coef) pqm_boundary_extrapolation N N h h u u edge_values edge_values ppoly_coef ppoly_coef Reconstruction by parabolas within boundary cells. The following explanations apply to the left boundary cell. The same reasoning holds for the right boundary cell. A parabola needs to be built in the cell and requires three degrees of freedom, which are the right edge value and slope and the cell average. The right edge values and slopes are taken to be that of the neighboring cell (i.e., the left edge value and slope of the neighboring cell). The resulting parabola is not necessarily monotonic and the traditional PPM limiter is used to modify one of the edge values in order to yield a monotonic parabola. 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. n Number of cells h cell widths (size N) [H] u cell averages (size N) [A] edge_values Edge value of polynomial [A] ppoly_coef Coefficients of polynomial, mainly [A] subroutine, public subroutine, public pqm_functions::pqm_boundary_extrapolation_v1 (N, h, u, edge_values, edge_slopes, ppoly_coef, h_neglect) pqm_boundary_extrapolation_v1 N N h h u u edge_values edge_values edge_slopes edge_slopes ppoly_coef ppoly_coef h_neglect h_neglect Reconstruction by parabolas within boundary cells. The following explanations apply to the left boundary cell. The same reasoning holds for the right boundary cell. A parabola needs to be built in the cell and requires three degrees of freedom, which are the right edge value and slope and the cell average. The right edge values and slopes are taken to be that of the neighboring cell (i.e., the left edge value and slope of the neighboring cell). The resulting parabola is not necessarily monotonic and the traditional PPM limiter is used to modify one of the edge values in order to yield a monotonic parabola. 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. n Number of cells h cell widths (size N) [H] u cell averages (size N) [A] edge_values Edge value of polynomial [A] edge_slopes Edge slope of polynomial [A H-1] ppoly_coef Coefficients of polynomial, mainly [A] h_neglect A negligibly small width for the purpose of cell reconstructions [H] hneglect_dflt mom_remapping::build_reconstructions_1d regrid_interp::regridding_set_ppolys Piecewise quartic reconstruction functions. Date of creation: 2008.06.06 L. White. This module contains routines that handle one-dimensionnal finite volume reconstruction using the piecewise quartic method (PQM).