\hypertarget{namespacep1m__functions}{}\doxysection{p1m\+\_\+functions Module Reference} \label{namespacep1m__functions}\index{p1m\_functions@{p1m\_functions}} \doxysubsection{Detailed Description} Linear interpolation functions. Date of creation\+: 2008.\+06.\+09 L. White. This module contains p1m (linear) interpolation routines. p1m interpolation is performed by estimating the edge values and linearly interpolating between them. \doxysubsection*{Functions/\+Subroutines} \begin{DoxyCompactItemize} \item subroutine, public \mbox{\hyperlink{namespacep1m__functions_a233a7aff25cf6581421f76bba053d758}{p1m\+\_\+interpolation}} (N, h, u, edge\+\_\+values, ppoly\+\_\+coef, h\+\_\+neglect, answers\+\_\+2018) \begin{DoxyCompactList}\small\item\em Linearly interpolate between edge values. \end{DoxyCompactList}\item subroutine, public \mbox{\hyperlink{namespacep1m__functions_a1a45cb8f3f794172d2a19b53e10416c6}{p1m\+\_\+boundary\+\_\+extrapolation}} (N, h, u, edge\+\_\+values, ppoly\+\_\+coef) \begin{DoxyCompactList}\small\item\em Interpolation by linear polynomials within boundary cells. \end{DoxyCompactList}\end{DoxyCompactItemize} \doxysubsection{Function/\+Subroutine Documentation} \mbox{\Hypertarget{namespacep1m__functions_a1a45cb8f3f794172d2a19b53e10416c6}\label{namespacep1m__functions_a1a45cb8f3f794172d2a19b53e10416c6}} \index{p1m\_functions@{p1m\_functions}!p1m\_boundary\_extrapolation@{p1m\_boundary\_extrapolation}} \index{p1m\_boundary\_extrapolation@{p1m\_boundary\_extrapolation}!p1m\_functions@{p1m\_functions}} \doxysubsubsection{\texorpdfstring{p1m\_boundary\_extrapolation()}{p1m\_boundary\_extrapolation()}} {\footnotesize\ttfamily subroutine, public p1m\+\_\+functions\+::p1m\+\_\+boundary\+\_\+extrapolation (\begin{DoxyParamCaption}\item[{integer, intent(in)}]{N, }\item[{real, dimension(\+:), intent(in)}]{h, }\item[{real, dimension(\+:), intent(in)}]{u, }\item[{real, dimension(\+:,\+:), intent(inout)}]{edge\+\_\+values, }\item[{real, dimension(\+:,\+:), intent(inout)}]{ppoly\+\_\+coef }\end{DoxyParamCaption})} Interpolation by linear polynomials within boundary cells. The left and right edge values in the left and right boundary cells, respectively, are estimated using a linear extrapolation within the cells. It is assumed that the size of the array \textquotesingle{}u\textquotesingle{} is equal to the number of cells defining \textquotesingle{}grid\textquotesingle{} and \textquotesingle{}ppoly\textquotesingle{}. No consistency check is performed here. \begin{DoxyParams}[1]{Parameters} \mbox{\texttt{ in}} & {\em n} & Number of cells \\ \hline \mbox{\texttt{ in}} & {\em h} & cell widths (size N) \mbox{[}H\mbox{]} \\ \hline \mbox{\texttt{ in}} & {\em u} & cell averages (size N) \mbox{[}A\mbox{]} \\ \hline \mbox{\texttt{ in,out}} & {\em edge\+\_\+values} & edge values of piecewise polynomials \mbox{[}A\mbox{]} \\ \hline \mbox{\texttt{ in,out}} & {\em ppoly\+\_\+coef} & coefficients of piecewise polynomials, mainly \mbox{[}A\mbox{]} \\ \hline \end{DoxyParams} Definition at line 68 of file P1\+M\+\_\+functions.\+F90. \begin{DoxyCode}{0} \DoxyCodeLine{69 \textcolor{comment}{! Arguments}} \DoxyCodeLine{70 \textcolor{keywordtype}{integer}, \textcolor{keywordtype}{intent(in)} :: N\textcolor{comment}{ !< Number of cells}} \DoxyCodeLine{71 \textcolor{keywordtype}{ real}, \textcolor{keywordtype}{dimension(:)}, \textcolor{keywordtype}{intent(in)} :: h\textcolor{comment}{ !< cell widths (size N) [H]}} \DoxyCodeLine{72 \textcolor{keywordtype}{ real}, \textcolor{keywordtype}{dimension(:)}, \textcolor{keywordtype}{intent(in)} :: u\textcolor{comment}{ !< cell averages (size N) [A]}} \DoxyCodeLine{73 \textcolor{keywordtype}{ real}, \textcolor{keywordtype}{dimension(:,:)}, \textcolor{keywordtype}{intent(inout)} :: edge\_values\textcolor{comment}{ !< edge values of piecewise polynomials [A]}} \DoxyCodeLine{74 \textcolor{keywordtype}{ real}, \textcolor{keywordtype}{dimension(:,:)}, \textcolor{keywordtype}{intent(inout)} :: ppoly\_coef\textcolor{comment}{ !< coefficients of piecewise polynomials, mainly [A]}} \DoxyCodeLine{75 } \DoxyCodeLine{76 \textcolor{comment}{! Local variables}} \DoxyCodeLine{77 \textcolor{keywordtype}{ real} :: u0, u1 \textcolor{comment}{! cell averages}} \DoxyCodeLine{78 \textcolor{keywordtype}{ real} :: h0, h1 \textcolor{comment}{! corresponding cell widths}} \DoxyCodeLine{79 \textcolor{keywordtype}{ real} :: slope \textcolor{comment}{! retained PLM slope}} \DoxyCodeLine{80 \textcolor{keywordtype}{ real} :: u0\_l, u0\_r \textcolor{comment}{! edge values}} \DoxyCodeLine{81 } \DoxyCodeLine{82 \textcolor{comment}{! -\/-\/-\/-\/-\/-\/-\/-\/-\/-\/-\/-\/-\/-\/-\/-\/-\/-\/-\/-\/-\/-\/-\/-\/-\/-\/-\/-\/-\/-\/-\/-\/-\/-\/-\/-\/-\/-\/-\/-\/-\/}} \DoxyCodeLine{83 \textcolor{comment}{! Left edge value in the left boundary cell}} \DoxyCodeLine{84 \textcolor{comment}{! -\/-\/-\/-\/-\/-\/-\/-\/-\/-\/-\/-\/-\/-\/-\/-\/-\/-\/-\/-\/-\/-\/-\/-\/-\/-\/-\/-\/-\/-\/-\/-\/-\/-\/-\/-\/-\/-\/-\/-\/-\/}} \DoxyCodeLine{85 h0 = h(1)} \DoxyCodeLine{86 h1 = h(2)} \DoxyCodeLine{87 } \DoxyCodeLine{88 u0 = u(1)} \DoxyCodeLine{89 u1 = u(2)} \DoxyCodeLine{90 } \DoxyCodeLine{91 \textcolor{comment}{! The standard PLM slope is computed as a first estimate for the}} \DoxyCodeLine{92 \textcolor{comment}{! interpolation within the cell}} \DoxyCodeLine{93 slope = 2.0 * ( u1 -\/ u0 )} \DoxyCodeLine{94 } \DoxyCodeLine{95 \textcolor{comment}{! The right edge value is then computed and we check whether this}} \DoxyCodeLine{96 \textcolor{comment}{! right edge value is consistent: it cannot be larger than the edge}} \DoxyCodeLine{97 \textcolor{comment}{! value in the neighboring cell if the data set is increasing.}} \DoxyCodeLine{98 \textcolor{comment}{! If the right value is found to too large, the slope is further limited}} \DoxyCodeLine{99 \textcolor{comment}{! by using the edge value in the neighboring cell.}} \DoxyCodeLine{100 u0\_r = u0 + 0.5 * slope} \DoxyCodeLine{101 } \DoxyCodeLine{102 \textcolor{keywordflow}{if} ( (u1 -\/ u0) * (edge\_values(2,1) -\/ u0\_r) < 0.0 ) \textcolor{keywordflow}{then}} \DoxyCodeLine{103 slope = 2.0 * ( edge\_values(2,1) -\/ u0 )} \DoxyCodeLine{104 \textcolor{keywordflow}{ endif}} \DoxyCodeLine{105 } \DoxyCodeLine{106 \textcolor{comment}{! Using the limited slope, the left edge value is reevaluated and}} \DoxyCodeLine{107 \textcolor{comment}{! the interpolant coefficients recomputed}} \DoxyCodeLine{108 \textcolor{keywordflow}{if} ( h0 /= 0.0 ) \textcolor{keywordflow}{then}} \DoxyCodeLine{109 edge\_values(1,1) = u0 -\/ 0.5 * slope} \DoxyCodeLine{110 \textcolor{keywordflow}{else}} \DoxyCodeLine{111 edge\_values(1,1) = u0} \DoxyCodeLine{112 \textcolor{keywordflow}{ endif}} \DoxyCodeLine{113 } \DoxyCodeLine{114 ppoly\_coef(1,1) = edge\_values(1,1)} \DoxyCodeLine{115 ppoly\_coef(1,2) = edge\_values(1,2) -\/ edge\_values(1,1)} \DoxyCodeLine{116 } \DoxyCodeLine{117 \textcolor{comment}{! -\/-\/-\/-\/-\/-\/-\/-\/-\/-\/-\/-\/-\/-\/-\/-\/-\/-\/-\/-\/-\/-\/-\/-\/-\/-\/-\/-\/-\/-\/-\/-\/-\/-\/-\/-\/-\/-\/-\/-\/-\/-\/}} \DoxyCodeLine{118 \textcolor{comment}{! Right edge value in the left boundary cell}} \DoxyCodeLine{119 \textcolor{comment}{! -\/-\/-\/-\/-\/-\/-\/-\/-\/-\/-\/-\/-\/-\/-\/-\/-\/-\/-\/-\/-\/-\/-\/-\/-\/-\/-\/-\/-\/-\/-\/-\/-\/-\/-\/-\/-\/-\/-\/-\/-\/-\/}} \DoxyCodeLine{120 h0 = h(n-\/1)} \DoxyCodeLine{121 h1 = h(n)} \DoxyCodeLine{122 } \DoxyCodeLine{123 u0 = u(n-\/1)} \DoxyCodeLine{124 u1 = u(n)} \DoxyCodeLine{125 } \DoxyCodeLine{126 slope = 2.0 * ( u1 -\/ u0 )} \DoxyCodeLine{127 } \DoxyCodeLine{128 u0\_l = u1 -\/ 0.5 * slope} \DoxyCodeLine{129 } \DoxyCodeLine{130 \textcolor{keywordflow}{if} ( (u1 -\/ u0) * (u0\_l -\/ edge\_values(n-\/1,2)) < 0.0 ) \textcolor{keywordflow}{then}} \DoxyCodeLine{131 slope = 2.0 * ( u1 -\/ edge\_values(n-\/1,2) )} \DoxyCodeLine{132 \textcolor{keywordflow}{ endif}} \DoxyCodeLine{133 } \DoxyCodeLine{134 \textcolor{keywordflow}{if} ( h1 /= 0.0 ) \textcolor{keywordflow}{then}} \DoxyCodeLine{135 edge\_values(n,2) = u1 + 0.5 * slope} \DoxyCodeLine{136 \textcolor{keywordflow}{else}} \DoxyCodeLine{137 edge\_values(n,2) = u1} \DoxyCodeLine{138 \textcolor{keywordflow}{ endif}} \DoxyCodeLine{139 } \DoxyCodeLine{140 ppoly\_coef(n,1) = edge\_values(n,1)} \DoxyCodeLine{141 ppoly\_coef(n,2) = edge\_values(n,2) -\/ edge\_values(n,1)} \DoxyCodeLine{142 } \end{DoxyCode} \mbox{\Hypertarget{namespacep1m__functions_a233a7aff25cf6581421f76bba053d758}\label{namespacep1m__functions_a233a7aff25cf6581421f76bba053d758}} \index{p1m\_functions@{p1m\_functions}!p1m\_interpolation@{p1m\_interpolation}} \index{p1m\_interpolation@{p1m\_interpolation}!p1m\_functions@{p1m\_functions}} \doxysubsubsection{\texorpdfstring{p1m\_interpolation()}{p1m\_interpolation()}} {\footnotesize\ttfamily subroutine, public p1m\+\_\+functions\+::p1m\+\_\+interpolation (\begin{DoxyParamCaption}\item[{integer, intent(in)}]{N, }\item[{real, dimension(\+:), intent(in)}]{h, }\item[{real, dimension(\+:), intent(in)}]{u, }\item[{real, dimension(\+:,\+:), intent(inout)}]{edge\+\_\+values, }\item[{real, dimension(\+:,\+:), intent(inout)}]{ppoly\+\_\+coef, }\item[{real, intent(in), optional}]{h\+\_\+neglect, }\item[{logical, intent(in), optional}]{answers\+\_\+2018 }\end{DoxyParamCaption})} Linearly interpolate between edge values. The resulting piecewise interpolant is stored in \textquotesingle{}ppoly\textquotesingle{}. See \textquotesingle{}ppoly.\+F90\textquotesingle{} for a definition of this structure. The edge values M\+U\+ST have been estimated prior to calling this routine. The estimated edge values must be limited to ensure monotonicity of the interpolant. We also make sure that edge values are N\+OT discontinuous. It is assumed that the size of the array \textquotesingle{}u\textquotesingle{} is equal to the number of cells defining \textquotesingle{}grid\textquotesingle{} and \textquotesingle{}ppoly\textquotesingle{}. No consistency check is performed here. \begin{DoxyParams}[1]{Parameters} \mbox{\texttt{ in}} & {\em n} & Number of cells \\ \hline \mbox{\texttt{ in}} & {\em h} & cell widths (size N) \mbox{[}H\mbox{]} \\ \hline \mbox{\texttt{ in}} & {\em u} & cell average properties (size N) \mbox{[}A\mbox{]} \\ \hline \mbox{\texttt{ in,out}} & {\em edge\+\_\+values} & Potentially modified edge values \mbox{[}A\mbox{]} \\ \hline \mbox{\texttt{ in,out}} & {\em ppoly\+\_\+coef} & Potentially modified piecewise polynomial coefficients, mainly \mbox{[}A\mbox{]} \\ \hline \mbox{\texttt{ in}} & {\em h\+\_\+neglect} & A negligibly small width \mbox{[}H\mbox{]} \\ \hline \mbox{\texttt{ in}} & {\em answers\+\_\+2018} & If true use older, less acccurate expressions. \\ \hline \end{DoxyParams} Definition at line 27 of file P1\+M\+\_\+functions.\+F90. \begin{DoxyCode}{0} \DoxyCodeLine{28 \textcolor{keywordtype}{integer}, \textcolor{keywordtype}{intent(in)} :: N\textcolor{comment}{ !< Number of cells}} \DoxyCodeLine{29 \textcolor{keywordtype}{ real}, \textcolor{keywordtype}{dimension(:)}, \textcolor{keywordtype}{intent(in)} :: h\textcolor{comment}{ !< cell widths (size N) [H]}} \DoxyCodeLine{30 \textcolor{keywordtype}{ real}, \textcolor{keywordtype}{dimension(:)}, \textcolor{keywordtype}{intent(in)} :: u\textcolor{comment}{ !< cell average properties (size N) [A]}} \DoxyCodeLine{31 \textcolor{keywordtype}{ real}, \textcolor{keywordtype}{dimension(:,:)}, \textcolor{keywordtype}{intent(inout)} :: edge\_values\textcolor{comment}{ !< Potentially modified edge values [A]}} \DoxyCodeLine{32 \textcolor{keywordtype}{ real}, \textcolor{keywordtype}{dimension(:,:)}, \textcolor{keywordtype}{intent(inout)} :: ppoly\_coef\textcolor{comment}{ !< Potentially modified}} \DoxyCodeLine{33 \textcolor{comment}{ !! piecewise polynomial coefficients, mainly [A]}} \DoxyCodeLine{34 \textcolor{keywordtype}{ real}, \textcolor{keywordtype}{optional}, \textcolor{keywordtype}{intent(in)} :: h\_neglect\textcolor{comment}{ !< A negligibly small width [H]}} \DoxyCodeLine{35 \textcolor{keywordtype}{logical}, \textcolor{keywordtype}{optional}, \textcolor{keywordtype}{intent(in)} :: answers\_2018\textcolor{comment}{ !< If true use older, less acccurate expressions.}} \DoxyCodeLine{36 } \DoxyCodeLine{37 \textcolor{comment}{! Local variables}} \DoxyCodeLine{38 \textcolor{keywordtype}{integer} :: k \textcolor{comment}{! loop index}} \DoxyCodeLine{39 \textcolor{keywordtype}{ real} :: u0\_l, u0\_r \textcolor{comment}{! edge values (left and right)}} \DoxyCodeLine{40 } \DoxyCodeLine{41 \textcolor{comment}{! Bound edge values (routine found in 'edge\_values.F90')}} \DoxyCodeLine{42 \textcolor{keyword}{call }bound\_edge\_values( n, h, u, edge\_values, h\_neglect, answers\_2018 )} \DoxyCodeLine{43 } \DoxyCodeLine{44 \textcolor{comment}{! Systematically average discontinuous edge values (routine found in}} \DoxyCodeLine{45 \textcolor{comment}{! 'edge\_values.F90')}} \DoxyCodeLine{46 \textcolor{keyword}{call }average\_discontinuous\_edge\_values( n, edge\_values )} \DoxyCodeLine{47 } \DoxyCodeLine{48 \textcolor{comment}{! Loop on interior cells to build interpolants}} \DoxyCodeLine{49 \textcolor{keywordflow}{do} k = 1,n} \DoxyCodeLine{50 } \DoxyCodeLine{51 u0\_l = edge\_values(k,1)} \DoxyCodeLine{52 u0\_r = edge\_values(k,2)} \DoxyCodeLine{53 } \DoxyCodeLine{54 ppoly\_coef(k,1) = u0\_l} \DoxyCodeLine{55 ppoly\_coef(k,2) = u0\_r -\/ u0\_l} \DoxyCodeLine{56 } \DoxyCodeLine{57 \textcolor{keywordflow}{ enddo} \textcolor{comment}{! end loop on interior cells}} \DoxyCodeLine{58 } \end{DoxyCode}