\hypertarget{namespaceppm__functions}{}\section{ppm\+\_\+functions Module Reference} \label{namespaceppm__functions}\index{ppm\_functions@{ppm\_functions}} \subsection{Detailed Description} Provides functions used with the Piecewise-\/\+Parabolic-\/\+Method in the vertical A\+LE algorithm. \subsection*{Functions/\+Subroutines} \begin{DoxyCompactItemize} \item subroutine, public \mbox{\hyperlink{namespaceppm__functions_a5c4e47be75ad413904902582b3d0d4a4}{ppm\+\_\+reconstruction}} (N, h, u, edge\+\_\+values, ppoly\+\_\+coef, h\+\_\+neglect, answers\+\_\+2018) \begin{DoxyCompactList}\small\item\em Builds quadratic polynomials coefficients from cell mean and edge values. \end{DoxyCompactList}\item subroutine \mbox{\hyperlink{namespaceppm__functions_a3d365f4992a6d3b5cbcaca630c502b95}{ppm\+\_\+limiter\+\_\+standard}} (N, h, u, edge\+\_\+values, h\+\_\+neglect, answers\+\_\+2018) \begin{DoxyCompactList}\small\item\em Adjusts edge values using the standard P\+PM limiter (Colella \& Woodward, J\+CP 1984) after first checking that the edge values are bounded by neighbors cell averages and that the edge values are monotonic between cell averages. \end{DoxyCompactList}\item subroutine, public \mbox{\hyperlink{namespaceppm__functions_ac8f382eb9d1f0df80aab9e07eb2ceebe}{ppm\+\_\+boundary\+\_\+extrapolation}} (N, h, u, edge\+\_\+values, ppoly\+\_\+coef, h\+\_\+neglect) \begin{DoxyCompactList}\small\item\em Reconstruction by parabolas within boundary cells. \end{DoxyCompactList}\end{DoxyCompactItemize} \subsection*{Variables} \begin{DoxyCompactItemize} \item real, parameter \mbox{\hyperlink{namespaceppm__functions_a86e3d1a796b4934167d563eda5310a0e}{hneglect\+\_\+dflt}} = 1.E-\/30 \begin{DoxyCompactList}\small\item\em A tiny width that is so small that adding it to cell widths does not change the value due to a computational representation. It is used to avoid division by zero. \end{DoxyCompactList}\end{DoxyCompactItemize} \subsection{Function/\+Subroutine Documentation} \mbox{\Hypertarget{namespaceppm__functions_ac8f382eb9d1f0df80aab9e07eb2ceebe}\label{namespaceppm__functions_ac8f382eb9d1f0df80aab9e07eb2ceebe}} \index{ppm\_functions@{ppm\_functions}!ppm\_boundary\_extrapolation@{ppm\_boundary\_extrapolation}} \index{ppm\_boundary\_extrapolation@{ppm\_boundary\_extrapolation}!ppm\_functions@{ppm\_functions}} \subsubsection{\texorpdfstring{ppm\_boundary\_extrapolation()}{ppm\_boundary\_extrapolation()}} {\footnotesize\ttfamily subroutine, public ppm\+\_\+functions\+::ppm\+\_\+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, }\item[{real, intent(in), optional}]{h\+\_\+neglect }\end{DoxyParamCaption})} Reconstruction by parabolas within boundary cells. \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 \mbox{\texttt{ in}} & {\em h\+\_\+neglect} & A negligibly small width for the purpose of cell reconstructions \mbox{[}H\mbox{]} \\ \hline \end{DoxyParams} Definition at line 134 of file P\+P\+M\+\_\+functions.\+F90. \begin{DoxyCode}{0} \DoxyCodeLine{134 \textcolor{comment}{!------------------------------------------------------------------------------}} \DoxyCodeLine{135 \textcolor{comment}{! Reconstruction by parabolas within boundary cells.}} \DoxyCodeLine{136 \textcolor{comment}{!}} \DoxyCodeLine{137 \textcolor{comment}{! The following explanations apply to the left boundary cell. The same}} \DoxyCodeLine{138 \textcolor{comment}{! reasoning holds for the right boundary cell.}} \DoxyCodeLine{139 \textcolor{comment}{!}} \DoxyCodeLine{140 \textcolor{comment}{! A parabola needs to be built in the cell and requires three degrees of}} \DoxyCodeLine{141 \textcolor{comment}{! freedom, which are the right edge value and slope and the cell average.}} \DoxyCodeLine{142 \textcolor{comment}{! The right edge values and slopes are taken to be that of the neighboring}} \DoxyCodeLine{143 \textcolor{comment}{! cell (i.e., the left edge value and slope of the neighboring cell).}} \DoxyCodeLine{144 \textcolor{comment}{! The resulting parabola is not necessarily monotonic and the traditional}} \DoxyCodeLine{145 \textcolor{comment}{! PPM limiter is used to modify one of the edge values in order to yield}} \DoxyCodeLine{146 \textcolor{comment}{! a monotonic parabola.}} \DoxyCodeLine{147 \textcolor{comment}{!}} \DoxyCodeLine{148 \textcolor{comment}{! N: number of cells in grid}} \DoxyCodeLine{149 \textcolor{comment}{! h: thicknesses of grid cells}} \DoxyCodeLine{150 \textcolor{comment}{! u: cell averages to use in constructing piecewise polynomials}} \DoxyCodeLine{151 \textcolor{comment}{! edge\_values : edge values of piecewise polynomials}} \DoxyCodeLine{152 \textcolor{comment}{! ppoly\_coef : coefficients of piecewise polynomials}} \DoxyCodeLine{153 \textcolor{comment}{!}} \DoxyCodeLine{154 \textcolor{comment}{! It is assumed that the size of the array 'u' is equal to the number of cells}} \DoxyCodeLine{155 \textcolor{comment}{! defining 'grid' and 'ppoly'. No consistency check is performed here.}} \DoxyCodeLine{156 \textcolor{comment}{!------------------------------------------------------------------------------}} \DoxyCodeLine{157 } \DoxyCodeLine{158 \textcolor{comment}{! Arguments}} \DoxyCodeLine{159 \textcolor{keywordtype}{integer}, \textcolor{keywordtype}{intent(in)} :: N\textcolor{comment}{ !< Number of cells}} \DoxyCodeLine{160 \textcolor{keywordtype}{ real}, \textcolor{keywordtype}{dimension(:)}, \textcolor{keywordtype}{intent(in)} :: h\textcolor{comment}{ !< cell widths (size N) [H]}} \DoxyCodeLine{161 \textcolor{keywordtype}{ real}, \textcolor{keywordtype}{dimension(:)}, \textcolor{keywordtype}{intent(in)} :: u\textcolor{comment}{ !< cell averages (size N) [A]}} \DoxyCodeLine{162 \textcolor{keywordtype}{ real}, \textcolor{keywordtype}{dimension(:,:)}, \textcolor{keywordtype}{intent(inout)} :: edge\_values\textcolor{comment}{ !< edge values of piecewise polynomials [A]}} \DoxyCodeLine{163 \textcolor{keywordtype}{ real}, \textcolor{keywordtype}{dimension(:,:)}, \textcolor{keywordtype}{intent(inout)} :: ppoly\_coef\textcolor{comment}{ !< coefficients of piecewise polynomials, mainly [A]}} \DoxyCodeLine{164 \textcolor{keywordtype}{ real}, \textcolor{keywordtype}{optional}, \textcolor{keywordtype}{intent(in)} :: h\_neglect\textcolor{comment}{ !< A negligibly small width for}} \DoxyCodeLine{165 \textcolor{comment}{ !! the purpose of cell reconstructions [H]}} \DoxyCodeLine{166 } \DoxyCodeLine{167 \textcolor{comment}{! Local variables}} \DoxyCodeLine{168 \textcolor{keywordtype}{integer} :: i0, i1} \DoxyCodeLine{169 \textcolor{keywordtype}{ real} :: u0, u1} \DoxyCodeLine{170 \textcolor{keywordtype}{ real} :: h0, h1} \DoxyCodeLine{171 \textcolor{keywordtype}{ real} :: a, b, c} \DoxyCodeLine{172 \textcolor{keywordtype}{ real} :: u0\_l, u0\_r} \DoxyCodeLine{173 \textcolor{keywordtype}{ real} :: u1\_l, u1\_r} \DoxyCodeLine{174 \textcolor{keywordtype}{ real} :: slope} \DoxyCodeLine{175 \textcolor{keywordtype}{ real} :: exp1, exp2} \DoxyCodeLine{176 \textcolor{keywordtype}{ real} :: hNeglect} \DoxyCodeLine{177 } \DoxyCodeLine{178 hneglect = hneglect\_dflt ; \textcolor{keywordflow}{if} (\textcolor{keyword}{present}(h\_neglect)) hneglect = h\_neglect} \DoxyCodeLine{179 } \DoxyCodeLine{180 \textcolor{comment}{! ----- Left boundary -----}} \DoxyCodeLine{181 i0 = 1} \DoxyCodeLine{182 i1 = 2} \DoxyCodeLine{183 h0 = h(i0)} \DoxyCodeLine{184 h1 = h(i1)} \DoxyCodeLine{185 u0 = u(i0)} \DoxyCodeLine{186 u1 = u(i1)} \DoxyCodeLine{187 } \DoxyCodeLine{188 \textcolor{comment}{! Compute the left edge slope in neighboring cell and express it in}} \DoxyCodeLine{189 \textcolor{comment}{! the global coordinate system}} \DoxyCodeLine{190 b = ppoly\_coef(i1,2)} \DoxyCodeLine{191 u1\_r = b *((h0+hneglect)/(h1+hneglect)) \textcolor{comment}{! derivative evaluated at xi = 0.0,}} \DoxyCodeLine{192 \textcolor{comment}{! expressed w.r.t. xi (local coord. system)}} \DoxyCodeLine{193 } \DoxyCodeLine{194 \textcolor{comment}{! Limit the right slope by the PLM limited slope}} \DoxyCodeLine{195 slope = 2.0 * ( u1 - u0 )} \DoxyCodeLine{196 \textcolor{keywordflow}{if} ( abs(u1\_r) > abs(slope) ) \textcolor{keywordflow}{then}} \DoxyCodeLine{197 u1\_r = slope} \DoxyCodeLine{198 \textcolor{keywordflow}{ endif}} \DoxyCodeLine{199 } \DoxyCodeLine{200 \textcolor{comment}{! The right edge value in the boundary cell is taken to be the left}} \DoxyCodeLine{201 \textcolor{comment}{! edge value in the neighboring cell}} \DoxyCodeLine{202 u0\_r = edge\_values(i1,1)} \DoxyCodeLine{203 } \DoxyCodeLine{204 \textcolor{comment}{! Given the right edge value and slope, we determine the left}} \DoxyCodeLine{205 \textcolor{comment}{! edge value and slope by computing the parabola as determined by}} \DoxyCodeLine{206 \textcolor{comment}{! the right edge value and slope and the boundary cell average}} \DoxyCodeLine{207 u0\_l = 3.0 * u0 + 0.5 * u1\_r - 2.0 * u0\_r} \DoxyCodeLine{208 } \DoxyCodeLine{209 \textcolor{comment}{! Apply the traditional PPM limiter}} \DoxyCodeLine{210 exp1 = (u0\_r - u0\_l) * (u0 - 0.5*(u0\_l+u0\_r))} \DoxyCodeLine{211 exp2 = (u0\_r - u0\_l) * (u0\_r - u0\_l) / 6.0} \DoxyCodeLine{212 } \DoxyCodeLine{213 \textcolor{keywordflow}{if} ( exp1 > exp2 ) \textcolor{keywordflow}{then}} \DoxyCodeLine{214 u0\_l = 3.0 * u0 - 2.0 * u0\_r} \DoxyCodeLine{215 \textcolor{keywordflow}{ endif}} \DoxyCodeLine{216 } \DoxyCodeLine{217 \textcolor{keywordflow}{if} ( exp1 < -exp2 ) \textcolor{keywordflow}{then}} \DoxyCodeLine{218 u0\_r = 3.0 * u0 - 2.0 * u0\_l} \DoxyCodeLine{219 \textcolor{keywordflow}{ endif}} \DoxyCodeLine{220 } \DoxyCodeLine{221 edge\_values(i0,1) = u0\_l} \DoxyCodeLine{222 edge\_values(i0,2) = u0\_r} \DoxyCodeLine{223 } \DoxyCodeLine{224 a = u0\_l} \DoxyCodeLine{225 b = 6.0 * u0 - 4.0 * u0\_l - 2.0 * u0\_r} \DoxyCodeLine{226 c = 3.0 * ( u0\_r + u0\_l - 2.0 * u0 )} \DoxyCodeLine{227 } \DoxyCodeLine{228 ppoly\_coef(i0,1) = a} \DoxyCodeLine{229 ppoly\_coef(i0,2) = b} \DoxyCodeLine{230 ppoly\_coef(i0,3) = c} \DoxyCodeLine{231 } \DoxyCodeLine{232 \textcolor{comment}{! ----- Right boundary -----}} \DoxyCodeLine{233 i0 = n-1} \DoxyCodeLine{234 i1 = n} \DoxyCodeLine{235 h0 = h(i0)} \DoxyCodeLine{236 h1 = h(i1)} \DoxyCodeLine{237 u0 = u(i0)} \DoxyCodeLine{238 u1 = u(i1)} \DoxyCodeLine{239 } \DoxyCodeLine{240 \textcolor{comment}{! Compute the right edge slope in neighboring cell and express it in}} \DoxyCodeLine{241 \textcolor{comment}{! the global coordinate system}} \DoxyCodeLine{242 b = ppoly\_coef(i0,2)} \DoxyCodeLine{243 c = ppoly\_coef(i0,3)} \DoxyCodeLine{244 u1\_l = (b + 2*c) \textcolor{comment}{! derivative evaluated at xi = 1.0}} \DoxyCodeLine{245 u1\_l = u1\_l * ((h1+hneglect)/(h0+hneglect))} \DoxyCodeLine{246 } \DoxyCodeLine{247 \textcolor{comment}{! Limit the left slope by the PLM limited slope}} \DoxyCodeLine{248 slope = 2.0 * ( u1 - u0 )} \DoxyCodeLine{249 \textcolor{keywordflow}{if} ( abs(u1\_l) > abs(slope) ) \textcolor{keywordflow}{then}} \DoxyCodeLine{250 u1\_l = slope} \DoxyCodeLine{251 \textcolor{keywordflow}{ endif}} \DoxyCodeLine{252 } \DoxyCodeLine{253 \textcolor{comment}{! The left edge value in the boundary cell is taken to be the right}} \DoxyCodeLine{254 \textcolor{comment}{! edge value in the neighboring cell}} \DoxyCodeLine{255 u0\_l = edge\_values(i0,2)} \DoxyCodeLine{256 } \DoxyCodeLine{257 \textcolor{comment}{! Given the left edge value and slope, we determine the right}} \DoxyCodeLine{258 \textcolor{comment}{! edge value and slope by computing the parabola as determined by}} \DoxyCodeLine{259 \textcolor{comment}{! the left edge value and slope and the boundary cell average}} \DoxyCodeLine{260 u0\_r = 3.0 * u1 - 0.5 * u1\_l - 2.0 * u0\_l} \DoxyCodeLine{261 } \DoxyCodeLine{262 \textcolor{comment}{! Apply the traditional PPM limiter}} \DoxyCodeLine{263 exp1 = (u0\_r - u0\_l) * (u1 - 0.5*(u0\_l+u0\_r))} \DoxyCodeLine{264 exp2 = (u0\_r - u0\_l) * (u0\_r - u0\_l) / 6.0} \DoxyCodeLine{265 } \DoxyCodeLine{266 \textcolor{keywordflow}{if} ( exp1 > exp2 ) \textcolor{keywordflow}{then}} \DoxyCodeLine{267 u0\_l = 3.0 * u1 - 2.0 * u0\_r} \DoxyCodeLine{268 \textcolor{keywordflow}{ endif}} \DoxyCodeLine{269 } \DoxyCodeLine{270 \textcolor{keywordflow}{if} ( exp1 < -exp2 ) \textcolor{keywordflow}{then}} \DoxyCodeLine{271 u0\_r = 3.0 * u1 - 2.0 * u0\_l} \DoxyCodeLine{272 \textcolor{keywordflow}{ endif}} \DoxyCodeLine{273 } \DoxyCodeLine{274 edge\_values(i1,1) = u0\_l} \DoxyCodeLine{275 edge\_values(i1,2) = u0\_r} \DoxyCodeLine{276 } \DoxyCodeLine{277 a = u0\_l} \DoxyCodeLine{278 b = 6.0 * u1 - 4.0 * u0\_l - 2.0 * u0\_r} \DoxyCodeLine{279 c = 3.0 * ( u0\_r + u0\_l - 2.0 * u1 )} \DoxyCodeLine{280 } \DoxyCodeLine{281 ppoly\_coef(i1,1) = a} \DoxyCodeLine{282 ppoly\_coef(i1,2) = b} \DoxyCodeLine{283 ppoly\_coef(i1,3) = c} \DoxyCodeLine{284 } \end{DoxyCode} \mbox{\Hypertarget{namespaceppm__functions_a3d365f4992a6d3b5cbcaca630c502b95}\label{namespaceppm__functions_a3d365f4992a6d3b5cbcaca630c502b95}} \index{ppm\_functions@{ppm\_functions}!ppm\_limiter\_standard@{ppm\_limiter\_standard}} \index{ppm\_limiter\_standard@{ppm\_limiter\_standard}!ppm\_functions@{ppm\_functions}} \subsubsection{\texorpdfstring{ppm\_limiter\_standard()}{ppm\_limiter\_standard()}} {\footnotesize\ttfamily subroutine ppm\+\_\+functions\+::ppm\+\_\+limiter\+\_\+standard (\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, intent(in), optional}]{h\+\_\+neglect, }\item[{logical, intent(in), optional}]{answers\+\_\+2018 }\end{DoxyParamCaption})\hspace{0.3cm}{\ttfamily [private]}} Adjusts edge values using the standard P\+PM limiter (Colella \& Woodward, J\+CP 1984) after first checking that the edge values are bounded by neighbors cell averages and that the edge values are monotonic between cell averages. \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}} & {\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 63 of file P\+P\+M\+\_\+functions.\+F90. \begin{DoxyCode}{0} \DoxyCodeLine{63 \textcolor{keywordtype}{integer}, \textcolor{keywordtype}{intent(in)} :: N\textcolor{comment}{ !< Number of cells}} \DoxyCodeLine{64 \textcolor{keywordtype}{ real}, \textcolor{keywordtype}{dimension(:)}, \textcolor{keywordtype}{intent(in)} :: h\textcolor{comment}{ !< cell widths (size N) [H]}} \DoxyCodeLine{65 \textcolor{keywordtype}{ real}, \textcolor{keywordtype}{dimension(:)}, \textcolor{keywordtype}{intent(in)} :: u\textcolor{comment}{ !< cell average properties (size N) [A]}} \DoxyCodeLine{66 \textcolor{keywordtype}{ real}, \textcolor{keywordtype}{dimension(:,:)}, \textcolor{keywordtype}{intent(inout)} :: edge\_values\textcolor{comment}{ !< Potentially modified edge values [A]}} \DoxyCodeLine{67 \textcolor{keywordtype}{ real}, \textcolor{keywordtype}{optional}, \textcolor{keywordtype}{intent(in)} :: h\_neglect\textcolor{comment}{ !< A negligibly small width [H]}} \DoxyCodeLine{68 \textcolor{keywordtype}{logical}, \textcolor{keywordtype}{optional}, \textcolor{keywordtype}{intent(in)} :: answers\_2018\textcolor{comment}{ !< If true use older, less acccurate expressions.}} \DoxyCodeLine{69 } \DoxyCodeLine{70 \textcolor{comment}{! Local variables}} \DoxyCodeLine{71 \textcolor{keywordtype}{integer} :: k \textcolor{comment}{! Loop index}} \DoxyCodeLine{72 \textcolor{keywordtype}{ real} :: u\_l, u\_c, u\_r \textcolor{comment}{! Cell averages (left, center and right)}} \DoxyCodeLine{73 \textcolor{keywordtype}{ real} :: edge\_l, edge\_r \textcolor{comment}{! Edge values (left and right)}} \DoxyCodeLine{74 \textcolor{keywordtype}{ real} :: expr1, expr2} \DoxyCodeLine{75 } \DoxyCodeLine{76 \textcolor{comment}{! Bound edge values}} \DoxyCodeLine{77 \textcolor{keyword}{call }bound\_edge\_values( n, h, u, edge\_values, h\_neglect, answers\_2018 )} \DoxyCodeLine{78 } \DoxyCodeLine{79 \textcolor{comment}{! Make discontinuous edge values monotonic}} \DoxyCodeLine{80 \textcolor{keyword}{call }check\_discontinuous\_edge\_values( n, u, edge\_values )} \DoxyCodeLine{81 } \DoxyCodeLine{82 \textcolor{comment}{! Loop on interior cells to apply the standard}} \DoxyCodeLine{83 \textcolor{comment}{! PPM limiter (Colella \& Woodward, JCP 84)}} \DoxyCodeLine{84 \textcolor{keywordflow}{do} k = 2,n-1} \DoxyCodeLine{85 } \DoxyCodeLine{86 \textcolor{comment}{! Get cell averages}} \DoxyCodeLine{87 u\_l = u(k-1)} \DoxyCodeLine{88 u\_c = u(k)} \DoxyCodeLine{89 u\_r = u(k+1)} \DoxyCodeLine{90 } \DoxyCodeLine{91 edge\_l = edge\_values(k,1)} \DoxyCodeLine{92 edge\_r = edge\_values(k,2)} \DoxyCodeLine{93 } \DoxyCodeLine{94 \textcolor{keywordflow}{if} ( (u\_r - u\_c)*(u\_c - u\_l) <= 0.0) \textcolor{keywordflow}{then}} \DoxyCodeLine{95 \textcolor{comment}{! Flatten extremum}} \DoxyCodeLine{96 edge\_l = u\_c} \DoxyCodeLine{97 edge\_r = u\_c} \DoxyCodeLine{98 \textcolor{keywordflow}{else}} \DoxyCodeLine{99 expr1 = 3.0 * (edge\_r - edge\_l) * ( (u\_c - edge\_l) + (u\_c - edge\_r))} \DoxyCodeLine{100 expr2 = (edge\_r - edge\_l) * (edge\_r - edge\_l)} \DoxyCodeLine{101 \textcolor{keywordflow}{if} ( expr1 > expr2 ) \textcolor{keywordflow}{then}} \DoxyCodeLine{102 \textcolor{comment}{! Place extremum at right edge of cell by adjusting left edge value}} \DoxyCodeLine{103 edge\_l = u\_c + 2.0 * ( u\_c - edge\_r )} \DoxyCodeLine{104 edge\_l = max( min( edge\_l, max(u\_l, u\_c) ), min(u\_l, u\_c) ) \textcolor{comment}{! In case of round off}} \DoxyCodeLine{105 \textcolor{keywordflow}{elseif} ( expr1 < -expr2 ) \textcolor{keywordflow}{then}} \DoxyCodeLine{106 \textcolor{comment}{! Place extremum at left edge of cell by adjusting right edge value}} \DoxyCodeLine{107 edge\_r = u\_c + 2.0 * ( u\_c - edge\_l )} \DoxyCodeLine{108 edge\_r = max( min( edge\_r, max(u\_r, u\_c) ), min(u\_r, u\_c) ) \textcolor{comment}{! In case of round off}} \DoxyCodeLine{109 \textcolor{keywordflow}{ endif}} \DoxyCodeLine{110 \textcolor{keywordflow}{ endif}} \DoxyCodeLine{111 \textcolor{comment}{! This checks that the difference in edge values is representable}} \DoxyCodeLine{112 \textcolor{comment}{! and avoids overshoot problems due to round off.}} \DoxyCodeLine{113 \textcolor{comment}{!\#\#\# The 1.e-60 needs to have units of [A], so this dimensionally inconsisent.}} \DoxyCodeLine{114 \textcolor{keywordflow}{if} ( abs( edge\_r - edge\_l )