test/dictionary/testCalcNewton: Example of #calc with #{...#} to find the root of a function

using Newton-Raphson iteration.

test/dictionary/Allclean

@@ -1,9 +0,0 @@
-#!/bin/sh
-cd ${0%/*} || exit 1    # Run from this directory
-
-# Source tutorial run functions
-. $WM_PROJECT_DIR/bin/tools/CleanFunctions
-
-cleanCase
-
-#------------------------------------------------------------------------------

test/dictionary/Allrun

@@ -6,6 +6,7 @@ cd ${0%/*} || exit 1    # Run from this directory
 
 runApplication -s testDict foamDictionary -expand testDict
 runApplication -s testCalc foamDictionary -expand testCalc
+runApplication -s testCalcNewton foamDictionary -expand testCalcNewton
 runApplication -s simpleBlockMeshDict foamDictionary -expand simpleBlockMeshDict
 
 #------------------------------------------------------------------------------

test/dictionary/testCalcNewton

@@ -0,0 +1,57 @@
+/*--------------------------------*- C++ -*----------------------------------*\
+  =========                 |
+  \\      /  F ield         | OpenFOAM: The Open Source CFD Toolbox
+   \\    /   O peration     | Website:  https://openfoam.org
+    \\  /    A nd           | Version:  dev
+     \\/     M anipulation  |
+\*---------------------------------------------------------------------------*/
+FoamFile
+{
+    format      ascii;
+    class       dictionary;
+    object      testCalcNewton;
+}
+// * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * //
+
+// Find the root of f(x) = x + B*x/sqrt(1 + sqr(x)) - A
+// using Newton-Raphson iteration
+
+A       1;
+B       1;
+
+x       #calc
+#{
+    // Lookup the coefficients
+    const scalar A = $A;
+    const scalar B = $B;
+
+    // Initial guess for x
+    scalar x = 0;
+
+    scalar x0 = x;
+
+    do
+    {
+        // Store the previous iteration x for the convergence check
+        x0 = x;
+
+        // Temporary sub-function evaluations
+        const scalar f1 = 1 + sqr(x);
+        const scalar f2 = sqrt(f1);
+
+        // Evaluate the function
+        const scalar f = x + B*x/f2 - A;
+
+        // Evaluate the derivative
+        const scalar df = 1 + B/(f1*f2);
+
+        // Update x
+        x = x0 - f/df;
+
+        // Test for convergence
+    } while (mag(x - x0) > 1e-6);
+
+    os << x;
+#};
+
+// ************************************************************************* //