CrankNicolsonDdtScheme: Add documentation

src/finiteVolume/finiteVolume/ddtSchemes/CrankNicolsonDdtScheme/CrankNicolsonDdtScheme.H

@@ -25,9 +25,37 @@ Class
     Foam::fv::CrankNicolsonDdtScheme
 
 Description
-    Second-oder CrankNicolson implicit ddt using the current and
+    Second-oder Crank-Nicolson implicit ddt using the current and
     previous time-step fields as well as the previous time-step ddt.
 
+    The Crank-Nicolson scheme is often unstable for complex flows in complex
+    geometries and it is necessary to "off-centre" the scheme to stabilize it
+    while retaining greater temporal accuracy than the first-order
+    Euler-implicit scheme.  Off-centering is specified via the mandatory
+    coefficient in the range [0,1] following the scheme name e.g.
+    \verbatim
+    ddtSchemes
+    {
+        default         CrankNicolson 0.9;
+    }
+    \endverbatim
+    With a coefficient of 1 the scheme is fully centred and second-order,
+    with a coefficient of 0 the scheme is equivalent to Euler-implicit.
+    A coefficient of 0.9 has been found to be suitable for a range of cases for
+    which higher-order accuracy in time is needed and provides similar accuracy
+    and stability to the backward scheme.  However, the backward scheme has
+    been found to be more robust and provides formal second-order accuracy in
+    time.
+
+    The advantage of the Crank-Nicolson scheme over backward is that only the
+    new and old-time values are needed, the additional terms relating to the
+    fluxes and sources are evaluated at the mid-point of the time-step which
+    provides the opportunity to limit the fluxes in such a way as to ensure
+    boundedness while maintaining greater accuracy in time compared to the
+    Euler-implicit scheme.  This approach is now used with MULES in the
+    interFoam family of solvers.  Boundedness cannot be guaranteed with the
+    backward scheme.
+
 SourceFiles
     CrankNicolsonDdtScheme.C
 
@@ -173,7 +201,7 @@ public:
                 (
                     "CrankNicolsonDdtScheme(const fvMesh& mesh, Istream& is)",
                     is
-                )   << "coefficient = " << ocCoeff_
+                )   << "Off-centreing coefficient = " << ocCoeff_
                     << " should be >= 0 and <= 1"
                     << exit(FatalIOError);
             }