ENH: robuster handling of inv() of fields with singular tensors (#2724)

- replace the "one-size-fits-all" approach of tensor field inv()
  with individual 'failsafe' inverts.

  The inv() field function historically just checked the first entry
  to detect 2D cases and adjusted/readjusted *all* tensors accordingly
  (to avoid singularity tensors and/or noisy inversions).

  This seems to have worked reasonably well with 3D volume meshes, but
  breaks down for 2D area meshes, which can be axis-aligned
  differently on different sections of the mesh.

applications/test/invTensor/Make/files

@@ -0,0 +1,3 @@
+Test-invTensor.C
+
+EXE = $(FOAM_USER_APPBIN)/Test-invTensor

applications/test/invTensor/Make/options

@@ -0,0 +1,2 @@
+/* EXE_INC = */
+/* EXE_LIBS = */

applications/test/invTensor/Test-invTensor.C

@@ -0,0 +1,96 @@
+/*---------------------------------------------------------------------------*\
+  =========                 |
+  \\      /  F ield         | OpenFOAM: The Open Source CFD Toolbox
+   \\    /   O peration     |
+    \\  /    A nd           | www.openfoam.com
+     \\/     M anipulation  |
+-------------------------------------------------------------------------------
+    Copyright (C) 2023 OpenCFD Ltd.
+-------------------------------------------------------------------------------
+License
+    This file is part of OpenFOAM.
+
+    OpenFOAM is free software: you can redistribute it and/or modify it
+    under the terms of the GNU General Public License as published by
+    the Free Software Foundation, either version 3 of the License, or
+    (at your option) any later version.
+
+    OpenFOAM is distributed in the hope that it will be useful, but WITHOUT
+    ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or
+    FITNESS FOR A PARTICULAR PURPOSE.  See the GNU General Public License
+    for more details.
+
+    You should have received a copy of the GNU General Public License
+    along with OpenFOAM.  If not, see <http://www.gnu.org/licenses/>.
+
+Application
+    Test-invTensor
+
+Description
+    Tests for regular and corner cases of tensor inversion.
+
+\*---------------------------------------------------------------------------*/
+
+#include "tensor.H"
+#include "symmTensor.H"
+#include "transform.H"
+#include "unitConversion.H"
+#include "Random.H"
+#include "scalar.H"
+#include "complex.H"
+#include "sigFpe.H"
+
+using namespace Foam;
+
+// * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * //
+
+template<class TensorType>
+void test_invert(const TensorType& tt)
+{
+    Info<< pTraits<TensorType>::typeName << nl
+        << "ten : " << tt << nl;
+
+    // Non-failsafe. try/catch does not work here
+    if (tt.det() < ROOTVSMALL)
+    {
+        Info<< "inv : " << "nan/inf" << nl;
+    }
+    else
+    {
+        Info<< "inv : " << tt.inv() << nl;
+    }
+
+    // Failsafe
+    Info<< "inv : " << tt.safeInv() << nl;
+
+    Info<< nl;
+}
+
+
+// * * * * * * * * * * * * * * * Main Program  * * * * * * * * * * * * * * * //
+
+int main(int argc, char *argv[])
+{
+    // Run with FOAM_SIGFPE=true to ensure we see divide by zero
+    Foam::sigFpe::set(true);
+
+    {
+        symmTensor st(1e-3, 0, 0, 1e-3, 0, 1e-6);
+        test_invert(st);
+    }
+
+    {
+        symmTensor st(1e-3, 0, 0, 1e-3, 0, 1e-30);
+        test_invert(st);
+    }
+
+    {
+        symmTensor st(1e-3, 0, 0, 1e-3, 0, 0);
+        test_invert(st);
+    }
+
+    return 0;
+}
+
+
+// * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * //