Info<< "Reading field U\n" << endl;
    volVectorField U
    (
        IOobject
        (
            "U",
            runTime.timeName(),
            mesh,
            IOobject::MUST_READ,
            IOobject::AUTO_WRITE
        ),
        mesh
    );

    volTensorField gradU //= fvc::grad(U);
    (
        IOobject
        (
            "grad(U)",
            runTime.timeName(),
            mesh,
            IOobject::NO_READ,
            IOobject::NO_WRITE
        ),
        mesh,
        dimensionedTensor("zero", dimless, tensor::zero)
    );
    surfaceVectorField snGradU // = fvc::snGrad(U);
    (
        IOobject
        (
            "snGrad(U)",
            runTime.timeName(),
            mesh,
            IOobject::NO_READ,
            IOobject::NO_WRITE
        ),
	mesh,
	dimensionedVector("zero", dimless, vector::zero)
    );

    volVectorField V
    (
        IOobject
        (
            "V",
            runTime.timeName(),
            mesh,
            IOobject::READ_IF_PRESENT,
            IOobject::AUTO_WRITE
        ),
        fvc::ddt(U)
    );

    volSymmTensorField epsilon
    (
        IOobject
        (
            "epsilon",
            runTime.timeName(),
            mesh,
            IOobject::READ_IF_PRESENT,
            IOobject::AUTO_WRITE
        ),
        mesh,
        dimensionedSymmTensor("zero", dimless, symmTensor::zero)
    );

    volSymmTensorField sigma
    (
        IOobject
        (
            "sigma",
            runTime.timeName(),
            mesh,
            IOobject::READ_IF_PRESENT,
            IOobject::AUTO_WRITE
        ),
        mesh,
        dimensionedSymmTensor("zero", dimForce/dimArea, symmTensor::zero)
    );

      volVectorField divSigmaExp
      (
        IOobject
        (
         "divSigmaExp",
         runTime.timeName(),
         mesh,
         IOobject::NO_READ,
         IOobject::NO_WRITE
         ),
        mesh,
        dimensionedVector("zero", dimForce/dimVolume, vector::zero)
       );

    constitutiveModel rheology(sigma, U);
    
    surfaceVectorField traction
    (
        IOobject
        (
            "traction",
            runTime.timeName(),
            mesh,
            IOobject::NO_READ,
            IOobject::NO_WRITE
        ),
        mesh,
        dimensionedVector("zero", dimForce/dimArea, vector::zero)
    );

  // for aitken relaxation
   volVectorField aitkenDelta
    (
        IOobject
        (
            "aitkenDelta",
            runTime.timeName(),
            mesh,
            IOobject::NO_READ,
            IOobject::NO_WRITE
        ),
        mesh,
	dimensionedVector("zero", dimLength, vector::zero)
    );
// aitken relaxation factor
scalar aitkenInitialRes = 1.0;
scalar aitkenTheta = 0.1;
if(mesh.relax(U.name()))
  {
    aitkenTheta = mesh.relaxationFactor(U.name());
  }


   volVectorField resid
    (
        IOobject
        (
            "resid",
            runTime.timeName(),
            mesh,
            IOobject::NO_READ,
            IOobject::AUTO_WRITE
        ),
        mesh,
	dimensionedVector("zero", dimless, vector::zero)
    );