oomph::SecondInvariantHelper Namespace Reference

Functions
double	second_invariant (const DenseMatrix< double > &tensor)
	Compute second invariant of tensor. More...

Detailed Description

Helper namespace containing function that computes second invariant of tensor

Function Documentation

second_invariant()

double oomph::SecondInvariantHelper::second_invariant

(

const DenseMatrix< double > &

tensor

)

Compute second invariant of tensor.

    {
      // get size of tensor
      unsigned n = tensor.nrow();
      double trace_of_tensor = 0.0;
      double trace_of_tensor_squared = 0.0;
      for (unsigned i = 0; i < n; i++)
      {
        // Calculate the trace of the tensor: T_ii
        trace_of_tensor += tensor(i, i);
        // Calculate the trace of the tensor squared: T_ij T_ji
        for (unsigned j = 0; j < n; j++)
        {
          trace_of_tensor_squared += tensor(i, j) * tensor(j, i);
        }
      }
 
      // return the second invariant: 1.0/2.0*[(T_ii)^2 - T_ij T_ji]
      return 0.5 *
             (trace_of_tensor * trace_of_tensor - trace_of_tensor_squared);
    }

References i, j, n, and oomph::DenseMatrix< T >::nrow().

Referenced by oomph::GeneralisedNewtonianAxisymmetricNavierStokesEquations::fill_in_generic_residual_contribution_axi_nst(), oomph::RefineableGeneralisedNewtonianAxisymmetricNavierStokesEquations::fill_in_generic_residual_contribution_axi_nst(), oomph::GeneralisedNewtonianNavierStokesEquations< DIM >::fill_in_generic_residual_contribution_nst(), oomph::RefineableGeneralisedNewtonianNavierStokesEquations< DIM >::fill_in_generic_residual_contribution_nst(), oomph::GeneralisedNewtonianNavierStokesEquations< DIM >::get_traction(), get_Z2_flux(), oomph::GeneralisedNewtonianAxisymmetricNavierStokesEquations::max_and_min_invariant_and_viscosity(), oomph::GeneralisedNewtonianNavierStokesEquations< DIM >::max_and_min_invariant_and_viscosity(), output(), square_of_norm_of_fixed_point(), square_of_norm_of_strain_invariant(), square_of_norm_of_viscosity(), and oomph::GeneralisedNewtonianAxisymmetricNavierStokesEquations::traction().