A fully explicit characteristic based split (CBS) scheme for viscoelastic flow calculations

In this paper, an explicit characteristic based split (CBS) scheme is proposed for the numerical solution of incompressible viscoelastic flow equations. The scheme proposed is free from simultaneous solution to the matrices arising from the finite element discretization of the governing equations. The experience gained from the solution of Newtonian fluid dynamics problems has been applied to the solution of viscoelastic flows. The Oldroyd-B model has been employed to solve two benchmark problems of viscoelastic flow. They are viscoelastic flow past a circular cylinder and viscoelastic flow through planar contraction geometry. The results show that the solutions obtained are stable for the Weissenberg or Deborah number range studied in this paper. The solutions obtained at lower Weissenberg or Deborah numbers are accurate and agree excellently with the majority of available numerical data. However at higher Weissenberg or Deborah numbers, results show some sign of negative influence of the artificial dissipation added to the discrete constitutive equations.