An explicit finite volume method for viscoelastic fluid flows

We discuss a finite volume method for computing solutions of steady incompressible viscoelastic fluid flows. A fourth-order Runge-Kutta method is used in the explicit time-stepping scheme. The computations are carried out mainly on unstructured grids on Newtonian, inelastic and differential-type constitutive equations, which include the Oldroyd-B and the upper-convected Maxwell models. The performance of the scheme on unstructured grids is investigated, with particular reference to the stick-slip problem for the modified upper-convected Maxwell fluid. The results are compared with those obtained by using the finite element method whenever possible.