A second-order hybrid finite element/volume method for viscoelastic flows

A second-order accurate cell-vertex nite volume / nite element hybrid scheme is proposed. A nite volume method is used for the hyperbolic stress equations and a nite element method for the balance equations. The nite volume implementation incorporates the recent advancement on fluctuation distribution schemes for advection equations. Accuracy results are presented for a pure convection problem, for which fluctuation distribution has been developed, and an Oldroyd-B benchmark problem. When source terms are included consistently, second-order accuracy can be achieved. However, a loss of accuracy is observed for both benchmark problems, when the flow near a boundary is (almost) parallel to it. Accuracy can be recovered in an elegant manner by taking advantage of the quadratic representations on the parent nite ele-ment mesh. Compared to the nite element method, the second-order accurate nite volume implementation is ten times as ecient