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 uctuation distribution schemes for advection equations. Accuracy results are presented for a pure convection problem, for which uctuation 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 ow 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 element mesh. Compared to the nite element method, the second-order accurate nite volume implementation is ten times as e cient.