### Peter Wapperom and Mike F. Webster

### A Second-order Hybrid Finite Element/Volume Method for Viscoelastic
Flows

* Journal of Non-Newtonian Fluid Mechanics* **79** (1998) 405-431

#### Abstract

A second-order accurate cell-vertex finite volume/finite element hybrid
scheme is proposed. A finite volume method is used for the hyperbolic stress
equations and a finite element method for the balance equations. The finite
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
finite element mesh.
Compared to the finite element method, the second-order
accurate finite volume implementation is ten times as efficient.
#### Keywords

Hybrid finite element/finite volume; fluctuation distribution;
second-order; Oldroyd-B; pure convection