Further results on the flow of a Maxwell fluid through an abrupt contraction
We report new finite element simulations of creeping flow of an upper- convected Maxwell fluid through a sudden planar contraction whose re- entrant corner is defined by a circular arc of small radius. A series of finite element meshes is used, with increasing resolution near the rounded corner. The latter is approximated by either \(C^ 0\) or \(C^ 1\) finite element mappings. We find that a limit point in the numerical solution family emanating from the Newtonian result is responsible for the loss of convergence of the iterative scheme beyond some critical value of the Weissenberg number We. The location of the limit point in We-space is not very sensitive to rather extensive mesh refinement, and is virtually invariant to the choice of either \(C^ 0\) or \(C^ 1\) discretizations of the rounded corner. These results suggest that the limit point is an intrinsic property of the Maxwell fluid. No definitive conclusion can be drawn, however, for the numerical solutions obtained at values of We close to the limit point show spurious wiggles near the corner.
\(C^ 0\) or \(C^ 1\) finite element mappings
scientific article; zbMATH DE number 4090988