Multiple solutions in the calculation of axisymmetric contraction flow of an upper convected maxwell fluid

2‐D time‐dependent viscoelastic flow calculations using connffessit

“…The journal bearing has been the subject of numerous investigations, analytical, numerical, and experimental (Ballal and Rivlin, 1976;Beris et al, 1983Beris et al, , 1984Beris et al, , 1986Beris et al, , 1987Burdette, 1989;Davies and Walters, 1973;Fix and Paslay, 1967;Lawler et al, 1986;Phan-Thien and Tanner, 1981;Rajagopalan, 1992;Reiner et al, 1969;Rivlin, 1979;Roberts and Walters, 1992;Sommerfeld, 1904;Tanner, 1963;Yeh et al, 1984). It consists of two nested cylinders of infinite length, the axes of which are parallel and separated by a distance e (Figure 3).…”

Computation of viscoelastic fluid flows using continuation methods

“…There are previous reports of the existence of a turning point in viscoelastic contraction flows [14,19,29,47] and other problem geometries [4,34,46]. Some observations indicate that the solution behavior is similar to that of a loss of temporal stability.…”

“…The authors observed numerically that, as the critical value of the Weissenberg number is approached, the length of the step that can be taken became infeasibly small. In [47], Yeh, et al used natural and arclength continuation methods to arrive at a bifurcation in the numerical solution of an upper convected Maxwell fluid, which the authors conjectured to be a product of the mathematical model of the fluid. However, later work has shown that the multiple solutions were an artifact of the numerical approximation (see [38]).…”

Further results on the flow of a maxwell fluid through an abrupt contraction

“…Table 1 shows that the picture is very different with the upper-convected Maxwell fluid. The limit point seems to settle in a meshindependent location, as seen by Yeh et al [4] in their simulations of circular contraction flows. It would thus appear that a true limit point (i.e.…”