Computational Rheology

Subcritical Instabilities in Plane Couette Flow of Visco-Elastic Fluids

“…There is also some evidence for non-linear parallel shear flow instabilities from numerical simulations of visco-elastic hydrodynamic equations (Atalik and Keunings, 2002). Partly because the numerical schemes used to solve these equations are known to break down when elastic stresses become large (Wi 1) -the socalled high Weissenberg number problem (Owens and Phillips, 2002) -it is open to debate whether an observed phenomenon is due to a numerical or a true physical instability.…”

A high-resolution finite-difference method for simulating two-fluid, viscoelastic gel dynamics

“…We do not explicitly nondimensionalize these equations because in doing so the number of parameters would not be reduced. Additionally, we avoid defining nondimensional parameters such as the Reynolds number, Weissenberg number, Deborah number, and elastic Mach number [20]. With 2 velocity fields, 4 viscosity parameters, 3 osmotic pressure parameters, a frictional drag coefficient, and a time-varying elastic modulus the rheology of the flow is difficult to characterize with these standard nondimensional numbers for single-phase viscoelastic flow.…”

“…An alternative method common for single-phase viscoelastic flows is to place the diagonal terms of τ at the cell centers and the off-diagonal terms of τ at the cell corners. This arrangement of unknowns gives a more natural way of calculating the divergence of the stress tensor since it does not require averaging any entries of τ [21,20]. However, for our two-phase model, this would have the unattractive consequence of coupling the stretching terms in (14) and (15) and increasing the total computational cost.…”

Numerical Analysis of Penetration Flow through Viscoelastic Fluids

“…In the present computation, we employed the elasticviscous split-stress (EVSS) method [14,19,20] to stabilize the numerical scheme. In the EVSS method, the stress tensor Sij is describe by…”