A Variable Time-Step Formulation for the Integral K–BKZ Model

Integral models such as K–BKZ are widely used in the simulation of viscoelastic flows, but the computational cost associated with evaluating the deformation history often limits their applicability in complex problems. In this work, we propose a simple strategy to reduce this cost, based on the use of variable time steps and on the efficient reconstruction of intermediate points along the memory interval. The methodology is assessed in three flow configurations: a two-dimensional cross-slot flow, a two-dimensional viscoelastic jet with a multimode fluid and PSM damping function, and an axisymmetric three-dimensional jet. In the cross-slot case, a reduction of up to 40 times in CPU time is observed without loss of accuracy. In the 2D jet, where flow stability imposes very small time steps, the computational cost remains essentially unchanged. In the 3D case, the use of a variable time step becomes essential to make the simulation feasible. The results indicate that the proposed approach is consistent, accurate, and applicable to complex viscoelastic flows.