A Fully Implicit Log-Conformation Tensor Coupled Algorithm for the Solution of Incompressible Non-Isothermal...

Area of Science:

• Computational Fluid Dynamics
• Rheology
• Polymer Science

Background:

• Viscoelastic fluid flow simulations require robust numerical methods.
• The log-conformation tensor approach offers advantages for modeling complex fluid behavior.
• Non-isothermal effects add complexity to viscoelastic flow simulations.

Purpose of the Study:

• To develop and validate a novel block-coupled algorithm for non-isothermal viscoelastic fluid flow.
• To implement the log-conformation tensor approach within a monolithic framework.
• To accurately capture the interplay between flow, heat transfer, and viscoelasticity.

Main Methods:

• A block-coupled algorithm integrating mass, momentum, log-conformation tensor, and energy equations.
• Rhie-Chow interpolation for inter-equation coupling of momentum and mass conservation.
• Implicit discretization of divergence terms and Taylor series expansion for constitutive equations.
• Monolithic solution framework assembling discretized equations into a block-matrix.

Main Results:

• Successful computation of laminar, incompressible, non-isothermal, viscoelastic flow problems.
• Implicit treatment of key terms enhances numerical stability and accuracy.
• Validation against the axisymmetric 4:1 planar sudden contraction benchmark for Oldroyd-B fluid.

Conclusions:

• The developed block-coupled algorithm provides a reliable tool for simulating complex viscoelastic flows.
• The implicit discretization and log-conformation tensor approach improve simulation fidelity.
• The method is validated for a standard benchmark, demonstrating its applicability.