Symmetric factorization of the conformation tensor in viscoelastic fluid models
This work offers a new mathematical formulation for viscoelastic fluid models that enhances numerical simulation stability and accuracy, benefiting researchers in computational fluid dynamics.
The authors reformulate the Oldroyd-B and FENE-P viscoelastic fluid models using the symmetric square root of the conformation tensor, which satisfies a closed evolution equation. This formulation yields a Hilbert space structure with an energy norm and provides significant improvements in accuracy and stability in direct numerical simulations.
The positive definite symmetric polymer conformation tensor possesses a unique symmetric square root that satisfies a closed evolution equation in the Oldroyd-B and FENE-P models of viscoelastic fluid flow. When expressed in terms of the velocity field and the symmetric square root of the conformation tensor, these models' equations of motion formally constitute an evolution in a Hilbert space with a total energy functional that defines a norm. Moreover, this formulation is easily implemented in direct numerical simulations resulting in significant practical advantages in terms of both accuracy and stability.