Oldroyd-B Viscoelastic Constitutive Model L1-477

Polymer PhysicsViscoelastic flowδ=5 · challengingL_DAG = 3.6📋 Stub — not mineable

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Unclaimed Principle — open for contribution

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Forward model E

r h o \cdot D v / D t = - g r a d (p) + d i v (t a u); t a u = t a u_{s} + t a u_{p}; t a u_{p} + λ_{1} \cdot s t r es s_{U} C M = 2 \cdot e t a_{p} \cdot D; s t r es s_{U} C M = d t a u / d t + v . g r a d (t a u) - (g r a d (v))^{T} t a u - t a ug r a d (v)

Oldroyd-B: Newtonian solvent + elastic dumbbell polymer stress tensor; upper-convected Maxwell evolution with relaxation time lambda_1 and retardation time lambda_2.

L-DAG

E.momentum -> E.UCM_stress -> O.iter -> O.stress_field

E.momentumE.UCM_stressO.iterO.stress_field

Well-posedness W

Existence:: true
Uniqueness:: true
Stability:: conditional
κ:: 500

High-Weissenberg number problem (HWNP); stress singularities near geometric corners; log-conformation reformulation needed for Wi>10.

Solvability C

Solver class:: DEVSS-G finite element with log-conformation; parameter inversion by adjoint-PDE optimization
Convergence rate q:: 2
Complexity:: O(N_mesh^{1.5}) per Newton step with preconditioned Krylov

Specs (0)

No L2 specs registered yet for this principle.