[EN] Developing a numerical and algorithmic tool which correctly identifies unyielded
regions in yield stress fluid flow is a challenging task. Two approaches are commonly used to
handle the singular behaviour at the yield surface, i.e. the Augmented Lagrangian approach and
the regularization approach, respectively. Generally in the regularization approach, solvers do
not perform efficiently when the regularization parameter gets very small. In this work, we use
a formulation introducing a new auxiliary stress. The three field formulation of the yield stress
fluid corresponds to a regularization-free Bingham formulation. The resulting set of equations
arising from the three field formulation is solved efficiently and accurately by a monolithic finite
element method. The velocity and pressure are discretized by the higher order stable FEM pair
Q2/Pdisc
1 and the auxiliary stress is discretized by the Q2 element.
Furthermore, this problem is highly nonlinear and presents a big challenge to any nonlinear
solver. Therefore, we developed a new adaptive discrete Newton method, which evaluates the
Jacobian with the divided difference approach. We relate the step length to the rate of the actual
nonlinear reduction for achieving a robust adaptive Newton method. We analyse the solvability
of the problem along with the adaptive Newton method for Bingham fluids by doing numerical
studies for a prototypical configuration ”viscoplastic fluid flow in a channel”.We would like to thank the Deutsche Forschungsgemeinschaft (DFG) for their financial support under the DFG Priority Program SPP 1962. The authors also acknowledge the support by LS3 and LiDO3 team at ITMC, TU Dortmund UniversityFatima, A.; Turek, S.; Ouazzi, A.; Afaq, MA. (2022). An adaptive discrete Newton method for regularization-free Bingham model. En Proceedings of the YIC 2021 - VI ECCOMAS Young Investigators Conference. Editorial Universitat Politècnica de València. 180-189. https://doi.org/10.4995/YIC2021.2021.12389OCS18018