Numerical Study of Viscoplastic Flows Using a Multigrid Initialization Algorithm

Abstract

In this paper, an innovative methodology to handle the numerical simulation of viscoplastic flows is proposed based on a multigrid initialization algorithm in conjunction with the SIMPLE procedure. The governing equations for incompressible flow, which consist of continuity and momentum equations, are solved on a collocated grid by combining the finite volume discretization and Rhie and chow interpolation for pressure–velocity coupling. Using the proposed solver in combination with the regularization scheme of Papanastasiou, we chose the square lid-driven cavity flow and pipe flow as test cases for validation and discussion. In doing so, we study the influence of the Bingham number and the Reynolds number on the development of rigid areas and the features of the vortices within the flow domain. Pipe flow results illustrate the flow’s response to the stress growth parameter values. We show that the representation of the yield surface and the plug zone is influenced by the chosen value. Regarding viscoplastic flows, our experiments demonstrate that our approach based on using the multigrid method as an initialization procedure makes a significant contribution by outperforming the classic single grid method. A computation speed-up ratio of 6.45 was achieved for the finest grid size (320 × 320).