GPU computing of yield stress fluid flows in narrow gaps

• Published in: Theoretical and computational fluid dynamics 2023-10, Vol.37 (5), p.661-680
• Main Authors: Medina Lino, Ivonne Leonor, Carrasco-Teja, Mariana, Frigaard, Ian
• Format: Article
• Language: English
• Subjects: Algorithms; Aquatic reptiles; Classical and Continuum Physics; Computational Science and Engineering; Engineering; Engineering Fluid Dynamics; Finite element method; Fluid flow; Fluids; Graphics coprocessors; Graphics processing units; Growth rings; Interfaces; Lagrange multiplier; Linear algebra; Non-Newtonian fluids; Nonlinearity; Original Article; Rheology; Yield stress
• ISSN: 0935-4964; 1432-2250
• DOI: 10.1007/s00162-023-00674-x

We present a Graphic Processing Units (GPU) implementation of non-Newtonian Hele-Shaw flow that models the displacement of Herschel-Bulkley fluids along narrow eccentric annuli. This flow is characteristic of many long-thin flows that require extensive calculation due to an inherent nonlinearity in the constitutive law. A common method of dealing with such flows is via an augmented Lagrangian algorithm, which is often painfully slow. Here we show that such algorithms, although involving slow iterations, can often be accelerated via parallel implementation on GPUs. Indeed, such algorithms explicitly solve the nonlinear aspects only locally on each mesh cell (or node), which makes them ideal candidates for GPUs. Combined with other advances, the optimized GPU implementation takes ≈ 2.5 % of the time of the original algorithm. Graphical abstract