Computational modelling of viscoplastic fluids based on a stabilised finite element method

This work is concerned with computational modelling of viscoplastic fluids. The flows considered are assumed to be incompressible, while the viscoplastic laws are obtained by incorporating a yield stress below which the fluid is assumed to remain non‐deformable. The Bingham fluid is chosen as a model problem and is considered in detail in the text. The finite element formulation adopted in this work is based on a version of the stabilised finite element method, known as the Galerkin/least‐squares method, originally developed by Hughes and co‐workers. This methodology allows use of low and equal order interpolation of the pressure and velocity fields, thus providing an efficient finite element framework. The Newton‐Raphson method has been chosen for solution of the incremental non‐linear problem arising through the temporal discretisation of the evolution problem. Numerical examples are provided to illustrate the main features of the described methodology.