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

Abstract

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.

A Fully Implicit Computational Strategy for Strongly Coupled Fluid–Solid Interaction

“…Such techniques have become standard in Eulerian finite element formulations and have been applied to various problems arising in fluid mechanics (see e.g. [4][5][6][7][16][17][18][19][20][21]). A review of a variety of stabilisation techniques may be found in [22].…”

Advanced FEM for free surface flow with application to landslides

“…Pressure can rise to infinity at large volumetric strain ε v = ρ0 ρ − 1 ensured by the state equation p = −K ln (1 − ε v ), in terms of bulk modulus K. The flow characteristics of the granular material is modelled by a Bingham fluid [1,6]. Hence the deviator stress is given by…”

“…An linear elastic material behaviour is assumed, which is described by the second Piola-Kirchhoff stress tensor S, the Green-Lagrangian strain tensor and the tensor C of elasticity. C is deduced from the strain-energy function Ψ of the St. Venant-Kirchhoff modelThe motion of viscous and compressible fluids is governed by the Navier-Stokes equations ∂ρv ∂tPressure can rise to infinity at large volumetric strain ε v = ρ0 ρ − 1 ensured by the state equation p = −K ln (1 − ε v ), in terms of bulk modulus K. The flow characteristics of the granular material is modelled by a Bingham fluid [1,6]. Hence the deviator stress is given by…”

On a finite element formulation for incompressible Newtonian fluid flows on moving domains in the presence of surface tension

“…Such techniques have become standard in Eulerian ÿnite element formulations for various problems arising in uid mechanics (see e.g. Reference [7]). A review of a variety of stabilization techniques may be found in Reference [8].…”