arXiv: Fluid Dynamics | 2019
An embedded boundary approach for efficient simulations of viscoplastics and other generalised Newtonian fluids in non-trivial domains
Abstract
We present a methodology for simulating three-dimensional flow of incompressible viscoplastic fluids modelled by generalised Newtonian rheological equations in non-trivial domains. It is implemented in a highly efficient framework for massively parallelisable computations on structured grids. In order to simulate flow in domains with non-trivial geometries, an embedded boundary approach is utilised, enabling a wide range of flow problems to be solved accurately and efficiently. This constitutes the first published implementation of embedded boundaries for simulating flow of viscoplastic fluids. The underlying algorithm employs a two-stage Runge-Kutta method for temporal discretisation, in which viscous terms are treated semi-implicitly and projection methods are utilised to enforce the incompressibility constraint. We augment the embedded boundary algorithm to deal with the variable apparent viscosity of the fluids. Since it depends strongly on the strain rate tensor, special care has been taken to approximate the components of the velocity gradients robustly near boundary cells, both for viscous wall fluxes in cut cells and for updates of apparent viscosity in cells adjacent to them. After validating the code against standard test cases, we demonstrate its capabilities by simulating fully three-dimensional creeping flow of Bingham plastics around objects moving through them for the first time. Our results shed new light on the flow fields around these objects.