Existing lattice Boltzmann models that have been designed to recover a macroscopic description of immiscible liquids are only able to make predictions that are quantitatively correct when the interface that exists between the fluids is smeared over several nodal points. Attempts to minimise the thickness of this interface generally leads to a phenomenon known as lattice pinning, the precise cause of which is not well understood. This spurious behaviour is remarkably similar to that associated with the numerical simulation of hyperbolic partial differential equations coupled with a stiff source term. Inspired by the seminal work in this field, we derive a lattice Boltzmann implementation of a model equation used to investigate such peculiarities. This implementation is extended to different spacial discretisations in one and two dimensions. We shown that the inclusion of a quasi-random threshold dramatically delays the onset of pinning and facetting.
Citation
Reis T, Dellar PJ (2010) A Stochastic Sharpening Method for the Propagation of Phase Boundaries in Multiphase Lattice Boltzmann Simulations. 12th European Conference on the Mathematics of Oil Recovery. Available: http://dx.doi.org/10.3997/2214-4609.20144959.
Acknowledgements
The authors’ research is supported by Award No. KUK-C1-013-04, made by King Abdullah Universityof Science and Technology (KAUST); and by an Advanced Research Fellowship, grant numberEP/E054625/1, from the UK’s Engineering and Physical Sciences Research Council (EPSRC).
