A volume-preserving sharpening approach for the propagation of sharp phase boundaries in multiphase lattice Boltzmann simulations
Lattice Boltzmann models that recover a macroscopic description of multiphase flow of immiscible liquids typically represent the boundaries between phases using a scalar function, the phase field, that varies smoothly over several grid points. Attempts to tune the model parameters to minimise the th...
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| Format: | Journal article |
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2010
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| _version_ | 1797072231720812544 |
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| author | Reis, T Dellar, P |
| author_facet | Reis, T Dellar, P |
| author_sort | Reis, T |
| collection | OXFORD |
| description | Lattice Boltzmann models that recover a macroscopic description of multiphase flow of immiscible liquids typically represent the boundaries between phases using a scalar function, the phase field, that varies smoothly over several grid points. Attempts to tune the model parameters to minimise the thicknesses of these interfaces typically lead to the interfaces becoming fixed to the underlying grid instead of advecting with the fluid velocity. This phenomenon, known as lattice pinning, is strikingly similar to that associated with the numerical simulation of conservation laws coupled to stiff algebraic source terms. We present a lattice Boltzmann formulation of the model problem proposed by LeVeque and Yee [J. Comput. Phys. 86, 187] to study the latter phenomenon in the context of computational combustion, and offer a volume-conserving extension in multiple space dimensions. Inspired by the random projection method of Bao and Jin [J. Comput. Phys. 163, 216] we further generalise this formulation by introducing a uniformly distributed quasi-random variable into the term responsible for the sharpening of phase boundaries. This method is mass conserving and the statistical average of this method is shown to significantly delay the onset of pinning. |
| first_indexed | 2024-03-06T23:04:45Z |
| format | Journal article |
| id | oxford-uuid:63653cbb-65f0-44b6-abbb-90b83d5abf8a |
| institution | University of Oxford |
| last_indexed | 2024-03-06T23:04:45Z |
| publishDate | 2010 |
| record_format | dspace |
| spelling | oxford-uuid:63653cbb-65f0-44b6-abbb-90b83d5abf8a2022-03-26T18:12:39ZA volume-preserving sharpening approach for the propagation of sharp phase boundaries in multiphase lattice Boltzmann simulationsJournal articlehttp://purl.org/coar/resource_type/c_dcae04bcuuid:63653cbb-65f0-44b6-abbb-90b83d5abf8aMathematical Institute - ePrints2010Reis, TDellar, PLattice Boltzmann models that recover a macroscopic description of multiphase flow of immiscible liquids typically represent the boundaries between phases using a scalar function, the phase field, that varies smoothly over several grid points. Attempts to tune the model parameters to minimise the thicknesses of these interfaces typically lead to the interfaces becoming fixed to the underlying grid instead of advecting with the fluid velocity. This phenomenon, known as lattice pinning, is strikingly similar to that associated with the numerical simulation of conservation laws coupled to stiff algebraic source terms. We present a lattice Boltzmann formulation of the model problem proposed by LeVeque and Yee [J. Comput. Phys. 86, 187] to study the latter phenomenon in the context of computational combustion, and offer a volume-conserving extension in multiple space dimensions. Inspired by the random projection method of Bao and Jin [J. Comput. Phys. 163, 216] we further generalise this formulation by introducing a uniformly distributed quasi-random variable into the term responsible for the sharpening of phase boundaries. This method is mass conserving and the statistical average of this method is shown to significantly delay the onset of pinning. |
| spellingShingle | Reis, T Dellar, P A volume-preserving sharpening approach for the propagation of sharp phase boundaries in multiphase lattice Boltzmann simulations |
| title | A volume-preserving sharpening approach for the propagation of sharp phase boundaries in multiphase lattice Boltzmann simulations |
| title_full | A volume-preserving sharpening approach for the propagation of sharp phase boundaries in multiphase lattice Boltzmann simulations |
| title_fullStr | A volume-preserving sharpening approach for the propagation of sharp phase boundaries in multiphase lattice Boltzmann simulations |
| title_full_unstemmed | A volume-preserving sharpening approach for the propagation of sharp phase boundaries in multiphase lattice Boltzmann simulations |
| title_short | A volume-preserving sharpening approach for the propagation of sharp phase boundaries in multiphase lattice Boltzmann simulations |
| title_sort | volume preserving sharpening approach for the propagation of sharp phase boundaries in multiphase lattice boltzmann simulations |
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