Spencer, Timothy J.; Halliday, Ian; Care, Chris M. A local lattice Boltzmann method for multiple immiscible fluids and dense suspensions of drops. (English) Zbl 1223.76091 Philos. Trans. R. Soc. Lond., Ser. A, Math. Phys. Eng. Sci. 369, No. 1944, 2255-2263 (2011). Summary: The lattice Boltzmann method (LBM) for computational fluid dynamics benefits from a simple, explicit, completely local computational algorithm making it highly efficient. We extend LBM to recover hydrodynamics of multi-component immiscible fluids, while retaining a completely local, explicit and simple algorithm. Hence, no computationally expensive lattice gradients, interaction potentials or curvatures, that use information from neighbouring lattice sites, need to be calculated, which makes the method highly scalable and suitable for high performance parallel computing. The method is analytical and is shown to recover correct continuum hydrodynamic equations of motion and interfacial boundary conditions. This LBM may be further extended to situations containing a high number \((O(100))\) of individually immiscible drops. We make comparisons of the emergent non-Newtonian behaviour with a power-law fluid model. We anticipate our method will have a range applications in engineering, industrial and biological sciences. Cited in 1 Document MSC: 76M28 Particle methods and lattice-gas methods 76T20 Suspensions Keywords:lattice Boltzmann; multi-component flow; deformable suspension; channel flow; power-law fluid Software:MUPHY PDFBibTeX XMLCite \textit{T. J. Spencer} et al., Philos. Trans. R. Soc. Lond., Ser. A, Math. Phys. Eng. Sci. 369, No. 1944, 2255--2263 (2011; Zbl 1223.76091) Full Text: DOI References: [1] COMP PHYS COMMUN 180 pp 1495– (2009) [2] PHYS REV E 47 pp 1815– (1993) [3] Swift, Physical Review Letters 75 (5) pp 830– (1995) [4] PHYS REV E 74 pp 046709– (2006) [5] Gunstensen 43 (8) pp 4320– (1991) [6] PHYS REV E 76 pp 026708– (2007) [7] PHYS REV E 68 pp 056302– (2003) [8] PHYS REV E 79 pp 016706– (2009) [9] PHYS REV E 77 pp 036702– (2008) [10] PHIL TRANS R SOC LOND A 360 pp 535– (2002) · Zbl 1037.76047 [11] J COMP PHYS 113 pp 134– (1994) · Zbl 0809.76064 [12] PHYS REV E 65 pp 046308– (2002) · Zbl 1244.76102 [13] PHYS FLUIDS 6 pp 80– (1994) [14] Philosophical Transactions of the Royal Society A: Mathematical, Physical and Engineering Sciences 362 (1822) pp 1885– (2004) · Zbl 1205.76216 This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.