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The Scientific World Journal
Volume 2014, Article ID 142907, 16 pages
Research Article

High-Accuracy Approximation of High-Rank Derivatives: Isotropic Finite Differences Based on Lattice-Boltzmann Stencils

1Laboratory of Porous Media and Thermophysical Properties, Mechanical Engineering Department, Federal University of Santa Catarina, 88040-900 Florianópolis, SC, Brazil
2Department of Petroleum Engineering, State University of Santa Catarina, 88330-668 Balneário Camboriú, SC, Brazil

Received 8 August 2013; Accepted 12 October 2013; Published 29 January 2014

Academic Editors: J. Banaś and C. Yiu

Copyright © 2014 Keijo Kalervo Mattila et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Citations to this Article [7 citations]

The following is the list of published articles that have cited the current article.

  • Tonino Biciuşcă, Adrian Horga, and Victor Sofonea, “Simulation of liquid–vapour phase separation on GPUs using Lattice Boltzmann models with off-lattice velocity sets,” Comptes Rendus Mécanique, 2015. View at Publisher · View at Google Scholar
  • Keijo K. Mattila, Luiz A. Hegele, and Paulo C. Philippi, “Investigation of an entropic stabilizer for the lattice-Boltzmann method,” Physical Review E, vol. 91, no. 6, 2015. View at Publisher · View at Google Scholar
  • D.R. Golbert, P.J. Blanco, A. Clausse, and R.A. Feijóo, “on the search of more stable second-order lattice-Boltzmann schemes in confined flows,” Journal of Computational Physics, 2015. View at Publisher · View at Google Scholar
  • Hongwu Zhang, Shaojuan Geng, and Kainan Hu, “Decoupled scheme based on the Hermite expansion to construct lattice Boltzmann models for the compressible Navier-Stokes equations with arbitrary specific heat ratio,” Physical Review E - Statistical, Nonlinear, and Soft Matter Physics, vol. 94, no. 4, 2016. View at Publisher · View at Google Scholar
  • Keijo K. Mattila, Paulo C. Philippi, and Luiz A. Hegele, “High-order regularization in lattice-Boltzmann equations,” Physics of Fluids, vol. 29, no. 4, pp. 046103, 2017. View at Publisher · View at Google Scholar
  • Abbas Fakhari, Travis Mitchell, Christopher Leonardi, and Diogo Bolster, “Improved locality of the phase-field lattice-Boltzmann model for immiscible fluids at high density ratios,” Physical Review E, vol. 96, no. 5, 2017. View at Publisher · View at Google Scholar
  • V. Sofonea, T. Biciuşcă, S. Busuioc, Victor E. Ambruş, G. Gonnella, and A. Lamura, “Corner-transport-upwind lattice Boltzmann model for bubble cavitation,” Physical Review E, vol. 97, no. 2, 2018. View at Publisher · View at Google Scholar