Least-squares finite-element scheme for the lattice Boltzmann method on an unstructured mesh

Yusong Li, Eugene J. Leboeuf, P. K. Basu

Research output: Contribution to journalArticle

41 Scopus citations

Abstract

A numerical model of the lattice Boltzmann method (LBM) utilizing least-squares finite-element method in space and the Crank-Nicolson method in time is developed. This method is able to solve fluid flow in domains that contain complex or irregular geometric boundaries by using the flexibility and numerical stability of a finite-element method, while employing accurate least-squares optimization. Fourth-order accuracy in space and second-order accuracy in time are derived for a pure advection equation on a uniform mesh; while high stability is implied from a von Neumann linearized stability analysis. Implemented on unstructured mesh through an innovative element-by-element approach, the proposed method requires fewer grid points and less memory compared to traditional LBM. Accurate numerical results are presented through two-dimensional incompressible Poiseuille flow, Couette flow, and flow past a circular cylinder. Finally, the proposed method is applied to estimate the permeability of a randomly generated porous media, which further demonstrates its inherent geometric flexibility.

Original languageEnglish (US)
Article number046711
JournalPhysical Review E - Statistical, Nonlinear, and Soft Matter Physics
Volume72
Issue number4
DOIs
StatePublished - Oct 2005

ASJC Scopus subject areas

  • Statistical and Nonlinear Physics
  • Statistics and Probability
  • Condensed Matter Physics

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