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

40 Citations (Scopus)

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 1 2005

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Unstructured Mesh
Lattice Boltzmann Method
Least Squares
mesh
Finite Element
flexibility
finite element method
Flexibility
Least-squares Finite Element Method
Crank-Nicolson Method
Advection Equation
numerical stability
Second-order Accuracy
Couette Flow
Poiseuille Flow
Couette flow
eccentrics
Numerical Stability
circular cylinders
Circular Cylinder

ASJC Scopus subject areas

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

Cite this

Least-squares finite-element scheme for the lattice Boltzmann method on an unstructured mesh. / Li, Yusong; Leboeuf, Eugene J.; Basu, P. K.

In: Physical Review E - Statistical, Nonlinear, and Soft Matter Physics, Vol. 72, No. 4, 046711, 01.10.2005.

Research output: Contribution to journalArticle

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