A Spectral-Element Discontinuous Galerkin Lattice Boltzmann Method for Incompressible Flows
Title | A Spectral-Element Discontinuous Galerkin Lattice Boltzmann Method for Incompressible Flows |
Publication Type | Journal Article |
Year of Publication | 2010 |
Authors | Min, MS, Lee, T |
Journal | J. Comput. Phys. |
Volume | 230 |
Pagination | 245-259 |
Date Published | 12/2010 |
Other Numbers | ANL/MCS-P1688-1009 |
Abstract | We present a spectral-element discontinuous Galerkin lattice Boltzmann method for solving single-phase incompressible flows. Decoupling the collision step from the streaming step offers numerical stability at high Reynolds numbers. In the streaming step, we employ high-order spectral-element discretizations using a tensor product basis of one-dimensional Lagrange interpolation polynomials based on Gauss-Lobatto-Legendre grids. Our scheme is cost-effective with a fully diagonal mass matrix, advancing time integration with the fourth-order Runge-Kutta method. We present a consistent boundary treatment allowing us to use both central and Lax-Friedrichs fluxes for the numerical flux in the discontinuous Galerkin approach. We present two benchmark cases: lid-driven cavity flows for Re=400-5000 and flows around an impulsively started cylinder for Re=550-9500. Computational results are compared with those of other theoretical, experimental, and computational work that used a multigrid method, a vortex method, and a spectral element model. |
http://www.mcs.anl.gov/papers/P1688.pdf |