A spectral-element discontinuous Galerkin lattice Boltzmann method for nearly incompressible flows

• Published in: Journal of computational physics Vol. 230; no. 1; pp. 245 - 259
• Main Authors: Min, Misun, Lee, Taehun
• Format: Journal Article
• Language: English
• Published: Kidlington Elsevier Inc 2011; Elsevier
• Subjects: Computation; Computational techniques; Cylinders; Discontinous Galerkin method; Exact sciences and technology; Fluid flow; Galerkin methods; Incompressible flow; Lattice Boltzmann method; Lattices; Mathematical methods in physics; Mathematical models; Physics; Spectra; Spectral element method; Spectral element method; Discontinous Galerkin method; Lattice Boltzmann method; Spectral method; Tensor product; Spectral model; Boundary conditions; Calculation methods; Galerkin-Petrov method; Large Reynolds number; Incompressible flow; Decoupling; Discretization; Lagrange interpolation; Diagonal matrix; Multigrid; Polynomial interpolation; Vortices; Couette flow; Mass matrix; Calculation; Runge-Kutta methods; Cylinders
• ISSN: 0021-9991; 1090-2716
• DOI: 10.1016/j.jcp.2010.09.024

We present a spectral-element discontinuous Galerkin lattice Boltzmann method for solving nearly 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 discontinuous Galerkin 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 treatment for imposing boundary conditions with a numerical flux in the discontinuous Galerkin approach. We show convergence studies for Couette flows and demonstrate two benchmark cases with 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 and computational work that used a multigrid method, a vortex method, and a spectral element model.