Some progress in lattice Boltzmann method. Part I: nonuniform mesh grids
Journal of Computational Physics
Journal of Computational Physics
Journal of Computational Physics
On the finite difference-based lattice Boltzmann method in curvilinear coordinates
Journal of Computational Physics
A novel thermal model for the lattice Boltzmann method in incompressible limit
Journal of Computational Physics
A characteristic Galerkin method for discrete Boltzmann equation
Journal of Computational Physics
An Eulerian description of the streaming process in the lattice Boltzmann equation
Journal of Computational Physics
Viscosity of finite difference lattice Boltzmann models
Journal of Computational Physics
A lattice Boltzmann algorithm for calculation of the laminar jet diffusion flame
Journal of Computational Physics
Journal of Computational Physics
Finite volume TVD formulation of lattice Boltzmann simulation on unstructured mesh
Journal of Computational Physics
Nodal Discontinuous Galerkin Methods: Algorithms, Analysis, and Applications
Nodal Discontinuous Galerkin Methods: Algorithms, Analysis, and Applications
Computers & Mathematics with Applications
Journal of Scientific Computing
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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.