📝 SummarXiv

Abstract

We develop a spectral element lattice Boltzmann method (SELBM) with the flux bounce-back (FBB) scheme, to enable accurate simulations of single-phase fluid dynamics in unstructured mesh. We adopt an Eulerian description of the streaming process in place of the perfect shift in the regular LBM. The spectral element method is used to spatially discretize the convective term, while the strong stability-preserving Runge-Kutta (SSPRK) method is used for time integration. To increase stability, we investigate the use of an explicit filter, particularly in the context of the sensitive double shear layer problem. The results indicate that by using the high-order polynomial, we can effectively eliminate the small vortices around the neck region. We introduce the flux bounce-back scheme to enable the current scheme to handle complex boundaries. The proposed scheme and flux boundary method are validated through benchmark simulations, including the unsteady Couette flow and the planar Poiseuille flow. Further validation is provided through the Taylor-Green vortex problem, demonstrating the accuracy and convergence of the scheme for isotropic turbulence. Finally, we consider a fully developed turbulent flow within a cylindrical pipe and correctly predict the turbulent boundary layer profile.