Semi-Lagrangian lattice Boltzmann model for compressible flows on unstructured meshes

Abstract

Compressible lattice Boltzmann model on standard lattices [M. H. Saadat, F. Bösch, and I. V. Karlin, Phys. Rev. E 99, 013306 (2019).] is extended to deal with complex flows on unstructured grid. Semi-Lagrangian propagation [A. Krämer et al., Phys. Rev. E 95, 023305 (2017).] is performed on an unstructured second-order accurate finite-element mesh and a consistent wall boundary condition is implemented which makes it possible to simulate compressible flows over complex geometries. The model is validated through simulation of Sod shock tube, subsonic and supersonic flow over NACA0012 airfoil and shock-vortex interaction in Schardin's problem. Numerical results demonstrate that the present model on standard lattices is able to simulate compressible flows involving shock waves on unstructured meshes with good accuracy and without using any artificial dissipation or limiter.

Semi-Lagrangian lattice Boltzmann method for compressible flows

“…The results accurately matched the reference solution [58] with only minor oscillations visible, comparable to other recently introduced methods [60].…”

“…To measure the accuracy of the SLLBM for compressible flows, the smooth density propagation [59,60] was evaluated.…”

A lattice Boltzmann model for reactive mixtures

“…As in [ 11 ], the lattice Boltzmann equations for the f - and g -populations are realized on the discrete velocity set and where relaxation parameters and are related to the viscosity and thermal conductivity. The equilibrium f -populations in ( 3.6 ) are evaluated using the product-form, with and in ( 2.6 ), The last term in ( 3.6 ) is a correction needed to compensate for the insufficient isotropy of the lattice in the compressible flow setting [ 11 , 13 – 15 ]: X is the vector with the components while the components of vectors are defined as The equilibrium and the quasi-equilibrium g -populations, and in ( 3.7 ), are ...…”

Lattice Boltzmann method for fluid-structure interaction in compressible flow

“…Another avenue are semi-Lagrangian methods [33][34][35][36][37], which start from a characteristic equation to resolve these issues. Promising results have been shown for wall-bounded turbulent flows [38] and even compressible flows [37,39,40].…”

“…In our previous works [39,40], it was demonstrated that by using an arbitrary Eulerian-Lagrangian (ALE) formulation in combination with a dual population LB formulation, highspeed compressible flows with moving geometries can be captured accurately and efficiently. However, in those works, only a single body was considered and the motion was prescribed.…”