Abstract
This work thoroughly investigates a semi-Lagrangian lattice Boltzmann (SLLBM) solver for compressible flows. In contrast to other LBM for compressible flows, the vertices are organized in cells, and interpolation polynomials up to fourth order are used to attain the off-vertex distribution function values. Differing from the recently introduced Particles on Demand (PoD) method [Dorschner, Bösch, and Karlin, Phys. Rev. Lett. 121, 130602 (2018)PRLTAO0031-900710.1103/PhysRevLett.121.130602], the method operates in a static, nonmoving reference frame. Yet the SLLBM in the present formulation grants supersonic flows and exhibits a high degree of Galilean invariance. The SLLBM solver allows for an independent time step size due to the integration along characteristics and for the use of unusual velocity sets, like the D2Q25, which is constructed by the roots of the fifth-order Hermite polynomial. The properties of the present model are shown in diverse example simulations of a two-dimensional Taylor-Green vortex, a Sod shock tube, a two-dimensional Riemann problem, and a shock-vortex interaction. It is shown that the cell-based interpolation and the use of Gauss-Lobatto-Chebyshev support points allow for spatially high-order solutions and minimize the mass loss caused by the interpolation. Transformed grids in the shock-vortex interaction show the general applicability to nonuniform grids.
Highlights
In the field of weakly compressible and isothermal flows, the lattice Boltzmann method (LBM) [1,2,3] has emerged as an efficient numerical solver that suits modern, highly parallel computing architectures
The Sod shock tube shows the general capability of the semi-Lagrangian lattice Boltzmann (SLLBM) to deal with shocks at the original density ratio presented by Sod [58]
The compressible SLLBM is related to the Particles on Demand (PoD) method, but operates in a static, nonmoving reference frame
Summary
In the field of weakly compressible and isothermal flows, the lattice Boltzmann method (LBM) [1,2,3] has emerged as an efficient numerical solver that suits modern, highly parallel computing architectures. While on-lattice approaches inherit the LBM’s exact, space-filling streaming step [6,7,8,9], off-lattice methods discretize the Boltzmann equation through finite volume [10,11,12,13] or finite difference schemes [14,15,16]. Orthogonal to this classification, single-population models [4,17] express all physical moments, including energy and heat flux, by a single distribution function. Double-population models [8,18,19] represent the local internal energy through a separate distribution function that is coupled with the density and momentum coming from the first distribution function
Sign-in/Register to view highlights & summary Sign-in/Register to access full text options 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a callDisclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.
