ColtBig: Compressible and thermal lattice Boltzmann methods on interpolation-based grids

• Applicant: Professor Dr.-Ing. Holger Foysi
• Subject Area: Fluid Mechanics
• Term: since 2020
• Project identifier: Deutsche Forschungsgemeinschaft (DFG) - Project number 439383920

Our goal is to study, improve, and apply novel lattice Boltzmann methods (LBM) for compressible flows. Despite the widely acknowledged success of LBM for the simulation of weakly compressible flows, an accepted framework for the simulation of thermal and fully coupled compressible flows is still lacking according to the literature, which is due to the large number of possible extensions and a lack of understanding of the strengths and weaknesses of the various approaches in reproducing variable density or intrinsic compressibility effects. A detailed analysis of the approaches to reproduce those effects is lacking. Firstly, the LBM model has to be energy conserving, a requirement not met by the standard LBM formulation when adopted to fully compressible flows. Secondly, the velocity sets have to be suited to high-speed flows and to a broad temperature range, being represented by a large number of energy shells with different particle velocities. Contrary to the standard LBM for weakly compressible flows, velocity sets coinciding with the Cartesian grid mostly do not fulfill these requirements. Lastly, the discretization of the advection step plays a decisive role in the flexibility of the methods. Standard schemes suffer from the fixed time step and from the enormous velocity sets that are used for the velocity discretization, since the sets have to both match the Cartesian grid and to obey symmetry in their shape. Recently, two very promising approaches were presented. The first is by Frapolli et al. called the entropic LBM (ELBM), representing an on-lattice LBM solver for compressible flows. Our project will compare the ELBM to our recently developed approach representing an off-lattice interpolation based semi-Lagrangian LBM solver (SLLBM). It represents a new generalized formulation of the LBM that allows for efficient simulations on irregular grids. Advantages of our new method include the geometric flexibility of the domain, the high-order advection step, a variable time step size and the easy application of sophisticated velocity sets. These advantages will turn the SLLBM into a high-potential candidate for the simulation of thermal and compressible flows. Succeeding a substantial analysis of the ELBM and the SLLBM in the first part of this proposal, simulations of compressible forced isotropic turbulence, compressible temporal mixing layers, and supersonic turbulent channel flows are performed in the second part of the project, partly for the first time with compressible LBM in general. This is necessary to analyze differences in the respective approaches and to gain required insights into finding an accepted and established approach to compressible flows using LBM. The test cases allow investigating intrinsic and variable density compressibility effects seperately, include shocklets and even allow (isotropic turbulence) a splitting into solenoidal and dilatational parts, in addition to a detailed comparison with the literature.

• DFG Programme: Research Grants