Octagonal lattices in thermal lattice Boltzmann & MHD simulations

Summary form only given. Lattice Boltzmann methods are an extremely efficient and highly parallelizable and vectorizable algorithm for mesoscopic representation of nonlinear macroscopic problems. The major hurdle facing the extensive use of TLBM is its numerical instability when wide parameter regimes are considered. Considerable research is underway to obviate this, but the root of the problem is clear: if one introduces discrete phase space velocity lattices one is forced to consider relaxation distribution functions that must be non-Maxwellian. The number of constraints needed to be enforced on the relaxed distribution function is reduced as one moves to higher isotropy lattice. We are investigating the use of octagonal lattices in 2D-and there generalization to 3D. However, since the octagonal lattice is no longer space filling the spatial grid is necessarily uncoupled from the velocity lattice. This uncoupling requires an extra step to, be incorporated into the TLBM algorithm an interpolation procedure that couples the free-streaming with the nodes of the chosen spatial grid 13. Even if one employed lower symmetry space-filling lattices, it would still be necessary to introduce interpolation if non-uniform spatial grids are employed (e.g., for wall-bounded flows..). We are currently looking into employing temperature-dependent velocity lattices, and will present some 2D jet flow simulations for Mach number flows up to 0.5. We are also investigating the use of octagonal lattices in MHD, rather than the customary square or hexagonal lattices. Besides aiming for higher numerical stability, one will test the accuracy to which div B=0 can be enforced in this non-vector potential representation. A reason for our continued interest in TLBM is its possible role in studying the scrape-off-layer in a tokamak.