A LB-based approach for adaptive flow simulations

This paper presents an approach for adaptive flow simulations based on Lattice-Boltzmann (LB) models in the sense, that in addition to an a priori distribution of degrees of freedom (DOF) a dynamic modification of the computational grid (coarsening and/or refinement) in the course of the transient computation is initiated, based on the local evaluation of error indicators in order to optimize the ratio of accuracy versus absolute number of DOF. Using quadtree-based data structures, both arbitrarily formed grid interfaces of different resolutions as well as their dynamic modification are facilitated. Efficiency aspects will be discussed based on laminar two-dimensional flow simulations. The obtained results compare well to reference solutions cited in the literature and indicate the usefulness and computational efficiency of the approach.