General characteristic-based algorithm for off-lattice Boltzmann simulations

The Lattice Boltzmann method offers an appealing potential for simulation of fluid flows. However, the intrinsic coupling of momentum and space discretization restricts the applicability of the traditional Lattice Boltzmann method to uniform, regular lattices which is often disadvantageous in practice. Available off-lattice Boltzmann algorithms have stability problems which are to be handled at the expense of additional computational cost. Here, we propose and validate a general characteristic-based algorithm for off-lattice Boltzmann simulations that preserves all appealing properties of the standard Lattice Boltzmann method while extending the method to unstructured grids. Both, finite-element and finite-difference implementations of the algorithms are exemplified.