Technical Note: Data Structures of ILBDC Lattice Boltzmann Solver

The lattice Boltzmann method (LBM) is used in computational fluid mechanics (CFD) to simulate flows. Introduced by McNamara [3] the LBM historically is based on lattice gas automata. Instead simulating each particle a statistical average for a sufficient small control volume is applied. The LBM can also be considered as the solution to a velocity-discrete Boltzmann equation with an appropriate collision operator. As the original collision operator is computational intensive the BGK operator [1] can be used instead. This results in the lattice BGK methods [2, 4]. For simulation the simulation domain is discretized by an equally spaced Cartesian grid. The resulting cells are then either fluid or solid. Every cell has N velocity vectors ei (i = 0, . . . , N − 1) and N particle distribution functions fi (i = 0, . . . , N − 1) which describe the probability of a certain number of particles being in the velocity range around ei. Depending on the dimensionality d of the simulation domain (2D or 3D) and the number of velocity vectors N several models exists. They are usually referred to as DdQN , e.g. D2Q7 or D3Q19. The lattice Boltzmann method solves the equation