Application of lattice Boltzmann method, finite element method, and cellular automata and their coupling to wave propagation problems

Three different computational techniques were applied to wave propagation problems. Those techniques were the lattice Boltzmann method, finite element method, and cellular automata. The formulation of each technique was presented, and the coupling procedures of those techniques were also presented. For example, a part of the problem domain was solved using one analysis technique while the other part was analyzed by another technique. Such coupled techniques may overcome the difficulties that a single technique has, and they may also provide their own advantages of two different methods in a single analysis depending on application problems. For example, one technique is computationally more efficient while another is useful to model a complex or irregular shape of domain. Combining the two techniques will be beneficial to solve a complex domain shape with computational efficiency. The accuracy of the different techniques including the coupled methods was numerically demonstrated by comparing their solutions to other solutions available for wave propagation problems in 1-D and 2-D.