Lee, H. and Lee, N., 2018. Lattice Boltzmann Simulation of Shallow Water Equations in Finite Element Framework. In: Shim, J.-S.; Chun, I., and Lim, H.S. (eds.), Proceedings from the International Coastal Symposium (ICS) 2018 (Busan, Republic of Korea). Journal of Coastal Research, Special Issue No. 85, pp. 106–110. Coconut Creek (Florida), ISSN 0749-0208.
The characteristic Galerkin finite element model for the discrete Boltzmann equation is developed for the depth-integrated shallow water equations. The lattice Boltzmann method (LBM) simulates microscopic collision and streaming of fluid particles and, then, evaluates the macroscopic velocity, pressure, etc. from the computed particle distribution. Due to the inherent geometric flexibility of the unstructured mesh in finite element method, the mesh clustering near large gradients and the numerical treatments of complex geometries has become possible. Some benchmark problems of practical importance (subcritical flow over hump, flow around cylinder, curved channel, etc.) are tested and the numerical results are in good agreement with previous experimental or analytic solutions.