Efficient simulations of long wave propagation and runup using a LBM approach on GPGPU hardware

We present an efficient implementation of the Lattice Boltzmann method (LBM) for the numerical simulation of the propagation of long ocean waves (e.g., tsunamis), based on the Nonlinear Shallow Water (NSW) wave equation. The LBM solution of NSW equations is fully nonlinear and it is assumed that the surface elevation is single-valued (hence, waves do not break or overturn). For the treatment of wet-dry states, a simple shoreline step-slot algorithm is used. The NVIDIA CUDA framework is used for the implementation, which gives access to the computational power of General Purpose Graphical Processing Units (GPGPUs). The initial analysis of LBM results for standard analytical benchmark problems shows a good agreement with the reference solutions. For all benchmarks, the run times of the numerical simulations are on the same order as the time scale of the real world event, or even less. The presented applications include wave runup studies on a plane beach and a more complex three-dimensional beach, as proposed in the tsunami community as part of the so-called Catalina(Liu et al., 2008) and PMEL sets of benchmark problems. Finally, the results and the performance of the LBM solver are compared to those of the Boussinesq solver FUNWAVE.