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

摘要

We present an efficient implementation of the Lattice Boltzmannmethod (LBM) for the numerical simulation of the propagation oflong ocean waves (e.g., tsunamis), based on the Nonlinear ShallowWater (NSW) wave equation. The LBM solution of NSWequations is fully nonlinear and it is assumed that the surface elevationis single-valued (hence, waves do not break or overturn).For the treatment of wet-dry states, a simple shoreline step-slotalgorithm is used.The NVIDIA CUDA framework is used for the implementation,which gives access to the computational power of GeneralPurpose Graphical Processing Units (GPGPUs). The initial analysisof LBM results for standard analytical benchmark problemsshows a good agreement with the reference solutions. For allbenchmarks, the run times of the numerical simulations are onthe same order as the time scale of the real world event, or evenless. The presented applications include wave runup studies on aplane beach and a more complex three-dimensional beach, as proposedin 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 comparedto those of the Boussinesq solver FUNWAVE.