  In this paper, we describe a numerical algorithm for the self-consistent
simulations of surface water and sediment dynamics. The method is based on the
original Lagrangian-Eulerian CSPH-TVD approach for solving the Saint-Venant and
Exner equations, taking into account the physical factors essential for the
understanding of the shallow water and surface soil layer motions, including
complex terrain structure and its evolution due to sediment transport.
Additional Exner equation for sediment transport has been used for the
numerical CSPH-TVD scheme stability criteria definition. By using OpenMP-CUDA
and GPUDirect technologies for hybrid computing systems (supercomputers) with
several graphic coprocessors (GPUs) interacting with each other via the PCI-E /
NVLINK interface we also develop a parallel numerical algorithm for the
CSPH-TVD method. The developed parallel version of the algorithm demonstrates
high efficiency for various configurations of Nvidia Tesla CPU + GPU computing
systems. In particular, maximal speed up is 1800 for a system with four C2070
GPUs compare to the serial version for the CPU. The calculation time on the GPU
V100~(Volta architecture) is reduced by 95 times compared to the GPU
C2070~(Fermi architecture).
