Abstract
The objectives of this study are to introduce a multiple-relaxation-time (MRT) lattice Boltzmann model (LBM) to simulate multilayer shallow water flows and to introduce graphics processing unit (GPU) computing to accelerate the lattice Boltzmann model. Using multiple relaxation times in the lattice Boltzmann model has an advantage of handling very low kinematic viscosity without causing a stability problem in the shallow water equations. This study develops a multilayer MRT-LBM to solve the multilayer Saint-Venant equations to obtain horizontal flow velocities in various depths. In the multilayer MRT-LBM, vertical kinematic viscosity forcing is the key term to couple adjacent layers. We implemented the multilayer MRT-LBM to a GPU-based high-performance computing (HPC) architecture. The multilayer MRT-LBM was verified by analytical solutions for cases of wind-driven, density-driven, and combined circulations with non-uniform bathymetry. The results show good speedup and scalability for large problems. Numerical solutions compared well to the analytical solutions. The multilayer MRT-LBM is promising for simulating lateral and vertical distributions of the horizontal velocities in shallow water flow.
Highlights
The shallow water equations are used to describe flow in bodies of water where the horizontal length scales are much greater than the fluid depth
The objective of this study is to develop a multiple-relaxation time (MRT)-lattice Boltzmann model (LBM) to simulate multilayer shallow water equations under graphics processing unit (GPU) high-performance computing
MATLAB GPU computing with Jacket starts at the most basic level through the replacement of low-level MATLAB data structures which normally reside on the central processing unit (CPU) with data structures that reside on the GPU
Summary
The shallow water equations are used to describe flow in bodies of water where the horizontal length scales are much greater than the fluid depth (e.g., river or lake hydrodynamics, coastal and estuarine circulation, overland flow, etc.). They have wide applications in hydraulic engineering [1,2,3]. When vertical effects are important, such as in baroclinic regimes, where density varies with salinity and temperature, three-dimensional flow should be used This would require the solution of a system of equations coupling the Navier–Stokes equation to a moving free surface boundary.
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