# MRT-Lattice Boltzmann Model for Multilayer Shallow Water Flow

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Engineering Science Program, Louisiana State University, 2228 Patrick F. Taylor Hall, Baton Rouge, LA 70803, USA

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Department of Civil and Environmental Engineering, Louisiana State University, 3325 Patrick F. Taylor Hall, Baton Rouge, LA 70803, USA

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Author to whom correspondence should be addressed.

Received: 21 June 2019 / Revised: 1 August 2019 / Accepted: 2 August 2019 / Published: 6 August 2019

(This article belongs to the Special Issue Lattice Boltzmann for Free Surface Flows)

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.