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High Performance Lattice Boltzmann Method for Shallow Water Flows


IGERT Trainee Kevin Tubbs with his IGERT professors (Tsai from Civil Engineering, Tohline from Physics and Allen from Computer Science) have developed a lattice Boltzmann method (LBM) for three-dimensional shallow water flows coupled to mass transport implemented in high performance computing (HPC) environments. Recently, the LBM has become an attractive numerical method to solve various fluid dynamics phenomena. However, LBM has not been extensively applied to shallow water equations.

The newly developed method extends previous studies to three dimensional flows which have wide applications in ocean, coastal and hydraulic engineering which can benefit from the advantages of the LBM including their performance in HPC environments. The LBM performance was investigated on central processing units (CPU)-based and graphics processing unit (GPU)-based HPC environments. As shown in Figure 1a, we have optimized the CPU-based code to achieve 16 times speedup on 16 processors. It shows the parallel scalability with increasing number of threads. Figure 1b shows the GPU-based code achieved 10 times speedup on one GPU. It shows the parallel speedup scalability with increasing problem size. This development could lead to new solvers that are optimized for next generation HPC systems involving both CPUs and GPUs.

The LBM code was successfully applied to mass transport in a dam break problem as shown in Figure 2. The high water (north) and low water (south) were initially separated by an impermeable boundary (dam). Water upstream contains 70% of passive solution concentration and downstream contains concentration of 20%. A portion of the impermeable boundary was immediately missing (dam break) triggers strong interaction between both waters in flow and concentration. The diffusion coefficient was set a very small value to test the LBM code for simulating advection-dominant mass transport problem. Figure 2a-d shows the concentration movement over different times. The distributions of flow velocities for different time are shown in Figure 2e-h. The developed LBM code is able to hand this problem.

Address Goals

The development of the LBM strategy for shallow water flows will allow a computationally cost effective rationalization of the multi-scale phenomena in such flow systems. This is enabling insight into new physics supporting the primary strategic goal.

The research is being conducted with the HPC infrastructure at LSU and is pushing the frontiers of high performance computing and cyber infrastructure from this perspective.