2015 , Volume 20, ¹ 4, p.3-16
Massively parallel Rayleigh - Taylor instability simulation using analytical expression of Greens function of the corresponding boundary value problem
A numerical algorithm for simulating Rayleigh - Taylor instability in high viscous incompressible Newtonian fluid was implemented. This algorithm uses analytical form of Green’s function of the corresponding boundary value problem, so solution can be found as an integral of the product of two known functions without necessity to use finite difference schemes. In other words, the algorithm makes it possible to calculate the flow field at any point in space independently of other points, like in the problem of gravitational interaction of N-bodies. Because of the simplicity and the high degree of parallelism, the method is very well suited for the effective implementation, especially on massively parallel devices such as graphics cards (GPU) and hybrid clusters. The developed software could employ an arbitrary number of GPU in hybrid cluster via MPI and CUDA technologies. The implementation for homogeneous clusters, which uses central processing units (CPU) with SSE instruction set via MPI, was proposed. In both cases the program shows a very high performance and more importantly the calculation productivity linearly depends on number of nodes. It happens due to exceptional properties of the algorithm which requires much less memory accesses than the difference methods. Thus, the computing speed depends largely on the peak performance of the system than the memory bandwidth. The program is used for fast numerical simulating of well known geological process, such as salt diapirism. It is a special case of Rayleigh - Taylor instability in solid rock, caused by lightness of solid rock salt, which is buried by more hard rocks. In geological time intervals (hundreds millions of years) this process is correctly described by fluid dynamics.
Keywords: NVIDIA CUDA, parallel programming, creeping flow, Greens function, Rayleigh - Taylor instability, salt diapirism
Position: Junior Research Scientist
Office: Trofimuk Institute of Petroleum-Gas Geology and Geophysics of the Siberian Branch of the RAS, Novosibirsk state University
Address: 630090, Russia, Novosibirsk
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Abramov T. Massively parallel Rayleigh - Taylor instability simulation using analytical expression of Greens function of the corresponding boundary value problem // Computational technologies. 2015. V. 20. ¹ 4. P. 3-16