Keywords: GPU computing, hybrid architecture, multiphase porous media flow, kinetic schemes, explicit finite difference schemes.

Mathematical modelling of multiphase flows in porous media is an important problem for scientific, economic, ecological, industrial and many other areas. The solution of industrial and technological problems connected with the difficult geometries of described designs is especially important and demands high precision of calculations. High-performance computing systems are opening unique opportunities for the solution of these tasks.

This paper is devoted to development of a new approach for simulation of multiphase flows in porous media using modern HPC systems. To provide the high solution accuracy at the sufficient scheme stability, the kinetic approach was applied [1]. For creation of a physical model"the principle of the minimum sizes" defining minimum characteristic sizes in space and time for this type of flows is applied.

Both two-phase and three-phase three-dimensional flows in homogeneous porous media were considered. All phases were immiscible. Compressibility of liquids and gas, gravitation and capillary pressure were taken into account. Accounting for the compressibility of liquids leads to a more complete and precise description of filtration processes in comparison with traditional approaches where liquids are considered as incompressible. Basic equations are the same for two-phase and three-phase flows but model equations of relative permeabilities and capillary pressure differ.

As a test problem the authors set themselves the task of infiltration of water to the impermeable box filled with water, oil and gas through the hole situated at the centre of boxs top.

To solve problems described above a software program was written. Program the language C/C++ in combination with CUDA and MPI libraries was chosen for the code. The reasons are the high speed of operation, compatibility with devices, cross-platform using (it works on both Windows and Linux), and similar structures for the code may be written for execution on CPUs and GPUs. The software program has a modular structure that enables jumping between different filtration problems without serious code modifications. All computations were performed with double-precision. To make computations more convenient for researchers task distribution was automated. It allowed increasing productivity by 5-30% depending on the current problem.

As for productivity, the achieved acceleration of one GPU in comparison with one CPU core was more than 108 times. Compared with one six-core CPU it was about 20.4 times. When a mesh composed of 1.5 billion points was considered, with a use of 80 graphics accelerators compared to a use of 80 CPU cores then problem time decreased by a factor of 72.

1

D.N. Morozov, B.N. Chetverushkin, N.G. Churbanova, M.A. Trapeznikova, "An Explicit Algorithm for Porous Media Flow Simulation using GPUs", in P. Iványi, B.H.V. Topping, (Editors), "Proceedings of the Second International Conference on Parallel, Distributed, Grid and Cloud Computing for Engineering", Civil-Comp Press, Stirlingshire, UK, Paper 19, 2011. doi:10.4203/ccp.95.19

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