The algorithm developed at the Trofimuk Institute of Petroleum Geology and Geophysics, Siberian Branch of the Russian Academy of Sciences, will facilitate rapid pore-scale simulation of multiphase processes, thus providing for a wide scope of its industrial applications.
Specifically, the mechanisms of multiphase flows in a porous medium must be investigated prior to injecting water and/or gas into an oil reservoir to enhance oil recovery rates. Whereas in powder metallurgy and ceramics processing where sintering is a major step, simulation of processes of grains sintering of various materials with different crystallographic orientations is imperative.
Multiphase processes are described by specialized sets of equations, including the Kahn-Hilliard equation. The algorithm created at IPGG SB RAS allows solving the latter, which is critical for obtaining a reliable model, with some calculations performed using supercomputer where necessary.
Dmitriy Prokhorov, PhD (phys.-math.), the algorithm developer
What are major advantages of the algorithm developed at IPGG SB RAS?
This is a parallel algorithm for the numerical solution of the Сahn–Hilliard equation in a three-dimensional formulation and is designed for heterogeneous system architecture, ensuring thereby its efficiency in scalability. The strong and weak scaling of the algorithm is investigated in application to the problem of phase separation for two different data exchange schemes between RAM and VRAM. Its performance draws heavily on advanced computing technologies. One MPI process is allocated for each subdomain, while the solution within the subdomain is calculated using CUDA technology for the GPU.
The algorithm’s efficiency has already been tested at the RSC-Tornado cluster of the Supercomputer Center at Peter the Great St. Petersburg Polytechnic University. According to Dmitriy Prokhorov, PhD (phys.-math.), a researcher at the Digital Rock Physics Laboratory, IPGG SB RAS, the goals set for the algorithm implementation are met, thus allowing it to be generally considered successful. Yet, new achievements still lie ahead.
– In the future, the parallel algorithm for solving the Cahn-Hilliard equation will be coupled with the Navier-Stokes solver for multiphase flow simulation. To this end, the function of handling complex boundary conditions arising in problems of digital rock physics will be added. Using the developed algorithm for modeling the sintering process will be next step in our research and a matter of the foreseeable future, - noted Dmitriy Prokhorov.
Published by IPGG Press Service
For more detail, please, see the article by :
Prokhorov, D.I. (2025). Domain decomposition for the numerical solution of the Cahn–Hilliard equation // NUMERICAL METHODS AND PROGRAMMING, 26 (1), 17-32