Application of kinetic approach to porous medium flow simulation in environmental hydrology problems on high-performance computing systems

Abstract

AbstractA kinetically-based system of equations for three-phase porous media flow simulation is considered. A simple case with the following assumptions is discussed: phase transitions are absent, phases do not dissolve and do not mix, the rock compressibility is negligible. Such systems are under consideration in applied problems when the pressure changes slightly and thermal processes are absent, for example, in environmental problems. The continuity equation is modified via introduction of the regularizing term and the second-order time derivative. Due to conversion to the hyperbolic type the corresponding difference equation stability is improved. An explicit algorithm is developed and adapted to high-performance computing systems. High parallelization efficiency is achieved on a classical cluster as well as on a hybrid cluster with graphics accelerators.