A kinetically-based system of equations for three-phase porous media ow 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 modi ed via introduction of the regularizing term and the second-order time derivative. Due to conversion to the hyperbolic type the corresponding di erence equation stability is improved. An explicit algorithm is developed and adapted to high-performance computing systems. High parallelization e ciency is achieved on a classical cluster as well as on a hybrid cluster with graphics accelerators.Keywords: Multiphase ow in a porous medium, quasigasdynamic system of equations, explicit nitedi erence schemes, parallel implementation.Mathematical modelling of multiphase uid ows in porous media is necessary for solving many practically important problems, for example, for the simulation of processes of contaminant in ltration into the soil [1, 9, 10, 17]. It is well known that numerical simulation of these processes is very time-consuming and impossible without the employment of high-performance computing systems. Nowadays the rapid growth in the computer performance is mainly achieved due to the use of hybrid architectures including multicore CPUs and di erent accelerators like graphics processing units (GPU). Use of GPU for general-purpose computations is a perspective modern trend to solve large scale applied problems with high accuracy for the reasonable time. However, such architectures cause serious di culties in the software development. For example, wellknown IMPES-method for modelling porous media ows [8] assumes the solution of elliptic equation. But the Laplace operator inversion requires high computational costs and leads to decrease of parallelization efciency. Computational algorithms with logically simple structure like explicit nite-di erence schemes can be adapted easily to hybrid supercomputers and allow to exploit them more e ciently [5]. Such algorithms show perfect scaling on parallel architectures therefore they are widely used in numerical investigations of subsurface ows [7, 12].In the present paper a new algorithm for porous medium ow simulation is discussed. Currently kinetic approaches such as Lattice Boltzmann schemes [2, 7, 11] and kinetically-consistent nite di erence (KCFD) [3] schemes seem to be the most promising methods in computational uid dynamics. The new model is constructed by the analogy with KCFD schemes and the related quasigasdynamic (QGD) system of equations [13].

Abstract. The work deals with the development of an original mathematical model of porous medium flow constructed by analogy with the quasigasdynamic system of equations and allowing implementation via explicit numerical methods. The model is generalized to the case of multiphase multicomponent fluid and takes into account possible heat sources. The proposed approach is verified by a number of test predictions.

No abstract

No abstract

No abstract