No abstract

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].

The paper deals with the development of software for traffic flow simulation combining the widest spectrum of mathematical approaches used in this field. Macro- and microscopic models, models of cellular automata as well as different numerical methods of their computer implementation are incorporated into a digital platform. Original developments of the authors of the paper  such as quasi-gas dynamic traffic model and multilane cellular automata model take the main place. Potential users of the software are students and researchers. The platform possesses an intuitive graphical interface ensuring interactivity. Microsoft Visual Studio with C# is chosen as the development environment, the Unity 3D engine is employed for visualization and collaboration with WinForm projects. In the future, the platform can be transformed into a network computer laboratory providing access to information resources via  Internet.

Работа посвящена апробации созданной авторами двумерной микроскопической модели движения автотранспорта на основе теории клеточных автоматов (СА) на тестовых задачах, приведенных в литературе. Проведено сравнение полученных пространственно-временных структур распределения скоростей транспортного потока с экспериментальными данными. Теоретически обоснован и проверен при помощи численного эксперимента выбор оптимального способа осреднения для более адекватного отражения результатов. Представленные результаты подтверждают, что предложенная СА-модель адекватно воспроизводит паттерны, наблюдаемые на диаграммах скоростей реальных транспортных потоков, а также обеспечивает большее сходство с экспериментальными данными по сравнению с другими приведенными моделями.