Marina A. Trapeznikova

Two-dimensional macroscopic model of traffic flows

The problem of simulating city and highway traffic flows is considered. Existing simulation techniques are reviewed in brief. A two-dimensional model of a synchronized traffic flow based on continuum approach and similar to kinetically consistent difference schemes is developed. Test problems are used to check the model.

Application of explicit schemes for the simulation of the two-phase filtration process

In the paper, the new model based on the kinetic approach is proposed to describe the process of two-phase slightly compressible fluid filtration. The capillary and gravity forces are taken into account. The obtained hyperbolic continuity equations for phase liquids are approximated by the explicit three-level schemes with a sufficiently mild stability condition. Due to its logical simplicity, the computational algorithm can be easily adapted to the hybrid architecture of modern supercomputers. The results of computations on a graphics accelerator are presented for the problem on contaminant infiltration into water-saturated soil and the high parallelization efficiency is demonstrated.

Three-phase filtration modeling by explicit methods on hybrid computer systems

An explicit algorithm constructed by the analogy with the kinetically-consistent difference schemes is proposed in the paper to solve problems of three-phase filtration. The filtration model includes the energy equation and allows taking into account possible sources of heat emission. Parallel implementation is directed to high performance computer systems with graphics accelerators. The computational domain decomposition is optimized in the code to additionally speed up the calculations.

Simulation of filtration problems on hybrid computer systems

The paper is devoted to the use of super-high performance hybrid computer systems for problems of mathematical physics. A program system for simulation of multi-phase filtration processes is described, allowing activation of the entire potential of multicore supercomputers with graphics accelerators. In the case of test computations of the problems of infiltration, it is shown that the logical simplicity of the suggested computation algorithms and implementation program significantly speed up computations.

Modeling the infiltration of multiphase fluid flows in a layered porous medium

Multiphase fluid flows in a layered porous medium are studied with allowance for capillary and gravitation forces. The developed computational algorithms have been tested on a number of test problems of two- and three-phase flows. The suggested approach can be used to deal with applied environmental problems of soil and ground water contamination by petroleum products and other agents.

Simulating multilane traffic flows based on cellular automata theory

A two-dimensional microscopic model of multilane traffic flows is proposed. Test calculations proved it to be adequate. The model was used to numerically analyze the traffic capacity of a crossing for different traffic lights modes, as well as to compare traffic capacities of roads depending on entries-exits and their number.

Parallel simulation of low Mach number flows based on the quasi gas dynamic model with pressure decomposition

Publisher Summary This chapter focuses on numerical simulation of viscous compressible gas flows at low Mach number and employment of distributed memory multiprocessors for solution of such large-scale problems. A new approach based on the quasi-gasdynamic system (QGDS) and on a parallel pressure correction algorithm is proposed. The QGDS of equations is an original model that has been proposed as an alternative to the Navier–Stokes equations. QGDS is a differential approximation of the kinetically consistent finite difference (KCFD) schemes. KCFD and QGDS can be interpreted as a new physical model for describing viscous compressible gas flows. The new approach based on QGDS and on a parallel pressure correction algorithm was validated by solving some tests. Computations were performed for uniform square grids of different sizes at different Reynolds numbers and at Mach number in the range from 0.0 to 0.1. Streamlines of the steady-state flow and velocity profiles of vertical and horizontal midsections of the cavity were analyzed. Results demonstrated good agreement between obtained results and benchmarks from the well-known papers.

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

Abstract A 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.

Simulation of Oil Recovery Processes with the Employment of High-Performance Computing Systems

The problems of mathematical modeling of two-phase flows in porous media, and in particular, the simulation of oil recovery processes, are considered. An economical numerical algorithm based on the kinetic approach with the use of explicit schemes is proposed to ensure the efficiency of the employment of modern supercomputers with a hybrid architecture.

Two-dimensional hydrodynamic model for traffic flow simulation using parallel computer systems

The problem of city and motorway traffic flow simulation is considered in the paper. An original 2D macroscopic model of multilane traffic is developed to depict flows for the real road geometry. The model uses the analogy with the quasi-gas-dynamic equations. Test predictions demonstrate good agreement with phenomena observed in practice. High parallelization efficiency is achieved at computations on a supercomputer system.