B. N. Chetverushkin

Resolution limits of continuous media mode and their mathematical formulations

In this work we present new mathematical formulations for several classical models of a continuum media. The developed formulations take into account the physical constraints on the details of its description. As compared to classical approaches, the presented ones introduce additional terms, which enable the effective solution of these problems on high-performance computer systems.

Simulating flows of incompressible and weakly compressible fluids on multicore hybrid computer systems

A logically simple algorithm based on explicit schemes for modeling flows of incompressible and weakly compressible fluids is considered. The hyperbolic variant of the quasi-gas dynamic system of equations is used as a mathematical model. An ingenious computer cluster based on NVIDIA GPUs is used for the computations.

An explicit scheme for the solution of the filtration problems

Different models of compressible fluid filtration are considered. Unlike the classical system of equations, the continuity equation is modified with allowance for the minimum scale of space averaging and for the internal relaxation time of the system. Three-level explicit finite difference schemes are proposed that are convenient for high-performance parallel implementation. The transition from the parabolic to the hyperbolic system of equations makes the stability requirements for them less stringent than for the two-level schemes.

Kinetic Models for Solving Continuum Mechanics Problems on Supercomputers

The application of kinetic models, describing one-particle distribution function, to constructing continuum mechanic models suitable for computer systems with extra-massive parallelism is considered. The construction of such models utilizes the existence of space–time scales below which there is no physical sense to further refine the solution. The proposed approach has been used to solve some three-dimensional problems involving approximations by grids with more than billion space nodes

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.

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.

A kinetic model for magnetogasdynamics

In this work the equations of ideal magnetogasdynamics are derived based on the introduced local complex Maxwellian distribution function. Using this kinetic model, we obtain the analog of a quasi-dynamic system of equations for magnetogasdynamics, including dissipative processes. The resulting model and the algorithm of its solution have been tested by applying them to a number of well-known problems. The given algorithm can be easily adapted to an architecture of high performance systems with extramassive parallelism.

Quasihydrodynamic model and small-scale turbulence

A model of the averaged quasihydrodynamic system of equations governing small-scale turbulence is proposed. In the case of plane geometry the model is tested against the problem of the flow past a rectangular cylinder. For this problem conservative finite-difference schemes on a rectangular grid are constructed and the algorithms of their numerical implementation are developed. Numerical experiments show that the model describes well the turbulent flow, both qualitatively and quantitatively. The results obtained are in good agreement with the results of other authors and the experimental data.

Unsteady Viscous Flow Simulation Based on QGD System

One approach to the validation of quasigasdynamic (QGD) equation system is discussed in this paper. There is close connection between kinetically consistent finite difference (KCFD) schemes1 and QGD system2. QGD system may be considered as some kind of differential approximation for KCFD schemes3. The new way of obtaining QGD system is demonstrated using the same physical ideas on which the KCFD schemes are based. For this purpose we take advantage of the well known BGK model for one particle distribution function.