Boris N. Chetverushkin

Hyperbolic type explicit kinetic scheme of magneto gas dynamics for high performance computing systems

Abstract The article presents the developments of the kinetic consistent approach of solution of the magneto gas dynamics problems on the high performance computing systems with massive parallelism. The main idea is to derive the magneto gas dynamic equations from the Boltzmann equation using a complex distribution function, including the electromagnetic terms. The derived equations were used for the formulation of the explicit numerical method of solution for the high performance parallel computing systems. The numerical experiments were performed for the verification of the chosen method.

Numerical simulation of the continuous media problems on hybrid computer systems

The paper presents some results of modeling continuous media problems on computer system with hybrid architecture on the base of Quasi Gas Dynamic (QGD) equations system. The successful experience in solving a wide variety of gas dynamic problems by means of QGD based schemes showed that they describe viscous heat conducting flows as good as schemes for Navier-Stokes equations, where the latter are applicable. The explicit scheme described here has a Courant stability condition even for very low Mach numbers. So, it is very convenient for computer systems with the hybrid architecture, in particular for GPU-based computers. Parallel realization is based on shmem programming technology. The calculations results show good parallelization efficiency.

Novel kinetically consistent algorithm for magneto gas dynamics

Abstract We propose a new kinetically consistent method for the modelling of magneto gas dynamic processes. The algorithm is consistent with viscous, thermally conducting, resistive flows. Through a computational test we show that it is robust in resolving the physical behaviour of shock structures and instabilities.

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.

Two-Phase porous media flow simulation on a hybrid cluster

A kinetically-based model is developed to describe flow of slightly compressible two-phase fluid in a porous medium. The continuity equations for phases are modified taking into account the minimal scales of averaging on space and on time, as a result regularizing terms and the second order time derivative with small parameters are present in the equations. They are approximated by the three-level explicit difference scheme with a mild enough stability condition. The proposed algorithm is easily adapted to modern hybrid supercomputers. The problem of contaminant infiltration into the soil is solved on a cluster with graphics accelerators. High speed-up of GPU computations in comparison with CPU is demonstrated.

Career of Prof. Yuri Kuznetsov

In what follows we provide a brief overview of the life and work of Professor Yuri Kuznetsov ( University of Houston)

On a hyperbolic perturbation of a parabolic initial-boundary value problem

Abstract We deal with a linear parabolic initial–boundary value problem and its hyperbolic perturbation with a small parameter e > 0 in front of the 2nd order time derivative. We derive bounds for the perturbation error of the orders O ( e ) and O ( e ) in several norms in dependence with smoothness of data (without a priori conditions on solutions) but for non-smooth coefficients and keeping the free terms in equations as distributions. They essentially complement or improve some previously known bounds. In addition, we discuss regularizations of the initial time derivative.

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.

STATISTICAL DISTRIBUTION FUNCTION OF CHARGED PARTICLES IN MAGNETIC FIELD

The statistical distribution function introduced by Boltzmann and his kinetic equation are the fundamental basis of the kinetic theory of gases and of the basic methods of solution of problems in the gas dynamics. At present time one of the areas of high interest in modern physics is the plasma in fusion processes and astrophysics which requires an extension of the kinetic description to charged particles dynamics, in particular regarding the electromagnetic interactions. We propose a unified distribution function which includes the electromagnetic interactions for charged particles in electromagnetic magnetic field and is suitable for the solution of problems of charged particle dynamics with Boltzmann type equations and kinetic consistent magneto gas dynamic equations.

KINETIC MODELS AND ALGORITHMS FOR SOLUTION OF THE MAGNETOGASDYNAMIC PROBLEMS ON THE MODERN SUPERCOMPUTING SYSTEMS

The impressive progress of the kinetic schemes in the solution of gas dynamics problems and the development of effective parallel algorithms for modern high performance parallel computing systems led to the development of advanced methods for the solution of the magnetohydrodynamics problem in the important area of plasma physics. The novel feature of the method is the formulation of the complex Boltzmann-like distribution function of kinetic method with the implementation of electromagnetic interaction terms. The numerical method is based on the explicit schemes. Due to logical simplicity and its efficiency, the algorithm is easily adapted to modern high performance parallel computer systems including hybrid computing systems with graphic processors.