V. M. Volokhov

Quantum chemical modeling of nanostructured silicon Si n (n = 2—308). The snowball-type structures

To search for advanced anode materials for Li-ion rechargeable batteries, the structures, stabilities, and electronic properties of crystalline silicon and those of the snowball-type (SB) and core-shell (CS) silicon clusters Sizyubin@icp.ac.ru (n = 2—308) were quantum chemically modeled within the framework of the density functional theory with inclusion of gradient correction and periodic boundary conditions. The formation of SB agglomerates from smaller Sizyubin@icp.ac.ru clusters (n ≤ 7) is energetically preferable. At n ≥ 105 and circumscribed sphere diameters (D) ≥ 17—20 Å, CS isomers comprised of quasi-crystalline cores surrounded by small clusters are energetically more favorable than the SB isomers.

Features of model hydrocarbon fuel oxidation for channel flow in the presence of electrostatic field

A mathematical model of the hydrocarbon fuel channel flow taking into account coke precursor deposit formation on the walls of aeroengine cooling systems and chemical transformations in the gas phase is presented. The model is based on the Navier—Stokes and Maxwell equations in the electric potential form. The description in the form of a radical-chain mechanism is used for the partial liquid-phase oxidation of hydrocarbons. The effect of the electric field intensity (E = 100—2000 V m–1) on the formation of coke precursors at different temperatures of the channel walls Tw is shown. The calculations in the range of wall temperatures 350 < Tw < 600 K showed that the temperature was the major factor affecting the deposit intensity. The influence of the electrostatic field on the deposit intensity is significantly lower: the difference in the weights of coke deposits for the variants with E = 0 and E = 2000 V m–1 differs by 10% on the average.

The Supercomputer Simulation of Nanocomposite Components and Transport Processes in the Li-ion Power Sources of New Types

As a result of a large amount of computational experiments on a number of supercomputer resources quantum-chemical and molecular dynamic modeling of various nanocomposite components of Li-ion power sources was performed. Various aspects of transport, structural and energy processes inside LPS during numerous cycles of charging and discharge were simulated. By tools of molecular dynamics estimated influence of various external conditions on structure of nanocomposites and characteristics of above-stated processes.

Supercomputer Simulation of Components and Processes in the New Type Li-ion Power Sources

As a result of a large amount of computational experiments (more than two thousand) performed on a number of supercomputing resources, we have developed quantum-chemical models of various constituent components of Li-ion power sources based on silicon-carbon nanostructure composites and promising solid electrolytes.

Supercomputer Simulation of Physicochemical Processes in Solid Fuel Ramjet Design Components for Hypersonic Flying Vehicle

A step-by-step computer simulation variant for making scramjet mathematical model is offered. The report considers an approach related to 3D mathematical models development of scramjet components further reduced to 1D models. Mathematical models of physicochemical processes in combustor cooling system are discussed with the aim of subsequent engine performance optimization depending on fuels used. Then 1D separate component models are used to make up a full-scale scramjet model. The one-dimensional models allow calculation times significantly reduce, and the simulation accuracy is conditioned by precision of 3D models to 1D models reduction.

Modeling processes of thermal decomposition of hydrocarbon fuels in heated channels

We introduce a mathematical model of the nonequilibrium process of thermal decomposition of hydrocarbon fuel in heated channels of a ramjet combustion chamber cooling system. This mathematical model is based on describing the process using intermediate asymptotics formed when taking into account the equilibrium gas composition, which is determined using open source software for calculating the equilibrium state of the chemical reaction products. A procedure was introduced allowing at different stages of the process of thermal decomposition of fuel to separate kinetically irreversible and reversible chemical reactions and to exclude from consideration chemical reactions which remained incomplete in a limited size engine. We present the features of the process of thermal decomposition of liquid and solid fuels which can be used in high-speed aircraft engines.

Relativistic Jahn—Teller effect Gg[3/2]×(t2g + eg) in cubic and octahedral molecules

The properties of the symmetry of the vibronic Hamiltonian of the multimode relativistic Jahn—Teller effect Gg[3/2]×(t2g + eg) in cubic and octahedral molecules are studied. The Hamiltonian considered corresponds to the half-integer spin of the electron shell and the linear approximation on the vibrational normal modes t2g and eg. The angular variables were separated, and biradial dynamic equations and analytical expressions for the biradial potential energy surfaces were obtained. The positions of the low-lying resonances in two upper potential “bowls” were found.

Parallel geometric multigrid

The paper describes practical approach for minimising the parallelisation overhead for a solution to the boundary value problems by geometric multigrid methods. It is shown that proposed multiple coarse grid correction strategy makes it possible not only to create the task of the smoother least demanding, but also to avoid load imbalance and limit the communication overhead. Estimation of maximum speedup and efficiency of parallel robust multigrid technique and parallel V-cycle are given.

PSEUDOMULTIGRID GAUSS–SEIDEL METHOD FOR LARGE SCALE AND HIGH PERFORMANCE COMPUTING

The paper represents a new approach for development of robust multigrid methods. The approach is based on minimization of the number of problem-dependent components in multigrid algorithm. Robust Multigrid Technique (RMT) is application of the essential multigrid principle in single-grid algorithm. Problem-dependent components of the technique are: 1) the number of smoothing iterations; 2) unknown ordering (for anisotropic problems); 3) underrelaxation parameter (for nonlinear problems); 4) stopping criterion of the multigrid iterations. The least number of the problem-dependent components makes it possible to use RMT in black box software. Disadvantage of RMT is extra computational efforts as compared with optimized multigrid. Since coarse grid correction is computed on the single grid, it is possible to avoid the large communication overhead and the processor idleness on the very coarse grids in parallel multigrid. The paper represents main components of RMT, results of numerical experiments, convergence and complexity analysis, estimation of speed-up and efficiency of parallel algorithm.

Structure of Highly Parallel, Efficient, Scalable, True Robust Pseudomultigrid Technique for Black-Box Solving a Large Class of the Boundary Value Problems on High Performance Computing Systems

In this paper, we discuss the true robust pseudomultigrid technique (RMT) for blackbox solving a large class of the boundary value problems on high performance computing systems. RMT has the same number of the problem-dependent components as Gauss-Seidel method and close-to-optimal algorithmic complexity. First, an algebraic approach to parallelization is introduced for a parallel smoothing on the fine levels. The algebraic approach is based on a decomposition of the given problem into a number of subproblems with an overlap. Second, a geometric approach to parallelization is introduced for a parallel smoothing on the coarse levels to avoid communication overhead and idling processes on the very coarse grids. The geometric approach is based on a decomposition of the given problem into a number of subproblems without an overlap. After that we discuss a combination of the algebraic and the geometric approaches for parallel RMT.