Singular problem for a third-order nonlinear ordinary differential equation arising in fluid dynamics

Results concerning singular Cauchy problems, smooth manifolds, and Lyapunov series are used to correctly state and analyze a singular “initial-boundary” problem for a third-order nonlinear ordinary differential equation defined on the entire real axis. This problem arises in viscous incompressible fluid dynamics and describes self-similar solutions to the boundary layer equation for the stream function with a zero pressure gradient (plane-parallel flow in a mixing layer). The analysis of the problem suggests a simple numerical method for its solution. Numerical results are presented.     

Response of a class of mechanical oscillators described by a novel system of differential-algebraic equations

We study the vibration of lumped parameter systems whose constituents are described through novel constitutive relations, namely implicit relations between the forces acting on the system and appropriate kinematical variables such as the displacement and velocity of the constituent. In the classical approach constitutive expressions are provided for the force in terms of appropriate kinematical variables, which when substituted into the balance of linear momentum leads to a single governing ordinary differential equation for the system as a whole. However, in the case considered we obtain a system of equations: the balance of linear momentum, and the implicit constitutive relation for each constituent, that has to be solved simultaneously. From the mathematical perspective, we have to deal with a differential-algebraic system. We study the vibration of several specific systems using standard techniques such as Poincaré’s surface of section, bifurcation diagrams, and Lyapunov exponents. We also perform recurrence analysis on the trajectories obtained.     

Mathematical simulation of electromagnetic fields inside an anechoic chamber of rectangular shape

A mathematical model for computing electromagnetic fields inside anechoic chambers of rectangular shape with walls covered with impedance coating has been developed for an operating frequency range from several kilohertz to tens of gigahertz. Numerical analysis is based on the solution of the corresponding difference Helmholtz problem. In the region of lower and medium frequencies, the solution is carried out using the method of variable directions, and, in the region of higher frequencies, this method uses multiprocessor systems with distributed memory for parallel computations. The computing results are given as well. The text was submitted by the authors in English.     

On the mathematical modelling of processes of peat firing and smoldering

Based on a mathematical model of a porous reacting medium the statement and mathematical solution are presented for a problem of the peat smoldering rise as a result of the effect of a lower seat of fire. It is found that at moderate temperatures T ≤ 750 K the firing and smoldering of the initial reagent are determined by the intensity of the external burning seat as well as by the processes of the peat drying, pyrolysis, and the oxidation reaction of the coked fixed bed. The work was financially supported by the Program of the Federal Agency for Education (Grant No. P 042242).     

Adaptation and optimization of basic operations for an unstructured mesh CFD algorithm for computation on massively parallel accelerators

The design of efficient algorithms for large-scale gas dynamics computations with hybrid (heterogeneous) computing systems whose high performance relies on massively parallel accelerators is addressed. A high-order accurate finite volume algorithm with polynomial reconstruction on unstructured hybrid meshes is used to compute compressible gas flows in domains of complex geometry. The basic operations of the algorithm are implemented in detail for massively parallel accelerators, including AMD and NVIDIA graphics processing units (GPUs). Major optimization approaches and a computation transfer technique are covered. The underlying programming tool is the Open Computing Language (OpenCL) standard, which performs on accelerators of various architectures, both existing and emerging.