Volume 29, Issue 4

An original technology of stability analysis of an airfoil boundary layer is presented in this paper. The technology includes an extraction of the boundary layer from the results of laminar flow computations, the computation of neutral curves and increments of Tollmien-Schlichting waves, and the computation of the location of laminar-turbulent transition zone by the e N -method for a given set of freestream turbulence levels. To be specific,we consider the flow around the NACA23012 airfoil with zero angle of attack at moderate Reynolds numbers.

Transformations of consistent discrete approximations of first derivatives in the passage from Cartesian coordinates to an orthogonal curvilinear system and transformations of discrete operations of vector analysis on skewed grids on a plane are studied in the paper. It is established that the transformation algorithm for discrete operators preserves symmetries of discrete solutions relative to coordinate curves inherent from differential system of equations. It also maintains the consistency of discrete operators, which allows us to construct completely conservative differential-difference schemes for discrete domains with curvilinear boundaries.

The new mixed finite element method with piece-wise constant fluxes was recently proposed for the diffusion equations on quadrilateral meshes. In this paper, we apply this method to the diffusion equations on general polygonal/polyhedral meshes

Numerical errors for models of the sea surface undulation are studied in the paper based on spectral decomposition of the stochastic field of water level. Such errors depend on the number of random harmonics in the spectral model and on the size of the domain for which the spectral model is constructed. Numerical errors are studied for temporal and spatial spectral models.

A three-dimensional parallel algorithm of the Monte Carlo method (ELSHOW) is developed for simulation of electron avalanches in gases. The parallel implementation is performed with the use of the well- proven PARMONC library, which accelerates the calculations of such integral characteristics as the number of particles in an avalanche, the coefficient of impact ionization, the drift velocity, and the others, as well as ways to select an appropriate size of the time step using the technique of dependent statistical tests. The algorithm consists of special methods of distribution modelling, a lexicographic implementation scheme for ‘branching’ of trajectories, a ‘Russian roulette’, justified construction of histograms and a polygon of frequencies, and the calculation of probabilistic error estimate of functionals. A comparison of the obtained results for nitrogen with previously published theoretical and experimental data is presented.