Vol 66, No 3 (2026)

This paper compares new, cost-effective versions of the double-sided rejection algorithm with piecewise constant majorant and minorant, and a modified ziggurat method, applied to computer simulation of the widely used Gaussian distribution. It is shown that these algorithms significantly outperform all known algorithms for simulating the Gaussian distribution (including the Box-Muller formulas, considered as the most cost-effective).

A new algorithm for finding the global minimizer of a one-dimensional multimodal function satisfying the Lipschitz condition with an unknown constant is considered and justified. It is assumed that the value of the function at the global minimizer is known (as is typical, e.g., in problems of minimizing the discrepancy between computed and experimental data). The convergence of the new algorithm is proved without using estimates of the Lipschitz constant, which are required in other Lipschitz optimization methods. Results of a numerical comparison of the efficiency of the proposed method with three well-known Lipschitz minimization algorithms are presented for functions from large random samples generated by two test problem generators widely used in such studies.

The Green’s function of the Dirichlet-2 boundary value problem for the polyharmonic equation in the unit ball is constructed, and an integral representation of the solution to this problem is given.

Several problems of mathematical physics in an angular junction of two thin rectangles, for example, beams, plates or canals, are considered. By means of an asymptotic analysis of all problems we derive onedimensional models including transmission conditions at the corner point where the segments, that is, midlines of the rectangles with the derived limiting ordinary differential equations of the models, meet each other. Among obtained transmission conditions we detect the Kirchhoff transmission conditions, classical, weighted and modified, but transmission conditions in the elasticity problem on deformation of the angular beam the transmission conditions become non-standard, namely constrained due to the Dirichlet conditions for the transverse displacements. A reason for formation of various structures of the transmission conditions and their relationship with the energy functional of the original problem are explained. Miscellaneous examples are given.

The paper considers a high-performance numerical method for modeling the stationary temperature field of a heterogeneous medium. A method for determining the effective thermal conductivity of porous media is presented. The algorithms developed by the authors correspond to the collocation schemes of boundary element methods. They are based on the decomposition of the desired solution into a series according to some pre-calculated analytical solutions of the equations of thermal conductivity. Using this approach, it is possible to calculate the temperature and the components of the heat flux density vector at any point in the medium under consideration, as well as, requiring engineering macroparameters of materials with high accuracy at a modest cost of computer resources. The paper analyzes the applicability and accuracy of the solution when using decomposition functions in the form of single layer and double layer potentials. The dependence of the effective thermal conductivity on the volume of heat-insulated pores and spheric inclusions with heat-conducting properties different from the surrounding material under random distribution has been studied. Well-known analytical solutions from other authors were used to verify the algorithm.

Direct numerical simulation (DNS) databases of developed turbulent channel flows are used for a priori and a posteriori testing of various formulations of wall-modeled large eddy simulation (WMLES). Average wall friction values and their root-mean-square deviations are compared with the exact data of the filtered DNS field; in addition, correlation coefficients between the exact friction field and that obtained using the wall function method are calculated. The equilibrium wall functions of Spalding, Werner and Wengle, Li et al. are considered, as well as various options for taking into account nonequilibrium effects in the approach of Li et al.: the contribution of the mean pressure gradient, the contribution of the total pressure gradient; additional inclusion of convective terms in the momentum equation are also considered. Conclusions are drawn on the applicability of wall functions when using instantaneous and time-averaged input data in LES simulations of wall-bounded flows.

The algorithm for calculating the Boltzmann collision integral for a minor impurity in a background gas has been developed. The method allows calculating the evolution of the impurity distribution function on a compact local grid in velocity space, which can be significantly smaller than the domain of the background distribution. The algorithm is based on the preliminary calculation of a transition frequency matrix from one grid cell to another. The calculation of the frequency matrix is reduced to integration over a plane in velocity space defined by the laws of conservation of energy and momentum. A modification of the method is presented that strictly conserves the number of particles in the computational domain. The method is generalized to the case of arbitrary cross-sections and inelastic collisions. Tests on relaxation to a Maxwellian distribution, scattering by a flow, and beam slowing-down confirmed the accuracy and applicability of the method for energy and momentum transfer problems in mixtures with significantly different temperatures.