This paper proposes a modification of the adaptive artificial viscosity (pseudoviscosity) method for constructing homogeneous difference gas dynamics schemes under the assumption of cylindrical flow symmetry. These schemes enable gas dynamic calculations with high flow structure resolution using arbitrary (both uniform and nonuniform) computational grids. Estimates are obtained for the pseudoviscosity function, ensuring the monotonicity of the numerical solution. Calculation results for a model problem are presented, demonstrating the possibility of obtaining a highly accurate solution using significantly nonuniform computational grids.

This paper presents an overview of technical solutions aimed at improving robustness and industrial applicability of computational fluid dynamics (CFD) methodology for high-fidelity simulations on hybrid supercomputers. This methodology, incorporated in the NOISEtte code, is based on higher-accuracy numerical schemes on unstructured meshes and modern turbulence modelling approaches. When it comes to industrial applicability on modern supercomputer architectures, in addition to the basic theoretical properties of methods and models, such as approximation accuracy, many other factors arise. These factors can ruin the whole computational methodology if not properly addressed. For instance: compliance with modern restricted parallel paradigms; low memory consumption; robustness of the simulation algorithm, which implies applicability for a wide range of meshing tools and approaches; simplicity of numerical method configuration for the end user. Simulation algorithms must produce reasonable results in as wide range of application conditions as possible, often far from ideal. The present paper describes how a heterogeneous CFD code is being adapted to the cruel reality of practical applications: compliance with modern hybrid architectures, robustness of the numerical scheme and turbulence modeling approach, acceleration of solution, improving computing pattern and reducing memory consumption.

The oscillation equation for an inhomogeneous lattice is obtained within the Fermi–Pasta–Ulam (FPU) model. Based on it, a generalized Korteweg–de Vries (KdV)-type equation with a variable coefficient, determined by the step of an inhomogeneous lattice, is derived. Inverse problems of recovering this coefficient by integrals of the solution to the equation are posed, investigated, and solved. Theorems on the existence and uniqueness of solutions to inverse problems are proved. A series of computational experiments confirming the obtained theoretical results are carried out. The results of the calculations in the form of computer images and graphs are presented.

To address the challenges of planning and managing organizational, technical, and economic structures, a new methodology for processing large factor models is proposed, based on graph condensation. This methodology involves restoring the dependencies between factors using machine learning techniques and artificial neural networks. For creating a condensed graph, approaches based on both content analysis and methods for identifying strong components are explored. Subsequently, the vertices of the graph are clustered based on the defining characteristics that describe them. The factor values for the vertices of the condensed graph are determined using a system of linear methods that describe their mutual influence. Unknown schemes dependent on parameters within a single cluster are controlled using machine learning methods. These schemes are processed independently, allowing their implementation in a hybrid computing system in the parallel mode. The mathematical methods used in this work are not original per se, but their novelty lies in their integration within a unified model for processing high-dimensional graphs. The proposed methodology is not tied to a specific subject area and is aimed at modeling simple organizational and technical systems when detailed behavior models of individual elements are absent, but there are small expert assessments of the degree of influence of industrial factors on one another, as well as some datasets on past interaction precedents among elements. The methodology for application to restore the factors of the economic activity of individual economic entities is considered at the level of the specified growth rates of industries, scientific and production enterprises, organizations, workshops, and laboratories.

Often the proceeding of physical and chemical processes (fluid flows in nozzles, channels and shock tubes, external flow around various objects, heat and mass transfer in porous bodies, etc.) has a preferentially spatial direction. Recently 1D models have been proposed for the mathematical description of such processes, but now more detailed 3D models are developed. The modeling complexity increases impressively with the transfer to 3D modeling. The article represents a computational approach based on the artificial extraction “1D terms” in the solution to reduce the amount of computational work in multidimensional modeling. Based on the Dirichlet boundary value problem for Poisson equation in a unit cube, the efficiency of proposed approach associated with solving d = 2.3 auxiliary 1D problems is demonstrated. The article represents results of the convergence analysis of the iterative methods with proposed solution decomposition for the discrete (initial-)boundary value problems. Previously, the efficiency of this approach was demonstrated for the numerical solution of saddle problems (the discrete Navier–Stokes equations).

This paper presents a computational technology for modeling unsteady gas mixture flows in the paths and chambers of solid-propellant rocket engines (SPREs). The technique is focused on the use of supercomputer technologies for three-dimensional modeling of propulsion systems with simulation of their operation with the specialized boundary conditions set close to realistic ones. The long-term goal is to transition to the virtual modeling of working processes instead of expensive full-scale experiments. The mathematical basis for describing the dynamics of a multicomponent gas mixture is the system of Navier–Stokes equations augmented by the convection–diffusion equations of the mixture’s components. The characteristics of the mixture (viscosity, thermal conductivity, heat capacity, and diffusion) are found by averaging the corresponding values of individual chemical components. The numerical model combines the advantages of splitting the system of determining equations, the reliability of the S.K. Godunov scheme for the realization of the convective stage, and the algorithmic efficiency of the Chebyshev scheme for solving the parabolic system of equations at the diffusion stage. The complete computational algorithm is implemented in C++ as a system of programs with tools to improve computational performance, including the use of parallel technologies for supercomputers with distributed and shared memory and graphics processors. The effectiveness of the approach is confirmed by computational studies of complex unsteady flows. The presented results of computations of gas-dynamic parameters of model devices testify to the correctness of the adopted problem formulation with the formulation of conditions determining the law of change in the mass flow of a high-temperature gas mixture at the given input boundary of the computational domain.

The advantages and disadvantages of using clustering methods using the Kohonen neural network and the density-based spatial clustering of applications with noise (DBSCAN) algorithm for solving problems of analyzing multidimensional medical data are presented. An example of using clustering methods to identify the relationship between the development of sensorineural hearing loss in newborns and the disease caused by the COVID-19 virus in the children themselves or in their mothers during pregnancy is analyzed. The considered methods are also used to prepare recommendations for monitoring newborns depending on the results of clustering data on their examination and anamnesis using various methods. The use of clustering methods in medicine expands the arsenal of tools for researchers and practicing doctors who use them for the purpose of diagnosing, predicting the course of diseases, the development of pathologies, and forming a treatment plan.

This paper formulates a model for assessing the risk of consequences from taking several medicines within the framework of an approach using intelligent processing of instructions for the use of drugs. The model also uses rank estimates of the relative severity of side effects and similar pharmacodynamics when taking several drugs. Using the example of the treatment of chronic heart failure, the use of this model as a basis for the development of a system to support medical decision-making in the field of polypharmacotherapy is shown. The assignment of a rank to the medicine–consequence pair is carried out taking into account the frequency of side effects, as well as the gender and age of the patient. The model allows for automatic correction of ranks within the framework of a personalized approach, when the severity of consequences increases if the patient has appropriate concomitant diseases. The compatibility of several drugs is determined on the basis of a graph model, when only those vertices are connected to each other (i.e., drugs) for which the total rank of consequences for each of the possible side effects is less than the critical level taken as one in the rank model. Therefore, the task of drug compatibility is reduced to the allocation of fully connected subgraphs, since a necessary, although not sufficient, condition for the compatibility of n drugs is their pairwise compatibility. This approach makes it possible to significantly reduce the computational complexity of the task, since clustering at the level of complete connectivity reduces the dimensionality of the possible number of drugs used simultaneously.

An Erratum to this paper has been published: https://doi.org/10.1134/S2070048225040015

This article presents a numerical study of the nonstationary vortex motion of gas arising over a conical body with a segmental bottom surface for various angles of attack in a transonic flow regime. The modeling is based on the viscous compressible gas model (Navier–Stokes model). For numerical simulation the conservative method of finite volumes is used. For various attack angles, the patterns of the vortex structure of the flow around a conical surface, bottom body surface, and in the near wake are presented. Data are provided on the nonstationary behavior of the flow in the area of conjugation of the conical and bottom surfaces, as well as the dependences of aerodynamic characteristics on the angle of attack. Numerical calculations are carried out on the basis of parallel algorithms and are realized on multiprocessor computing systems.