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This paper aims to clarify some aspects of the application of the Godunov method for the Baer–Nunziato equations solution on the example of the problem of shock wave – dense particles cloud interaction.

The statement of the problem corresponds to the natural experiment. Mathematical model is based on the Baer–Nunziato system of equations with algebraic right-hand side source terms that takes into account the interphase friction force. Two numerical approaches are used: Harten-Lax-van Leer method and Godunov method.

For the robust simulation using Godunov method, the application of the pressure relaxation procedure is proposed. The comparative analysis of the simulation results using two methods is carried out. The Godunov method provides significantly smaller numerical diffusion of the solid phase volume fraction in the cloud that leads to the much better agreement of the pressure curves on transducers and the dynamics of the cloud motion with the experimental data.

Godunov method for the Baer–Nunziato equations is applied for the simulation of the natural experiment on the shock wave particles cloud interaction. Up to now, the examples of the application of the Godunov method for the Baer–Nunziato equations to the investigation of the practical problems have been limited by the works of the authors of the method and the field of detonation in the heterogeneous explosives. For the robust simulations in the presence of interphase boundaries, it is proposed to use the Godunov method together with the pressure relaxation procedure.

This paper aims to perform a comparative study between capabilities of two numerical schemes from two main branches of numerical methods for solving hyperbolic conservation equations.

The accuracy and performance of a newly developed high‐resolution central scheme vs a higher‐order Godunov‐based method are evaluated in the context of black‐oil reservoir simulations. Both methods are modified enabling study of applications that are not strictly hyperbolic and exhibit local linear degeneracies in their wave structure.

The numerical computations show that while both schemes produce results with virtually the same accuracy, the Godunov method reproduces slightly more accurate results at the expense of calculation of eigen‐structures.

The paper investigates only one dimensional problems, but the idea can be easily extended to multi‐dimensional problems.

The paper shows the strengths and weaknesses of two practical numerical methods.

Such comparative study has not been published elsewhere and in particular, the performance of numerical methods on simulating hysteresis effect in hydrocarbon reservoirs has not been investigated in detail before.

The purpose of this paper is twofold. Firstly, to present a detailed account of the generalized Lagrangian formulation of Hui and Zhao, in which the stream function ζ and Lagrangian distance λ, are used as independent variables, and secondly to assess and compare the performance of various flux limiters in this formulation with their corresponding performance in the Eulerian formulation. The generalized Lagrangian formulation is obtained by a transformation from the cartesian co‐ordinates (x, y) to the Lagrangian co‐ordinates (λ, ζ). In this manner, the number of independent variables for steady, 3‐D flow is reduced from four to three, placing this formulation on the same footing as the Eulerian formulation even for steady flows (as opposed to the conventional Lagrangian formulation which apparently still requires four independent variables even for steady flows). The generalized Lagrangian formulation with the Godunov scheme (using flux limiters) appears to have distinct advantages over the corresponding Eulerian formulation, particularly with respect to accuracy. Furthermore, the method requires no grid generation.

The dynamics of coupling between spectrum and resolvent under ε‐perturbations of operator and matrix spectra are studied both theoretically and numerically. The phenomenon of non‐trivial pseudospectra encountered in these dynamics is treated by relating information in the complex plane to the behaviour of operators and matrices. On a number of numerical results we show how an intrinsic blend of theory with symbolic and numerical computations can be used effectively for the analysis of spectral problems arising from engineering applications.

This paper aims to improve the reliability of numerical methods for predicting the transient heat transfers in combustion chambers heated internally by moving heat sources.

A two-phase fluid dynamic model was used to govern the non-uniformly distributed moving heat sources. A Riemann-problem-based numerical scheme was provided to update the fluid field and provide convective boundary conditions for the heat transfer. The heat conduction in the solids was investigated by using a thermo-mechanical coupled model to obtain a reliable expanding velocity of the heat sources. The coupling between the combustion and the heat transfer is realized based on user subroutines VDFLUX and VUAMP in the commercial software ABAQUS.

The capability of the numerical scheme in capturing discontinuities in initial conditions and source terms was validated by comparing the predicted results of commonly used verification cases with the corresponding analytical solutions. The coupled model and the numerical methods are capable of investigating heat transfer problems accompanied by extreme conditions such as transient effects, high-temperature and high-pressure working conditions.

The work provides a reliable numerical method to obtain boundary conditions for predicting the heat transfers in solids heated by expanding multiphase reactive flows.

An optimized multigrid method (NSFLEX‐MG) for the NSFLEX‐code (Navier‐Stokes solver using characteristic flux extrapolation) of MBB (Messerschmitt Bolkow Blohm GmbH) is described. The method is based on a correction scheme and implicit relaxation procedures and is applied to two‐dimensional test cases. The principal feature of the flow solver is a Godunov‐type averaging procedure based on the eigenvalues analysis of the Euler equations by means of which the inviscid fluxes are evaluated at the finite volume faces. Viscous fluxes are centrally differenced at each cell face. The performance of NSFLEX‐MG is demonstrated for a large range of Mach numbers for compressible inviscid and viscous (laminar and turbulent) flows over a RAE‐2822 airfoil and over a NACA‐0012 airfoil.

The purpose of this paper is to investigate the performance of a specific class of high‐resolution central schemes in conjunction with the black oil models for hydrocarbon reservoir simulation.

A generalized black oil model is adopted, in which the solubility of gas in both oil and water and evaporation of oil are considered, leading to a system of equations prone to degeneracy. A computer code is generated and three test cases are solved to evaluate the performance of various schemes in terms of accuracy and discontinuity handling.

It is shown that, although some of the central schemes are highly sensitive to the choice of Courant‐Friedrich‐Levy (CFL) number and produce overly diffusive results, a certain type of this class is insensitive to the CFL number and can conveniently handle degenerate equations appearing in the reservoir simulation. The obtained results are compared with those available in the literature, showing merits of this class of schemes in complex reservoir simulation models.

This paper gives the one‐dimensional implementation of the above‐mentioned schemes. Extension to higher dimensional black oil model is currently under development by the authors.

The specific class of high‐resolution central schemes investigated here presents the same level of accuracy as more complicated numerical methods, yet keeping it much more simple, by avoiding Riemann solvers.

The high‐resolution central scheme used in this work has been newly developed and applied to simple scalar hyperbolic equations. It has been adopted for the black oil for the first time.

The purpose of this study is to investigate the convergence and divergence aspects of the Russian modernisation experience of c.1450–c.1600 and its role in both Russian history and management history.

This study combines in-depth data collection from multiple sources such as Russian Chronicles, eyewitness accounts (mostly by foreigners) and papers in history and management. The applied methodology also includes an examination of Ivan III’s modernisation initiative and its implementation in c.1450–c.1600. The analysis is conducted with an eye to understanding the extent to which Russian experiences converged or diverged from those found in Western Europe.

Russian modernisation is usually associated with Peter the Great. Early initiatives, such as those that occurred in Russia between 1462 (the ascent of Ivan III) and 1606 (the Time of Troubles) are overlooked. This paper, however, argues that without these earlier modernisation efforts Russia would not have survived as a country. Given the central role that Russia has played in European and world history, and understanding of this period is key to comprehending the modern world and global systems of management.

This paper seeks to understand a decisive period in Russian history and Russian management, highlighting the extent to which Russian experiences both diverged and converged with those found in Western Europe.

The paper helps us to understand both the successes and problems of Russian management since the 15th century.

To the best of author’s knowledge, this study is the first to consider Russian modernisation during the period c.1400–c.1600 with an eye to current debates in convergence/divergence theory.