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Mathematics
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Numerical Simulations and Mathematical Modelling in Engineering Physics
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Numerical Simulations and Mathematical Modelling in Engineering Physics

A special issue of Mathematics (ISSN 2227-7390). This special issue belongs to the section "Engineering Mathematics".

Deadline for manuscript submissions: closed (1 January 2024) | Viewed by 7344

Special Issue Editors

Dr. Victor V. Kuzenov

E-Mail Website
Guest Editor
Thermal Physics Department, Bauman Moscow State Technical University, 105005 Moscow, Russia
Interests: mathematical modeling (including hypersonic flows of a continuous medium around bodies of complex shape); numerical methods; MHD processes; low- and high-temperature plasma; radiative magnetogasdynamics
Dr. Sergei V. Ryzhkov

E-Mail Website
Guest Editor
Thermal Physics Department, Bauman Moscow State Technical University, 105005 Moscow, Russia
Interests: theoretical studies; mathematics and plasma physical analysis
Special Issues, Collections and Topics in MDPI journals

Special Issue Information

Dear Colleagues,

Mathematics is, and has generally been, present in many works involving high-precision calculations, parallel computing, hybrid methods, neural networks and multi-parameter problems, including large-scale modeling and optimization. Computer programs and software modifications for development, including network packets, are very important in fundamental and applied science from an engineering physics perspective.

In this Special Issue of Mathematics, we will focus on extended/improved models and numerical methods, multi-grid construction and calculation, nonlinear dynamics processes, and new schemes with high order accuracy, etc. Wide ranging applications of numerical methods and physical mathematical models, including numerical algorithms and computer codes for applied mathematics and physics, are also welcome. Model and method verification and validation can be presented as well. 

Dr. Victor V. Kuzenov
Dr. Sergei V. Ryzhkov
Guest Editors

Manuscript Submission Information

Manuscripts should be submitted online at www.mdpi.com by registering and logging in to this website. Once you are registered, click here to go to the submission form. Manuscripts can be submitted until the deadline. All submissions that pass pre-check are peer-reviewed. Accepted papers will be published continuously in the journal (as soon as accepted) and will be listed together on the special issue website. Research articles, review articles as well as short communications are invited. For planned papers, a title and short abstract (about 100 words) can be sent to the Editorial Office for announcement on this website.

Submitted manuscripts should not have been published previously, nor be under consideration for publication elsewhere (except conference proceedings papers). All manuscripts are thoroughly refereed through a single-blind peer-review process. A guide for authors and other relevant information for submission of manuscripts is available on the Instructions for Authors page. Mathematics is an international peer-reviewed open access semimonthly journal published by MDPI.

Please visit the Instructions for Authors page before submitting a manuscript. The Article Processing Charge (APC) for publication in this open access journal is 2600 CHF (Swiss Francs). Submitted papers should be well formatted and use good English. Authors may use MDPI's English editing service prior to publication or during author revisions.

Keywords

  • computer codes
  • high order accuracy
  • high-precision calculations
  • multigrid development
  • large-scale optimization
  • multiple processors
  • mathematical model
  • parallel computing
  • numerical algorithms
  • validation and verification

Published Papers (7 papers)

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Research

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17 pages, 3528 KiB  
Article
Numerical Analysis of a Drop-Shaped Aquatic Robot
by Evgeny V. Vetchanin and Ivan S. Mamaev
Mathematics 2024, 12(2), 312; https://doi.org/10.3390/math12020312 - 18 Jan 2024
Viewed by 570
Abstract
Finite-dimensional equations constructed earlier to describe the motion of an aquatic drop-shaped robot due to given rotor oscillations are studied. To study the equations of motion, we use the Poincaré map method, estimates of the Lyapunov exponents, and the parameter continuation method to [...] Read more.
Finite-dimensional equations constructed earlier to describe the motion of an aquatic drop-shaped robot due to given rotor oscillations are studied. To study the equations of motion, we use the Poincaré map method, estimates of the Lyapunov exponents, and the parameter continuation method to explore the evolution of asymptotically stable solutions. It is shown that, in addition to the so-called main periodic solution of the equations of motion for which the robot moves in a circle in a natural way, an additional asymptotically stable periodic solution can arise under the influence of highly asymmetric impulsive control. This solution corresponds to the robot’s sideways motion near the circle. It is shown that this additional periodic solution can lose stability according to the Neimark–Sacker scenario, and an attracting torus appears in its vicinity. Thus, a quasiperiodic mode of motion can exist in the phase space of the system. It is shown that quasiperiodic solutions of the equations of motion also correspond to the quasiperiodic motion of the robot in a bounded region along a trajectory of a rather complex shape. Also, strange attractors were found that correspond to the drifting motion of the robot. These modes of motion were found for the first time in the dynamics of the drop-shaped robot. Full article
(This article belongs to the Special Issue Numerical Simulations and Mathematical Modelling in Engineering Physics)
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24 pages, 12742 KiB  
Article
Numerical Modeling of Water Jet Plunging in Molten Heavy Metal Pool
by Sergey E. Yakush, Nikita S. Sivakov, Oleg I. Melikhov and Vladimir I. Melikhov
Mathematics 2024, 12(1), 12; https://doi.org/10.3390/math12010012 - 20 Dec 2023
Cited by 1 | Viewed by 685
Abstract
The hydrodynamic and thermal interaction of water with the high-temperature melt of a heavy metal was studied via the Volume-of-Fluid (VOF) method formulated for three immiscible phases (liquid melt, water, and water vapor), with account for phase changes. The VOF method relies on [...] Read more.
The hydrodynamic and thermal interaction of water with the high-temperature melt of a heavy metal was studied via the Volume-of-Fluid (VOF) method formulated for three immiscible phases (liquid melt, water, and water vapor), with account for phase changes. The VOF method relies on a first-principle description of phase interactions, including drag, heat transfer, and water evaporation, in contrast to multifluid models relying on empirical correlations. The verification of the VOF model implemented in OpenFOAM software was performed by solving one- and two-dimensional reference problems. Water jet penetration into a melt pool was first calculated in two-dimensional problem formulation, and the results were compared with analytical models and empirical correlations available, with emphasis on the effects of jet velocity and diameter. Three-dimensional simulations were performed in geometry, corresponding to known experiments performed in a narrow planar vessel with a semi-circular bottom. The VOF results obtained for water jet impact on molten heavy metal (lead–bismuth eutectic alloy at the temperature 820 K) are here presented for a water temperature of 298 K, jet diameter 6 mm, and jet velocity 6.2 m/s. Development of a cavity filled with a three-phase melt–water–vapor mixture is revealed, including its propagation down to the vessel bottom, with lateral displacement of melt, and subsequent detachment from the bottom due to gravitational settling of melt. The best agreement of predicted cavity depth, velocity, and aspect ratio with experiments (within 10%) was achieved at the stage of downward cavity propagation; at the later stages, the differences increased to about 30%. Adequacy of the numerical mesh containing about 5.6 million cells was demonstrated by comparing the penetration dynamics obtained on a sequence of meshes with the cell size ranging from 180 to 350 µm. Full article
(This article belongs to the Special Issue Numerical Simulations and Mathematical Modelling in Engineering Physics)
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19 pages, 3549 KiB  
Article
Fully Electromagnetic Code KARAT Applied to the Problem of Aneutronic Proton–Boron Fusion
by Stepan N. Andreev, Yuri K. Kurilenkov and Alexander V. Oginov
Mathematics 2023, 11(18), 4009; https://doi.org/10.3390/math11184009 - 21 Sep 2023
Viewed by 820
Abstract
In this paper, the full electromagnetic code KARAT is presented in detail, the scope of which is a computational experiment in applied problems of engineering electrodynamics. The basis of the physical model used is Maxwell’s equations together with boundary conditions for fields, as [...] Read more.
In this paper, the full electromagnetic code KARAT is presented in detail, the scope of which is a computational experiment in applied problems of engineering electrodynamics. The basis of the physical model used is Maxwell’s equations together with boundary conditions for fields, as well as material equations linking currents with field strengths. The Particle in Cell (PiC) method for the kinetic description of plasma is implemented in the code. A unique feature of the code KARAT is the possibility of the self-consistent modeling of inelastic processes, in particular, nuclear reactions, at each time step in the process of electrodynamic calculation. The aneutronic proton–boron nuclear reaction, accompanied by the release of almost only α-particles, is extremely in demand in medicine and, perhaps, in the future, will form the basis for obtaining “clean” nuclear energy. The results of a numerical simulation within the framework of the code KARAT of the key physical processes leading to the proton–boron fusion are presented and discussed both for laser-driven plasma and for a plasma oscillatory confinement scheme. Full article
(This article belongs to the Special Issue Numerical Simulations and Mathematical Modelling in Engineering Physics)
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21 pages, 1023 KiB  
Article
Black-Box Solver for Numerical Simulations and Mathematical Modelling in Engineering Physics
by Sergey I. Martynenko and Aleksey Yu. Varaksin
Mathematics 2023, 11(16), 3442; https://doi.org/10.3390/math11163442 - 08 Aug 2023
Cited by 1 | Viewed by 761
Abstract
This article presents a two-grid approach for developing a black-box iterative solver for a large class of real-life problems in continuum mechanics (heat and mass transfer, fluid dynamics, elasticity, electromagnetism, and others). The main requirements on this (non-)linear black-box solver are: (1) robustness [...] Read more.
This article presents a two-grid approach for developing a black-box iterative solver for a large class of real-life problems in continuum mechanics (heat and mass transfer, fluid dynamics, elasticity, electromagnetism, and others). The main requirements on this (non-)linear black-box solver are: (1) robustness (the lowest number of problem-dependent components), (2) efficiency (close-to-optimal algorithmic complexity), and (3) parallelism (a parallel robust algorithm should be faster than the fastest sequential one). The basic idea is to use the auxiliary structured grid for more computational work, where (non-)linear problems are simpler to solve and to parallelize, i.e., to combine the advantages of unstructured and structured grids: simplicity of generation in complex domain geometry and opportunity to solve (non-)linear (initial-)boundary value problems by using the Robust Multigrid Technique. Topics covered include the description of the two-grid algorithm and estimation of their robustness, convergence, algorithmic complexity, and parallelism. Further development of modern software for solving real-life problems justifies relevance of the research. The proposed two-grid algorithm can be used in black-box parallel software for the reduction in the execution time in solving (initial-)boundary value problems. Full article
(This article belongs to the Special Issue Numerical Simulations and Mathematical Modelling in Engineering Physics)
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19 pages, 8977 KiB  
Article
Eulerian-Eulerian Modeling of the Features of Mean and Fluctuational Flow Structure and Dispersed Phase Motion in Axisymmetric Round Two-Phase Jets
by Maksim A. Pakhomov and Viktor I. Terekhov
Mathematics 2023, 11(11), 2533; https://doi.org/10.3390/math11112533 - 31 May 2023
Cited by 2 | Viewed by 881
Abstract
The features of the local mean and fluctuational flow structure, carrier phase turbulence and the propagation of the dispersed phase in the bubbly and droplet-laden isothermal round polydispersed jets were numerically simulated. The dynamics of the polydispersed phase is predicted using the Eulerian–Eulerian [...] Read more.
The features of the local mean and fluctuational flow structure, carrier phase turbulence and the propagation of the dispersed phase in the bubbly and droplet-laden isothermal round polydispersed jets were numerically simulated. The dynamics of the polydispersed phase is predicted using the Eulerian–Eulerian two-fluid approach. Turbulence of the carrier phase is described using the second-moment closure while taking into account the presence of the dispersed phase. The numerical analysis was performed in a wide range of variation of dispersed phase diameter at the inlet and particle-to-fluid density ratio (from gas flow laden with water droplets to carrier fluid flow laden with gas bubbles). An increase in the concentration of air bubbles and their size leads to jet expansion (as compared to a single-phase jet up to 40%), which indicates an increase in the intensity of the process of turbulent mixing with the surrounding space. However, this makes the gas-droplet jet narrower (up to 15%) and with a longer range in comparison with a single-phase flow. The addition of finely dispersed liquid droplets to an air jet suppresses gas phase turbulence (up to 15%). In a bubbly jet, it is found that small bubbles (Stk < 0.1) accumulate near the jet axis in the initial cross-sections, while concentration of the large ones (Stk > 0.2) along the jet axis decreases rapidly. In the gas-droplet jet, the effect of dispersed phase accumulation is also observed in the initial cross-section, and then its concentration decreases gradually along the jet axis. For gas bubbles (Stk < 0.1), small turbulence attenuation (up to 6%) is shown. Full article
(This article belongs to the Special Issue Numerical Simulations and Mathematical Modelling in Engineering Physics)
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Review

Jump to: Research

30 pages, 2886 KiB  
Review
Mathematical Modeling of Structure and Dynamics of Concentrated Tornado-like Vortices: A Review
by Aleksey Yu. Varaksin and Sergei V. Ryzhkov
Mathematics 2023, 11(15), 3293; https://doi.org/10.3390/math11153293 - 26 Jul 2023
Cited by 3 | Viewed by 1915
Abstract
Mathematical modeling is the most important tool for constructing the theory of concentrated tornado-like vortices. A review and analysis of computational and theoretical works devoted to the study of the generation and dynamics of air tornado-like vortices has been conducted. Models with various [...] Read more.
Mathematical modeling is the most important tool for constructing the theory of concentrated tornado-like vortices. A review and analysis of computational and theoretical works devoted to the study of the generation and dynamics of air tornado-like vortices has been conducted. Models with various levels of complexity are considered: a simple analytical model based on the Bernoulli equation, an analytical model based on the vorticity equation, a new class of analytical solutions of the Navier–Stokes equations for a wide class of vortex flows, and thermodynamic models. The approaches developed to date for the numerical simulation of tornado-like vortices are described and analyzed. Considerable attention is paid to developed approaches that take into account the two-phase nature of tornadoes. The final part is devoted to the analysis of modern ideas about the tornado, concerning its structure and dynamics (up to the breakup) and the conditions for its occurrence (tornadogenesis). Mathematical modeling data are necessary for interpreting the available field measurements while also serving as the basis for planning the physical modeling of tornado-like vortices in the laboratory. Full article
(This article belongs to the Special Issue Numerical Simulations and Mathematical Modelling in Engineering Physics)
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20 pages, 1872 KiB  
Review
Mathematical Modeling of Gas-Solid Two-Phase Flows: Problems, Achievements and Perspectives (A Review)
by Aleksey Yu. Varaksin and Sergei V. Ryzhkov
Mathematics 2023, 11(15), 3290; https://doi.org/10.3390/math11153290 - 26 Jul 2023
Cited by 2 | Viewed by 1157
Abstract
Mathematical modeling is the most important tool for constructing theories of different kinds of two-phase flows. This review is devoted to the analysis of the introduction of mathematical modeling to two-phase flows, where solid particles mainly serve as the dispersed phase. The main [...] Read more.
Mathematical modeling is the most important tool for constructing theories of different kinds of two-phase flows. This review is devoted to the analysis of the introduction of mathematical modeling to two-phase flows, where solid particles mainly serve as the dispersed phase. The main problems and features of the study of gas-solid two-phase flows are included. The main characteristics of gas flows with solid particles are discussed, and the classification of two-phase flows is developed based on these characteristics. The Lagrangian and Euler approaches to modeling the motion of a dispersed phase (particles) are described. A great deal of attention is paid to the consideration of numerical simulation methods that provide descriptions of turbulent gas flow at different hierarchical levels (RANS, LES, and DNS), different levels of description of interphase interactions (one-way coupling (OWC), two-way coupling (TWC), and four-way coupling (FWC)), and different levels of interface resolution (partial-point (PP) and particle-resolved (PR)). Examples of studies carried out on the basis of the identified approaches are excluded, and they are also excluded for the mathematical modeling of various classes of gas-solid two-phase flows. Full article
(This article belongs to the Special Issue Numerical Simulations and Mathematical Modelling in Engineering Physics)
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