Pub Date : 2024-04-01DOI: 10.1134/s2070048224020170
A. Sukhinov, E. Protsenko, S. Protsenko, N. D. Panasenko
{"title":"Parallel Numerical Implementation of Mathematical Wave Hydrodynamics Models Taking into Account the Features of the Vertical Turbulent Exchange Using Remote Sensing Data","authors":"A. Sukhinov, E. Protsenko, S. Protsenko, N. D. Panasenko","doi":"10.1134/s2070048224020170","DOIUrl":"https://doi.org/10.1134/s2070048224020170","url":null,"abstract":"","PeriodicalId":38050,"journal":{"name":"Mathematical Models and Computer Simulations","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2024-04-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140790995","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2023-12-26DOI: 10.1134/s2070048223070104
O. A. Kovyrkina, V. V. Ostapenko
Abstract
A comparative accuracy analysis of three finite-difference schemes (the first order UpWind (UW), the second order TVD, and the third order in time WENO5 schemes) is carried out when calculating the nonlinear transport equation of the Cauchy problem with piecewise linear discontinuous periodic initial data. We show that in the case of stable initial discontinuities from which a sequence of shocks is formed, the convergence order of all three schemes between the shocks coincides with their formal accuracy. In the case of unstable initial discontinuities, when a sequence of centered rarefaction waves is formed, all three schemes have the first order of convergence within these waves. We obtain an explicit formula for the disbalances of the difference solutions in a centered rarefaction wave. This formula agrees closely with the numerical calculations in the case of high-order accurate schemes, does not depend on the scheme type, and is determined by the error in approximating the initial data in the vicinity of an unstable strong discontinuity.
{"title":"On the Accuracy of Finite-Difference Schemes in Calculations of Centered Rarefaction Waves","authors":"O. A. Kovyrkina, V. V. Ostapenko","doi":"10.1134/s2070048223070104","DOIUrl":"https://doi.org/10.1134/s2070048223070104","url":null,"abstract":"<h3 data-test=\"abstract-sub-heading\">Abstract</h3><p>A comparative accuracy analysis of three finite-difference schemes (the first order UpWind (UW), the second order TVD, and the third order in time WENO5 schemes) is carried out when calculating the nonlinear transport equation of the Cauchy problem with piecewise linear discontinuous periodic initial data. We show that in the case of stable initial discontinuities from which a sequence of shocks is formed, the convergence order of all three schemes between the shocks coincides with their formal accuracy. In the case of unstable initial discontinuities, when a sequence of centered rarefaction waves is formed, all three schemes have the first order of convergence within these waves. We obtain an explicit formula for the disbalances of the difference solutions in a centered rarefaction wave. This formula agrees closely with the numerical calculations in the case of high-order accurate schemes, does not depend on the scheme type, and is determined by the error in approximating the initial data in the vicinity of an unstable strong discontinuity.</p>","PeriodicalId":38050,"journal":{"name":"Mathematical Models and Computer Simulations","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2023-12-26","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140883951","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2023-12-26DOI: 10.1134/s2070048223070062
E. M. Kartashov
Abstract
This article considers the open problem of the thermal shock theory in terms of a generalized model of dynamic thermoelasticity under conditions of a locally nonequilibrium heat transfer process. The model is used for a massive body in the cases of three coordinate systems: Cartesian coordinates for a body bounded by a flat surface; spherical coordinates for a body with an internal spherical cavity; and cylindrical coordinates for a body with an internal cylindrical cavity. Three types of intensive heating and cooling are considered: temperature, thermal, and heating by the medium. The task is set to obtain an analytical solution, to carry out numerical experiments, and to give their physical analysis. As a result, generalized model representations of a thermal shock in terms of dynamic thermoelasticity are developed for locally nonequilibrium heat transfer processes simultaneously in three coordinate systems: Cartesian, spherical, and cylindrical. The presence of a curvature of the boundary surface of the thermal shock area substantiates the initial statement of the dynamic problem in displacements using the proposed corresponding compatibility equation. The latter made it possible to propose a generalized dynamic model of the thermal reaction of massive bodies with internal cavities simultaneously in Cartesian, spherical, and cylindrical coordinate systems under conditions of intense thermal heating and cooling, thermal heating and cooling, and heating and cooling by the medium. The model is considered in displacements on the basis of a local nonequilibrium heat transfer. An analytical solution for stresses is obtained and a numerical experiment is carried out; the wave nature of the propagation of a thermoelastic wave is described. A comparison is made with the classical solution without taking into account the local non-equilibrium. Based on the operational solution of the problem, design engineering relations that are important in practical terms for the upper estimate of the maximum thermal stresses are proposed.
{"title":"Generalized Model Representation of the Thermal Shock Theory","authors":"E. M. Kartashov","doi":"10.1134/s2070048223070062","DOIUrl":"https://doi.org/10.1134/s2070048223070062","url":null,"abstract":"<h3 data-test=\"abstract-sub-heading\">Abstract</h3><p>This article considers the open problem of the thermal shock theory in terms of a generalized model of dynamic thermoelasticity under conditions of a locally nonequilibrium heat transfer process. The model is used for a massive body in the cases of three coordinate systems: Cartesian coordinates for a body bounded by a flat surface; spherical coordinates for a body with an internal spherical cavity; and cylindrical coordinates for a body with an internal cylindrical cavity. Three types of intensive heating and cooling are considered: temperature, thermal, and heating by the medium. The task is set to obtain an analytical solution, to carry out numerical experiments, and to give their physical analysis. As a result, generalized model representations of a thermal shock in terms of dynamic thermoelasticity are developed for locally nonequilibrium heat transfer processes simultaneously in three coordinate systems: Cartesian, spherical, and cylindrical. The presence of a curvature of the boundary surface of the thermal shock area substantiates the initial statement of the dynamic problem in displacements using the proposed corresponding compatibility equation. The latter made it possible to propose a generalized dynamic model of the thermal reaction of massive bodies with internal cavities simultaneously in Cartesian, spherical, and cylindrical coordinate systems under conditions of intense thermal heating and cooling, thermal heating and cooling, and heating and cooling by the medium. The model is considered in displacements on the basis of a local nonequilibrium heat transfer. An analytical solution for stresses is obtained and a numerical experiment is carried out; the wave nature of the propagation of a thermoelastic wave is described. A comparison is made with the classical solution without taking into account the local non-equilibrium. Based on the operational solution of the problem, design engineering relations that are important in practical terms for the upper estimate of the maximum thermal stresses are proposed.</p>","PeriodicalId":38050,"journal":{"name":"Mathematical Models and Computer Simulations","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2023-12-26","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139055192","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2023-12-26DOI: 10.1134/s2070048223070165
Yu. V. Yanilkin, A. R. Guzhova, L. I. Degtyarenko, V. Yu. Kolobyanin, V. A. Shmelev
Abstract
A new approach to the direct numerical modeling (DNM) of the turbulent mixing of miscible and immiscible materials of different densities is proposed. The idea of the approach is to separate the states of homogeneous mixtures from heterogeneous ones, consisting of fragments with interfaces, in mixed cells containing mixing substances. This article describes a 2D technique developed in the Euler gas dynamics with concentrations (EGAK) code to realize the approach described above. The method is verified using a classical problem of turbulent mixing arising due to the Rayleigh–Taylor instability at the constant acceleration of the interface between two gases of different densities.
{"title":"Direct Numerical Simulation Method of Turbulence Taking the History of the Process into Account","authors":"Yu. V. Yanilkin, A. R. Guzhova, L. I. Degtyarenko, V. Yu. Kolobyanin, V. A. Shmelev","doi":"10.1134/s2070048223070165","DOIUrl":"https://doi.org/10.1134/s2070048223070165","url":null,"abstract":"<h3 data-test=\"abstract-sub-heading\">Abstract</h3><p>A new approach to the direct numerical modeling (DNM) of the turbulent mixing of miscible and immiscible materials of different densities is proposed. The idea of the approach is to separate the states of homogeneous mixtures from heterogeneous ones, consisting of fragments with interfaces, in mixed cells containing mixing substances. This article describes a 2D technique developed in the Euler gas dynamics with concentrations (EGAK) code to realize the approach described above. The method is verified using a classical problem of turbulent mixing arising due to the Rayleigh–Taylor instability at the constant acceleration of the interface between two gases of different densities.</p>","PeriodicalId":38050,"journal":{"name":"Mathematical Models and Computer Simulations","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2023-12-26","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139055754","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2023-12-26DOI: 10.1134/s2070048223070049
K. G. Garaev, I. R. Mukhametzyanov
Abstract
A variational problem for a conditional extremum of the Mayer type on the construction of the distribution law of the normal component of the velocity of injection of a cooled gas into a turbulent boundary layer under a supersonic flow regime that provides the minimum value of the convective heat flux transmitted from the hot gas to the streamlined surface is considered. The isoperimetric condition is the power of the injection control system, calculated taking into account Darcy’s filtration law. To solve the optimal problem, we use the first integral for the conjugate system with respect to Lagrange multipliers, obtained earlier by the authors using the classical theorem of E. Noether on invariant variational problems and the Lie-Ovsyannikov infinitesimal apparatus. A.A. Dorodnitsyn’s method of generalized integral relations, which has proven itself well in calculating the characteristics of boundary layers under various flow regimes, is used for the calculations. A computational experiment conducted for the case of a flow around a sphere shows the effectiveness of the optimal control law found in comparison with a uniform injection: the gain in the value of the minimized functional is 16.8%. The novelty of the study lies in the development of a method for solving the variational problem using the first integral for the conjugate system, as well as the Dorodnitsyn’s method of generalized integral relations. The scientific significance of the study lies in the development of the theory of an optimally controlled boundary layer under a turbulent flow regime in supersonic gas flows. The results obtained may be of interest in the design of systems for the active thermal protection of surfaces in high-velocity gas flows.
{"title":"Optimally Controlled Turbulent Boundary Layers in Supersonic Gas Flows","authors":"K. G. Garaev, I. R. Mukhametzyanov","doi":"10.1134/s2070048223070049","DOIUrl":"https://doi.org/10.1134/s2070048223070049","url":null,"abstract":"<h3 data-test=\"abstract-sub-heading\">Abstract</h3><p>A variational problem for a conditional extremum of the Mayer type on the construction of the distribution law of the normal component of the velocity of injection of a cooled gas into a turbulent boundary layer under a supersonic flow regime that provides the minimum value of the convective heat flux transmitted from the hot gas to the streamlined surface is considered. The isoperimetric condition is the power of the injection control system, calculated taking into account Darcy’s filtration law. To solve the optimal problem, we use the first integral for the conjugate system with respect to Lagrange multipliers, obtained earlier by the authors using the classical theorem of E. Noether on invariant variational problems and the Lie-Ovsyannikov infinitesimal apparatus. A.A. Dorodnitsyn’s method of generalized integral relations, which has proven itself well in calculating the characteristics of boundary layers under various flow regimes, is used for the calculations. A computational experiment conducted for the case of a flow around a sphere shows the effectiveness of the optimal control law found in comparison with a uniform injection: the gain in the value of the minimized functional is 16.8%. The novelty of the study lies in the development of a method for solving the variational problem using the first integral for the conjugate system, as well as the Dorodnitsyn’s method of generalized integral relations. The scientific significance of the study lies in the development of the theory of an optimally controlled boundary layer under a turbulent flow regime in supersonic gas flows. The results obtained may be of interest in the design of systems for the active thermal protection of surfaces in high-velocity gas flows.</p>","PeriodicalId":38050,"journal":{"name":"Mathematical Models and Computer Simulations","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2023-12-26","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139055757","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2023-12-26DOI: 10.1134/s2070048223070086
A. A. Kislitsyn
Abstract
The proposed method is based on calculations of the statistics of the nearest neighbor graph (NNG) structures, which are presented as a benchmark of the probabilities of the distribution of graphs by the number of disconnected fragments. The deviation of the actually observed occurrence of connectivity from the calculated one will allow us to determine the probability that this sample can be considered a set of statistically independent variables. The statements about the independence of the NNG statistics from the distribution of distances and from the triangle inequality are proved, which allows the numerical modeling of such structures. Estimates of the accuracy of the calculated statistics for graphs and their comparison with estimates obtained by modeling random coordinates of points in d-dimensional space are carried out. It is shown that the model of the NNGs without taking into account the dimension of the space leads to fairly accurate estimates of the statistics of graph structures in spaces of dimensionality higher than five. For spaces of smaller dimensionality, the benchmark can be obtained by directly calculating the distances between points with random coordinates in a unit cube. The proposed method is applied to the problem of analyzing the level of unsteadiness of the earthquake catalog in the Kuril–Kamchatka region. The lengths of samples of time intervals between neighboring events are analyzed. It is shown that the analyzed system as a whole is interconnected with a probability of 0.91, and this dependence is fundamentally different from the lag correlation between the sample elements.
{"title":"Modeling the Nearest Neighbor Graphs to Estimate the Probability of the Independence of Data","authors":"A. A. Kislitsyn","doi":"10.1134/s2070048223070086","DOIUrl":"https://doi.org/10.1134/s2070048223070086","url":null,"abstract":"<h3 data-test=\"abstract-sub-heading\">Abstract</h3><p>The proposed method is based on calculations of the statistics of the nearest neighbor graph (NNG) structures, which are presented as a benchmark of the probabilities of the distribution of graphs by the number of disconnected fragments. The deviation of the actually observed occurrence of connectivity from the calculated one will allow us to determine the probability that this sample can be considered a set of statistically independent variables. The statements about the independence of the NNG statistics from the distribution of distances and from the triangle inequality are proved, which allows the numerical modeling of such structures. Estimates of the accuracy of the calculated statistics for graphs and their comparison with estimates obtained by modeling random coordinates of points in <i>d</i>-dimensional space are carried out. It is shown that the model of the NNGs without taking into account the dimension of the space leads to fairly accurate estimates of the statistics of graph structures in spaces of dimensionality higher than five. For spaces of smaller dimensionality, the benchmark can be obtained by directly calculating the distances between points with random coordinates in a unit cube. The proposed method is applied to the problem of analyzing the level of unsteadiness of the earthquake catalog in the Kuril–Kamchatka region. The lengths of samples of time intervals between neighboring events are analyzed. It is shown that the analyzed system as a whole is interconnected with a probability of 0.91, and this dependence is fundamentally different from the lag correlation between the sample elements.</p>","PeriodicalId":38050,"journal":{"name":"Mathematical Models and Computer Simulations","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2023-12-26","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139055188","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2023-12-26DOI: 10.1134/s207004822307013x
E. V. Shilnikov, I. R. Khaytaliev
Abstract
The solution of a quasi-gas dynamic (QGD) system of equations using the local discontinuous Galerkin method (LDG) is considered. One-dimensional Riemann discontinuity problems with known exact solutions are solved. Strong discontinuities are present in the solutions of the problems. Therefore, to ensure the monotonicity of the solution obtained by the LDG method, the so-called slope limiters, or limiters, are introduced. A “moment” limiter is chosen that preserves as high an order as possible. The limiter is modified to smooth the oscillations in the areas where the solution is constant.
{"title":"Application of the Local Discontinuous Galerkin Method to the Solution of the Quasi-Gas Dynamic System of Equations","authors":"E. V. Shilnikov, I. R. Khaytaliev","doi":"10.1134/s207004822307013x","DOIUrl":"https://doi.org/10.1134/s207004822307013x","url":null,"abstract":"<h3 data-test=\"abstract-sub-heading\">Abstract</h3><p>The solution of a quasi-gas dynamic (QGD) system of equations using the local discontinuous Galerkin method (LDG) is considered. One-dimensional Riemann discontinuity problems with known exact solutions are solved. Strong discontinuities are present in the solutions of the problems. Therefore, to ensure the monotonicity of the solution obtained by the LDG method, the so-called slope limiters, or limiters, are introduced. A “moment” limiter is chosen that preserves as high an order as possible. The limiter is modified to smooth the oscillations in the areas where the solution is constant.</p>","PeriodicalId":38050,"journal":{"name":"Mathematical Models and Computer Simulations","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2023-12-26","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139055468","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2023-12-26DOI: 10.1134/s2070048223070050
N. V. Grigorevskiy, A. V. Zemskov, A. V. Malashkin
Abstract
We consider the unsteady problem of bending a homogeneous orthotropic hinged Timoshenko elastic-diffusion plate under the action of a mechanical load distributed over the surface. The initial mathematical formulation of the problem includes the system of elastic-diffusion equations for a continuum, which takes into account the finite propagation velocity of diffusion perturbations. The equations of unsteady elastic-diffusion vibrations of the plate are obtained from the equations for a continuum using the generalized principle of virtual displacements and hypotheses of Timoshenko’s theory. The solution is sought using the Laplace transform and expansion into Fourier series. The originals are found analytically using residues and tables of operational calculus.
{"title":"Modeling the Elastic-Diffusion Vibrations of a Hinged Timoshenko Plate under the Action of a Distributed Surface Load","authors":"N. V. Grigorevskiy, A. V. Zemskov, A. V. Malashkin","doi":"10.1134/s2070048223070050","DOIUrl":"https://doi.org/10.1134/s2070048223070050","url":null,"abstract":"<h3 data-test=\"abstract-sub-heading\">Abstract</h3><p>We consider the unsteady problem of bending a homogeneous orthotropic hinged Timoshenko elastic-diffusion plate under the action of a mechanical load distributed over the surface. The initial mathematical formulation of the problem includes the system of elastic-diffusion equations for a continuum, which takes into account the finite propagation velocity of diffusion perturbations. The equations of unsteady elastic-diffusion vibrations of the plate are obtained from the equations for a continuum using the generalized principle of virtual displacements and hypotheses of Timoshenko’s theory. The solution is sought using the Laplace transform and expansion into Fourier series. The originals are found analytically using residues and tables of operational calculus.</p>","PeriodicalId":38050,"journal":{"name":"Mathematical Models and Computer Simulations","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2023-12-26","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139055756","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2023-12-26DOI: 10.1134/s2070048223070128
M. Y. Nemtsev
Abstract
A mathematical model and numerical method for solving problems of the flow of two-phase mixtures of gas and fine solid particles are considered. The particles are assumed to be absolutely rigid, incompressible, and nondeformable. As the initial model, the continuum model of R.I. Nigmatulin is considered. The model has two drawbacks: it is not strictly hyperbolic (i.e., it degenerates into an elliptical one under certain flow regimes) and has a nonconservative form, which makes it difficult to solve numerically. This paper proposes a method for regularizing Nigmatulin’s model at a discrete level, which makes it possible to eliminate these shortcomings and develop a numerical model that is well-conditioned for evolutionary problems of the flow of gas-dispersed mixtures with nondeformable solid particles. The regularization method is based on splitting the original system into two subsystems, each of which is strictly hyperbolic and has a conservative form. Difference schemes of the Godunov type are developed for the numerical solution of these subsystems. Testing of the proposed model and implemented methods includes checking the preservation of a homogeneous solution and the formation of shock waves and rarefaction waves in a gas, as well as compaction and decompaction waves in the particle phase. The results of the numerical simulation of the interaction of a shock wave in a gas with a near-wall layer of particles are also presented.
{"title":"Numerical Simulation of Dynamic Processes in the Medium of Fine-Grained Solid Particles","authors":"M. Y. Nemtsev","doi":"10.1134/s2070048223070128","DOIUrl":"https://doi.org/10.1134/s2070048223070128","url":null,"abstract":"<h3 data-test=\"abstract-sub-heading\">Abstract</h3><p>A mathematical model and numerical method for solving problems of the flow of two-phase mixtures of gas and fine solid particles are considered. The particles are assumed to be absolutely rigid, incompressible, and nondeformable. As the initial model, the continuum model of R.I. Nigmatulin is considered. The model has two drawbacks: it is not strictly hyperbolic (i.e., it degenerates into an elliptical one under certain flow regimes) and has a nonconservative form, which makes it difficult to solve numerically. This paper proposes a method for regularizing Nigmatulin’s model at a discrete level, which makes it possible to eliminate these shortcomings and develop a numerical model that is well-conditioned for evolutionary problems of the flow of gas-dispersed mixtures with nondeformable solid particles. The regularization method is based on splitting the original system into two subsystems, each of which is strictly hyperbolic and has a conservative form. Difference schemes of the Godunov type are developed for the numerical solution of these subsystems. Testing of the proposed model and implemented methods includes checking the preservation of a homogeneous solution and the formation of shock waves and rarefaction waves in a gas, as well as compaction and decompaction waves in the particle phase. The results of the numerical simulation of the interaction of a shock wave in a gas with a near-wall layer of particles are also presented.</p>","PeriodicalId":38050,"journal":{"name":"Mathematical Models and Computer Simulations","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2023-12-26","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139055190","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2023-12-01DOI: 10.1134/s2070048223070141
Soledad Fioroni, A. Larreteguy, G. Savioli
{"title":"BlackOilFoam: Modelling Multiphase Flow from Laboratory Cells to Unconventional Reservoirs","authors":"Soledad Fioroni, A. Larreteguy, G. Savioli","doi":"10.1134/s2070048223070141","DOIUrl":"https://doi.org/10.1134/s2070048223070141","url":null,"abstract":"","PeriodicalId":38050,"journal":{"name":"Mathematical Models and Computer Simulations","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2023-12-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139194596","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
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