{"title":"Method and algorithm for calculating isobaric and non-isobaric three-dimensional turbulent jets of reacting gases","authors":"S. Khodjiev","doi":"10.26907/0021-3446-2023-11-41-58","DOIUrl":"https://doi.org/10.26907/0021-3446-2023-11-41-58","url":null,"abstract":"This paper presents a calculation method and algorithm, as well as numerical results of studying chemically reacting turbulent jets based on three-dimensional parabolic systems of Navier-Stokes equations for multicomponent gas mixtures.Continuity equations are used to calculate the mass imbalance when solving with constant pressure, and with variable pressures, with the equations of motion and continuity.Diffusion combustion of a propane-butane mixture flowing from a square-shaped nozzle in a submerged flow of an air oxidizer has been numerically studied. Pressure variability significantly affects the velocity (temperature) profiles in the initial sections of the jet, and when moving away from the nozzle exit, the pressure effect can be considered imperceptible, but the flame length is longer than at constant pressure, but it does not significantly affect the shape of the flame.The saddle-shaped behavior of the longitudinal velocity in the direction of the major axis is numerically obtained for large initial values of the turbulence kinetic energy of the main jet.Given method allows the study of non-reacting and reactive turbulent jets flowing from a rectangular nozzle.","PeriodicalId":507800,"journal":{"name":"Izvestiya Vysshikh Uchebnykh Zavedenii. Matematika","volume":"25 6","pages":""},"PeriodicalIF":0.0,"publicationDate":"2023-12-09","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139184813","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}
{"title":"Finite element modeling of the eigenvibrations of the square plate with attached oscillator","authors":"D. M. Korosteleva, S. I. Solov’ev","doi":"10.26907/0021-3446-2023-11-92-97","DOIUrl":"https://doi.org/10.26907/0021-3446-2023-11-92-97","url":null,"abstract":"For the problem on eigenvibrations of the plate with an attached oscillator, the new symmetric linear variational statement is proposed. It is established the existence of the sequence of positive eigenvalues of finite multiplicity with limit point at infinity and the corresponding complete orthonormal system of eigenvectors. The new symmetric scheme of the finite element method with Hermite finite elements is formulated. Error estimates consistent with the solution smoothness for the approximate eigenvalues and approximate eigenvectors are proved. The results of numerical experiments illustrating the influence of the solution smoothness on the computation accuracy are presented.","PeriodicalId":507800,"journal":{"name":"Izvestiya Vysshikh Uchebnykh Zavedenii. Matematika","volume":"8 3","pages":""},"PeriodicalIF":0.0,"publicationDate":"2023-12-09","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139184877","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}
{"title":"Approximation of the Lebesgue constant of the Fourier operator by a logarithmic-fractional-rational function","authors":"I. A. Shakirov","doi":"10.26907/0021-3446-2023-11-75-85","DOIUrl":"https://doi.org/10.26907/0021-3446-2023-11-75-85","url":null,"abstract":"The Lebesgue constant of the classical Fourier operator is uniformly approximated by a logarithmic-fractional-rational function depending on three parameters; they are defined using the specific properties of logarithmic and rational approximations. A rigorous study of the corresponding residual term having an indefinite (non-monotonic) behavior has been carried out. The obtained approximation results strengthen the known results by more than two orders of magnitude.","PeriodicalId":507800,"journal":{"name":"Izvestiya Vysshikh Uchebnykh Zavedenii. Matematika","volume":"8 4","pages":""},"PeriodicalIF":0.0,"publicationDate":"2023-12-09","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139184764","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}