{"title":"Calculation of Flows of Gas-Liquid Mixtures by a Modified Nodal Method of Characteristics","authors":"V. S. Surov","doi":"10.1134/s1995423923040079","DOIUrl":null,"url":null,"abstract":"<h3 data-test=\"abstract-sub-heading\">Abstract</h3><p>To calculate flows of a gas-liquid mixture, a modified inverse method of characteristics is proposed. An additional fractional time step is introduced in its algorithm, which makes it possible to carry out calculations with a large time step without loss of accuracy and stability. A formulation of boundary conditions on curvilinear walls is discussed in relation to a multidimensional nodal method of characteristics which is based on splitting along the coordinate directions of the original system of equations into a number of one-dimensional subsystems. For the boundary points located on curvilinear impenetrable surfaces, a calculation method based on a method of fictitious nodes is proposed. When testing the modified method, a supersonic interaction of a homogeneous dispersed flow with a barrier is calculated for a flow regime with an attached shock wave. Problems of steady mixture flows near an external obtuse angle, as well as near a cone, which are analogues of Prandtl–Meyer and Busemann flows in gas dynamics, are solved. The calculation results are compared with available self-similar solutions, and a satisfactory agreement is reached.</p>","PeriodicalId":43697,"journal":{"name":"Numerical Analysis and Applications","volume":"107 1","pages":""},"PeriodicalIF":0.4000,"publicationDate":"2023-12-07","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Numerical Analysis and Applications","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.1134/s1995423923040079","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q4","JCRName":"MATHEMATICS, APPLIED","Score":null,"Total":0}
引用次数: 0
Abstract
To calculate flows of a gas-liquid mixture, a modified inverse method of characteristics is proposed. An additional fractional time step is introduced in its algorithm, which makes it possible to carry out calculations with a large time step without loss of accuracy and stability. A formulation of boundary conditions on curvilinear walls is discussed in relation to a multidimensional nodal method of characteristics which is based on splitting along the coordinate directions of the original system of equations into a number of one-dimensional subsystems. For the boundary points located on curvilinear impenetrable surfaces, a calculation method based on a method of fictitious nodes is proposed. When testing the modified method, a supersonic interaction of a homogeneous dispersed flow with a barrier is calculated for a flow regime with an attached shock wave. Problems of steady mixture flows near an external obtuse angle, as well as near a cone, which are analogues of Prandtl–Meyer and Busemann flows in gas dynamics, are solved. The calculation results are compared with available self-similar solutions, and a satisfactory agreement is reached.
期刊介绍：
Numerical Analysis and Applications is the translation of Russian periodical Sibirskii Zhurnal Vychislitel’noi Matematiki (Siberian Journal of Numerical Mathematics) published by the Siberian Branch of the Russian Academy of Sciences Publishing House since 1998.
The aim of this journal is to demonstrate, in concentrated form, to the Russian and International Mathematical Community the latest and most important investigations of Siberian numerical mathematicians in various scientific and engineering fields.
The journal deals with the following topics: Theory and practice of computational methods, mathematical physics, and other applied fields; Mathematical models of elasticity theory, hydrodynamics, gas dynamics, and geophysics; Parallelizing of algorithms; Models and methods of bioinformatics.
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