Group Analysis of Gas Dynamics Equations for a Dissociating Gas in Two Spatial Dimensions in Eulerian and Lagrangian Coordinates

Group Analysis of Gas Dynamics Equations for a Dissociating Gas in Two Spatial Dimensions in Eulerian and Lagrangian Coordinates | Research Square window.SnipcartSettings = { analytics: { enabled: false } }; (function() { var accessVector = localStorage.getItem('access_vector') || ''; window.dataLayer = window.dataLayer || []; if (accessVector) { window.dataLayer.push({ user: { profile: { profileInfo: { snid: accessVector } } } }); } })(); (function(w,d,s,l,i){w[l]=w[l]||[];w[l].push({'gtm.start':new Date().getTime(),event:'gtm.js'});var f=d.getElementsByTagName(s)[0],j=d.createElement(s),dl=l!='dataLayer'?'&l='+l:'';j.async=true;j.src='https://www.googletagmanager.com/gtm.js?id='+i+dl;f.parentNode.insertBefore(j,f);})(window,document,'script','dataLayer','GTM-K279D39R'); Browse Preprints In Review Journals COVID-19 Preprints AJE Video Bytes Research Tools Research Promotion AJE Professional Editing AJE Rubriq About Preprint Platform In Review Editorial Policies Our Team Advisory Board Help Center Sign In Submit a Preprint Cite Share Download PDF Research Article Group Analysis of Gas Dynamics Equations for a Dissociating Gas in Two Spatial Dimensions in Eulerian and Lagrangian Coordinates Yurii N. Grigoryev, Eugene I. Kaptsov, Sergey V. Meleshko, Piyanuch Siriwat This is a preprint; it has not been peer reviewed by a journal. https://doi.org/ 10.21203/rs.3.rs-7913213/v1 This work is licensed under a CC BY 4.0 License Status: Posted Version 1 posted You are reading this latest preprint version Abstract comprehensive group analysis of two-dimensional flows of a chemically reacting ideal gas with a two-component mixture is carried out. The study covers both unsteady and stationary regimes, considered in Eulerian and Lagrangian coordinates. By exploiting equivalent transformations and use of optimal systems of subalgebras for classification procedure, the governing equations are classified into four distinct classes depending on the reaction rate function. The Lagrangian formulation of solutions stationary in Eulerian coordinates is given: the group classification of such equations is also presented. In addition, the case of a mixture of two non-interacting gases is analyzed as a natural limiting model. A class of partially invariant solutions is obtained through compatibility analysis and reduction to involutive form, followed by a generalization that reduces the governing equations to systems with two independent variables while retaining essential two-dimensional features. These generalized solutions admit self-similar forms and extend the classical similarity solutions of the strong explosion problem to incorporate transverse velocity components, thereby revealing the role of two-dimensionality. The results establish a coherent framework for the classification and construction of invariant and partially invariant solutions for reacting and non-reacting gas mixtures, with potential applications to twodimensional gas dynamics, magnetohydrodynamics, and invariant numerical schemes. Chemical reaction Lie point symmetries Invariant solution Lagrangian coordinates Group classification Group foliation Full Text Additional Declarations No competing interests reported. Cite Share Download PDF Status: Posted Version 1 posted You are reading this latest preprint version Research Square lets you share your work early, gain feedback from the community, and start making changes to your manuscript prior to peer review in a journal. As a division of Research Square Company, we’re committed to making research communication faster, fairer, and more useful. We do this by developing innovative software and high quality services for the global research community. Our growing team is made up of researchers and industry professionals working together to solve the most critical problems facing scientific publishing. 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