title: ÐÐ½Ð°Ð»Ð¸Ð·, Ð¿ÑÐ¾Ð³ÑÐ°Ð¼Ð¼Ð½Ð°Ñ ÑÐµÐ°Ð»Ð¸Ð·Ð°ÑÐ¸Ñ Ð¸ ÑÐµÑÑÐ¸ÑÐ¾Ð²Ð°Ð½Ð¸Ðµ ÑÑ ÐµÐ¼ Ð¿Ð¾Ð²ÑÑÐµÐ½Ð½Ð¾Ð³Ð¾ Ð¿Ð¾ÑÑÐ´ÐºÐ° ÑÐ¾ÑÐ½Ð¾ÑÑÐ¸ Ñ ÐºÐ²Ð°Ð·Ð¸Ð¾Ð´Ð½Ð¾Ð¼ÐµÑÐ½Ð¾Ð¹ ÑÐµÐºÐ¾Ð½ÑÑÑÑÐºÑÐ¸ÐµÐ¹ Ð³Ð°Ð·Ð¾Ð´Ð¸Ð½Ð°Ð¼Ð¸ÑÐµÑÐºÐ¸Ñ Ð¿ÐµÑÐµÐ¼ÐµÐ½Ð½ÑÑ
title: Ð²ÑÐ¿ÑÑÐºÐ½Ð°Ñ ÐºÐ²Ð°Ð»Ð¸ÑÐ¸ÐºÐ°ÑÐ¸Ð¾Ð½Ð½Ð°Ñ ÑÐ°Ð±Ð¾ÑÐ° Ð±Ð°ÐºÐ°Ð»Ð°Ð²ÑÐ°
titleType: Subtitle
title: Analysis, implementation and testing of high-order accuracy schemes with quasi-one-dimensional reconstruction of gas dynamic variables
Creators: name: ÐÐ°Ð±Ð¸Ñ, ÐÐ»ÐµÐ½Ð°
Publisher: name: Ð¡Ð°Ð½ÐºÑ-ÐÐµÑÐµÑÐ±ÑÑÐ³ÑÐºÐ¸Ð¹ Ð¿Ð¾Ð»Ð¸ÑÐµÑÐ½Ð¸ÑÐµÑÐºÐ¸Ð¹ ÑÐ½Ð¸Ð²ÐµÑÑÐ¸ÑÐµÑ ÐÐµÑÑÐ° ÐÐµÐ»Ð¸ÐºÐ¾Ð³Ð¾
Year: 2022
Subjects: ÑÐ¸ÑÐ»ÐµÐ½Ð½Ð¾Ðµ Ð¼Ð¾Ð´ÐµÐ»Ð¸ÑÐ¾Ð²Ð°Ð½Ð¸Ðµ
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Ð½ÐµÑÑÑÑÐºÑÑÑÐ¸ÑÐ¾Ð²Ð°Ð½Ð½ÑÐµ ÑÐµÑÐºÐ¸
ÐºÐ²Ð°Ð·Ð¸Ð¾Ð´Ð½Ð¾Ð¼ÐµÑÐ½Ð°Ñ ÑÐµÐºÐ¾Ð½ÑÑÑÑÐºÑÐ¸Ñ Ð¿ÐµÑÐµÐ¼ÐµÐ½Ð½ÑÑ
ÑÑ ÐµÐ¼Ð° Ð¿Ð¾Ð²ÑÑÐµÐ½Ð½Ð¾Ð³Ð¾ Ð¿Ð¾ÑÑÐ´ÐºÐ° ÑÐ¾ÑÐ½Ð¾ÑÑÐ¸
numerical simulation
finite volume method
unstructured meshes
quasi-one-dimensional reconstruction of variables
high-accuracy schemes

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description: The subject of the graduate qualification work is âAnalysis, implementation and testing of high-order accuracy schemes with quasi-one-dimensional reconstruction of gas dynamic variablesâ. The given work is devoted to studying the effectiveness of the use of high-order accuracy schemes with quasi-one-dimensional reconstruction of gas dynamic variables on unstructured meshes.Research objectives: 1. Literature review and analysis of various methods of variables reconstruction on the face using polynomials of the third and fifth order of accuracy. 2. Implementation of the procedure for restoring additional points necessary for constructing high order (3 and 5) of accuracy schemes to the Â«unstructuredÂ» finite-volume SINF/Flag-S code; implementation of the procedure for reconstructing variables on the face with high order of accuracy. 3. Performing calculations using implemented to the code SINF/Flag-S high-order accuracy schemes for the initial-value problem with periodic boundary conditions. Analysis of numerical error and evaluation of the schemesâ order of accuracy, performing calculations using unstructured meshes with different types of mesh elements. 4. Computation of inviscid subsonic flow past a cylinder with the use of implemented schemes. The calculations were performed using a finite-volume Â«unstructuredÂ» SINF/Flag-S program code developed at the SPbPU Institute of Physics and Mechanics. The schemes of an increased order of accuracy were introduced in the part of the code intended for calculating substantially compressible flows; to find the points of an extended reconstruction stencil a gradient-free procedure for reconstructing variables on the face was implemented.Using the extended by the author version of the code, a number of test calculations, demonstrating the effectiveness of the introduced schemes in terms of improving the accuracy of numerical solutions, were performed. The analysis of the order of accuracy was performed for one-dimensional and two-dimensional solutions of the scalar transport equations. The schemes were successfully approved on a computational study of subsonic inviscid flow around the cylinder.