title: Ð ÐµÐ°Ð»Ð¸Ð·Ð°ÑÐ¸Ñ Ð¸ ÑÐµÑÑÐ¸ÑÐ¾Ð²Ð°Ð½Ð¸Ðµ ÑÑ ÐµÐ¼ Ð¿Ð¾Ð²ÑÑÐµÐ½Ð½Ð¾Ð¹ ÑÐ¾ÑÐ½Ð¾ÑÑÐ¸ Ð¿ÑÐ¸ ÑÐ°ÑÑÐµÑÐ°Ñ ÑÐµÑÐµÐ½Ð¸Ð¹ Ñ ÑÐ°Ð·ÑÑÐ²Ð°Ð¼Ð¸ Ð½Ð° Ð½ÐµÑÑÑÑÐºÑÑÑÐ¸ÑÐ¾Ð²Ð°Ð½Ð½ÑÑ ÑÐµÑÐºÐ°Ñ
title: Ð²ÑÐ¿ÑÑÐºÐ½Ð°Ñ ÐºÐ²Ð°Ð»Ð¸ÑÐ¸ÐºÐ°ÑÐ¸Ð¾Ð½Ð½Ð°Ñ ÑÐ°Ð±Ð¾ÑÐ° Ð¼Ð°Ð³Ð¸ÑÑÑÐ°
titleType: Subtitle
title: Implementation and testing of high-order accuracy schemes for calculating flows with discontinuities on unstructured meshes
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: 2024
Subjects: ÐÐ°ÑÐµÐ¼Ð°ÑÐ¸ÐºÐ°
Ð¤Ð¸Ð·Ð¸ÐºÐ°
Ð¼ÐµÑÐ¾Ð´ ÐºÐ¾Ð½ÐµÑÐ½ÑÑ Ð¾Ð±ÑÐµÐ¼Ð¾Ð²
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 ÐµÐ¼Ñ Ð¿Ð¾Ð²ÑÑÐµÐ½Ð½Ð¾Ð¹ ÑÐ¾ÑÐ½Ð¾ÑÑÐ¸
ÑÐ°Ð·ÑÑÐ²Ð½ÑÐµ ÑÐµÑÐµÐ½Ð¸Ñ
finite volume method
unstructured meshes
quasi-one-dimensional reconstruction of variables
high-accuracy schemes
flow discontinuities

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description: The given work is devoted to studying the efficiency of high-order accuracy schemes with quasi-one-dimensional reconstruction of gas dynamic variables on unstructured meshes in modeling discontinuous flows. Research objectives: 1. Literature review on high-order accuracy schemes that are able to solve problems with gas-dynamic discontinuities. 2. Implementation of the procedure for reconstructing variables on the face using the fifth-order of accuracy WENO and MP schemes to the Â«unstructuredÂ» finite-volume SINF/Flag-S code. 3. Carrying out verification calculations using high-order schemes implemented to the code SINF/Flag-S for the isentropic vortex convection problem. 4. Test calculations of complex unsteady flows with shock-wave/vortex interaction. The calculations were performed using a finite-volume Â«unstructuredÂ» SINF/Flag-S program code developed at the SPbPU Institute of Physics and Mechanics. In the code part designed to calculate substantially compressible flows, the fifth-order of accuracy WENO and MP methods were 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 order of accuracy analysis was performed for the isentropic vortex convection problem. The schemes were successfully approved for modeling non-stationary problems in which a number of complex processes occur: the development of hydrodynamic instability, the interaction of shock waves with each other, contact discontinuities and vortex structures.