Space-time adaptive ADER-DG finite element method with LST-DG predictor and a posteriori sub-cell WENO finite-volume limiting for simulation of non-stationary compressible multicomponent reactive flows
{"title":"Space-time adaptive ADER-DG finite element method with LST-DG predictor and a posteriori sub-cell WENO finite-volume limiting for simulation of non-stationary compressible multicomponent reactive flows","authors":"I. S Popov","doi":"arxiv-2409.09932","DOIUrl":null,"url":null,"abstract":"The space-time adaptive ADER finite element DG method with a posteriori\ncorrection technique of solutions on subcells by the finite-volume ADER-WENO\nlimiter was used to simulate non-stationary compressible multicomponent\nreactive flows. The multicomponent composition of the reacting medium and the\nreactions occurring in it were described by expanding the original system of\nEuler equations by a system of non-stationary convection-reaction equations.\nThe use of this method to simulate high stiff problems associated with\nreactions occurring in a multicomponent medium requires the use of the adaptive\nchange in the time step. The solution of the classical problem related to the\nformation and propagation of a ZND detonation wave is carried out. It was shown\nthat the space-time adaptive ADER finite element DG method with a posteriori\ncorrection technique of solutions on subcells by the finite-volume ADER-WENO\nlimiter can be used to simulate flows without using of splitting in directions\nand fractional step methods.","PeriodicalId":501162,"journal":{"name":"arXiv - MATH - Numerical Analysis","volume":"16 1","pages":""},"PeriodicalIF":0.0000,"publicationDate":"2024-09-16","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"arXiv - MATH - Numerical Analysis","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/arxiv-2409.09932","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
引用次数: 0
Abstract
The space-time adaptive ADER finite element DG method with a posteriori
correction technique of solutions on subcells by the finite-volume ADER-WENO
limiter was used to simulate non-stationary compressible multicomponent
reactive flows. The multicomponent composition of the reacting medium and the
reactions occurring in it were described by expanding the original system of
Euler equations by a system of non-stationary convection-reaction equations.
The use of this method to simulate high stiff problems associated with
reactions occurring in a multicomponent medium requires the use of the adaptive
change in the time step. The solution of the classical problem related to the
formation and propagation of a ZND detonation wave is carried out. It was shown
that the space-time adaptive ADER finite element DG method with a posteriori
correction technique of solutions on subcells by the finite-volume ADER-WENO
limiter can be used to simulate flows without using of splitting in directions
and fractional step methods.